
Hans Janssen 
Adaptive integration of element matrices in finiteelement moisture transfer simulations 




Author(s) 
Hans Janssen^{1}; Jan Carmeliet^{1}; Hans Janssen^{1} 
Organisation(s) 
^{1}Laboratory for Building Physics, Faculty of Engineering, Katholieke Universiteit Leuven 
Abstract 
While serving different purposes, numerical simulations of moisture and heat
transfer
in soils and in building components are very similar in methodology: in both cases,
spatially and temporally discretised equations for transfer of moisture and heat in
porous materials are solved subject to (atmospheric) boundary conditions. The
strongly nonlinear transfer equations and boundary conditions however render such
hygrothermal simulations computationally very expensive, and an efficient numerical
solution algorithm is required. Such increasingly efficient numerical solution
schemes allow for more, larger, longer or more precise simulations, widening the
application capabilities of hygrothermal simulations.
The computational cost of hygrothermal simulations revolves around the serial
iterative composition and decomposition of the coefficient matrix of the system of
algebraic equations describing the discretised moisture and heat transfer, and is
thus determined by the cost of one (de)composition, and the number of required
(de)compositions. This article presents two optimisation measures for simulations
of moisture and heat transfer in building components under atmospherical
excitation:
adaptive integration and variations on the NewtonRaphson iterative scheme.
Adaptive
integration targets the cost of one (de)composition, while the variations on
NewtonRaphson aims at the number of required (de)compositions. While exemplified
by building physical simulations, the presented optimisation measures are equally
valid for simulations of moisture and heat transfer in soils.
It will be demonstrated that the common preference for loworder numerical
integration of the finite element matrices has an adverse effect on the required
spatial discretisation: a fine discretisation throughout is needed for accurate
simulation of the moving moisture fronts typical of infiltration problems. Adaptive
integration allows to merge loworder numerical integration with rougher spatial
discretisations, reducing the number of required integration points and of
discretisation nodes.
A second section of the article investigates the efficiency of (variations on) the
NewtonRaphson scheme. It will be demonstrated that appropriate application of
NewtonRaphson on the boundary conditions, of modified iteration and of separate
convergence criteria can drastically diminish the number of required (de)
compositions. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000750 


YuShu Wu 
Modeling Coupled Processes of Multiphase Flow and Heat Transfer in the Unsaturated Fractured Rock 




Author(s) 
YuShu Wu^{1}; Sumit Mukhopadhyay^{1}; Keni Zhang^{1}; G. Bodvarsson^{1}; YuShu Wu^{1} 
Organisation(s) 
^{1}Lawrence Berkeley National laboratory 
Abstract 
A multidimensional, mountainscale, thermalhydrologic (TH) numerical model is
developed for investigating unsaturated flow behavior in response to decay heat from
the radioactive waste repository in the Yucca Mountain unsaturated zone, Nevada, USA.
The TH model, consisting of both twodimensional and threedimensional
representations of the unsaturated repository system, is based on the current
repository design, drift layout, and thermal loading scenario under estimated current
and future climate conditions. More specifically, the TH model implements the current
geological framework and hydrogeological conceptual models, and incorporates the most
updated, bestestimated input parameters. This mountainscale TH model simulates the
coupled TH processes related to mountainscale multiphase fluid flow and evaluates
the impact of radioactive waste heat release on the natural hydrogeological system,
including thermally perturbed liquid saturation, gas and liquidphase fluxes, and
water and rock temperature elevations, as well as the changes in water flux driven by
evaporation/condensation processes and drainage between drifts. For a better
description of the ambient geothermal condition of the UZ system, the TH model is
first calibrated against measured borehole temperature data. The ambient temperature
calibration provides the necessary surface and water table boundary as well as
initial conditions. Then, the TH model is used to obtain scientific understanding of
TH processes in the Yucca Mountain unsaturated zone under the designed schedule of
repository thermal load. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000748 


Zhijiang Kang 
A TripleContinuum Numerical Model For Simulating Multiphase Flow in Vuggy Fractured Reservoirs 




Author(s) 
Zhijiang Kang^{1}; YuShu Wu^{2}; Jianglong Li^{1}; Yongchao Wu^{1}; Jie Zhang^{1}; Guangfu Wang^{1}; Zhijiang Kang^{1}; YuShu Wu^{2} 
Organisation(s) 
^{1}Research Inst. of Petroleum Exploration and Development, SINOPEC, Beijing, China; ^{2}Lawrence Berkeley National laboratory 
Abstract 
The existence of vugs (empty holes or cavities) in naturally fractured reservoirs has
long been observed and can be contributed significantly to reserves of underground
natural resources, such as oil, natural gas, and groundwater. A new multicontinuum
conceptual model has been developed for investigating multiphase flow behavior
through vuggy fractured reservoirs. The conceptual model, based on geological data
and observations of core examples from carbonate formations in China, has been
implemented into a threedimensional, threephase reservoir simulator using a
generalized multicontinuum modeling approach. In this conceptual model, vuggy
fractured rock is considered as a triplecontinuum medium, consisting of (1) highly
permeable fractures, (2) lowpermeability rock matrix, and (3) varioussized vugs.
The matrix system may contain a large number of small or isolated cavities (of
centimeters or millimeters in diameter), while vugs are larger cavities with sizes
from centimeters to meters in diameter, which are indirectly connected to fractures
through small fractures or microfractures. Similar to the conventional
doubleporosity concept, the fracture continuum is responsible for the occurrence of
global flow, while vuggy and matrix continua, providing largestorage space, are
locally connected to each other as well as directly interacting with globally
connecting fractures. Note that vugs directly connected with fractures are
considered as part of the fracture continuum. In the numerical implementation, a
controlvolume, integral finite difference method is used for spatial discretization,
and a firstorder finite difference scheme is adapted for temporal discretization of
governing massbalance equations for the threephase fluids in each continuum. The
resulting discrete nonlinear equations are solved fully implicitly by Newton
iteration. The numerical scheme has been verified by comparing its results against
those of analytical methods for the case of singlephase flow. In addition, to
demonstrate the model’s application, the new conceptual model and the associated
numerical modeling approach are used to obtain some insight into the behavior of flow
through vuggy fractured reservoirs. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000746 


Niels Schuetze 
Global optimization of deficit irrigation systems using evolutionary algorithms 




Author(s) 
Niels Schuetze^{1}; Thomas Woehling^{1}; Michael de Paly^{1}; Gerd H. Schmitz^{1}; Niels Schuetze^{1} 
Organisation(s) 
^{1}Institute of Hydrology and Meteorology at Dresden University of Technology 
Abstract 
Water is a limited resource and the dramatically increasing
world population requires a significant increase in food production.
For improving both crop yield and water use efficiency, the usual
optimization strategy in furrow irrigation at the field level considers
scheduling parameters, i.e. when and how much to irrigate, as well
as control parameters, i.e. the intensity and the irrigation time, for each
water application. Optimizing control and schedule parameters in
irrigation is considered as a nested problem. The objective of the
global optimization is to achieve maximum crop yield with a given,
but limited water volume, which can be arbitrary distributed over
the number of irrigations.
It is difficult to solve the global optimization problem, because
the target function has many locally optimal solutions and the number
of optimization variables, i.e. the number of irrigations is unknown
apriori. For this reason, a made to measure evolutionary optimisation
technique (EA) is employed to find a nearoptimal solution of the
global optimization problem within
acceptable computational time. The results
provided by the new optimization strategy are compared
with the popular SCEUA optimization algorithm and
MeshAdaptive Direct Search (MADS). The comparison demonstrated a striking
superiority of the new tool with respect to both the
achieved irrigation efficiency and the required computational time. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000744 


Guobiao Huang 
An Integrated Media, Integrated Processes Watershed Model – WASH123D: Part 1 – Model Descriptions and Features 




Author(s) 
Guobiao Huang^{1}; Fan Zhang^{2}; HsinChi (Jerry) Lin^{3}; JingRu (Ruth) Cheng^{3}; Earl V. Edris^{3}; David R. Richards^{3}; GourTsyh (George) Yeh^{4}; HwaiPing (Pearce) Cheng^{3}; GourTsyh (George) Yeh^{4} 
Organisation(s) 
^{1}Sutron Corp; ^{2}Oak Ridge National Laboratory; ^{3}ERDC, USACE; ^{4}University of Central Florida 
Abstract 
Parametricbased, lumped watershed models have been widely employed for integrated
surface and groundwater modeling to calculate surface runoff and pollution loads on
various temporal and spatial scales of hydrologic regimes. Physicsbased, process
level, distributed models that have the design capability to cover multimedia and
multiprocesses and are applicable to various scales have been practically
nonexistent until recently. It has long been recognized that only such models have
the potential to further the understanding of the fundamental biological, chemical,
and physical factors that take place in nature hydrologic regimes; to give
mechanistic predictions; and most importantly to be able to couple and interact with
weather/climate models. However, there are severe limitations with these models
that inhibit their use. These are, among other things, the ad hoc approaches of
coupling between various media, the simplistic approaches of modeling water quality,
and the excessive demand of computational time. This paper presents the development
of an integrated media (river/stream networks, overland regime, and subsurface
media), integrated processes (fluid flows and thermal, salinity, sediment, and water
quality transport) watershed model to address these issues. Rigorous coupling
strategies are described for interactions among overland regime,
rivers/streams/canals networks, and subsurface media. Generalized paradigms of
reactionbased water quality modeling are presented. The cultivation of innovative,
numerical algorithms and the implementation of high performance computing to
increase the computational speed are discussed. Various applicationdependent
numericaloptions to simulate scalar transport are provided. The necessities to
include various options in modeling surface runoff and river hydraulics are
emphasized. Several examples are used to demonstrate the flexibility and
efficiency of the model as applied to regionallevel large scale and projectlevel
small scale problems. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000742 


ChunWen Chen 
A Systematic Approach to Uncovering Scaleindependent Rate Formulations for Bioreduction of Hematite in Sediments at a Field Site 




Author(s) 
ChunWen Chen^{1}; GourTsyh (George) Yeh^{1}; William D. Burgos^{2}; Morgan L. Minyard^{2}; ChunWen Chen^{1} 
Organisation(s) 
^{1}University of Central Florida; ^{2}The Pennsylvania State University 
Abstract 
This presentation focuses on a systematic modeling approach in search of scale
independent rate formulations for biological reduction of hematite. Biological and
chemical processes controlling Fe(III) reduction are very complex including direct
bioreduction of ferric irons, microbial growth, secondary reactions of biogenic
ferrous iron adsorptions, iron complexation, precipitation of ferrous minerals, and
reoxidation. A reaction network of five reactions was proposed to describe these
processes under laboratorycontrolled batch and column experiments which were
conducted using sediments taken from a field site. The key reaction in the
experiments is the direct bioreduction of hematite. Four possible rate
formulations were proposed to describe this key reaction. Two kinds of simulations
were conducted to verify the rate formulations and reaction parameters: the first
one is batch modeling and the second one is column modeling. Simulation results
indicated that while all rate formulations can adequately model batch experiments,
only the formulation based on dual Monod kinetics with inhibition of ferrous iron
and the effect of DMRB is “universal.” Furthermore, only this rate formulation can
be upscaled to column experiments. Iterative modeling between batch and column
experiments revealed that the equilibrium assumptions for surface hydration of
hematite and adsorption of biogenic ferrous irons onto hematite may have to be
revoked and substituted with kinetic rate formulations. 
Track/Session 
Special Sessions / MultiDisciplinary Approaches To Reactive Transport Simulation In Aquifer Systems 
Date 
20060618 
DOI 
10.4122/1.1000000740 


Hua Shan 
A Bay/Estuary Model to Simulate Hydrodynamics and Water Quality Transport: Part 1  Hydrodynamics 




Author(s) 
Hua Shan^{1}; GourTsyh (George) Yeh^{2}; Gordon Hu^{3}; TienShuenn Wu^{4}; Hua Shan^{1} 
Organisation(s) 
^{1}University of Texas at Arlington; ^{2}University of Central Florida; ^{3}South Florida Water Management District; ^{4}Florida Department of Environmental Protection 
Abstract 
This paper presents the development and application of a bay/estuary model to
simulate hydrodynamics and thermal and salinity transport. The hydrodynamic module
solves threedimensional NavierStokes equations with or without the hydrostatic
assumptions. The turbulence is modeled with typical transport equations. The
Boussinesq approximation is employed to deal with the buoyancy force due to
temperature and salinity variations. The moving free surface is explicitly handled
by solving the kinematic boundary condition equation using a noderepositioning
algorithm. The transport module solves the energy equation for spatialtemporal
distributions of temperature and the mass transport equations for the salinity
field. The Arbitrary LagrangianEulerian (ALE) representation is adopted for all
transport equations including momentum transport. The solution is obtained with
finite element methods or a combination of finite element and SemiLagrangian
(particle tracking) methods. The model has been successfully calibrated with tides
and salinities and is applied to Loxahatchee Estuary for the investigation of its
minimum flow requirements to maintain ecological balance. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000738 


TienShuenn Wu 
A Bay/Estuary Model to Simulate Hydrodynamics and Water Quality Transport: Part 2  Water Quality 




Author(s) 
TienShuenn Wu^{1}; Gordon Hu^{2}; Jing Yu^{3}; GourTsyh (George) Yeh^{3}; Jing Yu^{3} 
Organisation(s) 
^{1}Florida Department of Environmental Protection; ^{2}South Florida Water Management District; ^{3}University of Central Florida 
Abstract 
This paper presents the development of a numerical water quality model using a
general paradigm of reactionbased approaches. In a reactionbased approach, all
conceptualized biogoechemical processes are transformed into a reaction network.
Through the decomposition of species governing equations via GaussJordan column
reduction of the reaction network, (1) redundant fast reactions and irrelevant
kinetic reactions are removed from the system, which alleviates the problem of
unnecessary and erroneous formulation and parameterization of these reactions, and
(2) fast reactions and slow reactions are decoupled, which enables robust numerical
integrations. The system of M species transport equations is transformed to M
reactionextent transport equations, which is then approximated with three subsets:
NE algebraic equations, NKI kineticvariables transport equations, and NC component
transport equations. As a result, the model alleviates the needs of using simple
partitions for fast reactions. With the diagonalization strategy, it makes the
inclusion of arbitrary number of fast and kinetic reactions relatively easy, and,
more importantly, it enables the formulation and parameterization of kinetic
reactions one by one. To demonstrate the flexibility and generality, the
eutrophication model in WASP5, QUAL2E, and CEQUALICM are recast in the mode of
reaction networks. This illustrates that the model embeds the most widely used water
quality models as specific examples. Based on these three examples, the
deficiencies of current practices in water quality modeling are discussed and the
actions that must be taken to improve these practices are addressed. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000736 


Christos Tsakiroglou 
A twoscale percolation approach to compute the effective twophase flow coefficients of heterogeneous porous media in the general case of a shearthinning nonwetting fluid 




Author(s) 
Christos Tsakiroglou^{1}; Christos Tsakiroglou^{1} 
Organisation(s) 
^{1}FORTH / ICEHT, Stadiou Street, Platani, P.O.Box 1414, GR26504 Patras, Greece 
Abstract 
Mechanistic simulators of the twophase flow in pore networks (length scale~1 cm)
have widely been used to determine the effective transport coefficients (e.g.
capillary pressure curvePc, relative permeability curve of wetting phasekrw and
nonwetting phasekrnw, resistivity indexIR) of macroscopically homogeneous porous
media. However, in the classical 1scale approach, very large networks, complicated
algorithms and enormous computational effort are required to (1) simulate the up
scaled multiphase transport coefficients of macroscopically heterogeneous porous
media (length scale~1 m), and (2) take into consideration the effects of buoyancy
and viscous forces on Pc, krw, krnw, IR.
In the present work, a twoscale percolation approach is developed to simulate the
displacement of a Newtonian wetting fluid by a power law fluid in a heterogeneous
porous medium. First, a gradient percolation model is developed by taking into
account the power law rheology of the nonwetting fluid and the flow of wetting
fluid along pore edges. In this manner, the smallscale Pc, krw, krnw, IR of each
homogeneous unit are calculated. Then, the smallscale effective transport
coefficients are fed as input data into a largescale sitepercolation model, where
the pore sizes are replaced by the smallscale Pc curves, and instead of the
critical pore pressure of penetration the critical breakthrough pressure is
employed. The effects of the power law parameters, Bond number (Bo), capillary
number (Ca), and contact angle (θe) on the small (homogeneous) and large
(heterogeneous) scale displacement growth pattern as well as on the corresponding
Pc, krw, krnw, IR are investigated. Finally, the calculated growth patterns and
effective transport coefficients are compared to results of drainage experiments
performed on glassetched dual pore networks. 
Track/Session 
Special Sessions / PoreScale Modelling: New Developments And Applications 
Date 
20060618 
DOI 
10.4122/1.1000000735 


Christos Tsakiroglou 
Solute dispersion coefficients in heterogeneous porous media as related with the migration of pesticides in groundwater 




Author(s) 
Christos Tsakiroglou^{1}; Dimitra Tzovolou^{1}; Christos Aggelopoulos^{1}; Maria Theodoropoulou^{2}; Theodora Dalkarani^{2}; Constantinos Pikios^{2}; Christos Tsakiroglou^{1} 
Organisation(s) 
^{1}FORTH / ICEHT, Stadiou Street, Platani, P.O.Box 1414, GR26504 Patras, Greece; ^{2}Technological Educational Institute of Patras, M. Alexandrou 1, GR26334 Patras, Greece 
Abstract 
During the last years, too much attention has been focused on problems related with
the diffuse pollution of groundwater by pesticides. However, in spite of the
numerous labscale and fieldscale experimental studies and numerical approaches,
one significant factor is usually overlooked: the transverse and longitudinal
dispersivities are scaledependent and sensitive to the variation of microscopic
properties of the pore structure and multiscale heterogeneities.
Miscible displacement and single sourcesolute transport experiments are performed
on long columns of disturbed soils of broad grain size distribution. The
geometrical and topological parameters of the pore space of soils are estimated by
fitting the experimental mercury intrusion/retraction curves to analytical
percolation models of the processes. The breakthrough curves of the tracer (NaCl)
concentration along the column is monitored by measuring the electrical resistance
at various axial positions from the column entrance. An inverse modeling algorithm
based on a Bayesian estimator is used to fit the experimental data to adequate
analytical and numerical solutions of the advection dispersion equation to estimate
the dispersion coefficients as functions of the pore structure heterogeneity, and
Peclet number. Moreover, this information is used to develop relevant
phenomenological models of the longitudinal and transverse dispersion coefficients.
Then, a 2D macroscopic numerical model of the transport / sorption /
biodegradation of pesticides in heterogeneous porous media is developed in the
environment of flexPDE (solver of partial differential equations with finite
elements) to simulate longterm fate of pesticides in groundwater. Sample
simulations are done by using literature and laboratory data concerning the
physicochemical and transport properties of four pesticides (glyphosate, phorate,
mancozeb, and 2,4D) that are widely utilized in agricultural cultivations of
Western Greece. The simulator is employed to investigate the potential errors
caused on (1) the longterm predictions of the fate of pesticides in aquifers, and
(2) the interpretation of labscale mobility experiments of pesticides, when
incorrect values of dispersion coefficients are used as input data. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000733 


Fred Tracy 
Improved Well Modeling Tools for Unsaturated Flow PumpandTreat Remediation Studies 




Author(s) 
Fred Tracy^{1}; Barbara Donnell^{1}; Stacy Howington^{1}; John Peters^{1}; Fred Tracy^{1} 
Organisation(s) 
^{1}Engineer Research and Development Center 
Abstract 
Many Department of Defense military sites and Environmental Protection Agency
superfund sites benefit from pumpandtreat systems for their remediation. One of
the ways used to determine the effectiveness of a pumpandtreat system is by using
a groundwater finite element method program to compute flow patterns from proposed
well placement. As the governing Richards’ equation for unsaturated flow is highly
nonlinear, the finite element discretization often has trouble converging. This is
especially true when (1) a significant part of the flow region has unsaturated flow,
(2) soils such as sand have relative hydraulic conductivities that go from almost
vertical to almost horizontal, (3) water in very dry soil is being applied at the
top of the flow region, and (4) the wells become partially above the free surface
when the pumping is turned on. This paper focuses on an improved wellmodeling
technique that allowed the finite element solution to go from nonconvergent to
converging in 15 nonlinear iterations for the Higgins Farm Superfund site
The Higgins Farm Superfund site, which is approximately 75 acres in size and
currently operated as a cattle farm, is located in a rural area along Route 518 in
Franklin Township, Somerset County, New Jersey. The site is primarily pastureland
where a drum burial dump was discovered. Extraction wells were placed around the
perimeter with an onsite treatment plant.
The finite element run not only did not converge but also the modeling of wells was
initially very tedious. A given well has a specified flow, and the user would
manually try to distribute this flow among the given set of nodes modeling the well.
During the iteration toward convergence, if a node of a well became above the free
surface (pressure head less than zero), the code stopped. The user then manually
redistributed the flow for that well and started the process again. However,
combining all of the nodes for a well into one well supernode was determined to be
the best solution. The nodes representing a partially penetrating well are combined
into a single degreeoffreedom well supernode. Now, one total value of flow is used
as input to the well supernode, and one single value of total head is computed as
output. Further improvement was added to the well model by implementing a
nonreversible elimination of well nodes above the water table. This paper will give
the details of this computational experience using the high performance computers at
the ERDC and illustrate the general applicability of this approach to other studies. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000731 


Ahmed AlFutaisi 
Impact of Microscopic NAPLWater Interface Configurations on Subsequent Gas Injection into WaterWet Permeable Rocks 




Author(s) 
Ahmed AlFutaisi^{1}; Tad Patzek^{2}; Ahmed AlFutaisi^{1} 
Organisation(s) 
^{1}Department of Civil & Architectural Engineering, Sultan Qaboos University; ^{2}Department of Civil & Environmental Engineering, UC Berkeley 
Abstract 
Predictive fieldscale models of the concurrent flow of three fluids require
accurate predictions of five macroscopic flow descriptors: three relative
permeabilities and two capillarypressures as functions of the fluid saturations
and saturation history. Since direct measurement of these descriptors is very
difficult, and empirical correlations are often unreliable, the use of physically
based porescale models has become an appealing alternative. In this paper, we
describe the features of our quasistatic pore network model for three immiscible
fluids. The model integrates a realistic representation of pore connectivity and
morphology reconstructed from 3D microfocused Xray CT images, a realistic
description of fluid displacement mechanisms, and a sound representation of the
wetting properties of the rock. All porelevel displacement mechanisms: piston
type, snapoff, cooperative porebody filling, and doubledisplacements are
considered with arbitrary contact angles and spreading coefficients. The proposed
model is used to simulate gas injection into waterwet permeable rocks that
initially contain water and NAPL after twophase drainage followed by twophase
imbibition. The gas injection is performed using a clusterbased invasion
percolation algorithm with trapping. The strong influence of the twophase
saturation history on the threephase transport properties of a permeable rock is
illustrated by performing a series of gas injections into Bentheimer and Berea
sandstones with different initial NAPL and water saturations, and different
microscopic fluid interface configurations. 
Track/Session 
Special Sessions / PoreScale Modelling: New Developments And Applications 
Date 
20060618 
DOI 
10.4122/1.1000000729 


Christos Tsakiroglou 
Correlation of the multiphase flow coefficients of porous media with wettability: A pore network approach 




Author(s) 
Christos Tsakiroglou^{1}; Christos Tsakiroglou^{1} 
Organisation(s) 
^{1}FORTH / ICEHT, Stadiou street, Platani, P.O.Box 1414, GR26504 Patras, Greece 
Abstract 
Information concerning the capillary pressure and relative permeability curves of
porous media is required by the multiphase flow simulators, developed to model NAPL
migration in the subsurface. Earlier experimental and theoretical studies have
revealed that both capillary pressure and relative permeability functions are
strongly affected by the solid surface wettability, which is commonly quantified by
the contact angle. However, there is still an ambiguity regarding the capillary
pressure and relative permeability functions of intermediatewet pore systems
(contact angle ~ 70o120o).
In the present work, a poreandthroat network including fractal roughness features
along its surface is employed to simulate primary drainage and secondary imbibition
by accounting for the quasistatic motion of menisci in pores and throats and
varying the contact angle from 0o (strongly waterwet conditions) to 180o (strongly
oilwet conditions). The roughness features of pores and throats are circular cones
and triangular prisms, respectively. The angle of sharpness of these features is
decided by the specific surface area, and defines a range of contact angles within
which the crosssection of the throat or pore is occupied entirely by one fluid
(conditions of intermediate wettability). In contrast, outside this range, both
fluids may coexist in a pore or throat. Such differences on the fluid distribution
at the pore level may have pronounced effects on the calculated effective twophase
flow coefficients and may interpret their nonlinear variation with the contact
angle. The simulator is used to calculate the capillary pressure and relative
permeability curves of a porous medium as the pore system transits from strongly
waterwet or strongly oilwet to intermediatewet conditions, and interpret
relevant experimental results collected from the literature. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000727 


Karen L. Ricciardi 
Optimal collocation applied to a onedimensional convectiondiffusion equation using a hybrid optimization algorithm 




Author(s) 
Karen L. Ricciardi^{1}; Stephen H. Brill^{2}; Karen L. Ricciardi^{1} 
Organisation(s) 
^{1}University of Massachusetts in Boston; ^{2}Boise State University 
Abstract 
The method of collocation can be used to determine highly accurate
solutions to the onedimensional steadystate convectiondiffusion equation
(which can be used to model the transport of contaminants
dissolved in groundwater). This accuracy is dependent upon
sufficient refinement of the finite element mesh as well as
applying upstream weighting to the convective term through the
determination of collocation locations which meet specified
constraints. Due to an increase in computational intensity of the
application of the method of collocation associated with increases
in the mesh refinement, minimal mesh refinement is sought. A
hybrid method that utilizes a genetic algorithm and a
hillclimbing approach is used to determine the optimal mesh
refinement for a number of models differentiated by their velocity
fields. The genetic algorithm is used to determine a mesh
refinement that results in feasible collocation locations that is
close to optimal. Following the genetic algorithm, a hillclimbing
approach is used to determine a local optimal mesh refinement that
is feasible. In most cases the optimal mesh refinements
determined with this hybrid method are equal to or better than
previous mesh refinements determined through direct search
methods. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000725 


Kathleen Fowler 
Approaching the Groundwater Remediation Problem Using Multifidelity Optmization 




Author(s) 
Kathleen Fowler^{1}; Genetha Gray^{2}; Genetha Gray^{2} 
Organisation(s) 
^{1}Clarkson University; ^{2}Sandia National Lab 
Abstract 
The objective of the hydraulic capture method for optimal groundwater remediation
design is containment of a contaminant plume using barrier wells to reverse the
direction of groundwater flow. Finding a solution involves applying optimization
algorithms in conjunction with simulators for groundwater flow and possibly for
contaminant transport. The formulation of the objective function and its
corresponding constraints dictates which optimization algorithms are appropriate and
usually eliminates gradient based approaches from consideration. In addition,
objective functions and constraints can be nonlinear, nonconvex, non
differentiable, or even discontinuous, and the simulations involved can be
computationally expensive.
Both computational efficiency and accuracy are important, and this further
influences the choice of solution method. With the advent and increasing
availability of massively parallel computers, computational speed has increased
tremendously. Unfortunately, the numerical and model complexities of problems like
groundwater remediation still demand significant computational resources. Moreover,
these expenses can be a limiting factor of optimization since obtaining solutions
often requires the completion of numerous computationally intensive jobs.
Therefore, we propose an algorithm designed to improve the computational efficiency
of an optimization method for a wide range of applications and apply it to
groundwater remediation.
Our approach takes advantage of the interactions between multifidelity models and is
applicable to problems for which models of varying fidelity are available. The
method can be described as follows: First, a direct search method is applied to the
high fidelity model over a reduced design space. In conjunction with this search, a
specialized oracle is employed to map the design space of this high fidelity model
to that of a computationally cheaper low fidelity model using space mapping
techniques. Then, in the low fidelity space, an optimum is obtained using gradient
based optimization, and it is mapped back to the high fidelity space.
To motivate this work, we consider a hydraulic capture problem proposed in the
literature for benchmarking purposes. The problem is to minimize the cost to install
and operate a set of wells subject to constraints on the concentration of a
contaminant at specified locations in the physical domain. We solve the problem by
applying the multifidelity approach described above using only flow information for
the low fidelity model and using concentration based constraints for the high
fidelity model. We present some promising results for this preliminary problem, and
explain how we plan to extend our study by considering more representative physical
models, simulators, objective function formulations, and by incorporating realsite
data. 
Track/Session 
Special Sessions / Groundwater Optimal Management Session 
Date 
20060618 
DOI 
10.4122/1.1000000723 


Umamahesh Nanduri 
Fuzzy Dynamic Programming Model for Operation of Multipurpose Reservoir 




Author(s) 
Umamahesh Nanduri^{1}; B Siva Naga Raju^{1}; Umamahesh Nanduri^{1} 
Organisation(s) 
^{1}National Institute of Technology, Warangal, India 
Abstract 
Multipurpose reservoir operation involves various interactions and tradeoffs
between purposes, which are sometimes complementary but often competitive or
conflicting. Reservoir operation may be based on the conflicting objectives of
maximizing the amount of water available for conservation purposes and maximizing
the amount of empty space for storing future flood waters to reduce the downstream
damages. A major complicating factor in water resources system management is
handling uncertainty. Reservoir management is one of the such complex problems
which involves the uncertainty. Various models have been reported in literature for
developing optimal operation policy for a reservoir. Most of these models consider
the uncertainty caused due to variability of inflows. However uncertainty caused
because of imprecise objectives and goals is also an factor in developing operation
policy of a reservoir. In recent years fuzzy optimization models have generated
considerable interest.
In the present study a Fuzzy Dynamic Programming (FDP) model is developed for
optimal operation of a multipurpose reservoir and is applied to Hirakud Reservoir
for deriving the ten daily operating policy for the reservoir. Hirakud project is a
multipurpose project on river Mahanadi in the State of Orissa in India. The main
objectives of the Hirakud project are irrigation, hydropower generation and flood
control. The objectives are treated as fuzzy, and membership functions are
developed for the linguistic variables describing the objectives. The objective
function of the FDP model is to maximize the minimum expected satisfaction level of
the fuzzy objectives. The FDP model is used to develop the optimal operating policy
of the reservoir. The reservoir is simulated using the operating policy derived
from FDP model and the performance of the reservoir is evaluated. The study
demonstrates the applicability of fuzzy optimization for reservoir operation. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000722 


Fan Zhang 
An Integrated Media, Integrated Processes Watershed Model – WASH123D: Part 6 – Sediment and Reactive Chemical Transport in Stream/River Networks 




Author(s) 
Fan Zhang^{1}; GourTsyh Yeh^{2}; Fan Zhang^{1} 
Organisation(s) 
^{1}Oak Ridge National Laboratory, USA; ^{2}2Dept of Civil and Environ. Eng., Univ. of Central Florida 
Abstract 
A watershed system includes river/stream networks, overland regions, and subsurface
media. This paper presents a numerical model of sediment and reactive chemical
transport in river/stream networks of watershed systems. The distribution of
mobile suspended sediments and immobile bed sediments is controlled by hydrological
transport as well as erosion and deposition processes. The distribution and fate of
chemical species with a variety of chemical and physical processes is
mathematically described by a system of advectivedispersivereactive species
transport equations. Each equation in the system simply states that the rate of
increase of a species is due to hydrology transport and the production rate from
all reactions contributing to the species. The system is very stiff if some of
reactions are very fast; in the limit with infinite rates. To circumvent the stiff
problem, fast reactions must be decoupled from slow reactions. A matrix
decomposition procedure is performed via the GaussJordan column reduction of the
reaction network. After matrix decomposition, the system of speciestransport
equations is transformed to a system of reaction extenttransport equations, in
which one and only one linearly independent reaction rate appears in any reaction
extent equation. This facilitates the decoupling of fast reactions from slow
reactions. Each of the reactionextent transport equations with the one and only
one fast reaction is then approximated with an algebraic equation and its reaction
extent is called an equilibrium variable. Thus the system of reactionextent
transport equations is reduced three subsets: (1) algebraic equations, (2) kinetic
variable transport equations, and (3) component transport equations. A variety of
numerical methods are investigated for solving the mixed differential and algebraic
equations (DAE). Two verification examples are compared with analytical solutions
to demonstrate the correctness of and to emphasize the need of implementing various
numerical options and coupling strategies for applicationdependent simulations. A
hypothetical example is employed to demonstrate the capability of the model to
simulate both sediment and reactive chemical transport and to handle complex
reaction networks involving both slow and fast reactions. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000720 


Fan Zhang 
An Integrated Media, Integrated Processes Watershed Model – WASH123D: Part 7 – Sediment and Reactive Chemical Transport in Surface Runoff 




Author(s) 
Fan Zhang^{1}; GourTsyh Yeh^{2}; Fan Zhang^{1} 
Organisation(s) 
^{1}Oak Ridge National Laboratory, USA; ^{2}2Dept of Civil and Environ. Eng., Univ. of Central Florida 
Abstract 
A watershed system includes river/stream networks, overland regime, and subsurface
media. This paper presents a numerical model of sediment and reactive chemical
transport in surface runoff of watershed systems. The distribution of mobile
suspended sediments and immobile bed sediments is controlled through hydrological
transport as well as erosion and deposition processes. Transport of chemical
species with a variety of chemical and physical processes is mathematically
described by system of M advectivedispersivereactive transport equations (where M
is the number of species). Decomposition via GaussJordan column reduction of the
reaction network transforms M speciestransport equations into three sets of
equations: a set of thermodynamic equilibrium equations representing NE equilibrium
reactions, a set of reactive transport equations of NKI kineticvariables involving
no equilibrium reactions (where NKI is the number of linearly independent kinetic
reactions), and a sent of NC component transport equations (where NC is the number
of components). The elimination of fast reactions from reactive transport equations
allows robust and efficient numerical integration. The model solves the PDEs of
kineticvariables and components rather than individual chemical species, which
reduces the number of reactive transport equations and simplifies the reaction
terms in the equations. A hypothetical example was used to demonstrate the
capability of the model in simulating sediment and reactive chemical transport
subject to a complex reaction network involving both slow and fast reactions, under
the effect of temperature. Based on the application of an eutrophication example,
the deficiency of current practices in the water quality modeling is discussed and
potential improvements over current practices using this model are addressed. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000718 


Fan Zhang 
An Integrated Media, Integrated Processes Watershed Model – WASH123D: Part 8 – Reactive Chemical Transport in Subsurface Media 




Author(s) 
Fan Zhang^{1}; GourTsyh Yeh^{2}; Jack Parker^{1}; Scott Brooks^{1}; Molly Pace^{1}; YoungJin Kim^{1}; Philip Jardine^{1}; Fan Zhang^{1} 
Organisation(s) 
^{1}Oak Ridge National Laboratory, USA; ^{2}2Dept of Civil and Environ. Eng., Univ. of Central Florida 
Abstract 
A watershed system includes river/stream networks, overland regions, and subsurface
media. This paper presents a reactionbased numerical model of reactive chemical
transport in subsurface media of watershed systems. Transport of M chemical species
with a variety of chemical and physical processes is mathematically described by M
partial differential equations (PDEs). Decomposition via GaussJordan column
reduction of the reaction network transforms M species reactive transport equations
into M reaction extenttransport equations (a reaction extent is a linear
combination of species concentrations), each involves one and the only one linearly
independent reaction. Thus, the reactive transport problem is viewed from two
different points of view. Descirbed with a speciestransport equation, the
transport of a species is balanced by a linear combinations of rates of all
reactions. Described by a reaction extenttransport equation, the rate of a linear
independent reaction is balanced by the transport of the linear combination of
species. The later description facilitates the decoupling of fast reactions from
slow reactions and circumvent the stiffness of reactive transport problems. This
is so because the M reaction extenttransport equations can be approximated with
three subsets of equations: NE algebraic equations describing NE fast reactions
(where NE is the set of linearly independent fast/equilibrium reactions), NKI
reactive transport equations of kineticvariables involving no fast reactions
(where NKI is the number of linearly independent slow/kinetic reactions), and NC
transport equations of components involving no reaction at all (where NC = M – NE –
NKI is the number of components). The elimination of fast reactions from reactive
transport equations allows robust and efficient numerical integration. The model
solves the PDEs of kineticvariables and components rather than individual chemical
species, which reduces the number of reactive transport equations and simplifies
the reaction terms in the equations. Two validation examples involving simulations
of uranium transport in soil columns are presented to evaluate the ability of the
model to simulate reactive transport with reaction networks involving both kinetic
and equilibrium reactions. A hypothetical threedimensional example is presented to
demonstrate the model application to a fieldscale problem involving reactive
transport with a complex reaction network. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000716 


chandra sekhar matli 
APPLICATION OF FUZZY INFERENCE SYSTEMS FOR WATER QUALITY MODELLING 




Author(s) 
chandra sekhar matli^{1}; chandra sekhar matli^{1} 
Organisation(s) 
^{1}national institute of technology 
Abstract 
The Krishna river is subjected to a varying degree of pollution, caused by numerous
outfalls  municipal and industrial effluents and by other human activities. The
main sources leading to pollution in the river include municipal wastewater from
urban areas of Hyderabad and Nalgonda, and wastewater from a variety of industries.
Nonpoint runoff is generated by precipitation that washes and cleanses the air and
land surface and then transports, a variety of materials, such as sediment, animal
wastes, fertilizers and leaves, to the nearest natural or man made collection
channel. Hence, it is becoming increasingly evident, that to establish the goals of
the water quality management programme, regulating and controlling only point
source pollution is not sufficient. In addition to the point sources, considerable
pollution reaches the river from various land use activities during the monsoon
period. Runoff from the agricultural lands, unsewered rural and urban areas, etc.,
is the source of nonpoint source pollution in this part of the basin.
Seasonal variations in quantity and quality of Krishna river water are significant
due to nonuniform distribution of rainfall and hence the discharge in the river.
During the dry season the river water is polluted due to discharge of
treated/partially treated/untreated domestic and industrial wastewaters. In wet
season, the river receives pollutants from nonpoint sources in addition to
pollutants from point sources. As the flow variations in the river are very large,
the flows are classified as wet flows (June  November) and dry flows (December 
May) for developing regression equations. A generalized regression equation which
can be used for water quality predictions did not yield in good predictions. To
incorporate the influence of previous flow on the present load of the pollutant,
ANFIS models are developed. Also, to develop generalized models for the river
stretch, Fuzzy Inference System is used for the first time and its applicability is
tested. Using concepts of fuzzy sets the flows are classified as low and high. The
influence of previous flow on the present pollutant load could be incorporated by
giving suitable weights by the ANFIS model.
Application of ANFIS for developing a generalized model for the river reach under
study yielded good results. The correlation coefficients in the range of 0.6 to 0.9
and low RMSE indicate suitability of the models to the study area. The models
successfully explained the variation in loads for different flow conditions in the
river. The peak flow and falling stage conditions indicated the influence of
previous flow on the load due to delayed effect. The models are verified using
linear regression. Agreement between model predictions and observed measurements is
within the uncertainty of data. However, for all the pollutants the observed values
fall within 95% confidence bands. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000715 


