The mathematical equivalence of a closed second-order transport equation fo
r 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 transformin
g the second-order equation to canonical form. The derivation of this equiv
alence is limited to media with heterogeneities in a plane orthogonal to th
e flow direction which represents a bidirectional generalization of the str
atified case. Results indicate how the parameters of the bicontinuum formul
ation can be obtained from statistical descriptions of this heterogeneity a
nd 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 spa
tially 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 thei
r variances.