XVI International Conference on Computational Methods in Water Resources (CMWRXVI) Ingeniørhuset  

Numerical evaluation of diffusive and dispersive transport in periodic porous media  Paper   

Author:  Alexandre Ern <ern@cermics.enpc.fr> (CERMICS  ENPC) 
 Luc Dormieux <dormieux@lmsgc.enpc.fr> (LMSGC  ENPC) 
 Pierre Tardif d'Hamonville <pierredh@cermics.enpc.fr> (CERMICS  ENPC) 
Presenter:  Pierre Tardif d'Hamonville <pierredh@cermics.enpc.fr> (CERMICS  ENPC) 
Date:
 20060618
Track:
Special Sessions
Session:
PoreScale Modelling: New Developments And Applications 
DOI:  10.4122/1.1000000231 
DOI:  10.4122/1.1000000232 

At the macroscopic scale, the transport of a fluid component
in a porous medium is governed by advective, diffusive, and dispersive
fluxes. The two latter fluxes are formulated using a
diffusion tensor and a dispersion tensor. The actual value of these
tensors depends on the pore geometry and on the magnitude of the
advection velocity.
Using the double scale expansion technique
and provided
the problem is homogeneizable, it is wellknown that the
the diffusion and
dispersion tensors can be evaluated from the following procedure.
First, a velocity field at the pore scale is obtained
by solving a Stokeslike problem. Then, this
velocity field is used in a vectorvalued
advectiondiffusion equation,
still posed at the pore scale, and from which solution the
the diffusion and
dispersion tensors are evaluated.
Since we are interested in 3D pore geometries for which
analytical solutions are not available,
we use the finite element method to approximate the pore scale velocity
field and to solve the vectorvalued
advectiondiffusion equation. Three strategies for approximating
the pore scale velocity field are proposed and analyzed. The first uses
nodal Lagrange finite elements with Galerkin/Least Squares
stabilization. The second uses mixed CrouzeixRaviart/P_0 finite
elements. The third uses the previous mixed finite elements and then
projects the velocity field onto a vector space of divergencefree
fields using BrezziDouglasMarini finite elements.
We perform numerical simulations for cubic and centered cubic networks
of spheres, with several values of the porosity. We also vary the
velocity magnitude to study its effect on the diffusion and dispersion
tensors. 