Helge K. Dahle 
Defining macroscale pressure from the microscale 




Author(s) 
Helge K. Dahle^{1}; S. Majid Hassanizadeh^{2}; Jan M. Nordbotten^{1}; Michael A. Celia^{3}; Jan M. Nordbotten^{1} 
Organisation(s) 
^{1}University of Bergen; ^{2}Utrecht University; ^{3}Princeton University 
Abstract 
Microscale models have proven to be powerful theoretical tools in groundwater flow
and transport modelling. In addition to being useful in estimating traditional
parameters, such as (relative) permeability and capillary pressure functions, micro
scale models have recently provided insight into complex multiphase flow
phenomena, such as the socalled dynamic capillary pressure, and are central in
investigating theoretical developments in multiphase flow modelling.
To transfer the results of a microscale model to larger scales, a proper
definition of macroscale variables in terms of microscale quantities is crucial.
One such variable is the pressure. Traditionally, macroscale pressure of a given
phase is defined in terms of the intrinsic phase average; i.e. the average of micro
scale pressure weighted by the volume of the phase. We show, by averaging of micro
scale momentum equations, that the macroscale pressure in the Darcy equation is
not necessarily the intrinsic phase average of its microscale equivalent. This
will be the case if there are gradients of porosity or saturation in the system,
and these gradients lead to nonnegligible changes on the scale of the averaging
volume. We have formulated a modified interpretation of macroscale pressure. The
implications of this modification for parameters on the macroscale are
significant, in particular for dynamic relative permeability and capillary
pressure. We show that recent interpretations of dynamic capillary pressure can
change significantly when this modified definition of macroscale pressure is used.
We also show, through simple example calculations, that inadmissible relative
permeability values (e.g. values larger than 1) can result when using the standard
average to define macroscale phase pressures, but that no such problems arise with
the new pressure definition. These simple calculations also imply that dynamic
capillary pressure effects may arise with the standard average, which do not appear
with the new pressure definition. The new pressure definition is further
investigated in the more complex setting of bundleoftubes and dynamic network
models. 
Track/Session 
Special Sessions / PoreScale Modelling: New Developments And Applications 
Date 
20060618 
DOI 
10.4122/1.1000000713 


Niklas Linde 
Reconstruction of the threedimensional Darcy velocity in a small catchment using selfpotential, electrical resistivity, and induced polarization data 




Author(s) 
Niklas Linde^{1}; André Revil^{1}; Barbara Suski^{1}; Cécile Dagès^{2}; Marc Voltz^{2}; Niklas Linde^{1} 
Organisation(s) 
^{1}CNRSCEREGE, Equipe Hydrogeophysique, AixenProvence, France; ^{2}INRA, Laboratoire d'étude des Interactions entre Sol, Agrosystème et Hydrosystème, Montpellier, France 
Abstract 
One of the ultimate goals of hydrogeophysics is to map the groundwater table
throughout a catchment and together with information about hydrogeological
properties of the saturated zone, derived from geophysical and hydrogeological
data, estimate the Darcy velocity in three dimensions throughout the saturated
zone. In this work, we present our first attempts to achieve this goal in the small
(~1 km2) catchment area of Roujan (Hérault, France), which is a well characterized
hydrogeological research site. Two mutually exclusive conceptual models to relate
selfpotential data to the determination of the water table were employed using a
maximum likelihood approach, where the resulting models were averaged according to
Bayesian model averaging. The estimated electrical resistivity structure derived
from resistivity surveys was used together with laboratory measurements to estimate
the streaming potential coupling coefficient and its spatial variation. Resistivity
and induced polarization surveys were employed to determine the spatial variation
of the thickness of the aquifer material (clayey silts) overlying the electrically
more conductive aquitard (Miocene marls). Induced Polarization measurements were
also performed to estimate the specific surface area and its variation in the
aquifer. The electrical conductivity of the pore water was sampled throughout the
aquifer and the formation factor was estimated in the laboratory. This allowed us
to use both the Kozeny and Carman model and sitespecific relationships to relate
electrical resistivity and normalized chargeability with permeability. A cokriging
method was applied to estimate large scale variations in the threedimensional
permeability structure by conditioning to available permeability data and several
collocated twodimensional models of electrical resistivity and normalized
chargeability. Our estimates of the variations of the depth to the aquitard, depth
to the water table, and the largescale variations in the permeability structure
allowed us to estimate the Darcy velocity throughout the saturated aquifer in the
Roujan catchment. 
Track/Session 
Special Sessions / Hydrogeophysical data fusion 
Date 
20060618 
DOI 
10.4122/1.1000000711 


Niklas Linde 
A structural approach to joint inversion of hydrogeophysical data 




Author(s) 
Niklas Linde^{1}; Andrew Binley^{2}; Ari Tryggvason^{1}; Laust Pedersen^{1}; Niklas Linde^{1} 
Organisation(s) 
^{1}Uppsala University, Department of Earth Sciences, Uppsala, Sweden; ^{2}Lancaster University, Department of Environmental Science, Lancaster, United Kingdom 
Abstract 
We have developed a flexible methodology to jointly invert different types of
geophysical and hydrogeological data, where the resulting models honour the spatial
correlation structure derived from geophysical borehole logs. Additionally, the
individual models are internally consistent. The key components in this work are:
(1) an efficient method to estimate stochastic regularization operators based on
geostatistical models; (2) to minimize the cross product of the gradients of two
models, which is used as a measure of structural dissimilarity. Electrical
resistances and Ground Penetrating Radar (GPR) traveltime data were collected
between boreholes in unsaturated Sherwood Sandstone close to Eggborough, UK. These
data were inverted for threedimensional models, where geophysical logs were used
to estimate the geostatistical model that we used to define appropriate
regularization operators. The forward computations and the calculations of the
Jacobians were performed with a finite element code for the electrical resistances
and a finite difference travel time algorithm for the traveltime data. The inverse
problem was solved using LSQR. The resulting models are more horizontally layered
when the regularization is based on the stochastic regularization operator instead
of the commonly used smoothness constraints; a pronounced layering is evident in
both EM conductivity and gamma logs at the Eggborough site. The interfaces between
lithological units are better defined in the models that were derived from joint
inversions compared to individual inversions. An advantage of this methodology is
that petrophysical relationships can be evaluated a posteriori without a priori
assumptions. The methodology allows us to test what features are resolved by the
data and to evaluate possible models that honour the data. This can be achieved by
defining a set of regularization operators that are based on different possible
geostatistical models and by giving different weights to the crossgradient
function. The methodology could readily be adapted to joint inversion of tracer
test and crosshole geophysical data. 
Track/Session 
Special Sessions / Hydrogeophysical data fusion 
Date 
20060618 
DOI 
10.4122/1.1000000709 


Robert Maier 
Sensitivity of PoreScale Flow and Dispersion to Properties of Random Bead Packs 




Author(s) 
Robert Maier^{1}; Mark Schure^{2}; Joe Seymour^{3}; Robert Maier^{1} 
Organisation(s) 
^{1}USACE; ^{2}Rohm and Haas Co.; ^{3}Montana State University 
Abstract 
Comparisons between porescale simulations and physical experiments are complicated
by the difficulty of reproducing the geometry of the experimental porous medium.
For example, obtaining the coordinates of the beads in experimental bead packings is
difficult, so porescale simulations typically develop geometry with some type of
spherepacking algorithm. Simulated and experimental geometries may have similar
porosity but otherwise no direct correspondence. Flow and dispersion are affected
by resulting differences in packing density, random packing variations, mild
polydispersity, nonrandom packing defects, and confining walls. The authors will
present recent results on the sensitivity of porescale simulations to these
physical parameters and to certain simulation parameters. Simulation and
experiment may also differ in methods for obtaining dispersion statistics.
Dispersion coefficients are often inferred from experimental column breakthrough
data, although more recently they have been inferred from changes in NMR signal
intensity within the measurement section of a column. Simulation techniques based
on particle tracking differ from breakthrough experiments but have some similarity
to NMR measurement techniques. The present method for longtime simulations of
dispersion will be presented and some issues in the experimental evaluation of
asymptotic dispersion will be discussed. As time permits, results will also be
presented on the sensitivity of flow and dispersion to the numerical treatment of no
slip boundaries, and a highly vectorizable implementation of the standard LBGK
algorithm for viscous fluid flow. 
Track/Session 
Special Sessions / PoreScale Modelling: New Developments And Applications 
Date 
20060618 
DOI 
10.4122/1.1000000707 


Jan M. Nordbotten 
Application of analytical solutions to storage of CO2 




Author(s) 
Jan M. Nordbotten^{1}; Michael A. Celia^{2}; Jan M. Nordbotten^{1} 
Organisation(s) 
^{1}University of Bergen; ^{2}Princeton University 
Abstract 
Many deep saline aquifers suitable for CO2 injection are located in mature, onshore
sedimentary basins of North America. These basins have been subjected to more than a
century of oil and gas exploration and production, as well as the more recent
practice of deep waste disposal. This legacy of drilling has resulted in large
numbers of wells, a significant fraction of which are abandoned. For example, the
number of wells is approaching 400,000 in the Alberta Basin in Canada, while in Texas
the number exceeds 1,000,000. Because the purpose of these wells is to allow for
easy transfer of fluids from the deep subsurface to the land surface, they have the
potential to serve as conduits along which injected CO2 could leak, especially if
they are improperly completed, operated, or abandoned.
To assess and understand different aspects of the flow and transport of injected CO2,
we have analysed the governing equations for twophase flow in porous media. In this
paper we will show how analytical solutions to the flow problem, both wellknown and
new, can be applied to CO2 sequestration scenarios to give substantial insight into
the order of magnitude of CO2 spread in the host aquifers, as well as the near well
flow patterns around abandoned wells. 
Track/Session 
Special Sessions / Geologic Sequestration of Carbon Dioxide 
Date 
20060618 
DOI 
10.4122/1.1000000705 


Alvaro A. Aldama 
Numerical solution of the twodimensional Richards equation via a TaylorFréchet ELLAM technique 




Author(s) 
Alvaro A. Aldama^{1}; Victor Arroyo^{1}; Alvaro A. Aldama^{1} 
Organisation(s) 
^{1}Mexican Institute of Water Technology 
Abstract 
The EulerianLagrangian Localized Adjoint Method (ELLAM) has been succesfully
employed in the solution of advectiondominated linear transport problems. Since
the concept of adjoint operator only exists for linear equations, ELLAM is strictly
speaking limited to linear problems. Some linearilization strategies have been
proposed, such as the one based on a Picard type of scheme. Nevertheless, these
strategies do not work well for the solution of highly nonlinear problems, such as
those governed by Richards’ equation, that describes the flow of liquids in
partially saturated soils. It is a well known fact that traditional Eulerian
techniques, such as the Finite Difference or the Finite Element Method require the
use of extremely fine meshes for the solution of Richards’ equation, particularly
in cases where sharp moisture content or pressure gradients propagate through
initially dry soils. This paper presents the development of a technique based on
the TaylorFréchet expansion of the nonlinear twodimensional Richards operator,
following the characteristics of the governing equation, properly cast in an
advectiondiffusionreaction format. Thus, the operator is linearized and a rapidly
convergent solution technique is generated. Several examples that illustrate the
application of the proposed procedure, incorporating a suite of different initial
and boundary conditions are presented. A comparison with conventional Eulerian
methods and the Picard linearlization procedure clearly show the superiority of the
TaylorFréchet ELLAM technique.
Keywords : Unsaturated soils, Richards’ equation, ELLAM, TaylorFréchet expansion. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000703 


Hiroshi Okabe 
Reconstruction of porespace images using multiplepoint statistics 




Author(s) 
Hiroshi Okabe^{1}; Martin Blunt^{2}; Hiroshi Okabe^{1} 
Organisation(s) 
^{1}Japan Oil, Gas and Metals National Corporation; ^{2}Imperial College London 
Abstract 
Quantitative prediction of petrophysical properties for reservoir rocks frequently
employs representative microscopic models of the pore space as input. Recently
digital imaging techniques such as microtomography have been used to provide void
space images at the resolution of a few microns. However, the sample size is
normally only a few mm when the highest resolutions are used, and even this may be
insufficient to capture some structures, particularly in carbonates. A larger image
may be necessary to predict representative flow properties. Focused ion beam images
can provide better resolution but only on even smaller samples. Twodimensional
(2D) thin sections can image microporosity, but do not directly capture the three
dimensional (3D) pore space.
We use 2D thinsections and 3D microtomography images as training data sets to
generate 3D pore space representations at high resolution using multiple point
statistics. The training images provide multiplepoint statistics, which describe
the statistical relation between multiple spatial locations and allow the
connectivity of the void space to be reproduced accurately. The method is tested on
sandstones and carbonates for which 3D images are available: these images capture
the connectivity of the larger pore spaces, while 2D thin sections accurately
characterize smallscale structure. The statistically generated images have
permeabilities computed using the latticeBoltzmann method (LBM) that are similar
to laboratorymeasured values. 
Track/Session 
Special Sessions / PoreScale Modelling: New Developments And Applications 
Date 
20060618 
DOI 
10.4122/1.1000000701 


Andreas Yiotis 
Pore network modeling of convective drying 




Author(s) 
Andreas Yiotis^{1}; Ioannis Tsimpanogiannis^{2}; Athanassios Stubos^{1}; Yanis Yortsos^{3}; Andreas Yiotis^{1} 
Organisation(s) 
^{1}NCSR 'Demokritos'; ^{2}Los Alamos National Laboratory; ^{3}University of Southern California 
Abstract 
Drying of porous media is a process of significant scientific and applied interest.
It involves several mechanisms at the pore scale that affect the macroscopic behavior
of the drying process. These include phase change at the liquidgas interface, mass
and heat transfer by diffusion and convection, capillarityinduced flow through
wetting liquid films and the receding of the liquid gas interfaces under combined
viscous, capillary and buoyancy forces.
In most typical applications, porous materials are subjected to a flow of a purge gas
along the external porous surface, which can significantly enhance the recovery
process and reduce drying times. The local mass transfer coefficient depends on the
mass transfer conditions within the convective layer over the surface as well as on
the liquid saturation at the surface. For a realistic solution of the drying problem,
mass transfer in the convective layer needs to be solved in conjunction with mass
transfer within the porous medium.
This paper presents a coupled porenetwork model that accomplishes such a solution.
The model accounts for isothermal evaporation at the liquidgas interface, mass
transfer by diffusion and flow through liquid films within the porous medium and
convective mass transfer through the convective layer over the surface. We study the
effect of velocity profiles in the convective layer, the Peclet number of the purge
gas and the thickness of the convective layer on the drying curves. Our results show
that the drying rate remains practically constant as long as the liquid films span
along the pore network and their density at the surface is sufficiently high. Our
results explain previously reported experimental findings and provide a rigorous
explanation of the constantrate period. 
Track/Session 
Special Sessions / PoreScale Modelling: New Developments And Applications 
Date 
20060618 
DOI 
10.4122/1.1000000699 


PalEric Oeren 
Porescale computation of material and transport properties of NorthSea reservoir rocks 




Author(s) 
PalEric Oeren^{1}; Stig Bakke^{1}; Rudolf Held^{2}; Rudolf Held^{2} 
Organisation(s) 
^{1}Numerical Rocks AS; ^{2}Statoil ASA 
Abstract 
The acquisition of digitized representations of rock microstructures has been
established in the workflow for investigation of petrophysical, material, and
transport properties. The availability of these data open the way for the
development of methods that directly predict effective properties based on
digitized topological information. The increasing number of effective properties
that may be numerically calculated includes elastic moduli, electrical
resistivities, fluid permeabilities, or constitutive relationships for multiphase
flow.
This work investigates different sandstone lithofacies in a North Sea field with
these analyses. We compare samples acquired by Xray Microtomography with digitized
samples of reconstructed lithofacies. The latter are based on backscattered
electron images of standard 2D petrographic thin sections. The study largely
shows an excellent agreement of the effective properties for the microCT and
reconstructed samples for these heterogeneous rock types. Limitation in resolution
of microCT data are revealed, where effective properties are sensitive to details
of the microstructure. Our results allow interpretation of effective medium
properties with respect to the investigated lithofacies and presentation of cross
property relations. Such crossproperty relationships become especially useful,
when one property is more readily obtained than another. 
Track/Session 
Special Sessions / PoreScale Modelling: New Developments And Applications 
Date 
20060618 
DOI 
10.4122/1.1000000697 


Mortazavi Naeini Seyed mohammad 
Application of Ant Algorithm in Calibration of RainfallRunoff Model 




Author(s) 
Mortazavi Naeini Seyed mohammad^{1}; Alireza B.Dariane^{2}; Mortazavi Naeini Seyed mohammad^{1} 
Organisation(s) 
^{1}Graduated Student; ^{2}Assistant Professor 
Abstract 
The successful application of a conceptual rainfallrunoff (CRR) model depends on
how it is calibrated. The CRR models generally represent the soil moisture
accounting phase of the hydrologic cycle as several interconnected subsystems, each
representing a certain component in the processing of the hydrologic event. Despite
the popularity of CRR models, reports in the literature indicate that difficulties
in calibrating the parameters.
Ant Colony Optimization (ACO) is one of the recent optimization methods which is
inspired by the fact that ants are able to find the shortest route between their
nest and a food source. This is accomplished by using pheromone trails as a form of
indirect communication. In this paper, calibration of a rainfallrunoff model is
presented by using Ant Colony Optimization (ACO) method. The results are compared
with the conventional calibration methods. 
Track/Session 
Special Sessions / Data assimilation in water resources modelling 
Date 
20060618 
DOI 
10.4122/1.1000000696 


Mortazavi Naeini Seyed mohammad 
Parameter Estimation of the Nonlinear Muskingum Model Using Ant Colony Optimization 




Author(s) 
Mortazavi Naeini Seyed mohammad^{1}; Mortazavi Naeini Seyed mohammad^{1} 
Organisation(s) 
^{1}Graduated Student 
Abstract 
There are two types of basic approaches to route floods : the hydrologic routing
approaches and the hydraulic routing approache. One of the hydrologic routing
techniques, the Muskingum method has been frequently used to route floods in
natural channels and rivers.In this paper, parameter estimation of the nonlinear
Muskingum model is presented by Using Ant Colony Optimization. Ant Colony
Optimization (ACO) is one of the recent optimization methods which is inspired by
the fact that ants are able to find the shortest route between their nest and a
food source. This is accomplished by using pheromone trails as a form of indirect
communication. In this paper, calibration of a rainfallrunoff model is presented
by using Ant Colony Optimization (ACO) method. The results are compared with the GA
and HS methods. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000695 


Masa Prodanovic 
Investigating pore scale configurations of two immiscible fluids via Level Set Method 




Author(s) 
Masa Prodanovic^{1}; Steven L. Bryant^{2}; Masa Prodanovic^{1} 
Organisation(s) 
^{1}Institute for Computational Engineering and Sciences, University of Texas at Austin; ^{2}Department of Petroleum and Geosystems Engineering and Institute for Computational Engineering and Sciences, University of Texas at Austin 
Abstract 
The study of pore level displacement of immiscible fluids has scientific appeal as
well as a plethora of engineering applications, notably in oil reservoir engineering
and in environmental problems in the shallow subsurface. Pore network models have
been used for numerical simulation of fluid displacement over relevant physical
volume sizes. An accurate description of the mechanics of 3D displacement could
significantly improve the predictions from network models of capillary pressure 
saturation curves, interfacial areas and relative permeability in real porous media.
If we assume quasistatic displacement, the criteria for interface movement can be
deduced from capillary pressure and local pore geometry. The capillary pressure
(pressure difference between the nonwetting and wetting fluid phase) at the fluid
interface is determined by the YoungLaplace equation Pc = 2*S*C, where S is the
interfacial tension and C is mean curvature of the interface. At constant pressure
and surface tension, pore scale interfaces are modeled as constant mean curvature
surfaces. Extremely irregular geometry of natural porous media makes it difficult to
evaluate surface curvature values and corresponding geometric configurations of two
fluids. A purely mechanistic set of pore level criteria for fluid advancement through
pore space implemented by [1] relied on idealizing the interfacial surface as locally
spherical. Even with spherical idealizations, simulating the topological changes of
the interface, such as splitting and merging fronts, is nontrivial.
We apply the Level Set Method (using Level Set Toolbox [2]) and the Surface Evolver
software [3] for tracking and propagating interfaces in order to robustly handle
topological changes and to obtain geometrically correct interfaces. For the level set
method, we describe a simple model for mechanical equilibrium between capillary
pressure and surface tension. The results from the models are illustrated at the pore
scale in two and three dimensions. The pore scale grain boundary conditions are
extracted from model porous media and from measured geometries in real rocks [4].
1. M. Gladkikh and S. L. Bryant. Prediction of imbibition in unconsolidated granular
materials. Journal of Colloid and Interface Science 288 (2005) 526539
2. K. Brakke. Surface Evolver, an interactive program for the modeling of liquid
surfaces shaped by various constraints.
http://www.susqu.edu/facstaff/b/brakke/evolver/html/intro.htm#overview
3. I. M. Mitchell and J. A. Templeton. A Toolbox of HamiltonJacobi Solvers for
Analysis of Nondeterministic Continuous and Hybrid Systems. SpringerVerlag. Lecture
Notes in Computer Science (LNCS) 3413, 480494.
4. W. B. Lindquist. 3DMARock, A Software Package for Automated Analysis of Rock Pore
Structure in 3D Computed Microtomography Images
http://www.ams.sunysb.edu/~lindquis/3dma/3dma_rock/3dma_rock.html 
Track/Session 
Special Sessions / PoreScale Modelling: New Developments And Applications 
Date 
20060618 
DOI 
10.4122/1.1000000693 


Michael Kuehn 
2D or not 2D: Are two dimensions enough to accurately model convective fluid flow through faults and surrounding host rocks? 




Author(s) 
Michael Kuehn^{1}; Conny Zeeb^{2}; Klaus Gessner^{3}; Michael Kuehn^{1} 
Organisation(s) 
^{1}Applied Geophysics, RWTH Aachen University; ^{2}Hydrology, University of Tübingen; ^{3}The University of Western Australia, School of Earth and Geographical Sciences 
Abstract 
In many studies of waterrock interaction, convective fluid flow has been invoked
to explain diagenetic processes, metamorphism, or metal precipitation. Fluid
convection in faults is increasingly recognised as an important mechanism for fluid
flow, heat transfer, and mass transport in hydrothermal systems, particularly in
consolidated and crystalline rocks. Convection is influenced not only by heat
transport processes within the fault but also by lateral heat transfer to and from
the surrounding rock mass. There is often a close spatial relationship between
major ore deposits and regional scale faults.
Most numerical studies simulate free convection in 2D only. This is because fluid
patterns are more easily recognised with less complicated geometries, less
computational time is required, or because some computer codes are restricted to
two dimensions.
Using the finite difference simulation code SHEMAT, a series of numerical
simulations of thermally driven fluid flow have been carried out to investigate the
difference in the fluid flow patterns in 2D and 3D models for the same geological
architecture. SHEMAT solves coupled problems involving fluid flow, heat transfer,
species transport, and chemical waterrock interaction on a Cartesian grid. In
SHEMAT, the different flow, transport, and reaction processes can be selectively
coupled.
The results of this study show that 2D and 3D models of convection in hydrothermal
systems produce significantly different results. In many cases 2D models represent
an oversimplification, and conclusions reached from such investigations are likely
to be irrelevant. In the case of planar high permeability regions, such as faults
and permeable stratigraphic units extending along strike, 2D and 3D modelling
outcomes vary significantly. Hence 3D models are absolutely essential to describe
the flow field in these cases.
An exception is incorporation of an impermeable basement, resulting in 2D
convection patterns identical to observed 3D fluid flow fields, but only if
vertical fault permeability equals horizontal host rock permeability. Conceptual
exemptions are 2D models of high permeability regions with close to radial or
linear symmetries, such as damage zones between fault jogs or at fault
intersections, giving reasonable results in 2D. 
Track/Session 
Special Sessions / MultiDisciplinary Approaches To Reactive Transport Simulation In Aquifer Systems 
Date 
20060618 
DOI 
10.4122/1.1000000691 


Andreas Bielinski 
Numerical Modeling of CO2 sequestration with MUFTE_UG 




Author(s) 
Andreas Bielinski^{1}; Anozie Ebigbo^{1}; Andreas Kopp^{1}; Holger Class^{1}; Rainer Helmig^{1}; Andreas Bielinski^{1} 
Organisation(s) 
^{1}Institute of Hydraulic Engineering, University of Stuttgart 
Abstract 
This presentation gives an overview of the modeling capabilities of
our group and our participation in various CO2related projects.
Furthermore, a benchmark example is discussed in detail.
We use the numerical simulator MUFTE_UG for computing nonisothermal
multiphase multicomponent flow and transport processes in porous media. It
has been extended by a twophase twocomponent model concept for the simulation
of CO2 sequestration in geological formations. It takes into account the
two phases CO2 and brine and the components CO2 and water which can dissolve
in the different phases. Furthermore, nonisothermal effects are considered
by solving an energy equation. Chemical reactions are not taken into account
by the code.
To show the capabilities of MUFTE_UG the results of principle calculations
will be presented, such as CO2 plume evolution in the subsurface, longterm
storage behavior of dissolved CO2, and nonisothermal effects especially
during leakywell scenarios.
Our work group currently participates in two research projects dealing with
CO2 sequestration; these are:
 "CO2SINK": this project is a fieldscale laboratory for testing CO2 injection
underneath a densely populated area close to Berlin. The largescale
numerical simulation of the CO2 injection process, of various scenarios
referring to scarce geological input data, and of longterm CO2 plume
evolution is the task that our group is dealing with. CO2SINK is
funded by the EU.
 "Numerical Investigation of CO2 Sequestration in Geological Formations 
ProblemOriented Benchmarks": the tasks of this project are the development
of benchmark problems to be used within the scientific community for the comparison
and verification of different numerical codes. The benchmark computations
deal with different subjects within the framework of CO2 sequestration,
e.g. storagecapacity estimation of aquifers, computation of plume evolution
and comparison with analytical solution methods, and enhanced coalbed methane
recovery. The project is funded by the German Research Foundation (DFG) and the
Federal Ministry of Education and Research (BMBF).
One of the benchmark examples will be presented in detail, including the assumptions
for the geology, the choice of the domain, and the grid generation. The initial and
boundary conditions will be motivated before showing and discussing the simulation
results.
Finally, we will summarize our work and give an overview of the next steps that we
plan to take in our research field. 
Track/Session 
Special Sessions / Geologic Sequestration of Carbon Dioxide 
Date 
20060618 
DOI 
10.4122/1.1000000689 


Karim DJADEL 
Discontinous Galerkin Methods for the SahllowWater Equations with bathymetric terms and dry areas 




Author(s) 
Karim DJADEL^{1}; Alexandre ERN^{1}; Serge PIPERNO^{1}; Karim DJADEL^{1} 
Organisation(s) 
^{1}Ecole Nationale des Ponts et Chaussées 
Abstract 
In this paper, we develop Discontinuous Galerkin Methods to deal with the
ShallowWater Equations involving bathymetric temrms and dry areas. Our major goals
are on the one hand to preserve quiescent flows and, more generally, steadystates
and on the other hand to ensure stability when the flow includes flooding and drying.
Drawing on earlier ideas for Finite Volume Methods [Aud,Ber], we design two
Discontinuous Galerkin Methods that preserve flows at rest. We investigate their
acuracy on various numerical tests including subcritical and trancritical flows.
Moreover, for one of the methods, we analyze its behaviour for some test cases
including flooding and drying.
[Aud] : E. Audusse, F. Bouchut, M.O. Bristeau, R. Klein, B. Perthame (2004) : "A fast
and wellbalanced scheme with hydrostatic reconstruction fo the shallow water flows",
SIAM J. Sci. Comput., Vol 25, n°6, p. 20502065.
[Ber] : A. Bermudez, M.E. Vazquez (1994) : "Upwind methods for hyperbolic conservation
laws with source terms", Computers and Fluids, 23, p.10491071. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000688 


Karim DJADEL 
Discontinous Galerkin Methods for the ShallowWater Equations with bathymetric terms and dry areas 




Author(s) 
Karim DJADEL^{1}; Alexandre ERN^{1}; Serge PIPERNO^{1}; Karim DJADEL^{1} 
Organisation(s) 
^{1}Ecole Nationale des Ponts et Chaussées 
Abstract 
In this paper, we develop Discontinuous Galerkin Methods to deal with the
ShallowWater Equations involving bathymetric terms and dry areas. Our major goals
are on the one hand to preserve quiescent flows and, more generally, steadystates
and on the other hand to ensure stability when the flow includes flooding and drying.
Drawing on earlier ideas for Finite Volume Methods [Aud,Ber], we design two
Discontinuous Galerkin Methods that preserve flows at rest. We investigate their
acuracy on various numerical tests including subcritical and trancritical flows.
Moreover, for one of the methods, we analyze its behaviour for some test cases
including flooding and drying.
[Aud] : E. Audusse, F. Bouchut, M.O. Bristeau, R. Klein, B. Perthame (2004) : "A fast
and wellbalanced scheme with hydrostatic reconstruction fo the shallow water flows",
SIAM J. Sci. Comput., Vol 25, n°6, p. 20502065.
[Ber] : A. Bermudez, M.E. Vazquez (1994) : "Upwind methods for hyperbolic conservation
laws with source terms", Computers and Fluids, 23, p.10491071. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000686 


Jonas Toelke 
Adaptive Lattice Boltzmann simulations of freesurface flows 




Author(s) 
Jonas Toelke^{1}; Manfred Krafczyk^{1}; Jonas Toelke^{1} 
Organisation(s) 
^{1}TU Braunschweig 
Abstract 
Recently LatticeBoltzmann (LB) methods have matured as complementary models and
simulation approaches for solving complex flow problems in engineering.
In our work we extend an existing laminar free surface LB model recently developed
by Koerner et al. by a Large Eddy model to describe turbulent flows and validate our
model by threedimensional computations of a rigid body impact on a shoreline and the
resulting wave generation. The results are compared to experimental and numerical
data obtained by Liu et al.
In addition, we present an adaptive 3D simulation of the classical dam break problem. 
Track/Session 
Special Sessions / Boltzmann Methods in Water Resources 
Date 
20060618 
DOI 
10.4122/1.1000000685 


Sarah E. Gasda 
Significance of slope on CO2 sequestration in deep sedimentary formations 




Author(s) 
Sarah E. Gasda^{1}; Michael A. Celia^{1}; Jan M. Nordbotten^{2}; Sarah E. Gasda^{1} 
Organisation(s) 
^{1}Princeton University; ^{2}University of Bergen 
Abstract 
Recent investigations regarding CO2 sequestration in deep, saline aquifers have
focused on characterization
of the injected plume, its migration within the aquifer over time, and possible
leakage out of the aquifer. As
part of our efforts to understand and quantify leakage potential in CO2 storage
systems, a semianalytical
solution has been developed that describes the plume shape evolution as well the
amount of leakage, with a
focus on leakage along abandoned wells. The semianalytical solutions require a
number of simplifying
assumptions, including a perfectly horizontal aquifer, negligible capillary pressure,
and symmetry of the
injection plume. Each of these assumptions can be tested systematically through
application of more general
numerical simulators. For example, in typical sedimentary basins, it is common to
have sloping aquifers with
a vertical rise of up to 34 km over the total horizontal length of the basin
(hundreds of kilometers).
Although the slope may only be 1% or less, the effects on the upward migration of the
CO2 plume may be
significant over the time scales appropriate for carbon sequestration. Similarly,
the role of capillarity in these
systems may be significant due to capillary diffusion or to capillary exclusion. In
this study, we use a general
twophase numerical simulator to assess the limitations of the assumptions required
to derive semianalytical
solutions to these systems. For example, we can simulate injection of CO2 into a
confined saline aquifer for
an extended period (we have used 30 years) and examine the effect of different
degrees of slope on the
centroid and maximum upslope extent of the plume. These measures of plume asymmetry
can then be
related to an appropriate dimensionless grouping that takes into account the fluid
properties and aquifer
characteristics. In this presentation we will present results from these simulations
and discuss their
implications regarding the extent to which CO2 injection systems can be simplified. 
Track/Session 
Special Sessions / Geologic Sequestration of Carbon Dioxide 
Date 
20060618 
DOI 
10.4122/1.1000000683 


JingRu Cheng Cheng 
Parallelization of the WASH123D Code—Phase III: 1Dimensional Channel, 2Dimensional Overland, and 3Dimensional Subsurface Flows 




Author(s) 
JingRu Cheng Cheng^{1}; Robert Hunter^{1}; HwaiPing Cheng^{1}; David Richards^{1}; JingRu Cheng Cheng^{1} 
Organisation(s) 
^{1}U.S. Army ERDC 
Abstract 
Watershed models are used to simulate and predict major hydrological processes, such
as surface or subsurface flows, which may occur on different spatial domains and
temporal scales. A key feature of watershed models is the ability to model
interactions among different processes and domains. Such interactions can be
strongly or weakly coupled depending on the relevant time scales for each process.
WASH123D is a firstprinciples, physicsbased model for simulating a coupled system
of channel flow, overland flow, and subsurface flow. A parallel version, pWASH, has
been used for the calibration, validation, and evaluation of proposed alternatives
of the Biscayne Bay Coastal Wetlands project. The goal is to rehydrate wetlands
using the best alternative based on the simulation results. In the pWASH code,
channel flow is modeled as a onedimensional (1D) channel network, overland flow as
a 2D process, and subsurface flow as a 3D process. Different algorithms are
implemented to account for the interactions between these different domains. The
pWASH code is designed to tackle large watershed problems on parallel high
performance computers. A softwareengineering approach was used to efficiently
parallelize the complex coupling algorithms. The resulting software toolkit
encapsulates the parallel data structures and message passing required for multi
domain/process interactions. In this paper, the authors briefly describe the
numerical methods in WASH123D, the parallelization of pWASH, and the scalability of
coupled flow problems running on parallel high performance computers. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000681 


Mortazavi Naeini Seyed mohammad 
APPLICATION OF ACO ALGORITHM IN SCSCN METHOD 




Author(s) 
Mortazavi Naeini Seyed mohammad^{1}; P. Suresh Babu^{2}; Mortazavi Naeini Seyed mohammad^{1} 
Organisation(s) 
^{1}Graduated Student; ^{2}PhD Candidate 
Abstract 
Calibrating the most appropriate parameter is one of the crucial stages in
dependable rainfallrunoff modeling. This paper evaluates the computational
performance of Ant Colony Optimization (ACO) and Marquardt Algorithms (MA) used for
calibration of CN and λ parameters of the Soil Conservation Service Curve Number
(SCSCN) model in optimization. Employing standard error of estimate (Se) and
standard error ratio (SER), the performance of both the algorithms was tested on a
large set of US data. 
Track/Session 
Special Sessions / Data assimilation in water resources modelling 
Date 
20060618 
DOI 
10.4122/1.1000000680 


Junhong LIANG 
BGK Boltzmann Model and Lattice Boltzmann Method for Shallow Water Flows 




Author(s) 
Junhong LIANG^{1}; Mohamed GHIDAOUI^{1}; Junhong LIANG^{1} 
Organisation(s) 
^{1}Department of Civil Engineering, the Hong Kong University of Science and Technology 
Abstract 
Both the BhatnagarGrossKrook (BGK) Boltzmann model and Lattice Boltzmann method
(LBM) are based on the numerical discretization of the Boltzmann equation with
collisional models, such as, the BGK model. The BGK Boltzmann scheme is a finite
volume scheme, where the timedependent distribution function with continuous
particle velocity space is constructed and used in the evaluation of the numerical
fluxes across cell interfaces. On the other hand, LBM tracks limited number of
particles and the viscous flow behavior emerges automatically from the intrinsic
particle stream and collisions process. In the field of computational methods for
water resources, BGK model is mainly used in shallow water flows and contaminant
transport, while application of LBM is focused on lowFroude number shallow water
flows, flows in porous media. No existing work has been contributed to compare the
performance of both models in the field. In this paper, comparisons for both models
are restricted to the shallow water flows. Both BGK and LBM for shallow water
equations will be first briefly formulated. Results by both schemes in several
benchmark problems in shallow water flows are presented. It is found that the
existing LBM model is not suitable for high Froude number flows and fails in the
dambreak tests where all three flow regimes, i.e., the supercritical flow, critical
flow and subcritical flow coexist, while the BGK model can accurately resolve both
bore and rarefaction wave in the test. For low Froude number flows, performances by
both models in flows over a hump and Poiseuille flow are comparable. 
Track/Session 
Special Sessions / Boltzmann Methods in Water Resources 
Date 
20060618 
DOI 
10.4122/1.1000000679 


Abhijit Chaudhuri 
Modeling of solute transport in a heterogeneous porous medium with a random source using stochastic finite element method 




Author(s) 
Abhijit Chaudhuri^{1}; Sekhar Muddu^{1}; Abhijit Chaudhuri^{1} 
Organisation(s) 
^{1}Indian Institute of Science 
Abstract 
Most of the probabilistic studies in solute transport literature are focused on
predicting the concentration uncertainty due to the heterogeneity of the governing
flow and transport parameters. The randomness in the source condition can also be a
major source of uncertainty in the concentration field. Some of the studies have
also looked into this aspect and analysed the effect of random source condition
while considering the system to be deterministic. For a deterministic system the
analysis of probabilistic behavior of concentration due to source uncertainty is
performed using a response/impulse function, which is obtained analytically or
numerically for a unit pulse source condition. However, a more general form of the
problem formulation is to consider both random source condition and system
parameters. Under this condition, the response function becomes a random function
and depends on the random system parameters.
In the present study an attempt is made to include the system uncertainty and to
assess the relative effects of system uncertainty and source uncertainty on the
probabilistic behavior of concentration. Here the random source is modeled as a
Poisson process, which results in concentration being a filtered Poisson process.
The probabilistic behavior of the random response function is obtained by using a
perturbation based stochastic finite element method. In this method the parameters
of each element are treated as random variables. The mean and covariance matrix are
obtained from the specified mean and covariance function of the parameters. The
proposed method is applied for analyzing the solute transport problem in one
dimensions considering flow and transport parameters as a random fields and
treating the amount and timing of the mass released from the source as random. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000677 


Håkon Hægland 
Streamline methods on fault adapted grids for risk assessment of storage of CO2 in geological formations 




Author(s) 
Håkon Hægland^{1}; Helge Dahle^{1}; Geir Terje Eigestad^{2}; Michael Celia^{3}; Jan Martin Nordbotten^{3}; Erlend Øian^{2}; Håkon Hægland^{1} 
Organisation(s) 
^{1}University of Bergen; ^{2}CIPR, University of Bergen; ^{3}Princeton University 
Abstract 
Streamline methods have shown to be effective for reservoir
characterization and simulation.
In this work we will
develop methodology which allows for tracing of streamlines in
fractured or faulted media including anthropogenic faults such as
abandoned wells.
The basis for a streamline method is a
sequential splitting of the
coupled pressure and saturation equations.
A massconservative
discretization, which handles general faulted grids in a consistent
manner, will be used for
the pressure equation.
The fact that the saturation equation is solved along the streamlines,
makes accurate tracing of streamlines essential. In earlier work we
have developed streamline tracing on
structured and unstructured matching grids.
Here we present an extension to grids adapting to faulted media.
For CO2 injection, probabilistic analysis within a risk assessment
framework requires multiple realizations. Therefore, fast numerical methods,
such as streamline simulation, are needed for screening.
The work is motivated in part by the need to assess potential of
geological storage of CO2 and is also highly relevant for reservoir
simulation. 
Track/Session 
Special Sessions / Geologic Sequestration of Carbon Dioxide 
Date 
20060618 
DOI 
10.4122/1.1000000675 


Håkon Hægland 
Adaptive streamline tracing for streamline simulation on irregular grids 




Author(s) 
Håkon Hægland^{1}; Helge Dahle^{1}; Geir Terje Eigestad^{2}; KnutAndreas Lie^{3}; Ivar Aavatsmark^{2}; Håkon Hægland^{1} 
Organisation(s) 
^{1}University of Bergen; ^{2}CIPR, University of Bergen; ^{3}SINTEF, Dept. of Applied Math., Oslo 
Abstract 
Streamline methods have shown to be effective for reservoir
simulation. Streamline simulation relies on an efficient an accurate
calculation of streamlines and timeofflight
coordinates (TOF).
Streamlines are commonly computed on a cellbycell basis using
a flux interpolation in the semianalytical
Pollock's method.
An alternative method is a gridcell cornerpoint
velocity interpolation, which is able to reproduce uniform flow in
three spatial dimensions. For this method numerical integration of
streamlines is required.
The shape of streamlines are affected by a change in
velocity direction over a cell, whereas TOF is sensitive to
variation in the absolute value of the velocity. Hence, an adaptive
method should be used
to control the error
in the numerical integration of the velocity.
In this work, we propose a method for adaptive step size selection
for numerical integration of streamlines,
and compare it with existing methods. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000673 


