Explaining longitudinal hydrodynamic dispersion using variance of pore size distribution

Arriaza, Juan Lopez and Ghezzehei, Teamrat A.

Journal of Porous Media, vol. 16(1), pp. 11–19 , 2013.

Keywords

porous media, transport, stochastic methods

Abstract

Hydrodynamic dispersion is responsible for spreading of dissolved mass within a single phase in porous media. It typically arises because of variability in local flow velocities. Because the pattern of spreading by dispersion is similar to Fickian diffusion, dispersion has been traditionally modeled as a pseudo-diffusive process that depends on the concentration gradient. However, there is no physical basis for this dependence of dispersion on concentration gradient. This unphysical formulation of dispersive flux has led to a number of major shortcomings including (a) lack of a self-consistent, mechanistic, and independent approach for predicting dispersion coefficient; and (b) dependence of the dispersion coefficient on transport distance. In this paper we show that the shape of dispersive spreading can be described using a model based on a variably sized bundle of capillaries and purely advective transport. The model suggests that dispersion can be described in terms of the variance of the pore size distribution only. Breakthrough curves of the proposed model can be exactly matched with the traditional diffusive-type dispersion model. By utilizing this equivalence, we derived relationships between the traditional dispersivity coefficient, pore size variance, and transport distance. The plausibility of the proposed expressions was tested using three illustrative examples that compare aspects of the proposed model with measurements obtained from the literature.