Equivalence of bicontinuum and second-order transport in heterogeneous soils and aquifers

The mathematical equivalence of a closed second-order transport equation for reactive solutes in saturated heterogeneous porous media (e.g., soils and aquifers) and a two-region, mobile-mobile, formulation is demonstrated in two ways: (1) by averaging the bicontinuum equations and (2) by transforming the second-order equation to canonical form. The derivation of this equivalence is limited to media with heterogeneities in a plane orthogonal to the flow direction which represents a bidirectional generalization of the stratified case. Results indicate how the parameters of the bicontinuum formulation can be obtained from statistical descriptions of this heterogeneity and establish a stochastic interpretation for the bicontinuum equations. One-dimensional analytical solutions of the equivalent transport equations are compared to a three-dimensional numerical simulation of transport in a spatially autocorrelated lognormal random conductivity field. Results indicate that the upscaled equations provide good approximations of the dynamics of the mean resident concentration, the flux-averaged concentration, and their variances.