Christophe Le Potier 
Positivity problem and reactive transport simulation in porous media 




Author(s) 
Christophe Le Potier^{1}; Alain Genty^{1}; Christophe Le Potier^{1} 
Organisation(s) 
^{1}Commissariat à l'energie atomique 
Abstract 
During the last decade, a large amount of work has been done in
reactive transport modeling in porous media leading today to
geochemical transport codes based on the coupling of transport
models and geochemistry modules.
In the framework of highlevel nuclear waste repository safety
calculations, we developed such a code with the numerical platform
ALLIANCES allowing the coupling of several classical transport
codes (Porflow, MT3D, Traces, Cast3m) and geochemistry
modules (PhreeqC, Chess).
In order to avoid negative concentration calculation stemming from
the transport model that may induce mass nonconservation, non
consistent concentration field or geochemistry module fail, one
generally use for reactive transport simulations orthogonal meshes
oriented with the main velocity direction in spite of the fact that
orthogonal meshes are not well adapted to the description of the
repository near field including cylindrical shapes (like wastes
canisters, repository vaults, galleries) and lead to coarse problem
description and/or time consuming calculations.
In this paper, we investigate with our ALLIANCES platform, on
unstructured 2D mesh of cylindrical shape, the impact of using
different spatial schemes (Mixed Hydrid Finite Elements, Finite
Volumes (MPFA)) for the transport model including anisotropic
heterogeneous dispersive tensor on negative concentration calculation
and on global impact on reactive transport model in term of
concentration field and mass conservation errors. 
Track/Session 
Special Sessions / MultiDisciplinary Approaches To Reactive Transport Simulation In Aquifer Systems 
Date 
20060618 
DOI 
10.4122/1.1000000671 


Gunnar Nuetzmann 
First attempts to model the virus  bacteria interaction in the context of bank filtration 




Author(s) 
Gunnar Nuetzmann^{1}; Rainer Brueggemann^{1}; Kilian Pramschiefer^{2}; Rainer Brueggemann^{1} 
Organisation(s) 
^{1}Institute of Freshwater Ecology and Inland Fisheries; ^{2}Technical University of Berlin 
Abstract 
In Berlin the bank filtration plays an important role to obtain drinking water.
During the passage of water in the saturated and unsaturated soil zone oxygen,
nutrients, pollutants, pathogens etc. pass the system of pores and different kind of
interactions take place.
Whereas the transport processes of pathogens coupled with sorption and sinks can
rather successfully described using different kinds of filtration and transport
models, the biological interaction of e. g. bacteriophages with biofilms is still not
well understood.
Modelling of this kind of interactions is hampered by the poor data availability and
by the difficult design of appropriate experiments. Therefore, simple mathematical
models with as few parameters as possible may useful for a first qualitative insight.
In this paper such a conceptual model is shown, taking into account virus and biofilm
interaction and steadystate flow in a porous medium. Further assumptions about the
role of transported solutes are made because of the nonlinearity and complexity of
the model. The concept of zeroisoclines is used to identify the fixpoints of the
system and in a second step the dependence of the virus and bacteria concentration on
the flow rate was studied. As a consequence of this modelling runs we cannot exclude
that hysteretic effects depending on the water flow may appear. 
Track/Session 
Special Sessions / Ecohydrology: From Detailed Descriptions To General Synthesis? 
Date 
20060618 
DOI 
10.4122/1.1000000669 


Gunnar Nuetzmann 
Combined watershed and groundwater modelling to investigate lowland runoff processes – illustrated for the Lietzengraben basin (Germany) 




Author(s) 
Gunnar Nuetzmann^{1}; Silke Mey^{2}; Bernd Pfützner^{2}; Silke Mey^{2} 
Organisation(s) 
^{1}Institute of Freshwater Ecology and Inland Fisheries; ^{2}Bureau of Applied Hydrology 
Abstract 
Since the last decades in several lowland watersheds of northeast Germany a
decreasing runoff combined with temporal hydrological droughts are observed. This
paper makes the case for a modular organised, fully distributed, comprehensive, multi
scaling model, which falls between the fully distributed, physically based
hydrological modelling system of the type of the MIKE SHE model and the lumped,
conceptual rainfallrunoff modelling system. This is achieved by integrating the
watershed model ArcEgmo with the groundwater model ASM. Both of them are fully
distributed models and their interaction is organised on the same rastergrid. The
advantage of this approach is the use of readily available data, the handling of
watershed heterogeneities (multiple land uses, soil layers, vegetation structures)
and the significantly increased flexibility in handling streamaquifer interactions.
The mechanics of integrating the components are outlined, and model calibration,
validation and simulation of realworld scenarios are briefly presented. Because of
the fact, that main part of this basin was influenced by additional water supply more
then 80 years, the aim of these scenarios was to derive management strategies to
support the water balance of the catchment area, especially taken into account the
interaction between surface and ground water.
These applications demonstrate the practicability and versatility of this relatively
simple and conceptual clear approach, making public acceptance of the integrated
watershed modelling system much easier. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000667 


Majken C Looms 
Monitoring unsaturated flow and transport using crossborehole geophysical methods 




Author(s) 
Majken C Looms^{1}; Karsten H Jensen^{1}; Lars Nielsen^{1}; Andrew Binley^{2}; Hans Thybo^{1}; Majken C Looms^{1} 
Organisation(s) 
^{1}Geological Institute, University of Copenhagen; ^{2}Department of Environmental Science, Lancaster University 
Abstract 
Recent research has shown that crossborehole georadar and electrical resistivity
tomography (ERT) can provide data on soil moisture content and conductivity
variations in the vadose zone at a more appropriate spatial scale than traditional
techniques.
A field site has been established in Denmark on a 2030 m layer of unsaturated melt
water sand and gravel deposits. Two identical field setups have been established
each having four ERT and four georadar boreholes. The boreholes are drilled to a
depth of 12 m, and form a cross consisting of two lines. Along each line the outer
two boreholes (7 m apart) are equipped with ERT instrumented PVCtubes (electrodes
every 50 cm) while the inner two boreholes (5 m apart) have access tubes for
georadar.
Two different tracer infiltration experiments have been performed; (i) natural
infiltration and (ii) forced infiltration experiments. In the natural infiltration
tracer experiment, 200 L tracer was distributed on a 10 m by 10 m area, simulating
a 2 mm rain event. In the forced infiltration tracer experiment, tracer was applied
during the first 4 hours of the experiment at a constant rate of 250 l/hr (5.1
mm/hr) followed by irrigation of clean water at the same rate to accelerate flow
during the successive 10 days.
When using the two geophysical monitoring techniques simultaneously, it is possible
to monitor variations in fluid conductivity resulting from tracer infiltration by
combining the water content images from crossborehole georadar with the bulk
conductivity images achieved from the crossborehole ERT.
In both experiments, water content and conductivity data were collected prior to
and after the applied tracer. The two sets of experiments provide data describing
two vastly different flow conditions. In the natural infiltration experiment the
upper boundary is determined by the naturally occurring precipitation and actual
evapotranspiration. In this case little temporal variation in soil moisture content
is observed and the tracer migration mainly takes place in autumn and winter where
a surplus netprecipitation exists. In contrast, flow and transport velocities are
much higher in the forced infiltration experiment and the upper boundary condition
for this experiment is much more welldefined.
Both experiments are interpreted by numerical hydraulic models which allow
estimation of largescale unsaturated hydraulic and transport parameters by
appropriate inverse modeling. 
Track/Session 
Special Sessions / Hydrogeophysical data fusion 
Date 
20060618 
DOI 
10.4122/1.1000000665 


Raphaèle Herbin 
ChemistryTransport coupling : Implicit schemes keeping a code coupling approach 




Author(s) 
Raphaèle Herbin^{1}; Philippe Montarnal^{2}; Nicolas Bouillard^{3}; Nicolas Bouillard^{3} 
Organisation(s) 
^{1}Université de Provence; ^{2}CEA; ^{3}CEA (French Atomic Energy Commission), DEN / DM2S / SFME / MTMS 
Abstract 
This work is linked with the field of reactive transport simulations in the context
of reactive waste storage in deep geological disposals. Indeed, the evolution of the
different materials and the species migration are deeply influenced by chemical,
hydraulic and transport interactions.
For these modeling issues it is necessary to deal with numerical codes involving
combined effect of transport and multiple geochemical species within groundwater
flow. Currently, many of the codes use a sequential iterative or noniterative
approach based on an operatorsplitting technique between the chemistry and transport
parts. One main advantage of this approach is the use of two different codes: one for
the transport and one for the chemistry. More recently, some codes have developed a
full implicit coupled approach dealing with chemistry and transport equations in one
global resolution. These types of algorithms are more robust than the sequential ones but
do not allow the use of existing geochemical codes.
In this work we present the development and application of two implicit schemes
keeping a code coupling approach: Newton and Nonlinear Conjugate Gradient methods. In
the former method, the computation of the full Jacobian matrix is required while in
the latter
one, a derivation along the descent direction is used. A derivation of the
chemistry operator is computed numerically by finite differences. The advantage of
the Nonlinear Conjugate Gradient method in comparison with the classical NewtonKrylov
algorithm is that we have only one loop of iterations and the original feature of the
implementation is the use of an explicit formula for the descent parameter. Different
preconditioning methods are tested. We present some comparisons of these methods in
one and two space dimensions.
This work is part of the Alliances project the aim of which is to produce a software
platform for the simulation of nuclear waste repository storage and disposal.
Alliances is jointly developing by CEA (French Atomic Energy Commission),
ANDRA(French Nuclear Waste Management Agency) and EDF (French Electricity Producer). 
Track/Session 
Special Sessions / MultiDisciplinary Approaches To Reactive Transport Simulation In Aquifer Systems 
Date 
20060618 
DOI 
10.4122/1.1000000663 


Martin Ferer 
Drainage with Unfavorable Viscosity Ratios: a porelevel model study 




Author(s) 
Martin Ferer^{1}; Grant Bromhal^{2}; Duane Smith^{2}; Martin Ferer^{1} 
Organisation(s) 
^{1}West Virginia University and National Energy Technology Laboratory, P. O. Box 880, Morgantown, WV 265070880; ^{2}U. S. Department of Energy, National Energy Technology Laboratory, P. O. Box 880, Morgantown, WV 265070880 
Abstract 
The applications of carbon dioxide sequestration in brinesaturated reservoirs,
as well as recovery of oil from oilwet reservoirs, involve the injection of a less
viscous, nonwetting fluid into a porous medium occupied by a moreviscous, wetting
fluid: i.e., drainage with an unfavorable viscosity ratio. In these cases, there is
a competition between capillary fingering and viscous fingering.
In standard treatments of twophase flow in porous media, the flow is assumed
to be compact, with a uniform residual saturation behind a front, which advances
linearly with time. This view of two phase flow is inconsistent with the cases of
fractal capillary fingering at zero capillary numbers, and fractal viscous fingering
resulting from injection of an inviscid fluid.
Earlier work has shown that when the flow characteristics are not precisely at their
fractal limit, the fractal fingering behavior crosses over to standard behavior at a
characteristic time which is inversely related to the distance of the flow
characteristics from their fractal limit. This earlier work was limited to
crossover from one type of fractal fingering to standard flow.
We present results from porelevel modeling for a range of capillary numbers
and unfavorable viscosity ratios. The results are analyzed to determine how the
competing capillary and viscous fingerings cross over to compact flow. These
results are compared with predictions of a scaling hypothesis based upon experience
with the aforementioned, simpler fractaltocompact crossovers from one type of
fractal fingering to standard/compact flow. 
Track/Session 
Special Sessions / PoreScale Modelling: New Developments And Applications 
Date 
20060618 
DOI 
10.4122/1.1000000661 


Michael Kuehn 
CO2 storage through mineral trapping in geothermal reservoirs 




Author(s) 
Michael Kuehn^{1}; Katrin Vosbeck^{2}; Martin Back^{3}; Christoph Clauser^{1}; Helge Stanjek^{2}; Stefan Peiffer^{3}; Michael Kuehn^{1} 
Organisation(s) 
^{1}Applied Geophysics, RWTH Aachen University; ^{2}Clay and Interface Mineralogy, RWTH Aachen University; ^{3}Hydrology, University of Bayreuth 
Abstract 
Costs for carbon dioxide sequestration into deep saline aquifers can be transformed
into a benefit when combined with ecologically desirable geothermal heat or power
production. The produced energy can be used and marketed. Aim is a scientifically
and technically feasible new technology to achieve a safe and economically
attractive longterm storage of CO2 trapped in minerals. We develop, study, and
evaluate a novel approach not only to sequester CO2 by physical trapping within a
reservoir, but to convert dissolved CO2 into the geochemically more stable form of
calcite.
Due to the geological situation exploitation of geothermal energy in Germany is
mainly provided from deep aquifers. The common arrangement of bore holes is the
well doublet, consisting of one well for hot water production and one well for
cooled water reinjection. The cooled water is loaded with dissolved CO2, and after
reinjection into the reservoir this cold water becomes enriched in calcium e.g.
due to dissolution of anhydrite (CaSO4). Subsequently CO2 precipitates as calcium
carbonate (CaCO3), provided that alkalinity is present either by the dissolution of
feldspars in the aquifer or by surface water treatment with fly ashes.
Processes are studied both in laboratory and by numerical simulations. The latter
are essential to quantify the entire process of CO2 storage and to deepen the
understanding of the detailed chemical processes. Reaction modelling and reactive
transport simulations are done on multiple scales since the combination of all
scales is not feasible in numerical models up to now. The relevant scales studying
CO2 storage in combination with geothermal energy production reach down from the
reservoir scale (ca. 10 km) to the micro scale (ca. 1 cm). Results from larger
scale models provide constraints for smaller scale scenarios. For processes which
cannot be resolved on the larger scale, due to restrictions of discretization of
the applied numerical mesh, functionalities are derived from the smaller scale. To
be predictive and capable of quantifying amounts of storable CO2 numerical
investigations on the reservoir scale are vital. Simulations on the borehole scale
are necessary, because the near vicinity of wells is vulnerable to permeability
decrease as a result of mineral reactions. Laboratory experiments are used to
calibrate the numerical tools and simulations on the micro scale allow further
investigation of the overall process of mineral dissolution and precipitation.
Simulation results as well as laboratory experiments prove that anhydrite can be
successfully transferred into calcite and thus are evidence for the feasibility of
the new technology. 
Track/Session 
Special Sessions / Geologic Sequestration of Carbon Dioxide 
Date 
20060618 
DOI 
10.4122/1.1000000659 


Sylvain WEILL 
Darcy multidomain approach for integrated surface/subsurface hydrologic models 




Author(s) 
Sylvain WEILL^{1}; Emmanuel MOUCHE^{1}; Sylvain WEILL^{1} 
Organisation(s) 
^{1}CEA 
Abstract 
A Darcy multidomain approach for modeling surface and subsurface hydrologic
processes is presented. The diffusive wave approximation is used to model runoff. The
resulting equation is formulated as a Darcy nonlinear one. Therefore, the water
dynamics in the three physical domains, ground surface, vadose zone and saturated
zone, is described through a single Darcy nonlinear equation with domaindependent
parameters. This multidomain Darcy equation is solved with Mixed Hybrid Finite
Element formulation. The time discretisation is implicit and the nonlinear equations
are solved within a sequential iterative Picard scheme. This model can describe
Hortonian runoff, runoff due to rainfall on saturated areas and seepage. In order to
evaluate this new modeling approach, different test cases are simulated: uniform
rainfall on nonconvergent hillslope topography with constant slope and a 3D open
book geometry, representing two hillslope sides with a stream in between. Simulation
results show that our model is able to model saturated area spreading and different
runoff generation processes. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000657 


Alain GENTY 
Unsaturated flow modeling in highlevel nuclear waste repository 




Author(s) 
Alain GENTY^{1}; Gilles BERNARDMICHEL^{1}; Alain GENTY^{1} 
Organisation(s) 
^{1}CEA 
Abstract 
In the context of highlevel nuclear waste repository safety
calculations, the modeling of desaturation and saturation
processes in low permeable porous media is of first importance.
Indeed these processes are strongly coupled with mechanics,
inducing host rock confinement properties changes. They also
control corrosion and the other geochemical processes responsible
for waste canister failure. Above all, desaturation and saturation
time scales of the repository components determine the
physicochemical behavior of the repository by trapping or not air
in the system.
In order to simulate unsaturated flow in the repository host rock
media, we developed, in the Cast3m tool, a modified Richard's model
with a storage coefficient. This allows to take into account the
transient head inside a fully saturated area of the domain.
Different spatial schemes are implemented (Mixed Hybrid Finite
Elements, Finite Volumes (MPFA)) as well as different nonlinear
solving algorithms (Picard and Newton).
In this paper, we present some classical validation cases of our
model. Then we perform a 3D saturation computation of a repository
drift seal and a repository gallery backfill. This enables us to
evaluate the occurrence of air entrapment and the presence of fully
saturated components. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000655 


Philip Binning 
Psuedokinetics arising from the upscaling of equilibrium 




Author(s) 
Philip Binning^{1}; Michael Celia^{2}; Li Li^{2}; Philip Binning^{1} 
Organisation(s) 
^{1}Technical University of Denmark; ^{2}Princeton University 
Abstract 
Multicomponent contaminant transport models in groundwater are typically based on
assumptions of local geochemical equilibrium on the grid scale. In heterogenous
systems there may be significant coupling between transport processes and
geochemical equilibrium at smaller than grid block scale. When these processes are
upscaled to grid scale, geochemical evolution may take on a kinetic character. We
have termed this upscaled kinetic behaviour as “pseudokinetics” and illustrate it
through some examples at the pore and aquifer scales. 
Track/Session 
Special Sessions / MultiDisciplinary Approaches To Reactive Transport Simulation In Aquifer Systems 
Date 
20060618 
DOI 
10.4122/1.1000000653 


Shaul Sorek 
Scale Dependent Fluid Momentum and Solute Mass Macroscopic Balance Equations: Theory and Observations 




Author(s) 
Shaul Sorek^{1}; Daniel Ronen^{1}; Shaul Sorek^{1} 
Organisation(s) 
^{1}BenGurion University of the Negev, ISRAEL 
Abstract 
A mathematical development is presented concerning extensions to the macroscopic
momentum balance equation for compressible Newtonian fluids flowing through
saturated porous matrices, and the macroscopic mass balance equation of solutes
transported with the fluids.
It is shown that each of these balance equations is composed of a dominant
macroscopic equation associated with a larger spatial scale, coupled with a
secondary macroscopic balance equation valid at a smaller spatial scale. The
dominant fluid momentum balance equation can govern the propagation of shock waves,
conform to Forchheimer's law or to Darcy's law when friction at the solidfluid
interface is dominant. Concurrently, the secondary momentum balance equation is
governed by inertia flow that conforms to a wave equation propagating the intensive
momentum and the dispersive momentum flux, both deviating from their corresponding
dominant average terms. The dominant macroscopic solute mass balance equation
accounts for advection and hydrodynamic dispersion. The secondary macroscopic solute
mass balance equation describes pure advection of the product of deviations from the
average solute mass fraction and the average fluid density.
Field observations under natural gradient flow conditions show excessive high
concentration of colloids (average of 50 mg/L) under land irrigated by sewage
effluents. The high concentration of colloids in a macroscopic flow field where
specific discharge varies between 4 to 16 m/yr, is suggested to be due to the
enhancement of colloidal mobility resulting from the secondary fluid momentum
equation governed by inertia and the secondary solute mass equation of pure
advection, both proven to be valid at a scale smaller then the one considered for
spatial averaging. 
Track/Session 
Special Sessions / Multiscale methods for flow in porous media 
Date 
20060618 
DOI 
10.4122/1.1000000651 


Peter Vermeulen 
Modelreduced Variational Data Assimilation in Groundwater Modeling 




Author(s) 
Peter Vermeulen^{1}; Arnold Heemink^{2}; Peter Vermeulen^{1} 
Organisation(s) 
^{1}Hydrological Engineer; ^{2}Department of Applied Mathematics 
Abstract 
This paper describes a new approach to variational data assimilation that with a
comparable computational efficiency does not require implementation of the adjoint
of the tangent linear approximation of the original model. In classical variational
data assimilation, the adjoint implementation is used to efficiently compute the
gradient of the criterion to be minimized. Our approach is based on model
reduction. Using an ensemble of forward model simulations, the leading EOFs are
determined to define a subspace. The reduced model is created by projecting the
original model onto this subspace. Once this reduced model is available, its
adjoint can be implemented very easily and be used to approximate the gradient of
the criterion. The minimization process can now be solved completely in reduced
space with negligible computational costs. If necessary, the procedure can be
repeated a few times by generating new ensembles closer to the most recent estimate
of the parameters. The reduced model based method has been tested on several
nonlinear synthetic cases for which the hydraulic conductivity was estimated. 
Track/Session 
Special Sessions / Data assimilation in water resources modelling 
Date 
20060618 
DOI 
10.4122/1.1000000650 


Peter Vermeulen 
Limitations to Upscaling of Groundwater Flow Models dominated by Surface Water Interaction 




Author(s) 
Peter Vermeulen^{1}; Peter Vermeulen^{1} 
Organisation(s) 
^{1}Hydrological Engineer 
Abstract 
Different upscaling methods for groundwater flow models are investigated. A suit of
different upscaling methods is applied to several synthetic cases with structured
and unstructured porous media. Although each of the methods applies best to one of
the synthetic cases, no performance differences is formed if the methods were
applied to a real 3Dcase. Furthermore, we focus on boundary conditions such as
Dirichlet, Neumann and Cauchy conditions, that characterize the interaction of
groundwater with e.g. surface water, recharge. It follows that the inaccuracy of
the flux exchange between driving forces on a finescale and the hydraulic head on
a coarse scale causes additional errors that are far more significant than the
errors due to an incorrect upscaling of the heterogeneity itself. Whenever those
errors are reduced, the upscaled model was improved by 70%. It thus follows that in
practise, whenever we focus on predicting groundwater heads, it is more important
to correctly upscale the boundary conditions than hydraulic conductivity. 
Track/Session 
Special Sessions / Multiscale methods for flow in porous media 
Date 
20060618 
DOI 
10.4122/1.1000000649 


Paolo Salandin 
WELL CATCHMENTS ESTIMATION IN HETEROGENEOUS AQUIFERS WITH A STRATIFIED MODEL 




Author(s) 
Paolo Salandin^{1}; Filomena Savini^{1}; Gianluca Marconi^{1}; Gianluca Marconi^{1} 
Organisation(s) 
^{1}Università Politecnica delle Marche 
Abstract 
A new method is proposed to delimitate wellhead protection areas in a confined
aquifer where hydraulic conductivity is assumed as spatially random function. In a
natural formation the heterogeneity of porous media influences the capture zone
delimitation and considerable differences can result from the homogenous case. In
the last decade several approaches were proposed to solve the problem but they need
of a priori description of statistical properties of aquifer that are usually
unknown or that requires a very expensive in situ investigation. To give a
probabilistic estimation of well catchments, we suggest here that a 3D aquifer can
be described with a perfectly stratified model. Only three parameters are needed to
completely define the latter: the logconductivity expected value and variance, and
the number of identical layers on the known depth of aquifers. While the log
conductivity expected value can be derived from a standard pumping test, the
variance and the number of layers need of a multilevel tracer test to be defined. To
validate the proposed method, pumping and tracer tests were developed in a fully 3D
synthetic aquifer and their results were adopted to define the parameters of the
stratified model. Several situations were investigated with different hydraulic log
conductivity spatial structure. In all cases the well catchment and isochrones
deduced from the latter show a good agreement with corresponding areas that can be
recognized in the synthetic aquifer. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000647 


Filippo Notarnicola 
MODELLING AND DESIGN IN BIOVENTING 




Author(s) 
Filippo Notarnicola^{1}; Filippo Notarnicola^{1} 
Organisation(s) 
^{1}Consiglio Nazionale Ricerche  Istituto Applicazioni del Calcolo, Sez. Bari 
Abstract 
Bioventing is a cleanup technology commonly used
for remediation of polluted unsaturated subsoil by
biodegradation.
The pollutant is considered as a nutrient, natural
bacteria destroy contaminants in an aerobic
situation and the needed oxygen is provided
by air injection and extraction wells.
The mathematical models for a bioventing system
are based on the theory of multiphase and multi
component fluid transport in porous media;
reactive terms describe the biological decay
phenomenon and the bacteria concentration obeys
population dynamic laws.
The problems involved in designing a bioventing
system consist of determining the number, the
positioning and the pumping rates of the air
injection/extraction wells considering the
pollutant distribution and the subsoil
characteristics. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000646 


Sergey Skachkov 
Twophase mixing in heterogeneous porous media 




Author(s) 
Sergey Skachkov^{1}; Mikhail Panfilov^{1}; Sergey Skachkov^{1} 
Organisation(s) 
^{1}Nancy School of Geology, LAEGO (LAboratoire Environnement, Geomecanique et Ouvrage) 
Abstract 
For a twophase immiscible flow through a heterogeneous porous medium a macroscale
model of first order is derived by a twoscale homogenization method while
capturing the effects of fluid mixing. The capillary pressure is taken in
consideration. An asymptotic twoscale homogenization method is applied which
derives homogenization equations as a twoscale limit of the system when the medium
heterogeneity tends to zero.
The obtained macroscale flow equation has revealed that the mixing is manifested in
the form of a nonlinear hydrodynamic dispersion and a transport velocity shift
("velocity renormalization"). The dispersion tensor is shown to be a nonlinear
function of saturation. In the case of flow without gravity and without capillarity
this function is proportional to the fractional flow derivative and depends on the
viscosity ratio. The capillary forces change the structure of the dispersion tensor
and the qualitative dependence on saturation.
The case of fractured medium is also considered in the form of a periodic
anisotropic network. In the case of asymptotically thin fractures the limit
solution to the cell problem is shown to become nonunique due to a physical effect
of stream configuration collapse in the nodes of fracture intersections. For a 2D
periodic network, all the probable stream configurations are determined. The
solution to the regularized problem and to the dispersion tensor is obtained in an
analytical form. The longitudinal dispersion is the linear function of
heterogeneity degree while the transverse dispersion is bounded. In the behaviour
of the dispersion tensor singular regimes are revealed which are characterized by
an infinite growth of dispersion. These regimes correspond to the trapping of a
phase. 
Track/Session 
Special Sessions / Multiscale methods for flow in porous media 
Date 
20060618 
DOI 
10.4122/1.1000000645 


Dustin Crandall 
Volume of Fluid Simulations of Multiphase Flow through Fractures: Analysis of Individual Fractures for Application in Reservoir Scale Models 




Author(s) 
Dustin Crandall^{1}; Kambiz Nazridoust^{2}; Goodarz Ahmadi^{1}; Grant Bromhal^{3}; Duane Smith^{3}; Duane Smith^{3} 
Organisation(s) 
^{1}Clarkson Univeristy and National Energy Technology Laboratory, Morgantown; ^{2}Clarkson Univeristy; ^{3}National Energy Technology Laboratory, Morgantown 
Abstract 
Geological Carbon Dioxide Sequestration requires a fundamental understanding of
modeling multiphase flows in fractured media. Subsurface flow is highly dependent
upon the rock structure within the flow domain, with high permeability and
fractured regions dominating the transport of the fluids. Discretefracture
simulators often assume the cubic law relationship for single phase flow through a
smooth set of parallel plates, and with good reason. The number of fractures that
need to be modeled at the reservoir scale may greatly exceed 10,000; and the
relationship between the pressure field and the fluid flow needs to be easily
describable in order for the model to be computationally efficient. The work
described in this paper examines twophase, immiscible flows through rough
fractures. Computations are performed utilizing the full multiphase NavierStokes
equations for flow through CT scanned fractures in Berea sandstone. A number of
computer simulations are performed, and an empirical model is generated that is
similar to the cubic law, yet accounts for the roughness of the fracture and the
interaction of the invading and defending fluids and the effect of capillary
forces. The fracture roughness and capillary forces are shown to restrict the
flow; hence the standard cubic law tends to overestimate the flow rate of the
invading fluid. 
Track/Session 
Special Sessions / Geologic Sequestration of Carbon Dioxide 
Date 
20060618 
DOI 
10.4122/1.1000000643 


GUOBIAO HUANG 
An Integrated Media, Integrated Processes Watershed Model – WASH123D: Part 2 – Simulating surface water flows with different water wave models 




Author(s) 
GUOBIAO HUANG^{1}; GourTsyh Yeh^{2}; GUOBIAO HUANG^{1} 
Organisation(s) 
^{1}Sutron Corporation, West Palm Beach, FL, USA; ^{2}Dept of Civil and Environ. Eng., Univ. of Central Florida, Orlando, FL, USA 
Abstract 
The complete Saint Venant equations/2D shallow water equations (dynamic wave
equations) and the kinematic wave or diffusion wave approximations were implemented
for 1D channel network flow and 2D overland flow in a watershed model, WASH123D.
Careful choice of numerical methods is needed even for the simple kinematic wave
model. Motha and Wigham (1995) reported numerical oscillation in Galerkin finite
element of kinematic wave overland flow. Since the kinematic wave equation is of
pure advection, the backward method of characteristics is used for kinematic wave
model. A characteristic based finite element method is chosen for the hyperbolic
type dynamic wave model. And the Galerkin finite element method is used to solve the
diffusion wave model.
Diffusion wave and kinematic wave approximations are found in many overland runoff
routing models. The error in these models has been characterized for some cases of
overland flow over simple geometry (e.g. Ponce 1978; Singh 2000 and Parlange 1990).
However, the nature and propagation of these approximation errors under more complex
2D flow conditions are not well known. These issues are evaluated within WASH123D
by comparison of simulation results on several example problems. The accuracy of the
three wave models for 1D channel flow was evaluated with several nontrivial (trans
critical flow; varied bottom slopes with frictions and nonprismatic crosssection)
benchmark problems (MacDonnell et al., 1997). The test examples for 2D overland
flow include: (1) a simple rainfallrunoff process on a single plane with constant
rainfall excess that has a kinematic analytical solution under steep slope
condition. A range of bottom slopes (mild, average and steep slope) are numerically
solved by the three wave models and compared; (2) Iwagaki (1955) overland flow
experiments on a cascade of three planes with shock waves; (3) overland flow in a
hypothetical wetland (infiltration bed). The applicability of dynamicwave,
diffusionwave and kinematicwave models to real watershed modeling is discussed
with simulation results from these numerical experiments. It was concluded that
kinematic wave model could lead to significant errors in most applications. On the
other hand, diffusion wave model is adequate for modeling overland flow in most
natural watersheds. The complete dynamic wave equations are required in lowterrain
areas such as flood plains or wetlands and many transient fast flow situations. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000641 


GUOBIAO HUANG 
An Integrated Media, Integrated Processes Watershed Model – WASH123D: Part 3 –a comparative study on different surface water/groundwater coupling approaches 




Author(s) 
GUOBIAO HUANG^{1}; GourTsyh Yeh^{2}; GUOBIAO HUANG^{1} 
Organisation(s) 
^{1}Sutron Corporation, West Palm Beach, FL, USA; ^{2}Dept of Civil and Environ. Eng., Univ. of Central Florida, Orlando, FL, USA 
Abstract 
In the core of an integrated watershed model is the coupling among surface water and
subsurface water flows. Recently, there is a tendency of claiming the fully coupled
approach for surface water and groundwater interactions in the hydrology literature.
One example is the assumption of a gradient type flux equation based on Darcy’s Law
(linkage term) and the numerical solution of all governing equations in a single
global matrix. We argue that this is only a special case of all possible coupling
combinations and if not applied with caution, the nonphysical interface parameter
becomes a calibration tool. Generally, there are two cases based on physical
nature of the interface: continuous or discontinuous assumption, when a sediment
layer exists at the interface, the discontinuous assumption may be justified. As for
numerical schemes, there are three cases: timelagged, iterative and simultaneous
solutions. Since modelers often resort to the simplest, fastest schemes in
practical applications, it is desirable to quantify the potential error and
performance of different coupling schemes. We evaluate these coupling schemes in a
finite element watershed model, WASH123D. Numerical experiments are used to compare
the performance of each coupling approach for different types of surface water and
groundwater interactions. These are in term of surface water and subsurface water
solutions and exchange flux (e.g. infiltration/seepage rate). It is concluded that
different coupling approaches are justified for flow problems of different spatial
and temporal scales and the physical setting of the interface. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000639 


GUOBIAO HUANG 
An Integrated Media, Integrated Processes Watershed Model – WASH123D: Part 4 – A characteristicsbased finite element method for 2D overland flow 




Author(s) 
GUOBIAO HUANG^{1}; GourTsyh Yeh^{2}; GUOBIAO HUANG^{1} 
Organisation(s) 
^{1}Sutron Corporation, West Palm Beach, FL, USA; ^{2}Dept of Civil and Environ. Eng., Univ. of Central Florida, Orlando, FL, USA 
Abstract 
The Method of Characteristics (MOC) in the context of finite element method was
applied to the complete 2D shallow water equations for 2D overland flow. For two
dimensional overland flow, finite element or finite volume methods are more flexible
in dealing with complex boundary. Recently, finite volume methods have been very
popular in numerical solution of the shallow water equations. Some have pointed out
that finite volume methods for 2D flow are fundamentally onedimensional (normal to
the cell interface). The results may rely on the grid orientation. The search for
genuinely multidimensional numerical schemes for 2D flow is an active topic. We
consider the Method of Characteristics (MOC) in the context of finite element method
as a good alternative. Many researchers have pointed out the advantage of MOC in
solving 2D shallow water equations that are of the hyperbolic type that has wave
like solutions and at same time, considered MOC for 2D overland flow being non
tractable on complex topography. The intrinsic difficulty in implementing MOC for 2
D overland flow is that there are infinite numbers of wave characteristics in the 2
D context, although there only three independent wave directions are needed for a
wellposed solution to the characteristic equations. We have implemented a numerical
scheme that attempts to diagonalize the characteristic equations based on pressure
and velocity gradient relationship. This new scheme was evaluated by comparison with
other choice of wave characteristic directions in the literature. Example problems
of mixed subcritical flow/supercritical flow in a channel with approximate
analytical solution was used to verify the numerical algorithm. Then experiments of
overland flow on a cascade of three planes (Iwagaki 1955) were solved by the new
method. The circular dam break problem was solved with different selections of wave
characteristic directions and the performance of each selection was evaluated based
on accuracy and numerical stability. Finally, 2D overland flow over complex
topography in a wetland setting with very mild slope was solved by the new numerical
method to demonstrate its applicability. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000637 


GUOBIAO HUANG 
An Integrated Media, Integrated Processes Watershed Model – WASH123D: Part 5 – Integrated modeling of surface water and groundwater interactions in a constructed wetland 




Author(s) 
GUOBIAO HUANG^{1}; GourTsyh Yeh^{2}; GourTsyh Yeh^{2} 
Organisation(s) 
^{1}Sutron Corporation, West Palm Beach, FL, USA; ^{2}Dept of Civil and Environ. Eng., Univ. of Central Florida, Orlando, FL, USA 
Abstract 
A pilot constructed wetland in south Florida, USA, the Everglades Nutrient Removal
(ENR) project was modeled with a physicsbased integrated approach by WASH123D.
Stormwater is routed into the treatment wetland for phosphorus removal by plant and
sediment intake. It overlies a highly permeable surficial groundwater aquifer.
Strong surface water and groundwater interactions are a key component of the
hydrologic processes. The site has extensive field measurement and monitoring that
provide point scale and distributed data on surface water levels, groundwater levels
and physical range of hydraulic parameters and hydrologic fluxes. Previous
hydrologic and hydrodynamic modeling studies have treated seepage losses empirically
by some simple regression equations and only surface water flows are modeled in
detail. Several years of operational data are available and were used in model
calibration and validation. The validity of diffusion wave approximation for 2D
overland flow in the region with very flat topography was also tested. The
uniqueness of this modeling study includes (1) the point scale and distributed
comparison of model results with observed data; for example, the spatial
distribution of measured vertical flux in the wetland is available. (2) Model
parameters are based on available field test data. (3) Water flows in the study area
consist of 2D overland flow, hydraulic structures/levees, 3D subsurface flow and 1
D canal flow and their interactions. This study demonstrates the need and the
utility of a physicsbased modeling approach for strong surface water and
groundwater interactions. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000635 


Stephen Brill 
A New Basis for the Solution of the OneDimensional ConvectionDiffusion Equation ConvectionDiffusion Equation 




Author(s) 
Stephen Brill^{1}; Stephen Brill^{1} 
Organisation(s) 
^{1}Department of Mathematics, Boise State University 
Abstract 
We present a family of functions that satisfy the
onedimensional convectiondiffusion equation.
This partial differential equation is widely used in
the sciences and engineering, including to model the
transport of contaminant dissolved in groundwater.
Combinations of these functions are formed to satisfy
boundary and initial conditions. The result is an
inexpensive and highly accurate solution methodology. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000633 


Harry Vereecken 
Inverse modeling of electrical conductivity distributions from ERT datasets: integrated analyses of the successive linear estimator and a smoothness constrained regularization approach 




Author(s) 
Harry Vereecken^{1}; TianChyi Jim Yeh^{2}; Andreas Englert^{1}; Andreas Kemna^{1}; Junfeng Zhu^{2}; Jan Vanderborght^{1}; Andreas Englert^{1} 
Organisation(s) 
^{1}Agrosphere Institute Agrosphere (ICG IV), Institute of Chemistry and Dynamics of the Geosphere (ICG), Research Centre Jülich; ^{2}Department of Hydrology and Water Resources, The University of
Arizona 
Abstract 
Recent field studies showed that electrical resistivity tomography
(ERT) potentially is a viable tool for characterizing subsurface
transport processes of substances with electrical conductivities
differing from the background. Popular approaches for interpreting
the electrical field measurements are based on inversion procedures
including regularization terms, which force the inverse solution to be
smooth. As a result, the image of a solute plume can be
unsatisfactory. Furthermore most inversion procedures do not
generally take advantage of in situ electrical conductivity
measurements or point concentration data. We further recognize that
while a solute plume in heterogeneous aquifers can be highly
irregular, it can be characterized in a geostatistical sense: its mean
position, lateral spreading, and spatial correlation structures.
These plume statistics can serve as our prior knowledge about the
plume. Based on existing stochastic theories of solute transport
processes, plume statistics can be easily estimated from statistics,
quantifying the heterogeneity of the hydraulic
conductivity. Therefore, we hypothesize that an ERT inversion,
incorporating our prior knowledge of the geostatistical
characteristics of a plume and some direct point measurements of the
plume concentration, could lead to more detailed images of subsurface
electrical conductivity distributions associated with the solute plume.
Using a synthetic salt tracer plume, we test our hypothesis by
investigating the quality of inversions with a smoothness constrained
regularization code as well as a geostatistic based, cokriging like
code, the successive linear estimator (SLE). The results of our
investigation based on measurements from different subsurface arrays
show that the quality of an investigation is, as expected, strongly
depending on the measurement geometry and the number of measurements.
The integrated analyses of inverse modeling procedures, SLE and
regularization, evidence that with only sparse measurements the
conditioning of the electrical inverse problem with the statistical
characteristics of the solute plume as well as with point values of
the plume concentration enhances the quality of the result
clearly. With an increasing number of measurements the effect of
conditioning however becomes less effective. 
Track/Session 
Special Sessions / Hydrogeophysical data fusion 
Date 
20060618 
DOI 
10.4122/1.1000000631 


