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arXiv · 1806.10628

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

Zhijie Xu·Alexandre M. Tartakovsky
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Abstract

This work presents a hierarchical model for solute transport in bounded layered porous media with random permeability. The model generalizes the Taylor-Aris dispersion theory to stochastic transport in random layered porous media with a known velocity covariance function. In the hierarchical model, we represent (random) concentration in terms of its cross-sectional average and a variation function. We derive a one-dimensional stochastic advection-dispersion-type equation for the average concentration and a stochastic Poisson equation for the variation function, as well as expressions for the effective velocity and dispersion coefficient. We observe that velocity fluctuations enhance dispersion in a non-monotonic fashion: the dispersion initially increases with correlation length λ, reaches a maximum, and decreases to zero at infinity. Maximum enhancement can be obtained at the correlation length about 0.25 the size of the porous media perpendicular to flow.

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Zhijie Xu, Alexandre M. Tartakovsky. 2018-06-25. Method of model reduction and multifidelity models for solute transport in random layered porous media. https://doi.org/10.1103/physreve.96.033314

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