
Abstract  We provide a physically based explanation for the complex macroscopic behavior of
longitudinal and transverse dispersion in porous media as a function of Peclet
number, Pe. A Lagrangian porescale transport model incorporating flow and molecular
diffusion is applied in 2D and 3D lattices of throats with square crosssection
whose characteristics are representative of Berea sandstone. The model accurately
predicts NMR, laser fluorescence and the classic breakthrough data for the
experimental dependence of the longitudinal dispersion coefficient, DL, on Pe. We
compute the probability, y(t)dt that a particle moves from one throat junction to a
nearest neighbor junction in the time interval t to t+dt and fit it to the simple
analytical expression, that depends on the mean advective transit time, a latetime
diffusive cutoff and a parameter b characterizing the distribution of transit
times between pores. Then, interpreting transport as a continuous time random walk,
we show: (1) that the powerlaw dispersion regime is controlled by the variation in
average velocity between throats (the distribution of local Pe rather than by
diffusion from boundary layers within throats, giving with d = 3b »1.2; (2) the
crossover to a linear regime for for Pe > Pecrit ≈ 400 is due to a transition
from a diffusioncontrolled latetime cutoff, to transport governed by advective
movement; and (3) that the transverse dispersion coefficient for all Pe >>1. We
provide a quantitative description of both asymptotic and preasymptotic dispersion
using CTRW with a physical interpretation of the parameters.
Hence, through an analysis of experiment, numerical modeling and theory we provide a
physical explanation of the subtle and surprising dependence of dispersion
coefficients in porous media on Pe. Our demonstration that the powerlaw dependence
of dispersion coefficient on Pe is due to the distribution of flow speeds in
individual pores contrasts with the traditional theories of Saffman and Koch and
Brady that emphasize the contribution to dispersion within pores or at pore
junctions. 
Track/Session  Special Sessions / PoreScale Modelling: New Developments And Applications 
Author(s)  Branko Bijeljic^{1}; Martin Blunt^{1}; Branko Bijeljic^{1} 
Organisation(s)  ^{1}Imperial College 
Dates  20060618 
DOI  10.4122/1.1000000218 