Sébastien Cadalen 
Macroscale models for Cesium transport in sandyclayed porous media 




Author(s) 
Sébastien Cadalen^{1}; Michel Quintard^{2}; Sébastien Cadalen^{1} 
Organisation(s) 
^{1}CEA (DEN / DM2S / SFME / MTMS); ^{2}IMFT 
Abstract 
This paper discusses the type of macroscale or Darcyscale model suitable for
modelling Cesium transport in sandyclayed soil. While the motivation for the study
comes from the context of nuclear risk control, this study may be viewed in the more
general framework of surface contaminations with reactive solute transport. The
adopted strategy consists in looking at an idealized soil composed of Fontainebleau
sand with a few percents of fine particules of Illite du Puy. This leads to a more
simple system in terms of geochemical reactions compared to natural systems which
present much more chemical components in the solid phases and in water.
In many geochemical studies, the first approximation made in Darcyscale models
consists in assuming that all macroscale concentrations correspond to equilibrium
conditions. Comparing chemical and diffusion characteristic times in the clay grain
to the advection in the intragranular porosity, it is plausible to find situations
where the porescale solute concentration is not homogeneous. This suggests that
twomedium effects are important, and this may be taken into account at the
Darcyscale by twoequation models. The remaining issue being the connection between
Darcyscale and microscale properties.
The first idea, is to perform porescale direct simulation simulations. The system to
be solved involves Stokes equation and a convectiondiffusion equation in the water
within the intragranular porosity, and a retardateddiffusive equation in the clay
grain. The results are used later as a reference for testing the Darcyscale models.
Two averaged models have been tested. The first model corresponds to a twoequation
model involving mainly dispersion in the macroporosity, and an exchange term with
the balance equation for the clay macroscale domain, which is estimated from the use
of a volume averaging upscaling technique. The second model corresponds to a
mixedmodel coupling a macroscale equation for the intragranular fluid phase with a
direct simulation of diffusion in the clay particle with special boundary conditions
involving the macroscale concentration. Indications are given on the implementation
of both models, and their ability to reproduce the direct simulations results. 
Track/Session 
Special Sessions / PoreScale Modelling: New Developments And Applications 
Date 
20060618 
DOI 
10.4122/1.1000000629 


Oscar Hartogensis 
ESTIMATING SURFACE FLUXES IN IRRIGATED AREAS WITH SCINTILLOMETERS 




Author(s) 
Oscar Hartogensis^{1}; Henk De Bruin^{2}; Oscar Hartogensis^{1} 
Organisation(s) 
^{1}Researcher; ^{2}Assistant Professor 
Abstract 
Scintillometry has proven to be a good alternative method to obtain surface fluxes
over heterogeneous areas over spatial scales of up to 10 km and in nonstationary
conditions in the stable surface layer (see e.g. [1]). This study concerns agro
hydrological scintillometer applications of estimating evaporation over homogeneous
irrigated areas on a scale of 50 to 500 m. Two types of scintillometers will be
considered, notably the displaced beam small aperture scintillometer (DBSAS) and the
large aperture scintillometer (LAS) deployed in two field campaigns in Idaho, USA in
1999 [2] and in the Yaqui Valley, Sonora, Mexico in 2000 [3].
The DBSAS and the LAS are optical instruments that consist of a transmitter and
receiver. The receiver records intensity fluctuations of the light beam emitted by
the transmitter, which are caused by refraction of the beam upon its passage through
the turbulent surface layer. These intensity fluctuations are a measure of the
structure parameter of temperature, CT2. The DBSAS obtains also the dissipation rate
of turbulent kinetic energy, e, from the correlation between the two displaced
beams. CT2 and e are related to the surface fluxes of heat, H, and momentum, t, by
virtue of MoninObukhov similarity theory. For the LAS  that provides CT2 only  t
is obtained from additional wind speed measurements and an estimate of the roughness
length. Evapotranspiration can then be estimated from net radiation and the soil
heat flux measurements.
In both field campaigns the irrigated agricultural area was surrounded by a desert.
In these conditions dry, warm desert air can be advected over the cool evaporating
surface by which sensible heat becomes negative and the water vapor deficit is
increased, both enhancing evapotranspiration. As a result the surface layer is
stably stratified and wind shear is the only turbulence generating mechanism. The
DBSAS directly gives information on this process, the LAS does not.
We will outline the potential of scintillometers of obtaining principle turbulence
parameters (CT2 and e) and fluxes of latent and sensible heat, and compare these
with eddy covariance method based estimates for the two experiments. We will present
evidence that scintillometers have advantages over the eddy covariance (EC) method
in the often nonstationary stable surface layer, since they can be used for short
fluxaveraging periods as they average turbulence not only in time but also in
space. Furthermore, scintillometers require less complex data processing and quality
control procedures. Last, the transmitter and receiver of the instrument can be
installed at the borders of the field by which the instrument does not interfere
with the farmer’s activities in the field.
Finally, the medium aperture scintillometer (MAS) will be discussed, which has an
aperture size that includes features of both the DBSAS and the LAS. Result of MAS
measurements over grass at Cabauw, Netherlands will be shown.
References
[1] De Bruin, H.A.R.: 2002, ‘Introduction, renaissance of scintillometry’, Boundary
Layer Meteorol. 105, 14. and the papers of this special issue on scintillometry.
[2] De Bruin, H.A.R., Hartogensis, O.K., Allen, R.G., and Kramer, J.W.J.L.,
2004: ‘Note on the Regional Advection Perturbations in an Irrigated Desert (RAPID)
Experiment’, Theor. Appl. Climatol. 80, 143152.
[3] Hoedjes, J.C.B., Zuurbier, R.M., and Watts, C.J.: 2002, ‘Large aperture
scintillometer used over a homogeneous irrigated are partly affected by regional
advection’, BoundaryLayer Meteorol. 105, 99117.
[4] Hartogensis, O.K., De Bruin, H.A.R., Van De Wiel, B.J.H.: 2002, ‘DisplacedBeam
Small Aperture Scintillometer Test. Part II: Cases99 Stable BoundaryLayer
Experiment’, BoundaryLayer Meteorol. 105, 149176. 
Track/Session 
Special Sessions / Field measurements and simulations of landatmosphere interaction 
Date 
20060618 
DOI 
10.4122/1.1000000627 


Geir Terje Eigestad 
Multi phase flow on complex 3D meshes by control volume methods 




Author(s) 
Geir Terje Eigestad^{1}; BjørnOve Heimsund^{2}; Erlend Øian^{2}; Ivar Aavatsmark^{2}; Jan Nordbotten^{1}; Geir Terje Eigestad^{1} 
Organisation(s) 
^{1}Department of Mathematics, University of Bergen; ^{2}Center for Integrated Petroleum Research 
Abstract 
Complex geometric and geological features of realistic reservoirs
motivate the need for flexible and robust flux discretization for
forecasting of fluid flow in porous media. Advanced seismic modelling
in combination with history matching reveal that faults and fractures
frequently occur in North Sea reservoirs, and may significantly affect
the flow patterns.
In this work we present a flexible grid structure which can
incorporate grid configurations due to complex faults and fractures in
a consistent manner. On these grids we have implemented general
control volume discretizations. This allows a consistent treatment of
the resulting skewed and nonmatching grid cells, heterogeneities
and general anisotropies.
The general fluxdiscretisation techniques may be combined with
streamline simulation on general grids. Such approaches utilize tools
for multiple realizations of general porous media flows and ranking of
models.
Numerical examples will here be given which illuminate the performance
on some representative largescale problems. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000626 


Anne Katrine Falk 
DATA ASSIMILATION TO IMPROVE FORECAST QUALITY OF RIVER BASIN MODELS 




Author(s) 
Anne Katrine Falk^{1}; Michael B. Butts^{1}; Henrik Madsen^{1}; Johan Hartnack^{1}; Anne Katrine Falk^{1} 
Organisation(s) 
^{1}DHI  Water & Environment 
Abstract 
Ideally, realtime flood management decisions must be based on an understanding of
the uncertainties and associated risks. It is therefore central for effective flood
management tools to provide reliable estimates of the forecast uncertainty. Only by
quantifying the inherent uncertainties involved in flood forecasting can effective
realtime flood management and warning be carried out. Forecast uncertainty requires
the estimation of the uncertainties associated with both the hydrological model
inputs (e.g. precipitation observations and forecasts), model structure,
parameterisation and calibration, and methodologies that predict how the
uncertainties from different sources propagate through the hydrological and
hydraulic system.
Within the EU 5th framework project FLOODRELIEF, an ensemblebased approach has been
developed to address the issue of handling and quantifying forecasting and modelling
uncertainties. A general stochastic framework for flood forecast modelling is
presented based on the Ensemble Kalman Filter (Evensen, 1994). The Kalman filter
provides a natural framework for determining how the different sources of
uncertainty propagate through the hydrological and hydraulic models and to reduce
forecast uncertainty via data assimilation of realtime observations. An evaluation
of this framework is presented for several case studies including the US NWS study
catchment, the Blue river basin and the Welland and Glen River Basin in the UK.
Two methods for introducing uncertainties into the model are compared:
1. Stochastic errors are added to the runoff calculated by the catchment model.
Only states in the river channel model are updated
2. Stochastic errors are added to the input to the catchment model (e.g.
precipitation and evaporation). States in both the catchment model and in the river
channel model are updated.
In particular, an investigation of the value of these two approaches for rapidly
responding river basins versus more slowly responding systems is presented. As
expected it is observed that updating in both the catchment model and the river
channel model has a longer lasting effect on the forecast than updating in the river
channel alone. Finally the results of this evaluation highlight the fact that one of
the major outstanding problems in estimating the forecast uncertainty is the
characterisation of the sources of uncertainty.
References:
Evensen, G. (1994), Sequential data assimilation with a nonlinear quasigeostrophic
model using Monte Carlo methods to forecast error statistics, J. Geophysical
Research, vol. 99, no. C5, pp. 1014310162. 
Track/Session 
Special Sessions / Data assimilation in water resources modelling 
Date 
20060618 
DOI 
10.4122/1.1000000624 


Christos Tsakiroglou 
Determination of the single and multi phase transport properties of a layered soil by combining laboratory experiments with numerical calculations 




Author(s) 
Christos Tsakiroglou^{1}; Christos Aggelopoulos^{1}; Christos Tsakiroglou^{1} 
Organisation(s) 
^{1}FORTH / ICEHT, Stadiou street, Platani, P.O.Box 1414, GR26504 Patras, Greece 
Abstract 
A military airport situated in Northern Poland has highly been contaminated by jet
fuel since 2nd world war. Geological characterization revealed that the unsaturated
zone is a highly heterogeneous soil consisting of three main layers dominated by
massive clay with desiccation fractures, homogeneous sand, and fractured sandy
till. In order to proceed in the implementation of an in situ stimulation
remediation program, information concerning the transport properties of the various
layers and their interfacial zones is required.
Depending on the texture of the (nonfractured) soil matrix, its single and multi
phase transport properties are either estimated with history matching of
displacement experiments or calculated from microscopic properties of the pore
structure. For the permeable sandy layers, immiscible and miscible displacement
experiments are performed on disturbed and undisturbed soil columns, and the
electrical resistance along the columns is monitored. The electrical measurements
are employed to calculate the transient response of the water saturation profile
along the column, as well as the solute concentration breakthrough curve at various
axial positions of the column. The experimental datasets are introduced into
numerical codes of inverse modeling of the twophase flow and advectiondispersion
equations to estimate the relative permeability curves, the capillary pressure
curve, and the longitudinal dispersion coefficient. For the low permeability
massive clay and sandy till layers, the pore and throatsize distributions along
with the network accessibility functions of the matrix are estimated by processing
the autocorrelation function of 2D BSEM images of polished crosssections of
porecasts, and inversing experimental data of Hg intrusion / retraction curves.
Then, critical path analysis is used to calculate the absolute permeability, and
formation factor, whereas a quasistatic pore network approach is employed to
calculate the relative permeability and capillary pressure curves. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000622 


L. Weihermüller 
The FLOWatchProject: Measuring water, carbon dioxide and energy fluxes at the field scale 




Author(s) 
L. Weihermüller^{1}; J. A. Huisman^{1}; M. Herbst^{1}; H. Vereecken^{1}; S. Lambot^{1}; L. Weihermüller^{1} 
Organisation(s) 
^{1}Forschungszentrum Jülich GmbH, Agrosphere Institute 
Abstract 
For water, energy and CO2 fluxes in agricultural landscapes, the field scale plays a
crucial role since it corresponds to the scale at which humans directly influence
fluxes by managing the system for crop cultivation. This leads to a humaninduced
spatiotemporal variability of these fluxes at the regional scale. Consequently, the
field scale is considered as the elementary scale for modelling of water, CO2 and
energy fluxes. Despite intensive research in the past, there is still a lack in
knowledge concerning the spatial and temporal interdependency of soil state variables
(e.g. moisture, soil temperature), matter fluxes from soil and vegetation (e.g.
water, carbon dioxide) as well as their variability and respective effective values
at the field scale. The FLOWatch project aims to improve our understanding of the
spatial and temporal variability of water, energy and carbon dynamics in the soil and
their role in determining effective evapotranspiration and carbon exchange fluxes at
the field scale. To this end, micrometeorological, geophysical and (groundbased)
remote sensing methods will be combined with mechanistic models describing the
dynamics of water, energy and CO2 in soils.
Modelling of Cdynamics involves the description of the turnover of different
organic matter pools. The turnover rates depend on soil temperature, soil water
content, and soil CO2 concentration amongst others. Therefore, an accurate
representation of these state variables is a key issue for the predictive modelling
of carbon turnover and CO2 efflux. Within the FLOWatch project, several noninvasive
and soil physical methods to measure soil water content at different scales will be
implemented. At the point scale, farfield ground penetrating radar (GPR), electrical
resistivity tomography (ERT), and time domain reflectrometry (TDR) will be used. For
plot scale estimates of soil water content, a passive
Lband radiometer will be installed. To obtain a spatial representation of the energy
balance components, meteorological measurements will be combined with 2D soil surface
temperature images from an IRcamera. Spatial and temporal variability of CO2 fluxes
will be measured with automated soil CO2 flux systems (LICOR Biosciences). Temporal
variability of the CO2 flux at the plot scale will be measured using the eddy
covariance method when conditions allow it. For the modelling of the water balance,
the energy balance and the CO2 efflux, a model containing the following processes
will be used: (I) water and heat transport in variably saturated soils, (II) organic
carbon turnover based on with multiple pools with variable turnover rates, (III)
multiphase CO2 transport from the soil to the atmosphere.
In this presentation, the experimental setup, the modelling concept and the first
results of the FLOWatch project will be presented. 
Track/Session 
Special Sessions / Field measurements and simulations of landatmosphere interaction 
Date 
20060618 
DOI 
10.4122/1.1000000620 


Mohsen Masihi 
Connectivity of fracture networks: The effects of anisotropy and spatial correlation 




Author(s) 
Mohsen Masihi^{1}; Peter R King^{1}; Peyman Nurafza^{1}; Mohsen Masihi^{1} 
Organisation(s) 
^{1}Imperial College London 
Abstract 
In fractured formations of very low matrix permeability connectivity of fractures
is a crucial parameter which may have a significant impact on the overall flow. The
connectivity behaviour of fracture networks can be analysed by using percolation
theory. The scaling law within this theory is used to predict the connectivity and
its associated uncertainty very rapidly. Although the effects of some geometrical
parameters of fractures (e.g. size distribution) on the universal connectivity
curves are extensively investigated, the effects of anisotropy or spatial
correlation of fractures has not yet been fully addressed.
In this paper we present a framework to derive and verify numerically the
scaling including the effects of anisotropy in two and three dimensions. Anisotropy
arises as a consequence of restricting the orientational disorder of fractures in
two dimensions and using fractures with different aspect ratios in three. The main
effect of anisotropy is to create an ‘easy’ direction for connectivity and
a ‘difficult’ direction. This leads to the concept of an ‘apparent’ percolation
threshold defined as the value which collapses all the anisotropic mean connected
fraction curves onto the same isotropic curve. This is changed as a function both
of the system size and the aspect ratio/s involved. We then used certain symmetry
relations involved and numerical results to formulate the aspect ratio/s dependency
of the apparent threshold. The curves for the fluctuations about this mean
connected fraction have to use this apparent threshold as well as a change in
magnitude which can be accounted for by rescaling with the geometric mean length.
Classical percolation usually used to study the connectivity assumes spatially
uncorrelated fractures. However, the same basic methodology still applies for
correlated systems with small modifications which depend on the nature of
correlation. A modelling technique based on the idea that the elastic free energy
due to the fracture density follows a Boltzmann distribution is presented to
generate realizations of correlated fracture networks. A simulated annealing
algorithm is used with an objective function based on the derived expression for
the spatial correlation in the elastic displacement. The connectivity aspects of
these networks are then analysed.
As a result this has extended the applicability of percolation concepts to the
anisotropic and correlated fracture systems which may be useful for practical
engineering purposes when a very rapid risk assessment is necessary. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000618 


Daria Spivakovskaya 
Risk analysis in the coastal zone using reversetime diffusion 




Author(s) 
Daria Spivakovskaya^{1}; Arnold W. Heemink^{1}; John G. M. Schoenmakers^{2}; Daria Spivakovskaya^{1} 
Organisation(s) 
^{1}Department of Applied Mathematical Analysis, Faculty of EEMCS, Delft University of Technology; ^{2}Weierstrass Institute for Applied Analysis and Stochastics 
Abstract 
Recently we have been faced with serious ecological problems due to calamities at
sea. For prediction the spreading of pollutants accurate methods must be available.
There are two main concepts for the simulation of the diffusion processes. One can
use the Eulerian approach and solve the advectiondiffusion equation numerically.
However, numerical methods often have problems with mass conservation or
positiveness in case of high concentration gradients of the pollutant.
Using a Lagrangian approach the advectiondiffusion equation is interpreted as a
FokkerPlanck equation and a system of underlying stochastic differential equations
for the behavior of the position of the individual particle of the pollutant can be
derived. By numerically simulating the positions of many different particles of the
pollutant the diffusion process can be described. This method is mass conserving
and the concentration can never become negative. Particle models are very
attractive from the computational point of view. Because of the independence of the
movements of all particles, particle models can be easily parallelized.
In this paper we investigate the risk of very high concentrations of the pollutant.
Suppose that for some locations a high concentration of the pollutant can be
dangerous or even fatal for life of some species. To prevent ecological disasters
we need to determine which areas in the sea are potentially dangerous and which
areas are safe, in other words we need to construct a risk map. By the risk map for
a given location of interest along the coast we mean the concentration of the
pollutant in this area for any locations (x,y) where the pollutant may be released.
From a risk map we can immediately determine the most dangerous as well as the safe
location of the pollutant release.
In this paper we develop an efficient method to construct the risk map based on the
concept of the reverse time diffusion. Using the reverse time model, which can be
derived from the original one, we can simulate backward particle trajectories. By
averaging the results of many independent realizations of the reverse time model we
can build the risk map. Comparing with the direct MonteCarlo method based on the
original random walk models, the proposed method is more attractive from the
computational point of view. In this paper we apply the reverse time method to
investigate the several critical locations along Dutch seaside and construct the
risk map for the Dutch coastal zone. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000616 


WANG Dong 
Period characteristics of representative hydrologic series in the Yellow River in China using maximum entropy spectra analysis(MESA) 




Author(s) 
WANG Dong^{1}; WANG Dong^{1} 
Organisation(s) 
^{1}Nanjing University 
Abstract 
In the field of stochastic hydrology, hydrologic series is formed with the non
periodic component, the periodic component and the stochastic component. Here the
period characteristics used include approximate periods in the nonperiodic
component, simple periods and complex periods in the periodic component. Spectral
analysis is an essential and effective tool for extracting such stochastic
characteristics of time series. In 1948, Shannon developed a mathematical theory of
entropy and applied it in communications. Nearly a decade later, Jaynes formulated
the Principle of Maximum Entropy (POME), which makes good winning in solution the
illposed problem. Maximum Entropy Spectra Analysis (MESA), introduced by BURG in
1975 and based on POME，has certain advantages over the classical and other new
methods. The statistical characteristics, which are used in stochastic model
identification, can be estimated using MESA, thus permitting integration of
spectral analysis and computations related to stochastic model development. It can
also be used in analyzing short time series, since it resolves lowfrequency
characteristics of the data. It is clear that studies with the use of entropy, POME
and MESA in hydrology, water resources and water environment have been relatively
few. Nevertheless, they are promising and justify further research. The former
studies provided motivation for our following work. Here MESA is used to detect the
period characteristics of the annual runoff series, monthly runoff series, and
annual maximum flood peak series of some stations in the Yellow River in China. The
subsection technique is used to compare whether the obtained periods have
consistency and stability. Such conclusions are drawn. (a) The 1st to 4th periods
of monthly runoff series takes the value of 12 month, 6 month, 4 month and 3 month
respectively; (b) The 1st to 2nd periods of annual runoff series takes the value of
3 year and 4 year respectively. (c) There is no significant period in the annual
maximum flood peak series.
Key words hydrologic series; maximum entropy spectra analysis (MESA); period
characteristics; the Yellow River; China 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000615 


WANG Dong 
Period characteristics of representative hydrologic series in the Yellow River in China using maximum entropy spectra analysis(MESA) 




Author(s) 
WANG Dong^{1}; WANG Dong^{1} 
Organisation(s) 
^{1}Nanjing University 
Abstract 
In the field of stochastic hydrology, hydrologic series is formed with the non
periodic component, the periodic component and the stochastic component. Here the
period characteristics used include approximate periods in the nonperiodic
component, simple periods and complex periods in the periodic component. Spectral
analysis is an essential and effective tool for extracting such stochastic
characteristics of time series. In 1948, Shannon developed a mathematical theory of
entropy and applied it in communications. Nearly a decade later, Jaynes formulated
the Principle of Maximum Entropy (POME), which makes good winning in solution the
illposed problem. Maximum Entropy Spectra Analysis (MESA), introduced by BURG in
1975 and based on POME，has certain advantages over the classical and other new
methods. The statistical characteristics, which are used in stochastic model
identification, can be estimated using MESA, thus permitting integration of
spectral analysis and computations related to stochastic model development. It can
also be used in analyzing short time series, since it resolves lowfrequency
characteristics of the data. It is clear that studies with the use of entropy, POME
and MESA in hydrology, water resources and water environment have been relatively
few. Nevertheless, they are promising and justify further research. The former
studies provided motivation for our following work. Here MESA is used to detect the
period characteristics of the annual runoff series, monthly runoff series, and
annual maximum flood peak series of some stations in the Yellow River in China. The
subsection technique is used to compare whether the obtained periods have
consistency and stability. Such conclusions are drawn. (a) The 1st to 4th periods
of monthly runoff series takes the value of 12 month, 6 month, 4 month and 3 month
respectively; (b) The 1st to 2nd periods of annual runoff series takes the value of
3 year and 4 year respectively. (c) There is no significant period in the annual
maximum flood peak series. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000614 


WANG Dong 
Two fuzzy and optimal models of water resources evaluation based on the Principle of Maximum Entropy (POME) and Engineering Fuzzy Set Theory 




Author(s) 
WANG Dong^{1}; WANG Dong^{1} 
Organisation(s) 
^{1}Nanjing University 
Abstract 
The randomness of characteristic value of water resources evaluation is inevitable
during its monitoring, experimenting, and data analyzing, as a result of the
physical process, the chemical process and biological process of water
contamination are all stochastic process. On the other hand, the fuzziness of water
resources evaluation is also inevitable, for the classification standard, the
evaluation class and pollution degree is impersonal fuzzy concept and phenomenon.
Entropy is a very important scientific conception. The entropy of a system was
first defined by Boltzmann in 1872. Shannon (1948) developed a mathematical theory
of entropy. Jaynes (1957) formulated the Principle of Maximum Entropy (POME), which
makes good winning in solution the illposed problem. Zadeh (1965)’s Fuzzy Sets has
been widely used in many fields. In 1998, Chen made a great progress, which was
named Engineering Fuzzy Set Theory. This new developed theory provides a new way to
ascertain membership degree and membership function. Now it is clear that studies
with the use of entropy, the Principle of Maximum Entropy (POME) and Engineering
Fuzzy Set Theory in water resources have been relatively few. Nevertheless, they
are promising and justify further research. It is the former studies that provided
motivation for our following work. The objective here is to consider both the
randomness and the fuzziness of water resources evaluation, based on the Principle
of Maximum Entropy (POME), and used the concept and method of Engineering Fuzzy Set
Theory. Two weighting generalized distances are defined respectively to build up
two fuzzy and optimal models for water resources evaluation. The validity and
reliability of modelⅠand modelⅡare proved by the results of eutrophication
evaluation of 12 representative lakes and reservoirs in China. The results of these
two models are basically identical, and consistent with the survey outcome.
Contrasting the fuzzy model in which only the fuzziness is taken into account, the
results of two models constructed here are more detailed, and possess lesser
Shannon entropy, which means the smaller uncertainty and more reliability. The
theory used and the models constructed here can be extended and applied to other
fields. 
Track/Session 
Special Sessions / Boltzmann Methods in Water Resources 
Date 
20060618 
DOI 
10.4122/1.1000000612 


Johannes Bruining 
Numerical validation of various mixing rules used for upscaled geophysical properties 




Author(s) 
Johannes Bruining^{1}; Evert Slob^{1}; WillemJan Plug^{1}; WillemJan Plug^{1} 
Organisation(s) 
^{1}Delft University of Technology 
Abstract 
Our objective is to interpret laboratory measurements of effective dielectric
permittivities as a function of water saturation during drainage and imbibition
processes in a porous medium. Mixing rules are widely used to express effective
properties of coefficients, e.g. diffusion coefficient, Darcy permeability, electric
conductivity and the dielectric permittivity, appearing in heterogeneous diffusion
like processes. Here we confine our interest to the electrostatic behaviour of a
mixture because most of the mixing rules were derived to compute the effective
dielectric permittivity. The validation of the so called mixing rules is obtained by
comparing them with the effective properties computed from the numerical solution of
the steady state diffusion equation, including boundary conditions. One of the
issues concerns the very large number of grid blocks required to obtain convergence.
The basic case considers a checkerboard permittivity distribution. From simulations
we can conclude that for the solution to converge to effective permittivity, a large
number of grid blocks is needed. Furthermore, the convergence rate depends on the
numerical method we use.
To analyze the validity of the results obtained, we make use of the HashinShtrikman
bounds that show the range of effective values for different spatial distributions,
for the given volume ratio of constituents. In agreement to the analytical solution,
the geometric mean is found to be the value for the effective permittivity in the 2
D case. However, a different choice of internodal dielectric coefficients can
enhance the computation for the finite difference simulation.
For the 3D case no analytical expression could be found and from the computations
we can conclude that the effective permittivity is close to the Bruggeman mixing law
and the third power law average.
Conclusions and significance:
1.For the 2D and 3D problem the convergence rate for the Finite Element (FE) model
is faster than for the Finite Difference (FD) model.
2.For the isotropic 2D case, a geometric mean for the internodal dielectric
permittivity leads to the fastest convergence rate, which corresponds to the
effective parameter value.
3.The solution for the 3 –D problem is close to the Bruggeman mixing rule and the
third power law average.
4.Coarse gridded FD computations, show results that do not satisfy the Hashin
Shtrikman bounds.
5.Fine gridded numerical computations can be used to analyze the measured effective
dielectric permittivity in terms of the spatial distribution of the components.
6.The results suggest that it is possible to obtain unambiguous mixing formula if
both the fraction of constituents and a geometric factor are specified.
7.Spatial distribution coefficients of the constituents (e.g. water, sand and rock)
are important to interpret and to analyse electric resistivity measurements, e.g.
borehole measurements.
8.This research shows that the conventional FD scheme used in reservoir simulators
can be improved by an optimal choice of internodal permeabilities. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000610 


Alexis Berne 
Pathaveraged rainfall estimation using a microwave link: uncertainty due to rainfall spatial variability 




Author(s) 
Alexis Berne^{1}; Remko Uijlenhoet^{1}; Hidde Leijnse^{1}; Alexis Berne^{1} 
Organisation(s) 
^{1}Wageningen University 
Abstract 
Microwave links offer the possibility to estimate (1) the latent and sensible heat
fluxes between landsurface and atmosphere, as well as (2) the pathaveraged rainfall
intensity along the link when precipitation occurs. In the latter case, a powerlaw
relation is assumed between the specific attenuation k affecting the electromagnetic
signal while propagating through precipitation and the rainfall intensity R, variable
of interest for many hydrological applications.
This work focuses on the influence of the spatial variability of rainfall along the
link on the parameterization of the kR relation, at the point and link scale. A
stochastic model is used to generate range profiles of raindrop size distributions
and subsequently to simulate link measurements. A Monte Carlo technique is then
applied to quantitatively analyze uncertainties on the kR powerlaw parameters for a
range of operating frequencies between 10 and 100 GHz and for different types of
rainfall events. 
Track/Session 
Special Sessions / Field measurements and simulations of landatmosphere interaction 
Date 
20060618 
DOI 
10.4122/1.1000000608 


WillemJan Plug 
Numerical Evaluation and Interpretation of Measured Effective Dielectric Permittivities during Two Phase Flow in a Porous Medium 




Author(s) 
WillemJan Plug^{1}; Johannes Bruining^{1}; Evert Slob^{1}; Ainhoa Gorriti^{1}; WillemJan Plug^{1} 
Organisation(s) 
^{1}Delft University of Technology 
Abstract 
An experimental procedure is presented where the capillary pressure and the
dielectric properties of a porous medium can be measured simultaneously. Our
objective is to determine a consistent relationship between capillary pressure
versus water saturation and its effect on the effective frequency dependent
dielectric permittivity. Applications are found in insitu subsurface measurements
like Ground Penetrating Radar, borehole measurements and logging tools.
We have built an experimental set up that can measure capillary pressure under
various pressures and temperature conditions. The sample holder is a parallel plate
capacitor with stainless steel plates, which also serve as support for the sample.
The plates are kept separated by a plastic ring, with an inner diameter of 89 mm
that also contains the sample. At the top of the sample holder we measure the
oil/gas pressure and at the outlet the water pressure and this pressure difference
is defined as the upscaled capillary pressure. Capillary pressure experiments have
already been conducted on sand stone samples where drainage processes were
investigated using CO2 and N2.
The second part of the experimental procedure is measuring the dielectric
permittivity. A precision component analyzer measures the impedance of the capacitor
as a function of frequency. The total impedance is directly related to the effective
value of the permittivity of the mixture of grains, water and oil/gas present in the
capacitor. Preliminary experiments suggest that the best results would be obtained
in the frequency range of 0.1 – 3.0 MHz.
To evaluate and interpret the measured effective permittivity of the different
constituents in the mixture and the influence on their distribution, we make use of
mixing laws and numerical models based on Finite Elements and Finite Difference. We
will present the results of this study between laboratory measurements and numerical
evaluation and interpretation in the resulting paper. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000607 


Henrik Madsen 
Data assimilation in a flood modelling system using the ensemble Kalman filter 




Author(s) 
Henrik Madsen^{1}; Johan Hartnack^{1}; Jacob Tornfeldt Sørensen^{1}; Henrik Madsen^{1} 
Organisation(s) 
^{1}DHI Water & Environment 
Abstract 
Data assimilation in a combined 1D2D numerical flood modelling system is
considered. The model is based on a dynamic linking between existing and well
established 1D and a 2D numerical modelling systems enhanced with new features which
are targeted specifically towards modelling of floods. This combination ensures a
maximum of flexibility by allowing modelling some areas in 2D detail (floodplain),
while other areas can be modelled in 1D (river network).
For this combined modelling system data assimilation facilities have been
implemen¬ted for assimilation of water level measurements. The data assimilation
system is based on the ensemble Kalman filter (EnKF) methodology. In the EnKF the
probability density of the model state is represented by an ensemble of model
states. In a model forecast each ensemble member is propagated according to the
dynamical system subjected to model errors, and the resulting ensemble then provides
estimates of the forecast state vector and the corresponding covariance matrix. When
measurements are available, the ensemble is updated using the standard Kalman filter
updating scheme to provide an updated probability density of the model state.
In this paper the implementation of the EnKF in the combined 1D2D model is
discussed and is demonstrated on a flood model application in Bangladesh. 
Track/Session 
Special Sessions / Data assimilation in water resources modelling 
Date 
20060618 
DOI 
10.4122/1.1000000605 


Han Stricker 
Estimation of pathaverage evaporation and precipitation using a microwave link 




Author(s) 
Han Stricker^{1}; Wouter Meijninger^{1}; Hidde Leijnse^{1}; Remko Uijlenhoet^{1}; Hidde Leijnse^{1} 
Organisation(s) 
^{1}Wageningen University 
Abstract 
The potential of a 27 GHz microwave link for measuring both evaporation and
precipitation is investigated. For the estimation of evaporation a combination of
the microwave link (radio wave scintillometer) and an energy budget constraint is
proposed. This Radio Wave ScintillometryEnergy Budget Method (RWSEBM) has been
tested using data from an experiment with a 27 GHz radio wave scintillometer over
2.2 km and four eddy covariance (EC) systems. Comparing one day of measurements (30
minute intervals) of the evaporation estimated using the RWSEBM to those measured
by eddy covariance systems leads to the conclusion that the method provides
consistent estimates under relatively wet conditions.
In the case of precipitation, analyses show that the specifc attenuation of an
electromagnetic signal at 27 GHz varies nearly linearly with the rainfall
intensity, which is ideal for lineintegrating instruments. Data from an experiment
with a 4.89 km microwave link and a line configuration of seven tippingbucket
raingauges are used to test whether this instrument is indeed suitable for the
estimation of pathaverage rainfall. Results from this experiment show that the
attenuation due to wet antennas can have a significant effect on
the retrieved rainfall intensity. However, when a twoparameter wet antenna
correction function is applied to the link data, comparisons with the raingauge
data show that the instrument is indeed wellsuited for the measurement of path
average rainfall. 
Track/Session 
Special Sessions / Field measurements and simulations of landatmosphere interaction 
Date 
20060618 
DOI 
10.4122/1.1000000603 


Hidde Leijnse 
Estimation of pathaverage precipitation using a 27 GHz microwave link 




Author(s) 
Hidde Leijnse^{1}; Remko Uijlenhoet^{1}; Han Stricker^{1}; Alexis Berne^{1}; Hidde Leijnse^{1} 
Organisation(s) 
^{1}Wageningen University 
Abstract 
Between May and July 1999 we operated a 27 GHz microwave link over a 5 km path
between the towns of Rhenen and Wageningen in the Netherlands. The instrument,
which was built at Eindhoven University of Technology, measures the power
arriving at the receiving antenna with a sampling frequency of 18 Hz. During
dry weather conditions, it can be used as a microwave scintillometer, i.e. the
(turbulent) fluxes of sensible and latent heat can be estimated from the
variance of the received power fluctuations. Here we focus on the use of the
instrument during rainy conditions, where it can be used to measure the
pathintegrated attenuation of the microwave signal due to intervening rain
between the transmitting and the receiving antenna. Owing to the fact that the
specific attenuation at this particular microwave frequency (in dB/km) is
closely proportional to the rainfall rate (in mm/h), as we demonstrate using
disdrometer observations from the Cabauw Experimental Site for Atmospheric
Research (CESAR), this instrument is well suited for pathaverage rainfall
estimation. This parameter is highly relevant for various hydrological and
meteorological applications. We present analyses for several rainfall events
during the mentioned period, where we have compared the pathaverage rainfall
estimates from the microwave link with rainfall measurements from a colocated
line configuration of tipping bucket rain gauges. Although the results of this
comparison are found to be promising, the need for an accurate absolute
calibration remains a serious drawback of singlefrequency microwave links. 
Track/Session 
Special Sessions / Field measurements and simulations of landatmosphere interaction 
Date 
20060618 
DOI 
10.4122/1.1000000602 


Jennifer Niessner 
Multiscale modeling of twophasetwocomponent processes in heterogeneous porous media 




Author(s) 
Jennifer Niessner^{1}; Rainer Helmig^{1}; Jennifer Niessner^{1} 
Organisation(s) 
^{1}Universitaet Stuttgart 
Abstract 
Flow and transport phenomena in porous media are the governing processes in many
natural and industrial systems. Not only do these flow and transport phenomena occur
on different space and time scales, but it is also the porous medium itself which is
heterogeneous where the heterogeneities are present on all spatial scales.
We consider a large domain with randomly distributed heterogeneities where complex
twophasetwocomponent processes are relevant only in a small (local) subdomain.
This subdomain needs fine resolution as the complex processes are governed by
smallscale effects. For a comprehensive finescale model taking into account
twophasetwocomponent processes as well as heterogeneities in the whole (global)
model domain, data collection is expensive and computational time is high. Therefore,
we developed a multiscale concept where on the one hand, the global flow field
influences the local twophasetwocomponent processes on the finescale. On the
other hand, a coarsescale saturation equation is solved where the effects of the
finescale twophasetwocomponent processes in the subdomain are captured by source
/ sink terms and the effects of finescale heterogeneities by a macrodispersion term.
The overall algorithm as well as results will be discussed for simplified applications. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000600 


Duane Smith 
The Use of a Realgas Potential Approach in a Multicomponent Simulator for Highly Fractured Reservoirs 




Author(s) 
Duane Smith^{1}; W. Neal Sams^{2}; Joseph Wilder^{1}; Duane Smith^{1} 
Organisation(s) 
^{1}National Energy Technology Laboratory, U. S. Department of Energy; ^{2}National Energy Technology Laboratory, EG&G 
Abstract 
Dualporosity simulators are ubiquitously used for fractured reservoirs. However,
explicitfracture simulators may be able to increase the accuracy and reliability of
simulations for highly fractured reservoirs, because they can directly use
descriptions (i.e., lengths, orientations, and apertures) of fractures as obtained
from well logs (especially, fmi), out crop analyses, and other geological data. Al
Hussainy et al developed the real gas potential primarily for use in gaswell
testing analyses and in singlephase simulators for a single, dry gas. The real gas
potential has been used in the current work to develop an explicit fracture
reservoir simulator for multicomponent, miscible fluids. This simulator considers
flow through explicitly defined fractures as well as storage/recharge in/from the
surrounding rock matrix. The simulator allows for the use of multiple geologic
layers in the reservoir, each of which has independently defined physical and/or
flow properties such as thickness, permeability, porosity, diffusivity of the fluids
through the rock matrix (important for lowpermeability situations), and adsorption
isotherms for one of more of the fluid components. Each of the fractures contained
in the reservoir also has independently defined physical properties such as height,
length, orientation, and aperture. Fluid flow between the layers of the geologic
strata is via userdefined multilayer fractures which extend through two or more
layers. Such multilayer fracture networks can be easily generated through the use
of such codes as NETL’s FRACGEN, the output of which can be used directly with the
flow simulator being reported on here. As a result of the explicit handling of
fractures as well as the use of the potential formulation, simulation of multilayer
reservoirs containing tens of thousands of fractures can be performed in shorter
times than those required by finite element codes.

