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This work presents a hierarchical model for solute transport in boundedlayered porous media with random permeability. The model generalizes theTaylor-Aris dispersion theory to stochastic transport in random layered porousmedia with a known velocity covariance function. In the hierarchical model, werepresent (random) concentration in terms of its cross-sectional average and avariation function. We derive a one-dimensional stochasticadvection-dispersion-type equation for the average concentration and astochastic Poisson equation for the variation function, as well as expressionsfor the effective velocity and dispersion coefficient. We observe that velocityfluctuations enhance dispersion in a non-monotonic fashion: the dispersioninitially increases with correlation length {\lambda}, reaches a maximum, anddecreases to zero at infinity. Maximum enhancement can be obtained at thecorrelation length about 0.25 the size of the porous media perpendicular toflow.

Method of model reduction and multifidelity models for solute transport in random layered porous media