(1)EG&G (2)U.S. Department of Energy 
Track/Session 
Special Sessions / Geologic Sequestration of Carbon Dioxide 
Date 
20060618 
DOI 
10.4122/1.1000000598 


Matteo Camporese 
Two dimensional hydrological simulation in swelling/shrinking peat soils 




Author(s) 
Matteo Camporese^{1}; Claudio Paniconi^{2}; Mario Putti^{1}; Paolo Salandin^{3}; Pietro Teatini^{1}; Matteo Camporese^{1} 
Organisation(s) 
^{1}Università di Padova; ^{2}INRS  ETE, Université du Québec; ^{3}Università Politecnica delle Marche 
Abstract 
Peat soils respond to drying/wetting cycles due to evapotranspiration
and precipitation with reversible deformations induced by
variations of water content in both the unsaturated and saturated
zone. This process results in shortterm vertical displacements
of the soil surface that superimpose to the irreversible longterm
subsidence typically occurring in drained cropped peatlands
because of biooxidation of the organic matter. Yearly sinking
rates due to the irreversible process can be comparable with
shortterm deformation rates (swelling/shrinkage) and the latter
must be assessed to achieve a thorough understanding of the whole
phenomenon.
A mathematical model describing swelling/shrinkage dynamics in peat soils
under unsaturated conditions has been derived from simple physical
considerations, and validated by comparison with laboratory shrinkage data.
The twoparameter model expresses the void ratio of the soil as a
function of the moisture ratio. This approach is implemented in a
model of subsurface flow in variably saturated porous media (Richards'
equation), by means of an appropriate modification of the general
storage term. The contribution of the saturated zone to the total
deformation is modeled by the theory of primary consolidation, in the
hypothesis of completely reversible compression and constant
coefficient of compressibility.
Simulations have been carried out for a drained cropped peatland south
of the Venice Lagoon (Italy), for which a large data set of
hydrological and displacement measurements has been collected since
the end of 2001. The considered domain is representative of a field
section bounded by ditches, subject to rainfall and evapotranspiration.
The comparison between simulated and measured quantities demonstrates
the capability of the model to accurately reproduce both
the hydrological and deformation dynamics of peat, with values of the
relevant parameters that are in good agreement with the literature. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000596 


Axel Malqvist 
A Mixed Adaptive Variational Multiscale Method 




Author(s) 
Axel Malqvist^{1}; Mats G. Larson^{2}; Axel Malqvist^{1} 
Organisation(s) 
^{1}Colorado State University; ^{2}Umea University 
Abstract 
We present a mixed adaptive variational multiscale method for
solving elliptic second order problems. This work is an extension of
the adaptive variational multiscale method (AVMS), introduced by
Larson and Malqvist, to a mixed
formulation. The method is based on a particular splitting into
coarse and fine scales together with a systematic technique for
approximation of the fine scale part based on solution of decoupled
localized subgrid problems. We present the mixed AVMS method and
derive a posteriori error estimates for both linear functionals and
the energy norm. Based on the estimates we propose an adaptive
algorithm for automatic tuning of critical discretization
parameters. Finally, we present numerical examples on a two
dimensional slice of an oil reservoir. 
Track/Session 
Special Sessions / Multiscale methods for flow in porous media 
Date 
20060618 
DOI 
10.4122/1.1000000594 


Dmitri Kavetski 
Analysis of potential CO2 leakage through abandoned wells using a semianalytical model 




Author(s) 
Dmitri Kavetski^{1}; Jan M. Nordbotten^{2}; Michael A. Celia^{1}; Stefan Bachu^{3}; Dmitri Kavetski^{1} 
Organisation(s) 
^{1}Princeton University; ^{2}University of Bergen; ^{3}Alberta Energy and Utility Board 
Abstract 
Potential injection sites for geological CO2 storage include deep formations in
mature sedimentary basins. Many of these basins have a long history of oil and gas
exploration and production and the vicinity of the injection site may therefore be
perforated by hundreds of wells, potentially penetrating into the injection
formation. Geosequestration models must therefore be able to simulate plume spreads
over large spatial areas (of order 1,000 km2), while resolving the local dynamics in
all the wells. Furthermore, many of these wells are abandoned and their locations and
hydraulic properties might be uncertain or unknown. Therefore, risk assessment based
on Monte Carlo simulations may be necessary to estimate the resulting uncertainty in
the leakage.
In this paper, we present a semianalytical model that simulates the evolution of CO2
plumes and leakage in multiple brine aquifers pierced by multiple passive wells over
decadal to century time scales. The model’s equations and state variables are
obtained from the selfsimilarity of the plume shapes and are defined solely at well
locations. Since the model does not require domain discretisation in the traditional
numerical sense, it is highly computationally efficient, potentially thousands of
times faster than existing numerical multiphase simulators. This paper demonstrates
the insights gained by applying this model to a potential injection site in the
Alberta Basin, Canada, involving more than 500 existing wells over a domain that is
900 km2. Different leakage measures and statistics are presented and discussed. 
Track/Session 
Special Sessions / Geologic Sequestration of Carbon Dioxide 
Date 
20060618 
DOI 
10.4122/1.1000000593 


liange zheng 
A DUAL CONTINUUM FLOW AND REACTIVE TRANSPORT MODEL WITH NTH ORDER SOLUTE TRANSFER TERM FOR STRUCTURED POROUS MEDIA: THEORY AND EVALUATION WITH SYNTHECTIC CASES 




Author(s) 
liange zheng^{1}; Javier Samper Calvete^{2}; liange zheng^{1} 
Organisation(s) 
^{1}PH. D student; ^{2}professor 
Abstract 
Compacted bentonite is foreseen to be used as backfill and sealing material for
highlevel radioactive waste disposal. Experimental evidence indicates that
bentonite exhibits two types of porous domains: macroporous domain which contains
free water and microporous domain mainly occupied by interlayer and sorbed water.
Geochemical nonequilibrium between macro and microdomains calls for a fully
coupled reactive transport Dual Continuum Model (DCM) to describe water flow and
hydrochemistry of bentonites. Most DCM in the literature assume a lumped first
order solute transfer term between both domains. However, it is well known that
such a term is not correct at all times. Here we present a formulation of flow and
reactive transport for a dual continuum with an nth order solute transfer term,
derived from an approximation of an analytical solution for diffusion through a
thin slab. Such formulation which has been implemented in a finite element code
which solves both for the forward and inverse problem greatly improves the ability
and accuracy of DCM to simulate reactive transport in bentonites. Solute transfer
terms of different orders (n) are evaluated for several 1 and 2D synthetic cases.
The order and the empirical coefficients of the solute transfer term are estimated
by inverse modelling. Optimum results for bentonite are achieved with n = 0.72 and
a scale term of 2.5. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000591 


Javier Samper 
An Approximate Analytical Solution for Multimonovalent Cation Exchange Reactive Transport in Groundwater 




Author(s) 
Javier Samper^{1}; Changbing Yang^{1}; Javier Samper^{1} 
Organisation(s) 
^{1}Universidad de Coruña, Spain 
Abstract 
Cation exchange in groundwater is one of the dominant surface reactions. Mass
transfer of cationexchanging pollutants in groundwater is highly nonlinear. This
makes difficult to derive analytical solutions for multication exchange reactive
transport which are of interest for stochastic analyses of multicomponent reactive
transport. Dou and Jin (1996) used the method of characteristics with a special
treatment of shock waves and worked out a closedform formulation for 1D transport
coupled to binary homovalent ion exchange. Jin and Ye (1999) extended this approach
and developed an approximate analytical solution to binary monovalentdivalent ion
exchange transport. Due to the complexity of the isotherms, most of the available
analytical solutions are suitable only for 1D transport with binary cation
exchange. Here we present an approximate analytical solution for the general case
of multimonovalent cation exchange reactive transport accounting for any arbitrary
number of monovalent cations. Time derivatives of concentrations of exchanged
cations (those sorbed on the solid phase), β’, are related to time derivatives of
concentrations of dissolved cations c’ through a Jacobian matrix J which is derived
by taking time derivatives of the logarithmic version of the nonlinear cation
exchange massactionlaw equations. The Jacobian matrix which in general depends on
β and c is evaluated at selected values of β* and c*. Substitution of β’ into the
reactive transport equations leads to a set of coupled partial differential
equations (PDEs). Such coupled set of PDEs can be effectively decoupled by means of
a similarity transformation which leads to a diagonal retardation matrix. By
performing such transformation on boundary and initial concentrations, the set of
linear uncoupled PDE’s can be solved in terms of transformed concentrations U by
using standard available analytical solutions. Concentrations of the original
problem c are obtained by performing the backwards transformation on U. Our
analytical solution has been tested with numerical solutions computed with a
general purpose reactive transport code (CORE2D)for several 1D cases. Analytical
solutions not only agree well with numerical results regardless of the choice of β*
and c*, but provide also additional insight into the nature of the retardation
factors caused by multicomponent monovalent cation exchange.
Cation exchange in groundwater is one of the dominant surface reactions. Mass
transfer of cationexchanging pollutants in groundwater is highly nonlinear. This
makes difficult to derive analytical solutions for multication exchange reactive
transport which are of interest for stochastic analyses of multicomponent reactive
transport. Dou and Jin (1996) used the method of characteristics with a special
treatment of shock waves and worked out a closedform formulation for 1D transport
coupled to binary homovalent ion exchange. Jin and Ye (1999) extended this approach
and developed an approximate analytical solution to binary monovalentdivalent ion
exchange transport. Due to the complexity of the isotherms, most of the available
analytical solutions are suitable only for 1D transport with binary cation
exchange. Here we present an approximate analytical solution for the general case
of multimonovalent cation exchange reactive transport accounting for any arbitrary
number of monovalent cations. Time derivatives of concentrations of exchanged
cations (those sorbed on the solid phase), β’, are related to time derivatives of
concentrations of dissolved cations c’ through a Jacobian matrix J which is derived
by taking time derivatives of the logarithmic version of the nonlinear cation
exchange massactionlaw equations. The Jacobian matrix which in general depends on
β and c is evaluated at selected values of β* and c*. Substitution of β’ into the
reactive transport equations leads to a set of coupled partial differential
equations (PDEs). Such coupled set of PDEs can be effectively decoupled by means of
a similarity transformation which leads to a diagonal retardation matrix. By
performing such transformation on boundary and initial concentrations, the set of
linear uncoupled PDE’s can be solved in terms of transformed concentrations U by
using standard available analytical solutions. Concentrations of the original
problem c are obtained by performing the backwards transformation on U. Our
analytical solution has been tested with numerical solutions computed with a
general purpose reactive transport code (CORE2D)for several 1D cases. Analytical
solutions not only agree well with numerical results regardless of the choice of β*
and c*, but provide also additional insight into the nature of the retardation
factors caused by multicomponent monovalent cation exchange. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000589 


Mikhail Gladkikh 
A PoreLevel Approach to Petrophysical Interpretation of Well Logging Measurements 




Author(s) 
Mikhail Gladkikh^{1}; Alberto Mezzatesta^{1}; Mikhail Gladkikh^{1} 
Organisation(s) 
^{1}Baker Hughes, Inc. 
Abstract 
An accurate description of water or oilbearing reservoirs and the assessment of
reserves strongly depend on a robust determination of their petrophysical
parameters, e.g., porosity, permeability and fluid distribution, reflecting fluid
type, content, and mobility. Downhole measurements provide means to formation
evaluation; however, they do not directly provide the petrophysical properties of
interest. To interpret well logging data, a range of empirical models are usually
employed. These empirical relationships, however, lack scientific basis and usually
represent generalizations of the observed trends. To provide a link between a
detailed description of the physical processes occurring at the pore scale and the
macroscopic properties of sedimentary rocks, a new porelevel approach to
petrophysical interpretation of logging measurements is suggested in this work.
A powerful means to create such a link is to develop quantitative relationships
between the petrophysical properties and the geologic processes involved in forming
the rocks. Here we describe the use of simple but physically representative models
of the results of several rockforming processes, e.g., sedimentation, cementation,
and the formation of authigenic clay minerals. The key feature of these models is
that they are geometrically determinate or precisely defined based on knowing the
location of every grain comprising the model rock and hence the morphology of the
pore space at the grain scale. We outline a method for computing macroscopic
petrophysical properties using the proposed rock models. Unlike many approaches to
porelevel modeling, our approach introduces no adjustable parameters and thus can
be used to produce quantitative, a priori predictions of the rock macroscopic
behavior. These a priori predictions, in turn, allow for successfully inverting and
interpreting logging data to obtain petrophysical parameters of sedimentary rocks,
such as absolute and relative permeabilities as well as capillary pressure curves.
For example, NMR (Nuclear Magnetic Resonance) logs contain information about grain
size, allowing for an accurate petrophysical interpretation by means of the pore
level approach presented in this work.
The proposed methodology is also applied to real field data and the corresponding
interpretation results are included in this paper. 
Track/Session 
Special Sessions / PoreScale Modelling: New Developments And Applications 
Date 
20060618 
DOI 
10.4122/1.1000000587 


Kristopher L. Kuhlman 
Recent Advances in Laplace Transform Analytic Element Method (LTAEM) Theory and Application to Transient Groundwater Flow 




Author(s) 
Kristopher L. Kuhlman^{1}; Shlomo P. Neuman^{1}; Kristopher L. Kuhlman^{1} 
Organisation(s) 
^{1}Department of Hydrology and Water Resources, University of Arizona 
Abstract 
Furman and Neuman (2003) proposed a Laplace Transform Analytic Element Method
(LTAEM) for transient groundwater flow. LTAEM solves the modified Helmholtz
equation in Laplace space and backtransforms it to the time domain using a Fourier
Series numerical inverse Laplace transform method (de Hoog, et.al., 1982). We have
extended the method so it can compute hydraulic head and flow velocity distributions
due to any twodimensional combination and arrangement of point, line and circular
area sinks and sources, nested circular regions having different hydraulic
parameters, and circular regions with specified head or flux. The strengths of all
sinks and sources, and the specified head and flux values, can all vary with time in
an independent and arbitrary fashion. Initial conditions may vary from one circular
element to another. A solution is obtained by matching heads and normal fluxes inside
and outside each circular element. The effect of each circular element on flow is
expressed in terms of generalized Fourier series which converge rapidly (<10 terms)
in most cases. As there are more matching points than Fourier terms, the matching is
accomplished in Laplace space by leastsquares. We illustrate the method by
calculating head and velocity as well as representative particle flow paths through a
distribution of circular inhomogeneities and transient sources and sinks. The
results are compared to a MODFLOW simulation. We are presently extending the method
to ellipses in two dimensions and spheroids in three dimensions. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000585 


Alexandre Tartakovsky 
Smoothed particle hydrodynamics model for porescale flow, reactive transport and mineral precipitation. 




Author(s) 
Alexandre Tartakovsky^{1}; Timothy Scheibe^{1}; George Redden^{2}; Yilin Fang^{1}; Paul Meakin^{2}; Prasad Saripalli^{1}; Alexandre Tartakovsky^{1} 
Organisation(s) 
^{1}Pacific Northwest National Laboratory; ^{2}Idaho National Laboratory 
Abstract 
We have developed a porescale numerical reactive transport model, based on
smoothed particle hydrodynamics (SPH), that incorporates heterogeneous
precipitation/dissolution reactions. Lagrangian particle methods such as SPH have
several advantages for modeling porescale flow and transport: i) in a Lagrangian
framework there is no nonlinear term in the momentum conservation equation, so that
SPH allows accurate solution of momentum dominated flows; ii) complicated physical
and chemical processes associated with realistic equations of state, changes in
solid boundaries due to dissolution or precipitation and chemical reactions are easy
to simulate. The SPH model was used to study the general effects of porosity, pore
scale heterogeneity, Damkohler numbers and Peclet numbers on reactive transport and
to estimate effective reaction coefficients and mass transfer coefficients. The
changes in porosity, conductivity and transport parameters resulting from mineral
precipitation were also investigated. Hysteresis in the reaction rate coefficient
and mass transport coefficient resulting from changing porosities, mass fluxes and
reactive surface areas was observed. Flow and transport with low Damkohler numbers
and high Peclet numbers was found to result in uniform precipitation. When the
Damkohler number was high and the Peclet number was low, precipitation occurred
mainly around the supersaturated solution injection areas. The porescale model was
coupled with a continuumscale reactive transport model and tested using data from a
mesoscale experimental investigation of calcite precipitation in a porous medium.
The results of the coupled porecontinuum modeling approach are compared to
simulation results from continuumscale modeling alone with existing formation
damage models drawn from the literature, and to the experimental observations. 
Track/Session 
Special Sessions / PoreScale Modelling: New Developments And Applications 
Date 
20060618 
DOI 
10.4122/1.1000000583 


Mark Porter 
Dynamic Effects in Oil/Water and Air/Water Capillary PressureSaturation Curves: Experiments and LatticeBoltzmann Simulations 




Author(s) 
Mark Porter^{1}; Marcel Schaap^{2}; Dorthe Wildenschild^{1}; Mark Porter^{1} 
Organisation(s) 
^{1}Oregon State University; ^{2}GEBJ Salinity Laboratory 
Abstract 
The capillary pressuresaturation curve is widely used to characterize hydraulic
properties of porous media. It is often assumed that curves measured under
equilibrium or steadystate flow conditions can be applied to transient flow
conditions, and vice versa. Yet, substantial experimental evidence suggests that
capillary pressuresaturation curves obtained during transient conditions differ from
those obtained under equilibrium or steadystate conditions. It has been shown that
the capillary pressuresaturation curve shows signs of dynamic behavior depending on
the inflow and outflow rate applied to the porous system. The exact cause of the
observed shift is not yet fully understood. It is hypothesized that the mechanisms
responsible for dynamic behavior include: (1) the geometry of the pore space, (2)
interfacial phenomena at the pore scale, and (3) the interplay of inertial and
viscous forces.
In this investigation, air/water and oil/water imbibition and drainage experiments
were conducted on a column of packed glass beads. Various inflow and outflow rates
were applied to each multiphase system, which resulted in capillary
pressuresaturation curves that exhibit varying degrees of dynamic behavior. The
dynamic behavior observed in preliminary oil/water experiments was less pronounced
than the behavior observed in past air/water experiments. This suggests that the
viscous and inertial forces may only be a major factor when the density and viscosity
ratios are large, as is the case for the air/water system.
The dynamic behavior was examined using conceptual 2D and 3D latticeBoltzmann (LB)
simulations. We used the multiphase, multicomponent model developed by Shan and
Chen for these simulations. The conceptual LB simulations can provide insights into
porescale interfacial phenomena and help explain the dynamic behavior observed in
the experiments. Scaling of time and space from LB parameters to physical parameters
was performed to make comparisons between simulation and experimental results possible. 
Track/Session 
Special Sessions / PoreScale Modelling: New Developments And Applications 
Date 
20060618 
DOI 
10.4122/1.1000000581 


Yilin Fang 
3D FieldScale Reactive Transport Modeling of In Situ Immobilization of Uranium in Structured Porous Media via Biostimulation 




Author(s) 
Yilin Fang^{1}; Timothy Scheibe^{1}; Eric Roden^{2}; Wiwat Kamolpornwijit^{1}; Scott Brooks^{3}; Yilin Fang^{1} 
Organisation(s) 
^{1}Pacific Northwest National Laboratory; ^{2}University of Wisconsin; ^{3}Oak Ridge National Laboratory 
Abstract 
A twomonthlong ethanol injection experiment was conducted to study the impacts of
porous media structure (i.e., heterogeneity existing at multiple scales) on the
effectiveness of metal/radionuclide bioremediation in a highly heterogeneous
unconfined aquifer near Oak Ridge, TN, USA. We have constructed a 3D fieldscale
groundwater flow and multicomponent reactive transport model to simulate the
experimental observations. The model incorporates a suite of abiotic reactions and
microbiallymediated redox reactions for multiple terminal electron accepting
processes (TEAPs) including soluble oxygen, nitrate, U(VI) and sulfate and solid
phase electron acceptors. Different biomass populations are considered in the
model. Growth of these populations is derived from the bioenergeticsbased approach
in which the partitioning of electron flow between energy generation and cell
biomass production is dependent on the free energy of the corresponding TEAP. TEAP
reaction rates were free energy constrained. The TEAP model and reaction system
have been formulated and used to simulate laboratory batch experimental
observations. We conducted the fieldscale simulation starting with the reaction
system and parameters obtained from the batch experiment and hydrologic parameters
estimated from the results of pumping tests and water level monitoring and model
interpretation of a tracer test conducted at the field in August 2004. Reaction
parameters were investigated to compare simulation results and field experiment
observations. 
Track/Session 
Special Sessions / MultiDisciplinary Approaches To Reactive Transport Simulation In Aquifer Systems 
Date 
20060618 
DOI 
10.4122/1.1000000580 


Steven Carle 
Simulating Effects of NonIsothermal Flow on Reactive Transport of Radionuclides Originating From an Underground Nuclear Test 




Author(s) 
Steven Carle^{1}; Mavrik Zavarin^{1}; Andrew Tompson^{1}; Reed Maxwell^{1}; Gayle Pawloski^{1}; Steven Carle^{1} 
Organisation(s) 
^{1}Lawrence Livermore National Laboratory 
Abstract 
In numerical simulation of radionuclide transport, a mechanistic reactive transport
model can account for nonelectrostatic surface complexation, ion exchange, and
mineral dissolution/precipitation reactions. However, in radionuclide transport
originating from an underground nuclear test, thermal effects must also be
considered because heat accounts for the majority of energy released from the test.
A large fraction of residual test heat is initially contained in a “puddle” of
solidified melt glass and rubble containing much of the lessvolatile
radionuclides. Residual test heat induces thermal convection by reducing fluid
density and viscosity. Residual test heat also increases glass dissolution rates
and, consequently, the rate of release of certain radionuclides into pore fluids.
We combine a transient streamline reactive transport simulation approach with a
hydrothermal flow model to predict the combined threedimensional effects of test
heat and nonlinear geochemistry on radionuclide transport within a scale of ~ 1 km.
This work was performed under the auspices of the U.S. Department of Energy by
Lawrence Livermore National Laboratory under contract No. W7405Eng48. 
Track/Session 
Special Sessions / MultiDisciplinary Approaches To Reactive Transport Simulation In Aquifer Systems 
Date 
20060618 
DOI 
10.4122/1.1000000578 


Ivan Lunati 
A multiscale finitevolume method for threephase flow influenced by gravity 




Author(s) 
Ivan Lunati^{1}; patrick jenny^{1}; Ivan Lunati^{1} 
Organisation(s) 
^{1}ETH Zurich 
Abstract 
A multiscale finitevolume (MSFV) method for solving multiphase flow problem in highly heterogeneous
media was recently developed. In contrast with classical upscaling techniques, the goal of multiscale methods
is not simply to capture the largescale effects of the finescale heterogeneity, but to provide an efficient tool
for solving large flow problems with finescale resolution.
The MSFV is based on a fractional flow formulation of the problem: first an equation for the total velocity is
solved, then a finescale velocity field is reconstructed, finally the phasesaturation distribution is obtained by
solving the nonlinear transport equations. In addition to the original fine grid the MSFV method employs an
imposed coarse grid and a dual coarse grid. The first step is to compute the effective parameters that have to
be used for solving the global flow problem on a coarse grid. This is done by means of a set of basis
functions, which are numerical solutions computed on the cells of the dual grid. From these basis functions,
the fluxes across the coarseblock boundaries are computed and the transmissibilities are extracted. Then the
conservative finescale totalvelocity field is reconstructed by solving a local flow problem in each coarse cell.
In this paper we extend the MSFV method to account for gravity effects, which enables our method to work for
fairly realistic problems, e.g. deadoil problems or blackoil problems. To correctly account for gravity effects
an additional local problem has to be solved on each block of the dual grid. This problem provides an
additional basis function (gravity basis function) that represents a local correction to the fluxes computed in
the absence of gravity. 
Track/Session 
Special Sessions / Multiscale methods for flow in porous media 
Date 
20060618 
DOI 
10.4122/1.1000000576 


Thomas Hemker 
DerivativeFree Optimization Methods for Handling Fixed Costs in Optimal Groundwater Remediation Design 




Author(s) 
Thomas Hemker^{1}; Kathleen Fowler^{2}; Thomas Hemker^{1} 
Organisation(s) 
^{1}Department of Computer Science, TU Darmstadt; ^{2}Department of Mathematics and Computer Science, Clarkson University 
Abstract 
Groundwater remediation design problems are routine in water resource management. The
starting point for such a design problem is to formulate an objective function that
represents a measure of the manager's goal. For example, in plume migration control,
we need to determine the cost to design a well field to alter the direction of
groundwater flow and thereby control the destination of a contaminant. Constraints
must be specified to ensure that the plume is captured, the physical domain is
protected, and the wells operate under realistic conditions. Optimization algorithms
must work in conjunction with groundwater flow and possibly contaminant transport
simulators to determine the minimal cost well design subject to the constraints, but
typically these numerical simulation codes have been developed for many years and
have usually not been designed to meet the specific needs of optimization methods as,
e.g., providing gradient information. Decision variables can be realvalued, in the
case of pumping rates and well locations, or integer valued in the case of the number
of wells in the design.
In this work we focus on formulations that include a fixed installation cost as well
as an operating cost, resulting in a simulationbased nonlinear mixedinteger
optimization problem. The motivation is that our preliminary studies have shown that
convergence to an unsatisfactory, local minimum with many wells operating at low
pumping rates is common when the fixed cost is ignored. The challenge in the fixed
cost formulation is the integer variable for the number of wells in the design.
Removing a well from the design space leads to a large decrease in cost meaning
optimizers must be equipped to either handle a mixedinteger or approximate mixed
integer, blackbox problem and discontinuities in the objective function. Moreover
since evaluation of the objective function requires numerical results from a
simulation, derivative information is unavailable. Gradient based optimization
methods are not appropriate for these applications, hence methods that rely only on
function values are more appealing.
We compare three methods for handling the installation cost on a hydraulic capture
benchmarking problem proposed in the literature. All the approaches described below
do not use the gradient of the objective function, only function values for
minimization. In one approach, we use penalty coefficients proposed in the literature
for the installation term to transform the discontinuous problem into a continuous
one. In another approach, we bypass including the number of wells as a decision
variable by defining an inactivewell threshold. In the course of the optimization,
if a well rate falls in this threshold, the well is removed from the design space,
leading to large discontinuities in the objective function. For the two above
formulations, we use the implicit filtering algorithm, a method which uses a sequence
of finite difference gradients, for minimization. In the third approach, we use
sequential stochastic modeling to build surrogate functions to approximate the
original objective function. With this procedure the use of a branch and bound
technique becomes possible to solve the mixed integer problem in contrast to methods
working directly on the simulation results, which impedes relaxation of integer
variables. We present promising preliminary numerical results on the benchmarking
problem and point the way towards improvement and future work. 
Track/Session 
Special Sessions / Groundwater Optimal Management Session 
Date 
20060618 
DOI 
10.4122/1.1000000574 


Javier Aparicio 
An optimal switching mechanism for a combined Picard Newton method for the solution of Richards´equation 




Author(s) 
Javier Aparicio^{1}; Álvaro Aldama^{1}; Claudio Paniconi^{2}; Mario Putti^{3}; Javier Aparicio^{1} 
Organisation(s) 
^{1}Mexican Institute of Water Technology; ^{2}Center for advanced Studies, Research and Development in Sardinia; ^{3}Dept. Mathematical Methods and Models for Scientific Applications 
Abstract 
Richards’ equation, describing flow in partially saturated porous media, contains
strong nonlinearities arising from pressure head dependencies in soil moisture and
hydraulic conductivity. Additionally, the time dependent nature of boundary
conditions can alter the nonlinear characteristics of equation during a transient
simulation.
Various iterative methods are used for solving this nonlinear equation, most
commonly the quadratically convergent Newton – Raphson technique and the simpler
but only linearly convergent Picard method (successive approximation). The initial
solution estimate can have a large influence on the behavior of these iterative
schemes, and we have observed through many applications of our numerical
subsurface flow models that the Newton scheme is more sensitive to the initial
solution than the Picard scheme is used to calculate improved initial guess
for the Newton iteration. This scheme should achieve quadratic convergence while
improving the global behavior of the iteration at less cost and complexity than
alternative globalization techniques such as line search and trust region
methods. In this work the combined Picard – Newton method is investigated via a
theoretical analysis, based on a Taylor – Frechét expansion of the nonlinear 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000572 


Javier Samper 
Numerical Evaluation of Multicomponent Cation Exchange Reactive Transport in Physically and Geochemically Heterogeneous Porous Media 




Author(s) 
Javier Samper^{1}; Changbing Yang^{1}; Javier Samper^{1} 
Organisation(s) 
^{1}Universidad de Coruña, Spain 
Abstract 
Sophisticated deterministic numerical models have been developed during the last
two decades for the analysis of multicomponent reactive solute transport. Most of
these models account for spatial heterogeneity by parameter zonation. Most
stochastic analyses of reactive transport in physically and geochemically
heterogeneous porous media consider a single reactive species. Attempts have been
made recently for the stochastic analysis of multicomponent reactive species which
rely on simplifying assumptions. Given the lack of theoretical stochastic analyses
of multicomponent cation exchange reactive transport in physically and
geochemically heterogeneous porous media here we use Montecarlo techniques. We
analyze cation exchange reactive transport through a twodimensional vertical
domain 40 m wide and 10 m deep. The 2D domain, initially filled with 1 mM NaNO3
and 0.2 mM KNO3, is flushed by 0.6 mM CaCl2 solution from left to right. This case
illustrates the chromatographic separation of Na and K. Na is weakly adsorbed and
is eluted first. K is more tenaciously held than Na, and it appears retarded in the
effluent. Both permeability and cation exchange capacity are assumed to be random
Gaussian functions with spherical semivariograms. Flow and reactive transport
equations are solved with a general purpose reactive transport code (CORE2D).
Spatial moments are calculated to characterize the longitudinal features of the
reactive plume assuming a single modal shape of the spatial derivative of depth
averaged concentrations of Na+, Ca+2 and Cl. Numerical results show that the
greater the variance of logK, the larger the displacement of the center of the
reactive plume while the larger the variance of logCEC, the smaller the
displacement of the reactive plume. The second order spatial moments of the plume
increase with increasing variances of logK and logCEC. Effective retardation
factor of Ca+2 is greater than that of Na+. Both of them increase with increasing
variances of logK and LogCEC and depend on the correlation structure between log
K and logCEC. Na+ and Ca+2 retardation factors for a negative correlation
structure between logK and logCEC are smaller than those for uncorrelated logK
and logCEC. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000570 


Reed Maxwell 
A Serendipitous, Longterm Infiltration Experiment: Water and Radionuclide Circulation Beneath the CAMBRIC Trench at the Nevada Test Site. 




Author(s) 
Reed Maxwell^{1}; Andrew Tompson^{1}; Steven Carle^{1}; Mavrik Zavarin^{1}; Stefan Kollet^{1}; Reed Maxwell^{1} 
Organisation(s) 
^{1}LLNL 
Abstract 
Underground atomic weapons testing at the Nevada Test Site introduced numerous
radionuclides that may be used to characterize subsurface hydrologic transport
processes in arid climates. Beginning in 1975, groundwater adjacent to the CAMBRIC
test, conducted beneath Frenchman Flat in 1965, was pumped steadily for 16 years to
elicit experimental information on the migration of residual radioactivity through
the saturated zone. Radionuclides in the pumping well effluent, including tritium,
36Cl, and 85Kr, were extensively monitored prior to their discharge into an unlined
ditch flowing toward a dry lake bed over a kilometer away. We have applied a large
(6km x 6km x 1km) and highly resolved (4 m) variably saturated flow model to
investigate infiltration into the 220m vadose zone underlying the ditch as well as
subsequent groundwater recharge and well recirculation processes. A Lagrangian
particletracking model has been used to compute flow pathways and estimate
radionuclide travel and residence times in various parts of the system based upon
the flow model. Results are consistent with rising tritium levels observed in a
monitoring well since 1991. They suggest that recirculation of the ditch effluent
through the vadose zone, into groundwater, and back to the test cavity and pumping
well are responsible for diluted, tritiumbased groundwater age dates observed in
2000 at these locations, as well as for increased tailing effects observed in the
pumping well elution curves. Altogether, the models and experimental observations
provide an improved basis to understand both historical and future movements of
testrelated radionuclides in groundwater near CAMBRIC.
This work was conducted under the auspices of the U. S. Department of Energy by the
University of California, Lawrence Livermore National Laboratory (LLNL) under
contract W7405Eng48. This work was funded by the UGTA program of the U. S.
Department of Energy. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000568 


Giovanna Darvini 
Examples of subsurface solute spreading driven by inhomogeneous velocity fields 




Author(s) 
Giovanna Darvini^{1}; Paolo Salandin^{1}; Giovanna Darvini^{1} 
Organisation(s) 
^{1}Università Politecnica delle Marche 
Abstract 
Most of solutions of flow and transport problems available in literature are
obtained under assumptions of stationarity of flow field and/or ergodicity of
transport, even though in realworld analyses these hypotheses cannot be always
verified. For instance, into problems that are met in practical applications, the
statistics of flow are often location dependent and the stationarity of flow is
violated. The nonstationarity of velocity field may originate from finite domain
boundaries, complex flow configurations (pumping and injecting), nonstationarity of
medium properties or conditioning of the log conductivity field to measurements of
head or conductivity. Moreover the lack of ergodicity related to the finite size of
solute sources makes difficult transport analyses that are often carried out by
rough schematizations. Some examples of solute dispersion of nonergodic passive
solute plume in heterogeneous formations with nonstationary flow conditions are here
considered and solved by a new approach. By this method the spatial moments of
finite initial volume of solute are obtained from the statistics of velocity field
evaluated by firstorder perturbation expansion of steady state flow equation in
Taylor series combined with a finite element discretization. The approach allows to
handle nonstationarity due to several causes and is here applied to some test cases
in bounded domains. A comparison of numerical results in terms of particle
displacements moments with known solutions available in literature and with Monte
Carlo simulations gives a measure of the effect related to the lack of plume
ergodicity and of flow spatial stationarity in realworld transport analyses. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000566 


Stefan Kollet 
Modeling Interactions of SurfaceSubsurface Flow Using a FreeSurface Overland Flow Boundary Condition in a Parallel Flow Simulator 




Author(s) 
Stefan Kollet^{1}; Reed Maxwell^{1}; Stefan Kollet^{1} 
Organisation(s) 
^{1}LLNL, Atmospheric, Earth, and Energy Sciences Department 
Abstract 
Models incorporating interactions between surface and subsurface flow are commonly
based on the conductance concept that presumes a distinct interface at the land
surface, separating the surface from the subsurface domain. In these models the
subsurface and surface domains are linked via an exchange flux that depends upon
the magnitude and direction of the hydraulic gradient across the interface and a
proportionality constant (a measure of the hydraulic connectivity). Because
experimental evidence of such a distinct interface is often lacking in the field, a
more general coupled modeling approach would be preferable.
We present a more general approach that incorporates a twodimensional overland
flow simulator into the parallel threedimensional variably saturated subsurface
flow code ParFlow developed at LLNL. This overland flow simulator takes the form of
an upper, freesurface boundary condition and is, thus, fully integrated without
relying on the conductance concept. Another advantage of this approach is the
efficient parallelism of ParFlow, which is exploited by the overland flow simulator.
Several verification and simulation examples are presented that focus on the two
main processes of runoff production: excess infiltration and saturation. The
usefulness of our approach is demonstrated in an application of the model to an
urban watershed. The influence of heterogeneity of the shallow subsurface on
overland flow and transport is also examined. The results show the uncertainty in
flow and transport predictions due to heterogeneity. This is important in
determining, for example, total maximum daily loads of surface water systems.
This work was conducted under the auspices of the U. S. Department of Energy by the
University of California, Lawrence Livermore National Laboratory (LLNL) under
contract W7405Eng48. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000565 


Michael Puma 
Spatial Scaling of Soil Moisture, Evapotranspiration, and Leakage 




Author(s) 
Michael Puma^{1}; Michael Celia^{1}; Ignacio RodriguezIturbe^{1}; Jan Nordbotten^{1}; Andrew Guswa^{2}; Michael Puma^{1} 
Organisation(s) 
^{1}Princeton University; ^{2}Smith College 
Abstract 
An outstanding issue in ecohydrological modeling is scaling nonlinear plantlevel
interactions among soil, vegetation, and water to larger spatial scales. Spatial
heterogeneity in precipitation and vegetation exert significant control on scaling
properties, especially in waterlimited ecosystems. Computational results indicate
that relationships between spatially averaged variables controlling soilmoisture
dynamics are nonunique at larger averaging scales, even when unique, nonhysteretic
relationships are defined at the plant level. The complexity of these relationships
evolves with increasing averaging area based on the characteristics of the spatial
heterogeneity. Through detail simulation studies, we can identify a threshold scale
for soil moisture, evapotranspiration, and leakage beyond which the nonunique
relationships will vary only slowly as averaging area becomes larger. The threshold
scale, which is analogous to the concept of a representative elementary area,
enables identification of a largescale relationship that is meaningful with respect
to the characteristics of the system.
We use numerical simulations to assess the effects of storm spatial structure,
rainfall intensity and frequency, and soil and vegetation characteristics on
thresholdscale values of the relevant variables. Results are generalized by
relating the threshold scales to a dimensionless group of parameters that includes
length scales characteristic of the heterogeneity and the model's resolution. We
then evaluate how the computationally derived nonunique relationships relate to
analytical approaches to obtain spatially averaged functional relationships.
Specific comparison of empirically obtained upscaled functions (based on the non
unique relationships) with the socalled statistical dynamic approach provides
guidelines to account for spatial heterogeneity in soil, plant, and climate systems. 
Track/Session 
Special Sessions / Ecohydrology: From Detailed Descriptions To General Synthesis? 
Date 
20060618 
DOI 
10.4122/1.1000000563 


Hendrik, A. R. De Bruin 
TURBULENT SURFACE FLUXES ON KILOMETER SCALE OBTAINED WITH SCINTILLOMETRY; A REVIEW. 




Author(s) 
Hendrik, A. R. De Bruin^{1}; Wouter, M. L. Meijninger^{2}; Wim Kohsiek^{3}; Frank Beyrich^{4}; Arnold, F. Moene^{5}; Oscar, K. Hartogensis^{5}; Hendrik, A. R. De Bruin^{1} 
Organisation(s) 
^{1}Wageningen University, Meteorology and Air Quality Group, 6701 AP Wageningen, Netherlands; ^{2}Wageningen University, Meteorology and Air Quality Group; ^{3}Royal Dutch Meteorological Society (KNMI), De Bilt, Netherlands; ^{4}Deutsche Wetter Dienst (DWD), Lindenberg, Germany; ^{5}Wageningen University, Netherlands, Meteorology and Air Quality Group 
Abstract 
A review will be presented of scintillometry work carried out by the Wageningen
University in collaboration with others. A scintillometer consists of a transmitter
and a receiver. The transmitter produces a parallel beam of light (here wavelengths
of about 1 micron and/or 1 mm) and the receiver detects light intensity fluctuations
cause by atmospheric turbulent motions. The latter are related to surface fluxes.
First, the performance of a large aperture scintillometer (LAS) over different
surface types, e.g. heterogeneous terrain types (Flevopolder, the Netherlands;
LITTFASS, Germany), grass (Cabauw, the Netherlands), savannah (GLOWA, Ghana) and
forest (LITFASS, Germany; Marrakech, Morocco), using path lengths between 1 and 10
km, will be discussed. Note that a LAS provides the sensible heat flux only.
Evaporation can be estimated next from a simplified energy balance equation. The so
called saturation effect appears to limit the maximum path length of a LAS. Recently
developed saturation correction procedures will be presented.
Next, the performance of a LAS combined with a millimeter wave scintillometer (MWS)
for estimating both the surface fluxes of sensible and latent heat over natural
landscape will be dealt with. Results of the Flevopolder and LITFASS2003 field
experiments will be shown, where a LASMWS system was installed over a heterogeneous
landscape over a path length of 2.1 and 4.7 km respectively. The scintillometer
derived surface fluxes will be compared with aggregated eddycovariance (EC)
measurements.
It is our aim also to discuss the question whether and how the scintillometer method
can be used in hydrology and agriculture. 
Track/Session 
Special Sessions / Field measurements and simulations of landatmosphere interaction 
Date 
20060618 
DOI 
10.4122/1.1000000561 


Jesper Overgaard 
DYNAMIC COUPLING OF HYDROLOGICAL AND ATMOSPHERIC MODELS TO EXAMINE FEEDBACK EFFECTS 




Author(s) 
Jesper Overgaard^{1}; Michael B. Butts^{1}; Dan Rosbjerg^{2}; Michael B. Butts^{1} 
Organisation(s) 
^{1}DHI  Water & Environment; ^{2}Environment & Resources  Technical University of Denmark 
Abstract 
Understanding the interaction between terrestrial microclimate, hydrology and
ecology is a key to determining the effect of landuse and climate change on
hydrological systems. Traditionally, the hydrological impacts of climate change have
been based on driving hydrological models with the output of regional climate
models. These climate models often operate at spatial and temporal scales that are
much larger than the scales required to analyse the effects on the hydrological
system. This is in part because of computational limitations and in part because of
the physics of the regional models do not justify much higher resolution.
Furthermore there is an inherent contradiction in this approach since these climate
models include their own hydrological model component. Similarly in analysing the
hydrological effects of landuse change the feedback to the meteorological system is
often neglected.
To address these issues a dynamically coupled hydrological and meteorological model
system has been developed for evaluating interactions at hydrological (catchment)
scales. Such a coupled system provides a unique framework for investigation of land
surface  atmosphere interactions at hydrological scales. A comprehensive
hydrological modelling system describing the terrestrial component of the
hydrological cycle MIKE SHE has been modified to allow coupling to a local scale
meteorological model. The coupling exploits the European Open Modelling Interface
and Environment (OpenMI) Open MI to link the two models systems. As simulations can
be run with and without coupling to the meteorological model, it is possible to
evaluate the impact of feedbacks between the two systems on hydrological
predictions. The uncoupled system has been validated against remote sensing and
eddy correlation measurements at the field and landscape scale describing the
hydrological and energy fluxes on the landsurface. The coupled system is then
validated against field data describing both the atmosphere and hydrological system.
Finally, a sensitivity analysis is carried out to examine the sensitivity of
hydrological predictions to atmospheric feedbacks to identify where feedback will
significantly affect the simulated impact. 
Track/Session 
Special Sessions / Field measurements and simulations of landatmosphere interaction 
Date 
20060618 
DOI 
10.4122/1.1000000559 


Haim Gvirtzman 
Mapping the saline/fresh groundwater interface beneath the Judean Desert using deep TDEM 




Author(s) 
Haim Gvirtzman^{1}; Mark Goldman^{2}; Eldad Levi^{1}; Haim Gvirtzman^{1} 
Organisation(s) 
^{1}Hebrew University; ^{2}Geophysical Institute of Israel 
Abstract 
A deep TDEM (Time Domain ElectroMagnetic) survey was carried out at the Judean
Desert to delineate the geometry of the interface between fresh, brackish and
saline groundwater bodies up to the depth of approximately 1.5 km. The survey was
conducted at 20 locations on the desert plateau, between Nebi Musa in the north and
Nahal Hever in the south. At this area, fresh groundwater flows from the
replenishment area at the eastern slopes of the Judea Mountains toward the Feshha,
Kaneh, Samar and EinGedi springs, whose total mean annual discharge is estimated
to be 85 million m3/y. At deeper aquifers, saline groundwater is found, which is
mixed at specific locations with the shallow fresh groundwater; thus the salinity
of some of these springs varies from fresh to saline.
Results of all TDEM soundings show that a low resistivity layer of 515 ohmm
exists below a relatively higher resistivity layer of 50500 ohmm. The low
resistivity layer is found at a depth range between 500 and 1000 m below land
surface. Comparison of these geoelectric results with stratigrafic data testifies
to the existence of an interface most likely separating fresh and brackish
groundwaters within the above mentioned depth range. Theoretical estimations using
Archie’s law as well as comparison of TDEM resistivities with groundwater
salinities measured in oil and deep water wells in the southern Judea desert and
central Israel verify this hypothesis. The expected resistivity of the DeadSea
brine is about 1 ohmm or less. Although not detected in most locations of this
survey, yet at three sites located at the eastern edge of the plateau (adjacent to
the rift faults), an additional interface probably separating the brackish
groundwater (515 ohmm) and the DeadSea brine (35 ohmm) is detected at greater
depth. These observations show that the upper Judea Group aquifer is usually
saturated with fresh groundwater, while the lower Judea Group aquifer, as well as
the underlying Kurnub Group aquifer, are saturated with brackish groundwater, the
salinity of which does not exceed the normal seawater salinity. The underlying
Jurassic formations are normally saturated with the DeadSea brine. 
Track/Session 
Special Sessions / Hydrogeophysical data fusion 
Date 
20060618 
DOI 
10.4122/1.1000000558 


Alex Furman 
Modeling the spatial and temporal patterns of infiltration and recharge in a phreatic nonfractured coastal aquifer 




Author(s) 
Alex Furman^{1}; Alex Furman^{1} 
Organisation(s) 
^{1}Soil, Water, and Environmental Sciences, ARO  Volcani center 
Abstract 
The accurate estimation of groundwater recharge is the key and a necessity for
sustainable use of groundwater resources. This is especially true for phreatic
coastal aquifers as the balance between the fresh and the saline water is more
fragile. Excluding the “one time reserve”, the safe yield of a groundwater system
must not accede, on the average, the average recharge. [Further, in most cases some
flushing of the aquifer must also be kept to prevent salination and accumulation of
solutes beyond an acceptable level]. Recharge is typically estimated using large
scale mass balance models based on water and/or isotopes. The two methods do provide,
when correctly applied, a good rough estimation of the groundwater recharge. However,
the estimation of recharge is lacking the understanding of the recharge process and
its spatial and temporal patterns, significant primarily for the understanding of
surface based aquifer pollution. Therefore, there is no practical ability to
influence recharge other than attempts to increase rainfall.
In this research we focus on matrix flow and transport in the vadose zone.
Specifically, we will examine through numerical modeling two different aspects of
groundwater recharge: a) the way natural large scale (order of km) inhomogeneities,
typical in many coastal aquifers, in the vadose zone alter flow and transport
patterns; b) the conditions for which surface infiltration becomes recharge. In the
case of largescale inhomogeneities, large vadose zone bodies can act as a resistance
or as an enhancement to the flow, depending on the size, shape, orientation,
hydraulic and transport properties of a single inhomogeneity in contras to the
background properties and, perhaps more important, the scale of recharge fluxes. In
the infiltration case, in arid conditions most infiltration (and for that matter also
irrigation water) is returned to the atmosphere by direct evaporation or by
evapotranspiration. Therefore the focusing of surface water by microdepressions and
by subsurface bending of microlayering may be crucial for matrix based recharge. 
Track/Session 
Special Sessions / Modeling and managing coastal aquifers 
Date 
20060618 
DOI 
10.4122/1.1000000557 


David Ahlfeld 
Can Global Climate Models be Used for Water Resource Planning? 




Author(s) 
David Ahlfeld^{1}; David Ahlfeld^{1} 
Organisation(s) 
^{1}Univ. of Massachusetts 
Abstract 
Water resources planning is needed to adapt to a changing climate. As precipitation,
wind and temperature patterns shift, water availability and demand by humans and
other ecosystems will change. These shifts have the potential to impact water
supply, agriculture, forestry and all nonhuman natural systems. Many large scale
water resource projects, such as reservoirs, distribution systems, groundwater
recharge facilities and desalinization systems can take many years to plan and
construct. Shifting the location of agricultural activities may also require large
lead times. Models are needed to predict climate one or more decades into the future
to assist in rational planning of water resource systems as water needs change. It
is important that these models predict trends at the decadal time scale, but also
provide an indication of the permanence of these changes to distinguish changes which
are permanent rather temporary excursions from the climate under which industrial
civilization has evolved.
Global Climate Models (GCM) and Regional Climate Models (RCM) have the potential to
be useful tools for water resource planning under a changing climate. GCMs have been
under development for many years with a primary goal of quantifying the longterm
impact, on climate, of emissions of greenhouse gases. The focus has been on global
average conditions. RCMs are a more recent development that seek to model climate at
finer grid scales and shorter time frames. Several major RCM projects are under
development including those that focus on North America and Europe.
In the present study, an intercomparison study is conducted of the ability of GCMs to
replicate observed 20th century climate. In addition, the GCMs are examined for
their ability to provide meaningful results at different spatial scales. Comparisons
are made with the CMAP observed precipitation data set which covers the period
19792000. GCM results are acquired from the IPCC database maintained by the Program
for Climate Model Diagnosis and Intercomparison at LLNL. A comparison is made in
three regions of North America. An additional comparison is conducted over a series
of successively smaller averaging regions in portions of eastern North America.
Precipitation and temperature averaged over monthly, seasonal and annual time periods
is considered. Most models compare well with observed precipitation for the central
and eastern regions at all time scales. For the western region, all models
overpredict precipitation at most time scales both for the entire averaging region
and for subdivisions of the region. 
Track/Session 
Special Sessions / Global Climate Change and Hydrologic Processes 
Date 
20060618 
DOI 
10.4122/1.1000000555 


Gianmarco Manzini 
Finite Volume Solutions of Strongly Anisotropic Porous Media Flow 




Author(s) 
Gianmarco Manzini^{1}; Mario Putti^{2}; Gianmarco Manzini^{1} 
Organisation(s) 
^{1}Istituto di Matematica Applicata e Tecnologie Informatiche, C.N.R Pavia, Italy; ^{2}Dept. Mathematical Methods and Models for Scientific Applications, University of Padua  Italy 
Abstract 
Anisotropic (i.e. direction dependent) porous media flow equations are characterized
by conductivities that may be space dependend full rank tensors. This class of
problems is also known as parameter dependent problems, the parameter being the
anisotropy ratio, i.e. the ratio between the smallest and largest eigenvalues of the
conductivity tensor. Efficient numerical discretization of strongly anisotropic
problems is generally obtained by means of ad hoc, mesh dependent scheme
modifications developed to overcome the problem known as parametric locking.
Locking is experimentally observed when the discretization error does not decrease at
the expected rate for limiting values of the parameter. This loss of convergence
disappears for sufficiently fine discretizations, but may involve costly or even
unfeasibly large calculations. The numerical solution of this type of problems
requires careful consideration of the errors that may be introduced by the
discretization scheme.
We propose a modification of Finite Volume approach based on the definition of a
diamond cell that makes optimal use of the reconstruction algorithm to yield an
accurate discretization of tangential gradients, a key ingredient for achieving
robustness of the numerical scheme for large values of the anisotropy ratio.
Numerical results are presented to show the performance of the proposed scheme.
Without introducing additional nonconsistent terms in the numerical scheme, as is
typically done in these cases (the so called variational crimes), the proposed
scheme robust with respect to the anisotropy ratio, as per the definition of Babuska
et al, 1992. We also show that the region of convergence of the method is defined by
a quadratic relationships between the anisotropy ratio and the mesh size parameter. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000554 


Véronique Naudet 
A review of the selfpotential method applied on groundwater resources 




Author(s) 
Véronique Naudet^{1}; Véronique Naudet^{1} 
Organisation(s) 
^{1}Lancaster University 
Abstract 
Standard geophysical methods detect the presence of water by changes of ground
physical properties, but none of them are sensitive to actual groundwater flow,
except the SelfPotential (SP) method. This method consists of measuring the natural
electric field within the subsurface with nonpolarisable electrodes. After
correcting for telluric currents and cultural noise, the remaining electrical
potentials are related to natural polarisation mechanisms occurring at depth. The
main contributions of SPsignals are associated to groundwater flow through the
electrokinetic effect and organic matterrich contaminant plumes through the
“electroredox” effect. We will present a review of recent advances in theoretical
and experimental aspects of the SP method to improve our knowledge on the
relationship between SPsignals and hydrogeochemical properties. These researches
can therefore open the door to the inversion of SPsignals to resolve some pertinent
information about the groundwater flow and contaminant transport, such as hydraulic
conductivity, geometry of the aquifer, and redox potential values. 
Track/Session 
Special Sessions / Hydrogeophysical data fusion 
Date 
20060618 
DOI 
10.4122/1.1000000552 


Hossein Ghazanfari 
Unsteady State Relative Permeability and Capillary Pressure Estimation of Porous Media 




Author(s) 
Hossein Ghazanfari^{1}; Morteza Khodabakhsh^{2}; Riaz Kharrat^{3}; Davood Rashtchian^{4}; Hossein Ghazanfari^{1} 
Organisation(s) 
^{1}phd student, Chemical and Petroleum Engineering Department, Sharif University of Technology, Petroleum Research Center, Tehran, Iran; ^{2}Ms Petroleum Engineer ,Chemical and Petroleum Engineering Department, Sharif University of Technology, Petroleum Research Center, Tehran, Iran; ^{3}Petroleum Research Center,Petroleum University of Technology,Tehran,Iran; ^{4}Chemical and Petroleum Engineering Department, Sharif University of Technology, Tehran, Iran 
Abstract 
To take capillary effect into account, a series of primary drainage experiments of
water by a sample oil fluid have been studied. The experiments performed under
different low flow rates on a horizontal high pressure glass type micromodel as a
model of porous media. Based on conventional macroscopic flow equations,the
relative permeabilities and capillary pressure are determined by parameter
estimation technique from history matching of saturation and pressure data of
unsteady state immiscible displacements. The Coery type of relative permeability
and capillary pressure functions are used. The results show that the end point
relative permeability of oil phase and the dynamic term of capillary pressure
function increase with flow rate, but the saturation exponent of relative
permeability functions are decreasing with flow rate. Also the results show that
the capillary pressure and relative permeability curves are rate dependent and the
relative permeability curves are increasing with flow rate.
Key Words: Rate Dependent,Relative Permeability,Capillary Pressure,Unsteady State,
History Matching,Micromodel 
Track/Session 
Special Sessions / PoreScale Modelling: New Developments And Applications 
Date 
20060618 
DOI 
10.4122/1.1000000550 


Jannette Frandsen 
Investigations of wave runup using a LBGK modeling approach 




Author(s) 
Jannette Frandsen^{1}; Jannette Frandsen^{1} 
Organisation(s) 
^{1}Louisiana State University 
Abstract 
In this paper, free surface water waves are predicted in nearshore regions. The
suitability of a LBGK modeling approach is examined. Boundary conditions are
reviewed on sloped beaches. Wave propagation in shallow water is presented. It is
assumed that the waves do not overturn; limiting the present study to steep waves.
The uniform grid solutions are compared with analytical solutions and other
findings reported in the literature. This study is important to a variety of
applications, in particular, the coastal engineering community. The present
investigations could potentially play a future role in storm surge predictions. 
Track/Session 
Special Sessions / Boltzmann Methods in Water Resources 
Date 
20060618 
DOI 
10.4122/1.1000000548 


Changbing Yang 
DIRECT AND INVERSE COUPLED THERMALHYDROBIOGEOCHEMICAL MODELS FOR POROUS AND FRACTURED MEDIA 




Author(s) 
Changbing Yang^{1}; Jorge Molinero^{2}; Mercedes BonillaFernandez^{1}; Ignasi Puigdomenech^{3}; Javier Samper^{1}; Changbing Yang^{1} 
Organisation(s) 
^{1}Universidad de Coruña, Spain; ^{2}Universidad de Santiago de Compostela, Spain; ^{3}SKB, Sweden 
Abstract 
It is well known that microbials play a major role controlling many redoxsensitive
geochemical processes. In the context of radioactive waste disposal it has been
recognized recently the need to evaluate the relevance of microbial processes in
the performance of a HLW repository. A large amount of data on the structure,
diversity and activity of native microbial populations has been collected in
underground laboratories such as those in deep Swedish granites. Laboratory and
field experiments such as the REX experiment have confirmed the relevance of
microbial processes and have been useful to obtain relevant hydrochemical and
microbial parameters and test conceptual biogeochemical models. Here we present
direct and inverse models for coupled flow, reactive solute transport and
biogeochemical processes in porous and fractured media. The inverse problem is
formulated as the minimization of a generalized leastsquares criterion by means of
a GaussNewton LevenbergMarquardt method. Different types of data can be taken
into account including hydraulic heads, aqueous and total concentrations, water
fluxes and water contents as well as prior information on model parameters. The
methodology can cope with the simultaneous estimation of flow, transport, microbial
and geochemical parameters as well as initial and boundary waters, such as pH, pE,
and abiotic and biotic concentrations. The mathematical formulation of inverse THBG
models has been implemented in a finite element code, INVERSEBIOCORE2D, which has
been verified with synthetic examples and tested for the estimation of microbial
parameters from the in situ REX experiment performed at a packed section of a
borehole drilled from the access tunnel in Äspö Hard Rock laboratory in Sweden The
hydrobiogeochemical model of the REX experiment considers microbiallymediated
methane oxidation and organic matter respiration. Numerical results indicate that
aerobic respiration of organic matter is much more efficient in consuming dissolved
oxygen than pyrite dissolution. Initial concentration of heterotrophic bacteria and
their growth rate constant are the two most sensitive parameters. Calibrated THBG
numerical models have been later used for testing quantitatively several scenarios
for a HLW repository in Sweden including: 1) Aerobic respiration associated to the
oxygen supplied during the preclosure stage; 2) Hydrochemical perturbations caused
by the construction of the repository during its operational stage; and (3)
Scenario of a glaciation in which melting waters rich in oxygen and no organic
matter might reach the repository. Results of these models should be relevant for
the performance assessment of a HLW repository in granites for the longevolution
of groundwater chemistry and redox conditions during pre and post repository
closure. 
Track/Session 
Special Sessions / MultiDisciplinary Approaches To Reactive Transport Simulation In Aquifer Systems 
Date 
20060618 
DOI 
10.4122/1.1000000546 


Busayamas Pimpunchat 
Water pollution modelling in Tha Chin River with Lattice Boltzmann method 




Author(s) 
Busayamas Pimpunchat^{1}; Wannapong Triampo^{2}; Tang I  Ming^{2}; Busayamas Pimpunchat^{1} 
Organisation(s) 
^{1}Mathematics; ^{2}Physics 
Abstract 
The Tha Chin River is one of the major rivers in Thailand. It passes through
agricultural land, industrial areas, farms, village and cites. It has become one of
the most polluted rivers in country. The factors causing the degradation of the
quality Tha Chin River’s water at different locations depend on the use of the land
that borders on the river banks. The Upper Tha Chin River basin runs through
agricultural land where germinating seedlings are cultivated. This requires the use
of fertilizer and insecticide at a high level. At the same time, the Lower Tha Chin
basin experiences runoff from urban and industrial areas as it descends to the
sea. It thus becomes polluted further by the combined discharges of industrial,
domestic and rural inflows. In addition, there is an inflow of salty water from the
sea. In monitoring the quality of the water in this river, one must measure all the
sources of the pollution feeding into the river. Clearly factors such as
precipitation, water flow rates, inundated seawater, chemical used in agricultural
and industry and land use information must be included in any model used to
understand and control the pollution in the Tha Chin river. Since the Tha Chin
ecosystems is a dynamic one, we will create a model based on the Lattice Boltzmann
methodology to analyze the interacting factors impacting the pollution of this river. 
Track/Session 
Special Sessions / Boltzmann Methods in Water Resources 
Date 
20060618 
DOI 
10.4122/1.1000000545 


Sjoerd Van der Zee 
Stochastic Analysis of Nonlinear Biodegradation in Regimes Controlled by both Chromatographic and Dispersive Mixing 




Author(s) 
Sjoerd Van der Zee^{1}; Gijs Janssen^{2}; Sjoerd Van der Zee^{1} 
Organisation(s) 
^{1}Hydrology Wageningen University NL; ^{2}Soil Quality Wageningen University NL 
Abstract 
Nonlinear biodegradation in natural porous media is affected by the heterogeneity of
the formation and dispersive mixing processes. We analyze these coupled effects by
combining recent advances in analytical onedimensional modeling of bioreactive
transport with stochastic concepts of dispersive mixing in heterogeneous domains.
Specifically, we model bioremediation of a sorbing contaminant undergoing nonlinear
biodegradation in heterogeneous aquifers applying the stochasticconvective and the
advectivedispersive stream tube approaches, in which we use a semianalytical
traveling wave solution for onedimensional reactive transport. The results of
numerical simulations agree excellently with both models, which establishes that the
traveling wave solution is an efficient and accurate way to evaluate the development
of intrastream tube concentration distributions, and that the advectivedispersive
stream tube approach is suitable to describe nonlinear bioreactive transport in
systems controlled by localscale dispersion. In contrast with conservative
transport, the mean contaminant flux is shown to be significantly influenced by
transverse dispersion, even for realistic Peclet values. Furthermore, asymptotic
front shapes are shown to be neither Fickian nor constant (traveling wave behavior),
which raises questions about the current practice of upscaling bioreactive
transport. The error caused by neglecting local dispersion was found to increase
with time and to remain significant even for large retardation differences between
electron acceptor and contaminant. This implies that, even if reaction rates are
dominated by chromatographic mixing, the dispersive mixing process can not be
disregarded when predicting bioreactive transport. 
Track/Session 
Special Sessions / MultiDisciplinary Approaches To Reactive Transport Simulation In Aquifer Systems 
Date 
20060618 
DOI 
10.4122/1.1000000544 


Johan Olav Helland 
The relationship between capillary pressure, saturation and interfacial area from a model of mixedwet triangular tubes 




Author(s) 
Johan Olav Helland^{1}; Svein M Skjaeveland^{1}; Johan Olav Helland^{1} 
Organisation(s) 
^{1}University of Stavanger 
Abstract 
Fluidfluid interfacial area is recognized as an important parameter in
understanding various multiphase flow processes in porous media. Mass transfer
processes such as dissolution, adsorption and volatilization occur across interfaces
and are strongly related to interfacial area. Moreover, the coefficient for
interfacial mass transfer is assumed to be proportional to the interfacial area. It
has also been observed experimentally that surfactants and bacteria may
preferentially accumulate at the interfaces and affect the subsequent fluid
transport. To quantify the efficiency and consequences of these processes, the
magnitude of the interfacial area is required.
In this paper we use a simple, yet physicallybased, bundleoftriangulartubes
model to calculate interfacial area for mixedwet conditions and contact angle
hysteresis. In such a representation of the pore network, capillary displacements
may either occur as pistonlike displacements of the fluids occupied in the bulk, or
as pistonlike displacements of fluids in layers. Accurate expressions for the
associated capillary entry pressures are implemented. The simulated interfacial area
vs. saturation data displays the same general trends as experimental measurements.
We also derive analytical expressions for the relationship between specific
interfacial area, capillary pressure and saturation for primary drainage. Based on
these expressions, we formulate flexible correlations for subsequent invasion
processes. The correlations are compared with the simulated data, and good agreement
is obtained. The proposed correlations are consistent with the wellknown Brooks
Corey correlation and may also be implemented in reservoir simulators.
Finally, we use our model to explore the conjecture by Hassanizadeh and Gray who
suggested that hysteresis can be eliminated in the relationship between capillary
pressure, saturation and specific interfacial area. We find that hysteresis may be
significant for both waterwet and mixedwet conditions as long as contact angle
hysteresis is assumed. 
Track/Session 
Special Sessions / PoreScale Modelling: New Developments And Applications 
Date 
20060618 
DOI 
10.4122/1.1000000542 


Wanderson Lambert 
Riemann Problems for a new class of equations modeling steam injection with applications in groundwater remediation. 




Author(s) 
Wanderson Lambert^{1}; Dan Marchesin^{1}; Wanderson Lambert^{1} 
Organisation(s) 
^{1}IMPA  Instituto de Matemática Pura e Aplicada 
Abstract 
Groundwater contamination by organic materials and petroleum products is a
preoccupying problem with environmental, social and health implications constituting
a menace to our highquality groundwater resources.
An important remediation technique is steam injection. The model that we
propose to describe this injection is a balance system, because it considers the
terms of mass transfer and chemical reactions in the different physical phases.
We have developed techniques to solve the Riemann problems associated to the
balance system for thermal flow in porous media. This theory was initially studied
in [1] and it is extended in [2]. As an example, we analyze the steam and water
injection in several proportions into a porous medium saturated with different
mixtures of steam, water and small amounts of NAPL’s. One disadvantage of pure
steam injection is the ecological impact of high temperatures. This can be
alleviated if we coinject nitrogen leading to a lower temperature, because the
boiling temperature depends on nitrogen concentration and it is lower than the
boiling temperature for pure water.
We consider a onedimensional porous medium filled with water, where steam
and nitrogen are injected. We neglect compressibility, heat losses and capillarity
effects and present a physical model for steam injection based on the mass balance
and energy conservation equations.
We show several Riemann solutions for different physical initial and injection
conditions. An interesting feature is that we can calculate the mass transfer
directly from the model, without knowing the expression for the mass transfer, see
[2] for more details.
[1] Bruining, J. and Marchesin, D. , Nitrogen and steam injection in a porous
medium with water, to appear to Transport in Porous Media (2006).
[2] Lambert, W., Doctoral Thesis, IMPA 2006, in preparation. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000540 


Christian Engwer 
A Discontinuous Galerkin Method for Simulations of Transport Processes on the Pore Scale 




Author(s) 
Christian Engwer^{1}; Christian Engwer^{1} 
Organisation(s) 
^{1}RuprechtKarlsUniversity of Heidelberg 
Abstract 
In the simulation of pore scale processes a good approximation to the
geometrical shape of the solid phase is crucial to good quality of the
numerical results, while on the other hand interest often focuses on a
small number of unknowns.
I will present a new approach for solving PDEs in complex domains. It
is based on a Discontinuous Galerkin (DG) discretization on a
structured grid, where the minimal number of unknowns is independent
of the shape of the domain, while this new method still allows the
provision of fine structures of the domains shape, even if their size
is significantly smaller than the grid cell size. Its advantage for
flow and transport simulation on the pore scale is that the resolution
of the simulation can be chosen freely between very large
domains, perhaps the size of several REVs, and very small domains,
just the size of few sandcorns, without changing the discretization
and without neglecting details in the shape of your domain.
I give an overview of the new technique and exemplify this with the
numerical simulation of solute transport in a 3D pore scale
domain. This is intended only as an introduction and does not involve
productive computations. Future applications might involve multiphase
flow on the pore scale or even upscaling simulations. 
Track/Session 
Special Sessions / PoreScale Modelling: New Developments And Applications 
Date 
20060618 
DOI 
10.4122/1.1000000538 


Mahsanam Mirzaei 
Dynamic Effects in TwoPhase Flow in Porous Media: Inclusion of 3D and Microscale Heterogeneity Effects 




Author(s) 
Mahsanam Mirzaei^{1}; Diganta Bhusan Das^{1}; Mahsanam Mirzaei^{1} 
Organisation(s) 
^{1}University of Oxford 
Abstract 
To quantify nonaqueous phase liquids (NAPLs) transport in the subsurface, one
requires a correct description of multiphase flow behaviour. This involves the
determination of various fluid and porous media parameters and, the constitutive
relationships among capillary pressure (Pc), fluid phase saturation (S) and
relative permeability (Kr). The determination of PcSKr relationships is
particularly difficult because of two effects: (i) presence of heterogeneities in
the flow domain and (ii) dynamic effects in PcSKr relationships (see below for
definition). While the significance of individual factor has been studied at
various scales using different approaches, the combination of the two effects on Pc
SKr relationships are not well characterised at any scale of observation.
Microscale heterogeneities in porous media occur at length scales below those of
typical laboratory measurement devices (core scale). These microheterogeneities
play a significant role in laboratory determination of PcSKr relationships. The
dependence of the PcSKr relationships on the rate of change of saturation is
known as the dynamic effect. Obviously, the dynamic effect stems from the fact that
the time duration necessary for obtaining equilibrium flow conditions may be long
(e.g., many days to weeks at laboratory conditions) depending on soil and fluid
properties, scale of observation, degree of saturation, boundary conditions, types
of media heterogeneity, if any, etc. One may also argue that since fluids do not
necessarily flow under static conditions at shorter time periods, the empirical
multiphase models, which assume that Pc is a unique function of fluid saturation,
are not sufficient to account for the physics of the flow. Hence, there is an
increasing interest in characterising the significance of dynamic effects for multi
phase flow in porous media. Most previous work on this area has assumed simple
scenarios ranging from pore scale and bundle of capillary tube model to 2D domain,
which may or may not include media heterogeneities. It seems that there is little
information on dynamic effects for twophase flow in 3D domains which include both
heterogeneity and gravity effects.
In this study, we carry out a systematic analysis of the effects of various flow
and media properties on dynamic twophase flow in 3D core scale domain, which
include microheterogeneities. A number of factors are considered, e.g., boundary
conditions; pore size distribution; permeability anisotropy, variations in nature,
amount and distribution of the microscale heterogeneity, etc. Their effects on
dynamic twophase flow behaviour are quantified in terms of a capillary damping
coefficient, which establishes the speed at which flow equilibrium is reached.
Binary combinations of fine sand imbedded in coarse sand are used. Drainage dynamic
and static curves for various 3D homogeneous and heterogeneous models have been
obtained and compared to determine the relative significance of the heterogeneity
patterns and intensity. Values of dynamic coefficient obtained in this work are
higher than most previously reported values, but this is plausible considering the
fact that we consider both 3D and microheterogeneity effects. Simulations have
also been conducted to compare dynamic effects in domains of various shapes but of
equal volume, namely, cylindrical, 3D rectangle (brick shape) and 2D rectangle. Our
results suggest that similar curves may be obtained; however, the dynamic
coefficient may be very different from one domain to another. This implies that the
dynamics of the flow depend on the shape of domain and PcSKr relationships
obtained for one domain shape may not be used directly for domain of another shape
at dynamic conditions.
All in all, the results obtained in our study give further evidence that the non
uniqueness in curves are caused by different factors: dynamic effects, applied
boundary condition, microheterogeneities, pore size distribution, media
anisotropy, domain shape and size, to mention just a few. For microheterogeneities
of the type used in our study, we find that, in general, with the increase in the
degree of heterogeneity, dynamic coefficient increases. However, this dependence is
not a linear function and depends on a complex interplay of various factors, as
mentioned above. 
Track/Session 
Special Sessions / Multiscale methods for flow in porous media 
Date 
20060618 
DOI 
10.4122/1.1000000537 


alain dimier 
Mesh Adaptation within the geochemistrytransport Alliances tool 




Author(s) 
alain dimier^{1}; Jérôme Gaombalet^{2}; maxime champagnac^{1}; michel kern^{3}; alain dimier^{1} 
Organisation(s) 
^{1}andra; ^{2}Andra; ^{3}inria 
Abstract 
Andra, CEA and EDF are conjointly developing a software platform for waste disposal
simulations. The core of the tool for solute plume evaluation is the geochemistry
transport coupling algorithm. Within Alliances, two geochemistry codes, PhreeqC and
Chess, and three transport codes, Castem, Traces and Mt3D are available and
interact within a sequential iterative algorithm for geochemistry transport coupling.
Considering the waste disposal, one of the main problematic of a repository is to
evaluate the alkaline perturbation in the host rock due to the cement interface with
bentonite and clay. In order to deal with the heterogeneities and the various scales
of the problem in two dimensions of space, a mesh adaptation method has been
introduced to better deal with sharp interfaces. The adaptation algorithm will be
described in details, pointing out its specificities due to the geochemistry
treatment, especially concerning mineral interfaces. Numerical results will
illustrate the algorithm performance for convection dominant and diffusion dominant
problems. 
Track/Session 
Special Sessions / MultiDisciplinary Approaches To Reactive Transport Simulation In Aquifer Systems 
Date 
20060618 
DOI 
10.4122/1.1000000536 


Jill Reese 
Simulating NonDarcy Flow through Porous Media using Sundance 




Author(s) 
Jill Reese^{1}; Kevin Long^{2}; Tim Kelley^{1}; Casey Miller^{3}; William Gray^{3}; Jill Reese^{1} 
Organisation(s) 
^{1}North Carolina State University; ^{2}Sandia National Laboratories; ^{3}University of North Carolina  Chapel Hill 
Abstract 
A nonDarcy partial differential equation (PDE) model for flow through porous media
is presented. The focus is on the numerical implementation of the model using Sandia
National Laboratories PDE simulation framework, Sundance. In particular, the
discussion will include the finite element discretization and how parallelism is
accomplished. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000534 


Freddy Alvarado 
ANOMOLOUS TWOPHASE FLOW BEHAVIOR IN FRACTURED SANDSTONE EXPLAINED USING XRAY COMPUTED TOMOGRAPHY 




Author(s) 
Freddy Alvarado^{1}; Phillip Halleck^{1}; Abraham Grader^{1}; Freddy Alvarado^{1} 
Organisation(s) 
^{1}The Pennsylvania State University 
Abstract 
Understanding fracture morphology in terms of a porous media is necessary for
accurate simulation of multiphase transport in fractured rocks. Although ambient
stress methods for obtaining fracture morphology exist, previous research lacks the
ability to map fracture closure as a function of stress or the distribution of
immiscible phases in the fracture.
A twentyfivemillimeter cylindrical sandstone sample was artificially fractured in
tension and placed under confining stress in an xray transparent vessel. The
fracture morphology was characterized under dry conditions using highresolution x
ray computed tomography. Multiphase fluid distributions in the fracture were
mapped between limits of the mobile saturation range using controlled fractional
flows. These distributions were correlated with flow rate and pressure drop
measurements. We observed order of magnitude differences in effective
permeabilities under conditions of nearly constant overall fracture saturations.
These differences in permeability are associated with rearrangement of the physical
distribution of the phases. Distributions associated with low permeability are
unstable on a time frame of several hours, much longer of the time frame associated
with snapoff phenomena. This phenomenon may be responsible for similar field
observations reported in the literature. 
Track/Session 
Special Sessions / PoreScale Modelling: New Developments And Applications 
Date 
20060618 
DOI 
10.4122/1.1000000532 


Yan Chen 
Data Assimilation by Ensemble Kalman Filter with Reparameterization for Nonlinear Problems 




Author(s) 
Yan Chen^{1}; Dean S. Oliver^{1}; Dongxiao Zhang^{1}; Yan Chen^{1} 
Organisation(s) 
^{1}The University of Oklahoma 
Abstract 
Owing to its simplicity and efficiency the Ensemble Kalman filter (EnKF) has
recently been applied for assimilating static and dynamic measurements to
continuously update the estimate of the state vector, such as reservoir properties
and responses. Many EnKF implementations showed promising results. However, the
Gaussian assumption is an implicit requirement for obtaining a satisfactory
estimate through EnKF or its variants. EnKF may not work properly when the state
vector is strongly nonlinear and thus nonGaussian. For instance, a direct
application of EnKF to estimating the saturation of twophase flow may lead to a
nonphysical behavior at the interface of the two immiscible phases. There exist
methods which reduce this nonGaussian effect, such as the iterative EnKF and the
Gaussian kernel filter. In this work, we propose a new approach which reduces the
nonGaussian effect through reparameterization. Instead of directly updating the
saturation, which is bimodally distributed, the time of saturation arrival (at a
particular location) is included in the state vector. The time of arrival is
correlated with the reservoir properties and other reservoir responses and can be
approximated by a Gaussian distribution without losing much information. After
updating the time of arrival through the EnKF, the local saturation history is used
to estimate the saturation of the reservoir at a particular time. The EnKF with
reparameterization provides reasonable and more accurate saturation estimation
which is the basis of assimilating further observations. The new approach is
illustrated on a heterogeneous reservoir of twophase flow with dynamic
measurements, and the results are compared with other methods, in terms of accuracy
and efficiency. 
Track/Session 
Special Sessions / Data assimilation in water resources modelling 
Date 
20060618 
DOI 
10.4122/1.1000000531 


Qinjun Kang 
Recent progresses in Lattice Boltzmann simulations of flow and multicomponent reactive transport in porous media 




Author(s) 
Qinjun Kang^{1}; Peter Lichtner^{1}; Dongxiao Zhang^{2}; Qinjun Kang^{1} 
Organisation(s) 
^{1}Los Alamos National Laboratory; ^{2}The University of Oklahoma 
Abstract 
In recent years, the Lattice Boltzmann (LB) method has become a powerful numerical
tool for simulating complex fluid flows and modeling physics and chemistry in
fluids. Derived from the continuum Boltzmann equation used in statistical
mechanics, the LB method has the advantage of describing nonequilibrium dynamics,
especially in fluidflow applications involving interfacial dynamics and complex
boundaries, without simplifying the physics. In addition, the parallel structure
inherent in the LB method makes it extremely suitable for parallel computing.
Because of these features, the LB method affords the most comprehensive porescale
approach to systematically investigate fundamental issues involving flow and
reactive transport in porous media. In this paper, the state of the art of this
method is discussed. Specifically, a multicomponent LB model for simulating
reactive transport in porous media at the pore scale is presented. In the model, a
set of distribution functions is introduced to simulate fluid flow and solute
transport. The LB equation for flow recovers the correct porescale continuity and
NavierStokes equations. The LB equations for solute transport are modified to
recover advectiondiffusion equations for total concentrations at the pore scale.
The model takes into account advection, diffusion, homogeneous reactions among
multiple aqueous species, heterogeneous reactions between the aqueous solution and
minerals, as well as changes in solid and pore geometry. Homogeneous reactions are
described through local equilibrium mass action relations. Mineral reactions are
treated kinetically through boundary conditions at the mineral surface. Simulation
examples presented include injection of carbon dioxide saturated brine into a
limestone rock with pore geometry derived from a thin section, crystal formation
from a supersaturated solution without flow, and crystal formation during carbon
dioxide sequestration in oceanic sediments. 
Track/Session 
Special Sessions / Boltzmann Methods in Water Resources 
Date 
20060618 
DOI 
10.4122/1.1000000529 


Qinjun Kang 
Role of pore–scale heterogeneity on reactive flows in porous materials: validity of the continuum representation of reactive transport 




Author(s) 
Qinjun Kang^{1}; Peter Lichtner^{1}; Peter Lichtner^{1} 
Organisation(s) 
^{1}Los Alamos National Laboratory 
Abstract 
Understanding multicomponent reactive transport in porous media is critical to a
wide range of fields. It poses great challenges to theoretical, experimental, as
well as numerical studies, because it usually involves multiple processes
(advection, diffusion, reaction) and multiple scales (molecular, pore, laboratory,
field). Current modeling approaches commonly employ a continuum description and
rely on volume averages. Because in porous media, averages are taken over length
scales much larger than typical grain sizes, spatial heterogeneity at smaller
scales is unresolved. This loss of information includes porescale velocities and
geometry, mineral texture, and other features. Therefore, understanding the impact
of porescale spatial heterogeneity on reactive processes in porous materials is a
key aspect in validating continuum models of reactive transport, and developing
predictive capabilities of system behavior. However, due to the complexity of the
multiprocess, multiscale problem, the majority of porescale modeling studies
have focused on the basic transport properties of porous media including effective
diffusion, conductivity, permeability, and elasticity.
In this study, using a Lattice Boltzmann (LB) model for multicomponent reactive
transport in porous media, we investigate the role of spatial heterogeneity related
to pore geometry on mass transport and reaction rates in porous materials and its
impact on the validity of the continuum representation of reactive transport.
Because of the ability of the LB method to accurately represent porescale
phenomena, it provides the most comprehensive approach to investigate the influence
of porescale heterogeneity on continuum formulations of reactive transport. We
apply our model to various chemical systems for twodimensional, artificially
constructed and natural multiscale fractured and porous media. The reactive
transport processes are simulated at the pore scale, with systematic consideration
of the porescale flow field, diffusion, homogeneous reactions among multiple
aqueous species, heterogeneous reactions between the aqueous solution and minerals,
as well as the resulting changes in solid and pore geometry. The results are
averaged over vertical slabs which are considered as REVs, and are compared with
onedimensional continuumscale simulations. From the LB simulations, it is
possible to determine macroscale properties of the medium such as tortuosity,
permeability, and reactive surface area. In addition, the LB simulations also
enable the most appropriate continuum formulation—single, dual, or multiple
continua—to be determined. Our results confirm that a multiple continuum model is
required to describe upscaled porescale results derived from multiscale
geometries. 
Track/Session 
Special Sessions / PoreScale Modelling: New Developments And Applications 
Date 
20060618 
DOI 
10.4122/1.1000000527 


Dongxiao Zhang 
An Efficient Stochastic Decomposition Approach for LargeScale Subsurface Flow Problems 




Author(s) 
Dongxiao Zhang^{1}; Zhiming Lu^{2}; Gaisheng Liu^{1}; Dongxiao Zhang^{1} 
Organisation(s) 
^{1}The University of Oklahoma; ^{2}Los Alamos National Laboratory 
Abstract 
Subsurface formations are of large scales and are inherently heterogeneous at a
multiplicity of scales. Significant spatial heterogeneity and a limited number of
measurements lead to uncertainty in characterization of formation properties and
thus, to uncertainty in predicting flow in the formations. Such uncertainties add
another dimension in probability space to the already largescale subsurface
problems. In this work, we develop an accurate yet efficient approach for solving
flow problems in largescale heterogeneous formations. We do so by obtaining higher
order solutions of the prediction and the associated uncertainty of reservoir flow
quantities using the momentequation approach based on KarhunenLoéve decomposition
(KLME). In the KLME approach, the log permeability (lnK) field is first expanded
into a multiscale series in terms of orthogonal standard Gaussian random variables
with their coefficients obtained from the eigendecomposition of the lnK
covariance. Next, the pressure and velocity fields are all decomposed with
perturbation expansions in which each individual term is further expanded into a
polynomial series of orthogonal Gaussian random products. The coefficients
associated with these series are deterministic and solved recursively from low to
high expansion orders. The pressure and velocity moments (such as the means,
covariances, and higher moments) can then be calculated from these coefficients
using simple algebraic operations. There are two attractive computational features
in this new approach. First, all equations for the deterministic coefficients share
exactly the same structure as the original equation, which greatly simplifies its
implementation as the existing simulators/solvers can be utilized as well as
significantly reduces the computation effort as the coefficient matrix remains
unchanged and only the righthandside vector needs to be updated across different
orders. Second, at each expansion order, the equations are independent of each
other, which allows for performing massively parallel computation. The new approach
is validated and its efficiency and accuracy is demonstrated with traditional Monte
Carlo simulations in largescale threedimensional subsurface problems. 
Track/Session 
Special Sessions / Multiscale methods for flow in porous media 
Date 
20060618 
DOI 
10.4122/1.1000000525 


seong lee 
black oil formulation for the multiscale finite volume method 




Author(s) 
seong lee^{1}; christian wolfsteiner^{1}; hamdi tchelepi^{2}; seong lee^{1} 
Organisation(s) 
^{1}chevron etc; ^{2}stanford u. 
Abstract 
until now, the multiscale finite volume (msfv) method has shown great promise in petroleum subsurface flow
simulation when applied to large and highly heterogeneous reservoirs. recently, the method was extended
from incompressible multiphase flow to a standard black oil formulation, i.e., compressible rock/fluid system
with gravity and solution gas. the new formulation requires modified basis functions and handles upstream
consistently in pressure and transport calculations. in our approach we split the governing operator is into an
incompressible, a compressible and a gravity contribution to handle the physics correctly on fine and coarse
scale. we detail the formulation and assess the accuracy of the new method with numerical examples relative
to detailed fine grid simulations.
keywords
multiscale, finite volume, subsurface, black oil 
Track/Session 
Special Sessions / Multiscale methods for flow in porous media 
Date 
20060618 
DOI 
10.4122/1.1000000523 


Zhiming Lu 
Parameter Structure Identification Using the Level Set Methods 




Author(s) 
Zhiming Lu^{1}; Zhiming Lu^{1} 
Organisation(s) 
^{1}Los Alamos National Laboratory 
Abstract 
We introduce an inverse approach for efficiently identifying the spatial distribution
of binary materials (say, a lower permeable material D embedded in the background
material) using the level set method, given head measurements at some locations and
times. No assumption has been made on the shape, size, and locations of these
embedded zones, as well as the correlation structure and the proportion of two
materials. By this method, instead of handling D directly, the lower permeable zones
(or their boundaries) are represented by a level set function, which is negative in
the interior of D, positive in its exterior, and zero on its boundary. Since a level
set function uniquely defines the region of embedded zones, we manipulate D
explicitly through evolution of its boundary. Our aim is to find a level set function
such that the hydraulic head solved using the spatial distribution of lower permeable
zones defined by this level set function matches the observed values. Because D is
unknown, so is the level set function. In the method, we generate a sequence of level
set functions such that the regions they defined approach D. We start from an initial
level set function (i.e., an initial boundary of lower permeable zones) and
sequentially propagate the boundary by solving a level set equation. The speed of
propagation of boundary, which is an input to the level set equation, is related to
the sensitivity of head to permeability and the error between the measured head and
modeled head using the current time. A synthetic example shows that this method can
locate those embedded zones efficiently. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000521 


John van esch 
Adaptive Multi Scale modeling of groundwater flow and transport 




Author(s) 
John van esch^{1}; John van esch^{1} 
Organisation(s) 
^{1}geodelft 
Abstract 
Usually the permeability tensor is the most dominant parameter affecting groundwater
flow and transport, while it is also the most heterogeneous parameter. Permeability
can be measured on laboratory scale and subsequently a spatially correlated random
field generator is often used to construct a field scale model. This procedure
results in a very fine grid with discrete tensor coefficients for each cell. To
reduce the number of unknowns in the flow model fine scale permeabilities have to be
upscaled to coarse scale permeabilities that relate the spatial averaged pressure,
flux and dissipation to each other. However exact values cannot be found in general
and traditional upscaling methods depend heavily on the local boundary conditions
chosen.
This paper presents an operator based scaling technique that is applied for
communication between scales in combination with adaptive mesh refinement that
balances the loss in accuracy due to the averaging procedure. The technique is used
to solve three dimensional groundwater flow and transport problems in partly
saturated highly heterogeneous porous media. The subdomain collocation finite
element method discretizes the flow and transport equation. Both sets of linearized
equations are then solved sequentially in a number of multigrid cycles where mesh
refinement is restricted to elements for which a local error criterion does not
hold. Picard iterations resolve the nonlinearities due to unsaturated flow and
density and viscosity coupling.
One example illustrates this adaptive multi scale technique by simulating flow and
transport through a heterogeneous embankment. The application shows the reduction of
computational work required to obtain the desired level of accuracy by refining the
mesh only in regions of interest where high concentration fronts or high
permeability contrast exist. 
Track/Session 
Special Sessions / Multiscale methods for flow in porous media 
Date 
20060618 
DOI 
10.4122/1.1000000520 


Nils van Velzen 
COSTA a Problem Solving Environment for data assimilation 




Author(s) 
Nils van Velzen^{1}; Nils van Velzen^{1} 
Organisation(s) 
^{1}Delft University of Technology / VORtech Computing 
Abstract 
Nils van Velzen
Delft University of Technology
Faculty of Electrical Engineering, Mathematics and Computer Science
Dept. of Appl. Mathematical Analysis
Mekelweg 4, 2628 CD Delft
The Netherlands
c.vanvelzen@ewi.tudelft.nl
affiliated with VORtech Computing
P.O. Box 260
2600 AG Delft
www.vortech.nl
Data assimilation techniques are widely used in various modeling areas
like meteorology, oceanography and chemistry. Most implementations of
these data assimilation methods however are custom implementations
specially designed for a particular model.
These custom implementations are in general very computationally efficient
but they are expensive to implement and maintain and it is hard to reuse
the implementation for an other model. Similarly, a lot of programming has
to be done in order to tryout an alternative assimilation method in an
existing system.
The COSTA project offers a modular
framework for data assimilation, containing methods and tools that can be
easily applied for general applications. Another goal of the COSTA project
is to simplify the application of data assimilation methods such that they
become available to a larger group of researchers and models.
The COSTA framework consists of a large number generic building blocks, called
components. The interfaces of the components are chosen such that the
complete system forms a flexible environment that can be used to build,
incorporate and/or replace implementations of data assimilation methods and
tools. A default implementation will be available for most of the building
blocks but the user can easily replace them with own implementations.
The software systems WAQUA and TRIWAQ for 2D and 3D shallow water
simulation of the Dutch National Institute for Coastal and
Marine Management (Rijkswaterstaat/RIKZ) are provided with a number of data
assimilation methods. There is however a need to apply the same
assimilation methods for other models and to extent the number of
assimilation methods in the existing software. The COSTA framework have
therefore been introduced in the system.
In the development of COSTA, the team collaborates with Delft Hydraulics,
where the generic data assimilation package DATools is being developed. The
collaboration focuses on sharing concepts and experiences, which is expected
to lead to improved design and a more efficient development cycle of both
systems.
The preliminary results from these applications will also be discussed in
this paper. 
Track/Session 
Special Sessions / Data assimilation in water resources modelling 
Date 
20060618 
DOI 
10.4122/1.1000000518 


Luis Gallardo 
Crossgradients joint inversion of disparate geophysical data for improved subsurface characterization: multiplephysics field examples 




Author(s) 
Luis Gallardo^{1}; Luis Gallardo^{1} 
Organisation(s) 
^{1}Earth Science Division, CICESE, Mexico 
Abstract 
The characterization and monitoring of hydrogeological and other complex subsurface
processes requires a detailed knowledge of several properties of the composing
rocks and fluids. Whilst some of these properties can be measured directly, other
properties have to be estimated by indirect measurements such as geophysical data.
However, it is not uncommon that the geophysical data yield models of limited
accuracy that may not contribute significantly to our understanding of the
subsurface processes.
Interestingly, the distribution of apparently uncorrelated physical properties
seems to be controlled by common subsurface attributes that, when taken into
account, can improve the accuracy and meaning of the otherwise independent
geophysical models. For instance, a highly porous rock that is saturated with water
can be sharply defined by a combined low seismic velocitylow electrical
resistivity area. However, such a correlation can not be generalised to different
environments. An outstanding feature of the subsurface that is common to the
geophysical data is the geometrical distribution of the physical properties which
can be measured by the physical property changes. This condition of commonality can
be incorporated in the process of estimation to obtain meaningful and more reliable
subsurface models in a process of joint inversion.
In this work I define the joint inversion of disparate geophysical data as the
search of those models that satisfy their respective geophysical data in a least
squares sense and are geometrically similar. I quantify the geometrical similarity
with the null values of the crossproducts of the gradients of two physical
properties and pose solutions for these objective functions that account for
multiplephysics models (P and Swave velocities as well as DC and MT
resistivity). I present several test and field examples that show the improvements
attained in parameter accuracy and geometrical resemblance as well as their
implications for petrophysical and structural associations for several nearsurface
field sites. 
Track/Session 
Special Sessions / Hydrogeophysical data fusion 
Date 
20060618 
DOI 
10.4122/1.1000000516 


BENJAMIN BELFORT 
A New Mass Lumping Scheme for the Mixed Hybrid Finite Element Method: Application to unsaturated water flow modelling 




Author(s) 
BENJAMIN BELFORT^{1}; FRANCOIS LEHMANN^{1}; ANIS YOUNES^{1}; PHILIPPE ACKERER^{1}; BENJAMIN BELFORT^{1} 
Organisation(s) 
^{1}Institut de Mecanique des Fluides et des Solides de Strasbourg 
Abstract 
Abstract:
Groundwater flow modelling is of interest in many sciences and engineering
applications for scientific understanding and/or technological management. Accurate
numerical simulation of infiltration in the vadose zone remains a challenge,
especially when very sharp fronts are present.
This study is focused principally on an alternatively numerical approaches referred
to in the literature as the mixed hybrid finite element (MHFE) method. MHFE schemes
simultaneously approximate both the pressure head and its gradient. For some
problems of unsaturated water flow, the MHFE solutions contain oscillations. Various
authors ( see [1]) suggest the use of a mass lumping procedure to avoid this
unphysical phenomenon. An analyse of the resulting matrix system shows that the
recommended technique differs from the standard masslumping wellestablished for
Galerkin finite element methods.
A “new” effective masslumping scheme adapted from [2] has been specially developed
for the MHFE method. Its ability for eliminating oscillations have been tested in
unsaturated conditions. Various test cases in a 2D domain, for homogeneous and
heterogeneous dry porous media and subject to different boundary conditions are
presented.
References:
[1] Farthing, M. W., C. E. Kees, and C. T. Miller. 2003. Mixed finite element
methods and higher order temporal approximations for variably saturated groundwater
flow. Adv. Water Resour. 26:373394.
[2] Younes A., Ackerer P. and Lehmann F., 2005.A new mass lumping scheme for the
mixed hybrid finite element method, Int. J. Numer. Meth. Engng. (submitted). 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000514 


HwaiPing Cheng 
Model Calibration and Validation of South Florida Biscayne Bay Coastal Wetlands Watershed 




Author(s) 
HwaiPing Cheng^{1}; HsinChi Lin^{1}; Charles Tate^{1}; Earl Edris^{1}; David Richards^{1}; Mitch Granat^{2}; David Richards^{1} 
Organisation(s) 
^{1}US Army Engineer Research and Development Center; ^{2}US Army Corps of Engineers, the Jacksonville District 
Abstract 
Among the 40 projects in the Florida Comprehensive Everglade Restoration Plan, the
Biscayne Bay Coastal Wetlands (BBCW) project has a purpose of rehydrating wetlands
and reducing point source discharge to Biscayne Bay. Seven project alternatives
that include rulecontrolled coastal canal structures, rulecontrolled pump
stations, spreader swales, stormwater treatment areas, flowways, levees, culverts,
roads, and backfilling canals have been proposed to achieve the purpose. These
alternatives are evaluated with the WASH123D modela firstprinciple, physicsbased
numerical model that computes flow and transport in a watershed system that is
conceptualized as a combination of 1D channel network, 2D overland regimes, and 3
D subsurface media. The WASH123DBBCW model needs to be calibrated and validated
before being used to evaluate the alternatives. This paper presents the
calibration and validation of the model. A threestep approach that is used for
model calibration and validation is presented, discussed, and evaluated in this
paper. The three steps are: calibration of the overland Manning’s roughness
coefficients (n2) and subsurface hydraulic conductivities (K) with the coupled 2
D/3D WASH123DBBCW model where the historical data of canal stage is used as the
boundary condition; calibration of the canal Manning’s roughness coefficients (n1)
where the calibrated n2 and K from the previous step are used; and validation of
the calibrated n1, n2, and K with a second set of historical data. The calibration
validation results of the WASH123DBBCW model are also presented in the paper. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000512 


Julius Harry Sumihar 
Data assimilation study of the DCSM model using full measurement 




Author(s) 
Julius Harry Sumihar^{1}; Martin Verlaan^{2}; Julius Harry Sumihar^{1} 
Organisation(s) 
^{1}Faculty of Electrical Engineering, Mathematics and Computer Science, Department of Applied Mathematics, Delft University of Technology, Delft, Netherlands; ^{2}Faculty of Electrical Engineering, Mathematics and Computer Science, Department of Applied Mathematics, Delft University of Technology, Delft, Netherlands and Rijkswaterstaat, Rijksinstituut voor Kust en Zee (RIKZ), Netherlands 
Abstract 
The operational water level prediction method in the Netherlands is based on the
decomposition of water level into the astronomical tides and the surge. While the
astronomical components are analysed and predicted by using Harmonic Analysis, the
surge is predicted by using numerical hydrodynamics model named Dutch Continental
Shelf Model, DCSM. Using this approach the nonlinear interaction between the
components is not well accomodated. Moreover, the performance of the system now seems
to have reached its limit. Hence, as an attempt to further improve the prediction we
are going to apply data assimilation using the DCSM model with the full water level
measurements without any decomposition. In the first step of the study we use the
steadystate Kalman filter as the method for data assimilation. Selection of
measurement locations is also discussed to find the best configuration. As the
success of data assimilation depends largely on the error representation, we are also
going to work with new error representation for the boundary condition. In the new
representation, a colored noise process, modelled using AR(1), is assigned to each
harmonic parameters defining the water level boundary conditions. This choice is made
based on the fact that the harmonic parameters of the astronomical tides are in fact
slowly varying in time. We are going to present and discuss some results of this study.
~ 
Track/Session 
Special Sessions / Data assimilation in water resources modelling 
Date 
20060618 
DOI 
10.4122/1.1000000510 


CARINE FAMY 
ACCURATE MODELLING OF MATRIXFRACTURE TRANSFERS IN FRACTURED POROUS MEDIA THROUGH SUBGRIDDED DUALPOROSITY MODELS 




Author(s) 
CARINE FAMY^{1}; BERNARD BOURBIAUX^{1}; PATRICK LEMONNIER^{1}; MICHEL QUINTARD^{2}; CARINE FAMY^{1} 
Organisation(s) 
^{1}Institut Français du Pétrole (I.F.P.); ^{2}Institut de Mécanique des Fluides de Toulouse (I.M.F.T.) 
Abstract 
Conventional models to represent fractured media are often based on the “dual
porosity” concept (Warren and Root, 1963). In most simulators, to represent the
exchange between the fracture and matrix media, we use an approximate pseudosteady
state mass exchange formulation resulting from an upscaling of the matrix block
scale flow (Landereau et al., 2001). This formulation is reasonably predictive for
singlephase flows, but generally inaccurate for multiphase flows. This is mainly
due to the impact of nonlinearities and the coupling between several physical
mechanisms, especially capillarity and gravity, that do not yield the same
homogenised flow behaviour at the matrix block scale. A numerical approach to
overcome this limitation consists in subgridding the matrix blocks (Pruess and
Narasimhan, 1985), which may be viewed as a mixed model as obtained from
homogenization theory (Arbogast et al., 1990). However, this method is still unused
in practical situations because of its high computational cost. This paper describes
the optimisation of this subgridding technique in the capillary imbibition case, by
taking into account the physical specificities of this mechanism and with a
criterion of minimal computational cost. Implemented in a conventional flow
simulator, this technique allows the calculation of very reliable exchange terms
between matrix blocks and fractures.
The study of the capillary imbibition mechanism on a single matrix block (possibly
anisotropic) allows one to create an optimised onedimensional model. This sub
gridding methodology has been validated by comparison with reference finegrid
simulations, for various rockfluid properties and anisotropic flow conditions. The
reference solutions are reproduced very accurately, including the detailed time
evolution of the matrixfracture transfer rates. Since the subgridding methodology
provides accurate exchange terms, it has been implemented in a conventional flow
simulator dedicated to fractured porous media. The subgridding methodology improves
the calculation of matrixfracture exchanges driven by capillary forces. Moreover,
matrix and fractures unknowns have been decoupled in order to reduce the
computational cost. Therefore, short and longterm flows of waterdrive fractured
media can be reliably predicted. This methodology can be applied to other multiphase
flow problems solved with an industrial fractured reservoir simulator.
The main technical contributions of this work are the development of an optimised
method for subgridding matrix blocks, and the implementation of this subgridding
methodology into a conventional flow simulator dedicated to fractured media.
T. Arbogast, J. Douglas Jr and U. Hornung (1990), Derivation of the double
porosity model of single phase flow via homogenization theory, SIAM J. Math. Anal,.
21(4), 823836.
P. Landereau, B. Noetinger and M. Quintard (2001), Quasisteady twoequation
models for diffusive transport in fractured porous media: largescale properties for
densely fractured systems, Advances in Water Resources 24, 863876
K. Pruess and T.N. Narasimhan (1985), A practical method for modeling fluid and
heat flow in fractured porous media, SPE Journal.
J.E. Warren and P.J. Root (1963), The behavior of naturally fractured reservoirs,
SPE Journal. 
Track/Session 
Special Sessions / Multiscale methods for flow in porous media 
Date 
20060618 
DOI 
10.4122/1.1000000508 


CRISTINA CATA 
A randomwalk approach for simulating transport and transformations in the unsaturated zone 




Author(s) 
CRISTINA CATA^{1}; ULF MOHRLOK^{1}; CRISTINA CATA^{1} 
Organisation(s) 
^{1}University Karlsruhe, Institute for Hydromechanics 
Abstract 
A new reactive transport modelling approach and its applications are presented,
dealing with the impact of the transformation processes, e.g. redoxreactions, on
the spreading of solutes, e.g. wastewater, in unsaturated zone. This method is based
on the random walk approach, balancing the water and associated mass transport in
the unsaturated zone. It allows the quantification of the mass transfer between
different phases (i.e. mobile fluid phase, immobile solid phase) and of the reactive
processes. It is applied for investigating the plume development from a point
source, e.g. sewer leak, in unsaturated zone and its impact on groundwater. One
advantage of the model is that the water and the solute transport are simultaneous
calculated, without having to first run a flow model and then a transport model,
saving simulation effort.
Transport of dissolved solutes in the unsaturated soil zone depends on the
unsaturated water flow, which is usually described by the Richard’s equation. As the
Richard’s equation is reformulated as a FokkerPlanck equation for the water
transport, the random walk approach can be used for balancing the water flow in the
unsaturated zone by moving particles representing a defined water volume. Also,
defining mass loadings for each particle represents the mass transport. Thus, the
unsaturated water transport and mass transport are computed together. When a
particle moves, it represents the mobile fluid phase and brings the solute mass from
one location to another one. At the same time it exchanges mass with the immobile
solid phase (i.e. the cell). This approach is implemented in the numerical model
Water and Solute Transport Model (WSTM), where this exchange takes place between
individual particles and the respective cell. The method was applied to simulate a
sewer leak infiltration in unsaturated soils considering conservative and reactive
solutes. The distributions of the water content and the solutes concentration are
well represented.
For the complete assessment of the wastewater impact on soils and groundwater
detailed understanding of migration and transformation of solutes in the subsurface
is required. The implementation of the relevant transformation processes (e.g. redox
reactions) into the numerical model enables detailed investigation of their
interactions on transport. Simulation results considering transformation processes
will be validated by the use of the experimental results in order to provide a tool
with predictive capability. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000507 


HwaiPing Cheng 
Numerical Strategies to Model Surface and Groundwater Interactions for the Biscayne Bay Coastal Wetlands Project Alternatives 




Author(s) 
HwaiPing Cheng^{1}; JingRu cheng^{1}; David Richards^{1}; GourTsyh Yeh^{2}; HwaiPing Cheng^{1}; David Richards^{1} 
Organisation(s) 
^{1}US Army Engineer Research and Development Center; ^{2}University of Central Florida 
Abstract 
WASH123D is a firstprinciple, physicsbased numerical model that computes flow and
transport in a watershed system that is conceptualized as a combination of 1D
channel network, 2D overland regimes, and 3D subsurface media. It has been
selected as the tool to help evaluate the proposed alternatives of the Biscayne Bay
Coastal Wetlands project that is one of the 40 projects included in the Florida
Comprehensive Everglade Restoration Plan. In order to best rehydrate wetlands and
reduce point source discharge to Biscayne Bay, rulecontrolled coastal canal
structures, rulecontrolled pump stations, spreader swales, stormwater treatment
areas, flowways, levees, culverts, roads, and backfilling canals are included in
these project alternatives. Specified target freshwater flows for Biscayne Bay and
the wetlands within the redistribution system are to be computed in each
alternative, which will be used in performance measurement to determine the most
adequate alternative for further investigation. In this paper, the numerical
strategies to incorporate all the aforementioned hydrological features and
processes included in the alternatives are presented. An example alternative will
be used for demonstration. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000505 


Vural Suicmez 
Porescale simulation of water alternate gas injection 




Author(s) 
Vural Suicmez^{1}; Mohammad Piri^{2}; Martin Blunt^{3}; Vural Suicmez^{1} 
Organisation(s) 
^{1}PhD student at Imperial College; ^{2}Research Associate at Princeton University; ^{3}Prof at Imperial College 
Abstract 
We use a threedimensional mixedwet random network model representing Berea
sandstone to compute displacement paths and relative permeabilities for water
alternating gas (WAG) flooding. First we reproduce cycles of water and gas
injection observed in previously published experimental studies. We predict the
measured oil, water and gas relative permeabilities accurately. We discuss the
hysteresis trends in the water and gas relative permeabilities and compare the
behavior of waterwet and oilwet media. We interpret the results in terms of pore
scale displacements. In waterwet media the water relative permeability is lower
in the presence of gas due to an increase in oil/water capillary pressure that
causes a decrease in wetting layer conductance. The gas relative permeability is
higher for displacement cycles after first gas injection at high gas saturation due
to cooperative pore filling, but lower at low saturation due to trapping. In oil
wet media, the water relative permeability remains low until waterfilled elements
span the system at which point the relative permeability increases rapidly. The
gas relative permeability is lower in the presence of water than oil because it is
no longer the most nonwetting phase. 
Track/Session 
Special Sessions / PoreScale Modelling: New Developments And Applications 
Date 
20060618 
DOI 
10.4122/1.1000000503 


Mohamed S. Ghidaoui 
A BGK MODEL FOR THREEDIMENSIONAL SHALLOW WATER PROBLEMS 




Author(s) 
Mohamed S. Ghidaoui^{1}; Jun Hong Liang^{1}; Mohamed S. Ghidaoui^{1} 
Organisation(s) 
^{1}Dept of Civil Engineering, The Hong Kong University of Science & Technology 
Abstract 
This paper focuses on illustrating how the Boltzmann theory can be used to
formulate numerical algorithms for threedimensional shallow water equations. The
paper begins by showing that the classical threedimensional shallow water
equations are obtainable from the moments of the Boltzmann BhatnagarGrossKrook
(BGK) equation. This connection is then exploited to formulate a threedimensional
finite volume for shallow flows in which the fluxes are obtained on the basis of
the BGK equation. The resulting scheme is illustrated using a variety of surface
water problems. The advantages of using the Boltzmannbased to formulate numerical
algorithms for surface water flows are summarized. 
Track/Session 
Special Sessions / Boltzmann Methods in Water Resources 
Date 
20060618 
DOI 
10.4122/1.1000000501 


Peter BauerGottwein 
INTERACTION OF DENSITY FLOW AND GEOCHEMICAL PROCESSES ON ISLANDS IN THE OKAVANGO DELTA, BOTSWANA 




Author(s) 
Peter BauerGottwein^{1}; Henning Prommer^{2}; Thomas Langer^{3}; Piotr Wolski^{4}; Peter BauerGottwein^{1} 
Organisation(s) 
^{1}Environment & Resources, Technical University of Denmark; ^{2}CSIRO, Perth, Australia; ^{3}CSDGeoklock, São Paulo, Brazil; ^{4}Okavango Research Centre 
Abstract 
The Okavango Delta in Northern Botswana is a large wetland system (about 20’000
km2) located at the downstream end of the Okavango River basin. The endorheic
Okavango River originates on the crystalline Benguela Plateau in Southern Angola,
flows southwards into the Kalahari sedimentary basin, where it terminates in the
Okavango Delta. The system is open with respect to water (evapotranspiration) but
closed with respect to solutes. Consequently, about 300’000 tons of salts
accumulate in the Okavango Delta per year.
Significant salt accumulation is observed on small to mediumsized islands (100
1000 m diameter) that are scattered throughout the wetland system. Due to
relatively shallow groundwater levels below the islands, groundwater is
continuously withdrawn from the surrounding swamps by the combined action of
transpiration and evaporation. Whereas transpiration dominates in the belt of
vigorous riverine vegetation along the islands’ fringes, evaporation is the
dominant process in the centre of the islands. Due to elevated groundwater
salinities (up to 30 g/l), only specialized grass species can survive in the
islands’ centre.
Salt accumulation on three islands in the Okavango Delta was studied in detail.
Electrical resistivity tomography was used to derive the 3D salinity distribution
on one island and its surroundings. Multiple boreholes and piezometers were drilled
to various depths and water samples were analyzed for major ions and tracers. The
field data suggests that density fingering against the evaporationinduced upward
flow occurs on the islands. At the same time, various minerals precipitate
(carbonates, silica and others) and form cemented layers and efflorescent salt
crusts.
A coupled multispecies flow and reactive transport model was used to analyze the
chemical evolution of the groundwater below the islands in the Okavango Delta. The
model takes into account both geochemical reactions and density flow. It is based
on the PHREEQC and SEAWAT codes. Of particular interest is the interaction between
density flow and geochemical reactions. To study these interactions, four numerical
island models of increasing complexity were developed and results were compared. In
a first step, advectivedispersive transport of one conserved species (salinity)
was simulated. Subsequently, variable fluid density was taken into account. The
third step considers advectivedispersive transport of multiple reactive species,
disregarding variable density effects. The final model formulation includes multi
species reactive transport and variable density flow. In the final model, mineral
precipitation delays the onset of fingering instabilities, due to the removal of
salinity. The vertical transport of solutes into deeper subsurface strata is
therefore less efficient as compared with the single species, conservative density
flow simulation.
The results enhance our understanding of reactive variable density flow in porous
media. They are relevant for all evaporative systems, where significant evapo
concentration occurs. An important application is soil and groundwater salination,
which is presently one of the major global environmental problems. 
Track/Session 
Special Sessions / MultiDisciplinary Approaches To Reactive Transport Simulation In Aquifer Systems 
Date 
20060618 
DOI 
10.4122/1.1000000499 


Hans Petter Langtangen 
Building Programmable Problem Solving Environments for Porous Media Flow 




Author(s) 
Hans Petter Langtangen^{1}; Hans Petter Langtangen^{1} 
Organisation(s) 
^{1}Simula Research Laboratory 
Abstract 
Scientists and engineers tend to use increasingly more complex
mathematical models to describe water resources systems. Efficient
use of such models often demands access to appropriate problem solving
environments (PSEs). This talk focuses on programmable PSEs where the
user has great flexibility to configure the PSE by writing and combining
software components.
Because software complexity often increases much faster than the
complexity of the underlying mathematical models, it is important to
adopt programming techniques that can meet the modern demands to
extensibility, maintenance, and verification. Some important
techniques, such objectoriented programming and generic (template)
programming, will be reviewed and exemplified in the context of
partial differential equation solvers. The importance of easytouse,
interpreted, highlevel languages, of which Matlab and Python are
examples, will also be emphasized. Then we outline a promising hybrid
software approach to constructing PSEs, based on domain decomposition
and combination of interpreted and compiled languages. We will show
how such an approach simplifies multiphysics problems,
parallellization, and reuse of legacy codes. Applications of the
mentioned techniques to porous media flow and shallow water waves also
will be shown. 
Track/Session 
Special Sessions / Keynote speakers (reserved for keynotes only) 
Date 
20060618 
DOI 
10.4122/1.1000000498 


Venkat Nageshwar Rao Shedimbi 
CONJUNCTIVE USE OF SURFACE AND GROUNDWATER IN COASTAL DELTAS USING SIMULATED ANNEALING AND NEURAL NETWORKS 




Author(s) 
Venkat Nageshwar Rao Shedimbi^{1}; Venkat Nageshwar Rao Shedimbi^{1} 
Organisation(s) 
^{1}National Institute of Hydrology, Roorkee, UA, INDIA. 
Abstract 
The hydrology of Indian deltas is largely influenced by vagaries of monsoon
rainfall that affects groundwater recharge during monsoon season and surface water
availability during both monsoon and nonmonsoon seasons. The irrigation here is
well developed from diversion structures. However, often the demand is not met
adequately during the nonmonsoon season through surface water sources only,
especially in the lower reaches of deltaic plains. Excessive groundwater extraction
in these regions to meet the demand may lead to significant SWI. These twin issues
of water availability and SWI in coastal and deltaic regions may be addressed in
several approaches. Conjunctive utilization of surface and groundwater sources is
one of the approaches. The demand at any point in space during a given time period
may be met either from the surface source or groundwater source or from both.
Similarly, if enough surface water is available during a particular time period, it
can be used to recharge the groundwater reservoir at several demand centers, for
use at a later time. This increases the groundwater levels so that pumpage at a
later stage does not induce too much of SWI.
A conceptual conjunctive use model is presented for a nearreal deltaic aquifer
system, irrigated from a diversion system, with some reference to hydrogeo
climatic conditions prevalent in the east coastal deltas of India. Water resources
are sufficiently available in these regions under average monsoon rainfall
conditions. However, their distribution in space and time has been ever challenging
to water managers. The surfacewater availability shows temporal fluctuations in
terms of floods and droughts. The groundwater availability shows mainly spatial
variability in terms of quality and quantity due to the hydro geologic setting,
boundary conditions, and aquifer properties. The combined simulationoptimization
model proposed in this study is solved as a nonlinear, nonconvex combinatorial
problem using a simulated annealing algorithm and an existing sharp interface
model. The computational burden is managed within practical time frames by
replacing the flow simulator with artificial neural networks (ANN) and using
efficient algorithmic guidance. 
Track/Session 
Special Sessions / Boltzmann Methods in Water Resources 
Date 
20060618 
DOI 
10.4122/1.1000000497 


Mortazavi Naeini Seyed mohammad 
Application of Genetic Algorithm for Optimal Reservoir Operation 




Author(s) 
Mortazavi Naeini Seyed mohammad^{1}; Mortazavi Naeini Seyed mohammad^{1} 
Organisation(s) 
^{1}Graduated Student 
Abstract 
Genetic Algorithms (GAs) application in the field of water resources engineering is
of recent origin. Genetic Algorithms is one of the tools, which handle nonlinear
optimization problems in an efficient manner. Optimal reservoir operation of
reservoir for hydropower production involves constrained nonlinear optimization.
The constrained problem is converted into unconstrained problem by using penalty
function method. Genetic algorithm was then used to optimize the reservoir
operation for hydropower production. This approach was used to develop optimal
operating policy for Dez reservoir. Various steps involved in deriving the optimal
operating policy for the reservoir using GA are discussed in the paper. For fixing
the GA parameters via Crossover probability and mutation probability, the model is
run for different values of crossover and mutation probabilities. The operating
policy thus obtained can be used for optimal operation of the reservoir. Results
from the model and possible extensions were discussed 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000496 


Insa Neuweiler 
Upscaling for unsaturated flow including connectivity of the soil structure 




Author(s) 
Insa Neuweiler^{1}; Insa Neuweiler^{1} 
Organisation(s) 
^{1}Institute of Hydraulic Engineering, University of Stuttgart 
Abstract 
Modelling of flow processes in the unsaturated zone on a large scale requires often
upscaling of the flow problem. The soil parameter distribution is mostly not known,
so that the upscaled problem is based on a characterization of the soil
heterogeneity, which is obtained from local measurements. Effective flow parameters
are therefore often derived in a stochastic framework, where the heterogeneity of a
field is quantified by its second order stochastic properties (the mean, variance
and a twopoint covariance model with an integral scale and anisotropy parameters).
A field has to be Gaussian to be quantified completely by these parameters. However,
soil structure resembles rarely Gaussian fields. It has connected and isolated
structures of different material types. The connectedness of material has a large
influence on the upscaled models, yet these properties can in general not be derived
from second order stochastic field parameters. Therefore upscaling methods are
needed which take connectivity into account.
In this contribution we first discuss how soil connectivity can be quantified from
local data in a reasonable way. We then discuss how the information about
connectivity can be taken into account into the upscaled models. This is done here
by applying different effective medium approaches to derive unsaturated effective
permeability. The methods are all derived assuming capillary equilibrium on the
small scale. Effective parameters are obtained using the selfconsistent approach,
the Maxwell approach, the differential effective medium approach and a generalized
percolation approach. We compare the methods and discuss their advantages and
limits. The results obtained for different test fields are compared to the exact
solution for the effective parameters, derived by homogenization theory. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000494 


Marc Honnorat 
Variational data assimilation of lagrangian data for fluvial hydraulics simulations. 




Author(s) 
Marc Honnorat^{1}; FrançoisXavier Le Dimet^{1}; Jérôme Monnier^{1}; Marc Honnorat^{1} 
Organisation(s) 
^{1}LMCIMAG 
Abstract 
A major difficulty in the simulation of river hydraulics flows is bound to model
parameters definition. Solutions of the shallow water equations are determined by
initial conditions, boundary conditions, bed elevation, physical and numerical
parameters. Data assimilation methods make it possible to combine optimally physical
information from the model and observation data of the physical system to identify
the value of model inputs that correspond to a numerical simulation which is
consistent with reality.
Variational data assimilation consists in finding the control variables that minimize
a cost function measuring the discrepancy between the model state variable and
observation data of the physical system. An efficient minimization using a
QuasiNewton algorithm requires the computation of the gradient of the cost function.
The latter is easily computed from the adjoint state which is solution of an adjoint
model.
However, in river hydraulics, observation data are available only in very small
quantities. Local water level measurements are usually very sparse in space and
velocity measurements are even rarer, especially in case of extreme events such as
floods. Consequently, in practice these eulerian observations are usually not
sufficient to take advantage of data assimilation.
We present a method to use lagrangian data from remote sensing observation in the
assimilation process, in addition to classical eulerian observations of the flow. The
trajectory of particles advected by the flow can bring information on the surface
velocity thanks to an appropriate transport model. Numerical twin experiments
demonstrate that this additional information makes it possible to improve the
identification of model parameters. In order to deal with real data, an observation
operator based on a multiscale filtering scheme is proposed. 
Track/Session 
Special Sessions / Data assimilation in water resources modelling 
Date 
20060618 
DOI 
10.4122/1.1000000492 


Taef ASWED 
Modeling of the Contamination in the Alsatian Aquifer by Chlorinated Solvents 




Author(s) 
Taef ASWED^{1}; Phillippe ACKERER^{1}; Taef ASWED^{1} 
Organisation(s) 
^{1}Institut de mécanique des fluides et des solides de Strasbourg 
Abstract 
The Alsatian aquifer in the upper Rhine area, northeastern of France, was
contaminated with CCl4 on account of an accident happened on 1970. After several
years of the accident, certain concentrations of CCl4, which are far away higher
than the acceptable safety norm, have been detected in the underground water
aquifer. Measured data have been collected from different locations of the aquifer
during the period between 1992 and 2004. To match the history and predict the
distribution of the contaminant, one requires knowledge of: (i) the behavior of the
contaminant source, (ii) the geophysical parameters that affect water flow and
contaminant transfer in the aquifer. In this work, we show the mathematical and
numerical modeling of the problem. All measured data collected between 1992 and 2004
were used to validate our model. The chemical CCl4 is modeled as a tracer in water
(that is, singlephase flow). Numerical results were obtained with an efficient, 3D
singlephase code “TRACES”, developed at the IMFS. This code combines the mixed
hybrid finite element and discontinuous Galerkin methods to solve both the flow and
the transport problems.
No information is available about the behavior of the contaminant at the source. To
estimate the contaminant concentration at the source, the travel time between the
source and measurementwells by the method of moments. Another difficulty one had to
overcome was because no measured data of the rock and fluid parameters such as
hydraulic conductivity, porosity, longitudinal and transversal dispersivities, were
available. Several simulations were thus performed to get the parameters that match
best the history. The permeability was calibrated with several runs carried out by
changing randomly the permeability of each grid block. Porosity, longitudinal and
transversal dispersivities were also fitted to the transport model. We have found
that the results are rather insensitive to changes in permeability, while they are
sensitive to changes in the longitudinal and transverse dispersivities. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000490 


Richard Ogilvy 
Constraining coastal aquifer models by hydrogeophysical imaging of seawater intrusion dynamics: a case study from the Lower Andarax delta, SE Spain 




Author(s) 
Richard Ogilvy^{1}; Oliver Kuras^{1}; Frederic Nguyen^{3}; Andreas Kemna^{3}; Philip Meldrum^{1}; Juan Gisbert^{4}; Sara Jorreto^{4}; Francisco Sanchez Martos^{4}; Antonio Pulido Bosch^{4}; Peter Engesgaard^{2}; Arni Antonsson^{2}; Karsten Jensen^{2}; Oliver Kuras^{1} 
Organisation(s) 
^{1}British Geological Survey; ^{2}University of Copenhagen; ^{3}Institute of Chemistry and Dynamics of the Geosphere; ^{4}University of Almeria 
Abstract 
Appropriate characterisation, modelling and management of coastal aquifers requires
knowledge of the dynamic balance between freshwater and saltwater present in the
aquifer as a result of natural marine intrusion or other salinisation processes of
geological or anthropogenic origin. Monitoring this balance is essential for the
timely detection and prediction of groundwater deterioration and the sustainable
management of abstraction schemes. Recent advances in hydrogeophysical methods
allow more accurate noninvasive assessments of intrusion dynamics and evolution,
thus providing vital input to the generation and refinement of conceptual and
numerical hydraulic models of coastal aquifers.
The purpose of this study of the Lower Andarax delta in the Andalucía region of
southeast Spain is to combine timelapse electrical resistivity tomography (ERT)
with conventional intrusive methods (borehole sampling, wireline and core logging)
and hydraulic tests in order to (1) image the saline/freshwater interface, (2)
obtain an improved understanding of the intrusion process and its seasonal
variation and (3) generate detailed and realistic models of a coastal aquifer. The
Andarax river basin is an alluvial valley situated in one of the most arid regions
in Europe. Its infrequent and irregular precipitation determines the regime of land
use and groundwater abstraction. The Lower Andarax catchment serves as a test area
for the project “Sustainable Management of Water Resources by Automated Realtime
Monitoring (ALERT)” under the European Union Sixth Framework Programme, which aims
to develop strategies for monitoring and managing vulnerable coastal zones.
A number of manual ERT surveys conducted in the Andarax riverbed over a period of
several months have revealed the shape of the mixing zone at high resolution.
Presentday seawater intrusion appears to be confined to the shallow Quaternary
part of the aquifer, where a sloping front has been detected down to depths of 70
80 m over a distance of approximately 1300 m from the shore. Early indications show
that this front is subject to seasonal change. Deeper formations of Pliocene age
appear to store significant amounts of saline water, however the results suggest
that these formations may exhibit much lower permeabilities and that therefore the
deeper regions of the aquifer may remain static over the timescale of the
observations.
The manual surveys will be followed by the permanent deployment of an automated
monitoring system during 2006. This system will provide volumetric images of the
subsurface at regular intervals or “on demand”, thereby obviating the need for
expensive repeat surveys and manual intervention. Using calibrated geophysical
hydrological relationships, the geophysical monitoring data will be integrated with
hydraulic data obtained from newly drilled exploratory boreholes as well as a range
of existing freshwater abstraction wells. 
Track/Session 
Special Sessions / Hydrogeophysical data fusion 
Date 
20060618 
DOI 
10.4122/1.1000000489 


Marwan Fahs 
Comparison between global and operator splitting approaches for modeling multicomponent reactive transport in porous media 




Author(s) 
Marwan Fahs^{1}; Jérôme Carrayrou^{1}; Anis Younes^{1}; Ackerer Philippe^{1}; Marwan Fahs^{1} 
Organisation(s) 
^{1}Institut de mécanique des fluides et des solides de strasbourg 
Abstract 
Multicomponent reactive transport with chemical equilibrium reactions, involving
advective and dispersive solute transport coupled with the nonlinear reaction, is
fundamental feature of subsurface environments. At the equilibrium, the governing
system of equations is formed by the partial differential equations (PDEs) of the
transport operator and the nonlinear algebraic equations (AEs) describing the
chemical reactions. These two sets of equations are coupled and needed to be solved
using the operator splitting (OS) approach or the global approach.
With (OS), the transport and reaction equations are separated and solved
sequentially for each time step. The OS includes the Sequential noniterative
approach (SNIA) and the Sequential iterative approach (SIA), which iterates between
transport and chemistry until convergence for each time step.
With the global approach, the governing equations of transport and reaction are
solved simultaneously. We distinguish two methods in the global approach. (i) The
Differential Algebraic Equations Approach (DAE) solves a large system formed by both
transport and chemistry equations (Miller, 1983). (ii) The direct substitution
approach (DSA) solves a reduced system obtained after substituting the chemistry
algebraic equations in the transport partial differential equations (Shen and
Nikolaidis, 1997; Jenning et al., 1982).
Since the reference work of Yeh and Tripathi (1989), the (OS) approach is widely
used to simulate reactive transport problems since it allows different numerical
methods to be used for the reactive and transport components. However, the (OS)
approach can introduce operatorsplitting errors which are avoided with the global
approach.
In this work, we show that DSA and DAE have the same numerical behavior. For a fine
discretization and/or for a large number of chemical species, DSA is shown to be
more efficient then DAE.
Both DSA and SIA give accurate results. Contrarily to DSA, SIA solves sequentially
two small systems (transport and chemistry). It was shown in Saaltink (2001) that
DSA runs faster than SIA in chemically difficult cases and the SIA may become faster
than the DSA for very large, chemically simple problems. In this work, we combine
DSA with a very efficient linear solver UMFPACK. Our numerical experiments suggest
that for all cases, DSA is shown to be more efficient than SIA. DSA requires less
iteration to reach the convergence and allows large time steps contrarily to SIA.
Comparisons between DSA and SNIA show that SNIA spends less CPU time than DSA.
However OS errors introduced with SNIA are proportional to the time step size and
can therefore be significant. When SNIA is combined with an adaptative time stepping
procedure based on a posteriori control error, DSA can be more efficient then SNIA. 
Track/Session 
Special Sessions / MultiDisciplinary Approaches To Reactive Transport Simulation In Aquifer Systems 
Date 
20060618 
DOI 
10.4122/1.1000000488 


Anis YOUNES 
An alternative procedure to avoid excessive numerical diffusion with the ELLAM 




Author(s) 
Anis YOUNES^{1}; Philip ACKERER^{1}; Anis YOUNES^{1} 
Organisation(s) 
^{1}Institut de mécanique des fluides Strasbourg 
Abstract 
In this work, the EulerianLagrangian Localized Adjoint Method (ELLAM) is improved
to better reduce the numerical diffusion when solving Advection Diffusion Equations
(ADE). The ELLAM preserves the performance of characteristic methods and treats
general boundary conditions naturally in their formulations. ELLAM is accurate for
large time steps. However, when using several time steps, it is known that they
suffer from numerical diffusion [2].
Because the location of the foot of the characteristic does not coincide with a grid
point, interpolation is necessary at each time step. When many interpolations are
necessary (many time steps), numerical diffusion becomes significant. With higher
order interpolation, negative weights will be necessary to avoid numerical
diffusion, creating potential spurious oscillations [1]. This phenomenon is reduced
for the onedimensional problem in [4] by combining ELLAM with a moving grid
procedure. However, this approach cannot be extended in the same way to 2 or 3
dimensions.
Moreover, masslumping is often used to avoid oscillations with numerical methods
and is known to add excessive numerical diffusion with EulerianLagrangian methods
[3]. To reduce this problem, one dimensional ELLAM scheme with a selective lumping
has been developed in [3].
In this work, an alternative procedure is used to avoid excessive numerical
diffusion with Eulerain Lagrangian methods when performing several time steps.
Compared to the selective lumping approach, it adds less numerical diffusion and can
be more easily extended to multidimensional problems and unstructured meshes.
References
[1] Ruan, F. and D. McLaughlin, An investigation of EulerianLagrangian methods
for solving heterogeneous advectiondominated transport problems, Water Resources
Research (1999), Vol 35, No 8, pp 23592373.
[2] Russell TF, Numerical dispersion in EulerianLagrangian methods.
Computational Methods in Water Resources, Vol. 2, S. M. Hassanizadeh et al., ed.,
Elsevier, Amsterdam (2002), pp. 963970.
[3] Russell TF, and P. Binning, Oh No, not the Wiggles Again! A Revisit of an
Old Problem and a New Approach, Computational Methods in Water Resources, Vol. 1, C.
T. Miller et al., ed., Elsevier, Amsterdam, (2004), pp. 483494.
[4] Younes A, An accurate moving grid Eulerian Lagrangian Localized Adjoint
Method for solving the onedimensional variablecoefficient ADE, Int. J. Numer.
Meth. Fluids, 45, (2004), 157178. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000487 


Arni Antonsson 
Constraining a 2D/3D density dependent saltwater intrusion model using timelapse electrical imaging data 




Author(s) 
Arni Antonsson^{1}; Peter Engesgaard^{1}; P.I. Meldrum^{2}; Andreas Kemna^{3}; Frederic Nguyen^{3}; Oliver Kuras^{2}; R.D. Ogilvy^{2}; Jose Gisbert^{4}; Sara Jorreto^{4}; Fransisco Sanchez Martos^{4}; Antonio PulidoBosch^{4}; Arni Antonsson^{1} 
Organisation(s) 
^{1}Geological Institut of University of Copenhagen; ^{2}British Geological Survey, Electrical Tomography Programme, Keyworth, Nottingham NG12 5GG, UK; ^{3}Institue of Chemistry and Dynamics of the Geosphere, Forschungszentrum Juelich; ^{4}Department of Hydrogeology, University of Almeria, Spain 
Abstract 
In groundwater model development, calibration is one of the critical aspects that
determine its reliability and applicability in terms of e.g. system
(hydrogeological) understanding, groundwater quality predictions, and general use in
water resources context. The result of a groundwater model calibration is determined
by different factors, where both data quantity and quality is of crucial importance.
A density dependent saltwater intrusion model has been established for a coastal
aquifer in Almeria, SE Spain, where hydraulic and solute transport parameters had to
be calibrated in order to simulate the intrusion dynamics realistically.
Furthermore, the sources of saltwater in the coastal aquifer are not unambiguously
defined yet but current state of knowledge seems to suggest the possibility of
multiple sources e.g. present seawater intrusion, solution of evaporites, fossil
waters and anthropogenic influences.
Typically the availability of conventional monitoring installations (e.g. depth
specific monitoring wells for Chloride measurements) and the cost of constructing
new ones limit the amount of obtainable data. These factors can seriously hinder a
successful monitoring strategy and consequently limit the reliability of the
calibrated model. An effective alternative to conventional measurements is the use
of geophysical methods to monitor the saltwater intrusion front. If applied in a
timelapse manner, electrical images give both spatial and temporal information on
the salinity distribution compared to conventional methods, which only give (few)
point information. As a result a more comprehensive understanding of the
hydrogeological system is obtained and a greater confidence in the calibrated model
is achieved.
In this (case) study from Almeria, we demonstrate how the use of timelapse
electrical imaging data improve the calibration of a density dependent intrusion
model compared to using data from conventional (existing) measurements
installations. This was achieved by calibrating the model with the different data
sets and subsequently evaluate the performance of the model.
The results illustrate the benefit of using electrical images for calibration
purposes but also its contribution to system understanding and how it, together with
modeling, can assist in the identification of saltwater sources in the area. 
Track/Session 
Special Sessions / Modeling and managing coastal aquifers 
Date 
20060618 
DOI 
10.4122/1.1000000485 


Hans van Duijn 
Crystal dissolution and precipitation in porous media: the case of fixed geometry 




Author(s) 
Hans van Duijn^{1}; Tycho van Noorden^{1}; Iuliu Sorin Pop^{1}; Iuliu Sorin Pop^{1} 
Organisation(s) 
^{1}Technische Universiteit Eindhoven 
Abstract 
In this talk we propose a pore scale model for precipitation and dissolution
in porous media. We assuming that a fluid is flowing through the pores.
Dissolved cations and anions are transported by the fluid. These ions can
precipitate and form a crystalline solid, which is attached to the surface
of the porous skeleton, and thus is immobile. The reverse reaction of
dissolution is also possible.
The proposed model includes the following components: the Stokes flow and
the transport of the dissolved ions by convection and diffusion, which are
processes in the void space of the medium, and the dissolution/precipitation
reactions occurring on the surface of the grains (the porous skeleton). We
pay a special attention to the dissolution rate, which is modelled by a
Heaviside type graph and thus is multivalued.
Here we assume that the flow geometry as well as the fluid properties are not
affected by the chemical processes. The case of variable geometry is
considered in another presentation given at this conference. We start with
some qualitative properties of the model for general domains, and then
consider simpler geometries. In particular, if the void space is a strip,
with dissolution and precipitation occurring at the lateral boundaries, we
investigate the formation of a dissolution front.
Further, as a first step for a rigorous derivation of the macroscopic model
we let the ratio between the thickness and the length of the strip vanish.
We end up with the upscaled transportreaction model proposed by
C.J. van Duijn and P. Knabner.
We conclude our talk with numerical experiments sustaining the theoretical
results. Some details concerning the numerical algorithm will also be
presented. 
Track/Session 
Special Sessions / MultiDisciplinary Approaches To Reactive Transport Simulation In Aquifer Systems 
Date 
20060618 
DOI 
10.4122/1.1000000483 


Vegard Kippe 
MULTISCALE METHODS FOR ELLIPTIC PROBLEMS IN POROUS MEDIA FLOW 




Author(s) 
Vegard Kippe^{1}; Jørg E. Aarnes^{1}; Vegard Kippe^{1} 
Organisation(s) 
^{1}SINTEF ICT/Applied Mathematics 
Abstract 
We will review three multiscale methods for elliptic equations in porous media flow, namely the
Mixed Multiscale Finite Element Method (MsMFEM) [1], the Multiscale Finite Volume Method
(MsFVM) [5] and Numerical Subgrid Upscaling (NSU) [2]. Common for the methods is that they are
able to produce massconservative finescale solutions as well as upscaled solutions, and may thus be
utilized as either efficient (approximate) finescale solvers or robust upscaling methods. We shall
consider the methods in both these respects, and compare them to a stateoftheart upscaling method
(Coupled LocalGlobal Upscaling [3]) combined with a finescale reconstruction procedure (Nested
Gridding [4]). In order to investigate the properties of the methods, we perform a series of numerical
experiments designed to reveal differences with regard to robustness and flexibility. In this process we
discover some shortcomings of the methods, and we discuss alternative approaches to remedy these. We
will also comment on implementational aspects and present an analysis of the computational effort
required by each of the methods.
References:
1. J. E. Aarnes, On the use of a mixed multiscale finite element method for greater flexibility and
icreased speed or improved accuracy in reservoir simulation, SIAM Multiscale Modeling and
Simulation 2 (2004), no. 3, 421439.
2. T. Arbogast, Numerical subgrid upscaling of twophase flow in porous media, Numerical Treatment
of Multiphase Flows in Porous Media (Z. Chen et. al., ed.), Lecture Notes in Physics, vol. 552, Springer,
Berlin, 2000, pp. 3549.
3. Y. Chen, L. J. Durlofsky, M. Gerritsen, and X. H. Wen, A coupled localglobal upscaling approach
for simulating flow in highly heterogeneous formations, Advances in Water Resources 26 (2003), 1041
1060.
4. Y. Gautier, M. J. Blunt, and M. A. Christie, Nested gridding and streamlinebased simulation for fast
reservoir performance prediction, Computational Geosciences 3 (1999), 295320.
5. P. Jenny, S. H. Lee, and H. A. Tchelepi, Multiscale finitevolume method for elliptic problems in
subsurface flow simulation, Journal of Computational Physics (2003), no. 187, 4767. 
Track/Session 
Special Sessions / Multiscale methods for flow in porous media 
Date 
20060618 
DOI 
10.4122/1.1000000481 


Ahmed Hassan 
Uncertainty Reduction for Parameters of a Seawater Intrusion Model using Markov Chain Monte Carlo 




Author(s) 
Ahmed Hassan^{1}; Hesham Bekhit^{2}; Jenny Chapman^{3}; Ahmed Hassan^{1} 
Organisation(s) 
^{1}Desert Research InstituteUSA and Cairo University Egypt; ^{2}Cairo University  Egypt; ^{3}Desert Research Institute  USA 
Abstract 
The Milrow underground nuclear test was one of three tests that were conducted on
Amchitka Island, Alaska. A stochastic groundwater flow and contaminant transport
model was created for the site which propagated uncertainty in input parameters
through flow and transport simulations to yield an output with a wide range of
uncertainty. The Consortium for Risk Evaluation with Stakeholder Participation
(CRESP) sponsored field efforts in the summer of 2004, which yielded data pertaining
to the location of the freshwater lens, derived from geophysical surveys on the
island. These data are compared to the groundwater model input distributions for
verification, and then the distributions are tightened around the new data for
uncertainty reduction using a Markov Chain Monte Carlo approach. The geophysical data
resulted in a transition zone location much deeper than that identified from the
salinity profile at a borehole drilled on the island near Milrow ground zero. A
number of scenarios are investigated in which reduction of parameter uncertainty
through the use of Markov Chain Monte Carlo is evaluated using the salinity data
alone, the geophysical data alone, and all data together. Due to the inconsistency
between the salinity data and the geophysical logs, the use of these data sets
combined does not yield a reduction of uncertainty similar to that obtained by using
the geophysical logs alone. A hypothetical scenario is used where the geophysical
interpretation is assumed to be consistent with the salinity data and the resulting
reduction of uncertainty is found to be significant. 
Track/Session 
Special Sessions / Modeling and managing coastal aquifers 
Date 
20060618 
DOI 
10.4122/1.1000000479 


Lieke van Roosmalen 
Effects of future climate change on groundwater in Denmark 




Author(s) 
Lieke van Roosmalen^{1}; Jens Hesselbjerg Christensen^{2}; Jens Christian Refsgaard^{3}; Karsten Høgh Jensen^{4}; Michael Butts^{5}; Lieke van Roosmalen^{1} 
Organisation(s) 
^{1}PhD. student Geological Institute, Copenhagen University; ^{2}Senior researcher, Danish Meteorological Institute; ^{3}Research professor, Geological Survey of Denmark and Greenland (GEUS); ^{4}Professor, Geological Institute, Copenhagen University; ^{5}Senior hydrologist, Danish Hydrological Institute 
Abstract 
The water supply in Denmark is entirely based on groundwater and it is therefore of
concern how climate change will affect the groundwater reserves in the future. We
have analyzed this problem by retrieving climatological output data from a regional
climate model and using this data in a distributed hydrological model, focusing on a
selected watershed in the country.
Global climate models simulate the global climate system with greenhouse gas
concentrations representing observed and possible future conditions, but their
limited regional detail makes them less suitable for hydrological impact studies.
Therefore, regional climate models with a limited model domain and higher resolution
are utilized. In this study the regional climate model HIRHAM from the Danish
Meteorological Institute is used with boundary conditions generated by the global
climate model HadAM3H from Hadley Centre. The concentrations of greenhouse gas and
aerosols, have been applied based on the IPCC SRES A2 emission scenario.
The climate model output consists of data for two time slices, one for a period
representing recent climate (19611990; control run) and one for the future climate
(20712100; scenario run). The climate output used is daily precipitation,
temperature and potential evapotranspiration, all at a 12x12 km resolution.
Climate models are subject to systematic biases, so climate model data cannot be
used directly in hydrological models. Different transfer methods exist to transfer
the signal of climate change, of which two will be examined in this study. One is
the socalled delta change approach, that alters the original hydrological model
input data with a factor deduced from the climate model output data to generate the
input data for the hydrological simulation of the future scenario. The other method
is the direct method, that uses the climate model output directly as input for the
hydrological model after correcting the climate output with factors based on the
bias between the climate model control scenario data and the original hydrological
model input data.
We use the socalled DK model as the model for the hydrological analysis. The DK
model divides Denmark into 10 regions and it is based on the distributed
hydrological model code MIKE SHE with a horizontal spatial discretization of 1 x 1
km2. One of these regions has been selected as the study area for the impact
analysis. 
Track/Session 
Special Sessions / Global Climate Change and Hydrologic Processes 
Date 
20060618 
DOI 
10.4122/1.1000000477 


Ahmed Hassan 
Assessment of Hydraulic Conductivity Upscaling Techniques and Associated Uncertainty 




Author(s) 
Ahmed Hassan^{1}; Farag Botros^{2}; Ahmed Hassan^{1} 
Organisation(s) 
^{1}Desert Research InstituteUSA and Cairo University Egypt; ^{2}Desert Research Institute and University of Nevada, Reno USA 
Abstract 
The use of numerical models for studying subsurface flow and transport has become
common practice in hydrology over the last three decades. However, hydraulic
parameters introduced to these models are still of a major concern. Data are usually
collected at a scale much smaller than that used in numerical models but by using
geostatistical techniques, available measurements can be used to stochastically
populate the entire domain of the studied area. Models built based on these
geostatistical techniques should be on the same scale as the supporting measurements
which lead to models with very large number of cells. Dealing with these numerical
models stochastically is beyond the capabilities of current computational resources.
Upscaling is the process of transforming the detailed description of hydraulic
parameters in a grid constructed at measurement scale (fine grid) to a coarser grid
with less detailed description (coarse grid) for the purpose of numerical subsurface
modeling. The fact that the coarse grid hydraulic conductivity should have a value
between the harmonic mean and arithmetic mean of the fine grid conductivities inside
this coarse grid cell led researchers to use the power average technique for the
upscaling process with exponent varying from 1.0 to 1.0. The objective of this study
is to develop a technique for assessing the uncertainty in upscaling flow and
transport parameters and the impact of this uncertainty on prediction uncertainty of
models relying on upscaled parameter values. This technique is tested using
lognormal distribution of hydraulic conductivity with small variance and exponential
covariance, results were found to match with analytical solution. 
Track/Session 
Special Sessions / Multiscale methods for flow in porous media 
Date 
20060618 
DOI 
10.4122/1.1000000475 


Rink van Dijke 
Criterion for threefluid configurations including layers in pores with nonuniform wettability 




Author(s) 
Rink van Dijke^{1}; Mohammad Piri^{2}; Ken Sorbie^{1}; Martin Blunt^{3}; Rink van Dijke^{1} 
Organisation(s) 
^{1}HeriotWatt University, Edinburgh, UK; ^{2}Princeton University, Princeton, USA; ^{3}Imperial College, London, UK 
Abstract 
Recently, a considerable effort has been made to determine the precise criteria for
threefluid configurations in pores of angular crosssections, based on capillary
entry pressures (van Dijke et al., J. Colloid Interface Sci. (2004) 184; van Dijke
and Sorbie, Proc. CMWR XV, Chapel Hill (2004); Piri and Blunt, Phys. Rev. E, 70
(2004) 061603; Helland and Skjaeveland, Proc. 8th Int. Symposium on Reservoir
Wettability, Houston (2004)). It has been shown that implementation of these
criteria in pore network models may have a large effect on the simulation of three
phase displacements processes, such as NAPL migration in the unsaturated zone and
gas injection for improved oil recovery. These configurations may contain thick
conducting fluid layers, such as oil layers residing between gas in the centre and
water in the corners of the pore, which significantly affect oil relative
permeability. For pores of uniform, but arbitrary, wettability and in the absence
of contact angle hysteresis a precise, thermodynamic, criterion for the existence
of such layers has been established before. In this paper, we derive a similar
criterion for pores of nonuniform wettability, a condition that commonly occurs
when only parts of the pore walls are exposed to oil. Moreover, we show how this
criterion depends on the different processes by which these layers form or
collapse, such as gas invasion or oil extraction, as in each process different
values of the various contact angles (advancing, receding or stationary) are
involved. This criterion for formation and collapse of layers is consistent with
the capillary entry conditions for the accompanying threephase bulk phase
displacements, which is essential for the accurate porescale modelling of three
phase flow. 
Track/Session 
Special Sessions / PoreScale Modelling: New Developments And Applications 
Date 
20060618 
DOI 
10.4122/1.1000000473 


Bernhard Becker 
THREE LARGE SCALE GROUNDWATER MODELS AT THE LOWER RHINE – COUPLING AND DATA MANAGEMENT 




Author(s) 
Bernhard Becker^{1}; Felix Notermanns^{1}; Jürgen Köngeter^{1}; Bernhard Becker^{1} 
Organisation(s) 
^{1}RWTH Aachen University, Institute of Hydraulic Engineering and Water Resources Management 
Abstract 
Three finite element groundwater models were developed to forecast the impact of
draining measures from open pit mining in the Lower Rhine Brown Coal Mining Area on
the groundwater balance. Different scenarios of resource management shall be simulated
and evaluated. One major attitude is the evaluation of measures to protect wetlands,
which are endangered by the mining drainage.
The groundwater models represent the geological units of "Erftscholle", "Rurscholle",
and "Venloer Scholle". In total, the three models cover an area of about 3070 square
kilometers
and take into account seven, eight, or nine aquifers and their separating aquitards.
We introduce the models and show the challenges of large scale modeling: besides the
multiple boundary conditions, drainage wells, infiltrations, and public and
industrial withdrawal
result in a large amount of different transient sources and sinks. Additionally, the
modeling of the open pit mining process requires a transient behaviour of soil
parameters.
The complex groundwater exchange rates between the three units used to be calculated
in an iterative process of boundary condition adjustment. To improve modeling results and
to avoid the timeconsuming process of generating boundary conditions, the groundwater
interchange now is realized by numerical coupling: finite beam elements are inserted
between the boundary nodes and replace the exchange boundary conditions. The coupled
models now are treated as one model. From the model coupling also further information
about the interaction of the geological units are expected. We describe the coupling
concept and show how the numerical coupling improves the model results.
The coupling induces various new data management tasks. Aspects of model handling
and data management are presented: The combined usage of advanced visualisation tools,
geographic information systems (GIS) and databases allows an efficient handling, updating
and checking of the large amount of model input and output data. 
Track/Session 
Special Sessions / Groundwater Optimal Management Session 
Date 
20060618 
DOI 
10.4122/1.1000000471 


Tycho Van Noorden 
Crystal dissolution and precipitation in porous media flow: variable geometry 




Author(s) 
Tycho Van Noorden^{1}; Sorin Pop^{1}; Hans Van Duijn^{1}; Tycho Van Noorden^{1} 
Organisation(s) 
^{1}Eindhoven University of Technology 
Abstract 
In this work we propose a pore scale model for crystal dissolution and
precipitation in a porous medium. Our investigations are a first step towards
an upscaled model for crystal formation in reactive porous media flows and
are motivated by the work of P. Knabner et al. (Adv. Water Res. 1995) and
C.J. van Duijn et al. (J. reine angew. Math. 2004).
We consider a porous medium that is fully saturated by a fluid in which
cations (e.g. sodium ions) and anions (e.g. chlorine ions) are dissolved.
In a precipitation reaction, n cations and m anions can precipitate in the
form of one particle of crystalline solid (e.g. sodium chloride) attached to
the surface of the grains (the porous matrix). The reverse reaction of
dissolution is also possible. As a result of the precipitation and dissolution
of crystals the geometry of the flow domain may change.
The model we propose consists of a system of coupled partial differential
equations on a variable domain. The changes in the flow domain, which occur due
to the dissolution and precipitation of crystals are modeled by a Stefanlike
boundary condition. This describes the movement of the interface between the
fluid and the crystal layer.
For simple geometries we show that solutions exist and we study their
qualitative behavior using both analytic and numerical techniques. 
Track/Session 
Special Sessions / MultiDisciplinary Approaches To Reactive Transport Simulation In Aquifer Systems 
Date 
20060618 
DOI 
10.4122/1.1000000469 


Birgitte Eikemo 
Computing singlephase transport (Timeofflight) in fractured media using a discontinuous Galerkin method 




Author(s) 
Birgitte Eikemo^{1}; Inga Berre^{1}; Helge K. Dahle^{1}; KnutAndreas Lie^{2}; Jostein R. Natvig^{2}; Birgitte Eikemo^{1} 
Organisation(s) 
^{1}Department of Mathematics, University of Bergen; ^{2}Dept. of Applied Mathematics, SINTEF ICT, Oslo 
Abstract 
Recent numerical results show that the discontinuous Galerkin method is efficient
and accurate in solving the timeofflight equation and the stationary tracer
distribution for singlephase transport in porousmedia reservoirs; see [Natvig et
al., 2006]. The efficiency is obtained by taking advantage of prior knowledge of
the direction of flow in solving the resulting system of unknowns.
In this work, we investigate the methodology presented in [Natvig et al., 2006] for
computing timeofflight in media with fractures. In particular, we examine the
discretisation of the transport model in the fractured regions of the reservoir.
Comparing the numerical results of the discontinuous Galerkin approximation with
those from a streamline simulator, we demonstrate the importance of a sufficient
gridresolution across the fractures even though they are modelled as one
dimensional lines in the twodimensional reservoir
model. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000468 


Axel Tillmann 
3D noninvasive monitoring of water flow and solute transport processes with MERIT 




Author(s) 
Axel Tillmann^{1}; Egon Zimmermann^{1}; Andreas Kemna^{1}; Harry Vereecken^{1}; Axel Tillmann^{1} 
Organisation(s) 
^{1}Forschungszentrum Jülich GmbH 
Abstract 
The noninvasive measurement of physical parameters in soils is an important
tool for observation and sustainable management of soils and aquifers so as to
preserve or to restore groundwater quantity and quality from natural or
anthropogeneous effects.
Therefore, a spatially and temporally highly resolved monitoring and
characterization of soils and aquifers is often required.
A broad range of mechanistic models that predict water flow and solute transport
in the subsurface environment is available now.
However, to use and validate these models a proper set of data must be collected,
preferrably without disturbing the soil or aquifer system.
We present MagnetoElectrical Resistivity Imaging Technique (MERIT) to monitor
fluid flow and solute transport processes at multiple scales by simultaneous
measurement
of electric potential and magnetic field data.
We performed numerical modeling of the electric potential and magnetic field
during a solute transport process in a cylindrical soil column.
The obtained synthetic data sets of the electric potential and magnetic field
were simultaneous processed by a 3D inversion algorithm of GaussNewtontype in
order to determine
the electrical conductivity distribution within the sample.
The inversion algorithm itself is based on a parameterization of the cylindrical
column as a set of functionals.
Additional knowledge about the specific hydrological process can be introduced into
the inversion scheme by chosing
an appropriate set of functionals.
The results of the inversion process depending of the chosen functional set vary in
it's reproduction
of the true model, convergence behaviour and computational speed. 
Track/Session 
Special Sessions / Hydrogeophysical data fusion 
Date 
20060618 
DOI 
10.4122/1.1000000467 


Owen Eslinger 
Discontinuous Galerkin Methods Applied to TwoPhase Flow Problems 




Author(s) 
Owen Eslinger^{1}; Mary Wheeler^{2}; Owen Eslinger^{1} 
Organisation(s) 
^{1}ERDC; ^{2}The University of Texas at Austin 
Abstract 
A set of discontinuous Galerkin (DG) finite element methods are proposed to solve
the twophase flow equations, such as the airwater system that arises in shallow
subsurface flow problems. The two timesplitting approaches detailed incorporate
primal formulations, such as the OdenBaumannBabuska DG (OBBDG), Symmetric
Interior Penalty Galerkin (SIPG), NonSymmetric Interior Penalty Galerkin (NIPG),
and Incomplete Interior Penalty Galerkin (IIPG), as well as a local discontinuous
Galerkin (LDG) method applied to the saturation equation. The twophase flow
equations presented are split into sequential and implicit pressure/explicit
saturation (IMPES) formulations.
The IMPES formulation introduced in this work uses a primal DG formulation to solve
the pressure equation implicitly at every time step, and then uses an explicit LDG
scheme for saturation equation. The LDG scheme employed advances in time via
explicit RungeKutta time stepping, while employing a Kirchoff transformation for
the local solution of the degenerate diffusion term.
DG finite element methods are naturally suited to problems subsurface flow and
transport. They can handle general meshes which may be nonconforming, they can
treat higher order approximations, and they are locally mass conservative, among
many other desirable properties. In particular, due to different rock properties
at the interface between two materials, fluid saturations may be discontinuous.
Therefore DG methods are a natural fit for this class of problems. Computational
results showing that the IMPES method proposed will hold capillary barriers while
using two capillary pressure curves in different materials are presented. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000465 


Peter King 
Connectivity Modelling of Heterogeneous Systems: Analysis and Field Study 




Author(s) 
Peter King^{1}; Mohsen Masihi^{2}; Peyman Nurafza^{2}; Peyman Nurafza^{2} 
Organisation(s) 
^{1}Professor, Imperial College London; ^{2}PhD Student, Imperial College London 
Abstract 
A statistical approach is proposed and validated against a realistic field dataset
to model connectivity of heterogeneous systems such as low to intermediate netto
gross reservoirs. An object based technique is used to model the spatial
distribution of aligned isotropic and anisotropic facies bodies. The connectivity
of the model is estimated using percolation theory. First account is made to
evaluate the effect of the aspect ratio of the facies. The outcome is two universal
curves for the connectivity and its associated uncertainty which can be used to
estimate the connectivity of all sorts of body sizes and aspect ratios very quickly.
The approach is then developed to be applicable for variable body sizes as well as
a system with oriented bodies. An effective size based on the square root of the
average area of bodies is used to represent the distribution of body sizes. For
systems with oriented bodies, a new aspect ratio is defined and the reduced
percolation thresholds of the system are determined. The results show that with
above changes the universal curves are still applicable for both orientated and
variable size systems.
Finally, a conventional facies modelling of a carbonate layered reservoir is used
to be compared with the results of the proposed method. The comparisons were in
good agreement. It is found that the new method gave reliable and broad estimate of
connectivity of the system in compare with exact and uncertain results from
modelling of real data, while the first one is so fast, the latter is so costly and
time consuming. This framework can be further extended to evaluate recovery factor
and sweep efficiency of a reservoir. The technique can also be used for preliminary
evaluation of a reservoir as a quick method which offers fast estimates of
important parameters of a reservoir based on its simple basic data. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000463 


Sayyed Hassan Tabatabaei 
Simulation model for water resource management in North MAHYAR aquifer by using of Modflow Model 




Author(s) 
Sayyed Hassan Tabatabaei^{1}; Masoud Tavasoli^{2}; Sayyed Hassan Tabatabaei^{1} 
Organisation(s) 
^{1}Shahrekord University; ^{2}Isfahan Regional Water Organization 
Abstract 
In the world today, along the development of computer science and improvement of
mathematical techniques, mathematical models can used as a strong and useful mean
to solve different problems of ground water. By means of these models, acceptable
and relatively precise results can be obtained with the lowest cost. The precision
of results obtained from mathematical model are completely dependent on the
precision of required data and definition of boundary conditions. In this research,
a widespread mathematical model (Modflow) used to simulate ground water flow in
North Mahyar aquifer. The necessary data for the model were obtained from the
information collected by Isfahan regional water organization, and field surveys.
The model was calibrated in two cases, steady and unsteady state, using information
of water year 199596. In steady state, calibration of model was done by a one
month time step with change of hydraulic conductivity using trial and error method.
In unsteady state, it was done by one eightmonth period with 30day time step and
changing storage coefficient. Then for every selected hydrodynamic coefficient in
calibration stage, a sensitivity analysis was done. Finally, the model was
verificated using water year 199697 data and after the validity of results was
proved, the model was used to assess future condition of aquifer and effect of
different management alternatives. To do these, different methods of multiple
operations of regional ground water and the water transferred from ZayandehRud
River to Mahyar plain was investigated and superior alternative was selected.
Keywords: Groundwater modeling, Modflow, North Mahyar plain and water resource
management. 
Track/Session 
Special Sessions / Groundwater Optimal Management Session 
Date 
20060618 
DOI 
10.4122/1.1000000462 


Leonardo Traversoni 
Hypercomplex approximation to vorticity 




Author(s) 
Leonardo Traversoni^{1}; Leonardo Traversoni^{1} 
Organisation(s) 
^{1}Universidad Autonoma Metropolitana 
Abstract 
We present a new approach to vortex methods using quaternionic analysis in order to
represent Navier Stokes equations only depending on vorticity as a quaternionic
variable. There are great computational advantages on doing that as well as more
accurate approximation. This approach also allows a more natural use of several
computational tools as wavelets, particularly what is called quaternionic
multiresollution analysis. Several computational results are shown. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000460 


Jantine Bokhorst 
The hydrological component of the Cabauw Experimental Site for Atmospheric Research (CESAR) 




Author(s) 
Jantine Bokhorst^{1}; Remko Uijlenhoet^{2}; Han Stricker^{2}; Jantine Bokhorst^{1} 
Organisation(s) 
^{1}Hydrology and Quantitative Water Management Group, Wageningen University, Wageningen,The Netherlands; ^{2}Hydrology and Quantitative Water Management Group, Wageningen University, Wageningen, The Netherlands 
Abstract 
It is well recognized in the weather and climate modelling community that over
shorter time scales (rainfall, surface runoff) and over longer time scales (latent
heat flux, soil moisture storage) the parameterisation of the exchange processes
from the atmosphere to the land surface and vice versa still needs considerable
improvement. Over the past decade the atmospheric research site at Cabauw has
already served as one of the prominent sites in intercomparison studies of land
atmosphere interactions (PILPS, AMIP). From the latter study it was concluded that
next to clouds and radiation interactions, the consistent description of the
interactions between the atmospheric and terrestrial hydrologic processes remains to
be achieved. However longterm time series of measurements of all the terms of the
terrestrial water budget around validation sites are in general lacking. To further
expand the opportunities at Cabauw for testing and validating landatmosphere
parameterisations, extra efforts are being put in the hydrological component.
Ultimately, this will increase the confidence in the realism of such
parameterisations.
Our goal is to improve the parameterisation of the hydrological component of land
surface  atmosphere exchanges in regional climate models through: 1) monitoring the
water budget of two nested polder areas around the Cabauw tower that are
representative for the region; 2) upscaling of the hydrologic processes and their
parameterisations to the scale of regional climate models, taking into account sub
grid variability. In this contribution, we focus on the former. The concrete
question we address is: Are we able to close the water budget for two selected areas
around Cabauw? Since 1.5 years, we have been observing the components of the water
budget in two nested areas of approximately 0.3 and 0.5 km2 around the Cabauw tower.
We employ a combination of in situ measurements (groundwater level from divers, soil
moisture storage from time domain reflectometry, water intake and discharge from
weirs, evapotranspiration by eddy covariance and precipitation from rain gauges) and
remotely sensed observations (scintillometry, weather surveillance radar). Here we
present an analysis of the data collected thus far.
Our work is part of a larger effort, called the Cabauw Experimental Site for
Atmospheric Research (CESAR). The CESAR observatory is located near the village of
Cabauw, approximately 20 km SW of Utrecht (http://www.cesarobservatory.nl) and is
operated by a consortium of major universities and research institutes. The overall
purpose of CESAR is to enhance the possibilities of the Cabauw site and to setup
and operate an observational facility with a comprehensive set of remote sensing and
in situ equipment for studies on atmospheric and land surface processes, monitoring
of longterm tendencies in climate parameters, the development of new measurement
techniques, the validation of satellite observations and climate models, and the
training of young scientists. 
Track/Session 
Special Sessions / Field measurements and simulations of landatmosphere interaction 
Date 
20060618 
DOI 
10.4122/1.1000000459 


Jostein R. Natvig 
An efficient domain decomposition method for transport in porous media. 




Author(s) 
Jostein R. Natvig^{1}; KnutAndreas Lie^{1}; Jørg Aarnes^{1}; Jostein R. Natvig^{1} 
Organisation(s) 
^{1}SINTEF ICT 
Abstract 
Convection dominated transport of fluids in a porous media is governed
by a nonlinear equation. Explicit time discretisations of this
equation are subject to a very restrictive stability condition on the
time step, due to variable background velocity and porosity fields. It
is therefore common to resort to implicit time discretisation. This
results in better stability, but one has to solve large systems of
nonlinear equations for each time step.
We present an efficient solver for hyperbolic transport equations with
positive characteristics. Our solver is based on an implicit discretisation
combined with overlapping domain decomposition. By applying an optimal
ordering algorithm for each subdomain, the discrete system of nonlinear
equations can be solved in one grid block at a time. This way, we avoid assembly
in each subdomain of a full nonlinear system. Our approach allows us to handle
large numbers of grid blocks with modest requirements on memory. Physical terms
violating our assumptions of positive characteristics (e.g., gravity and
capillary forces) can be treated by a standard operator splitting. 
Track/Session 
General Sessions / General 
Date 
20060618 
DOI 
10.4122/1.1000000457 
