Stochastic reactive transport in porous media: higher-order closures

An Eulerian moment expansion through σvN (σv2 is the velocity variance) is developed for reactive chemical transport in heterogeneous porous media with linear non-equilibrium sorption. Both the hydraulic conductivity and sorption partition coefficients are treated as spatial random variables to account for physical and chemical heterogeneities. The theory provides a self-consistent recursive solution to the closure problem associated with Eulerian methods. The closed form of the mean concentration up to O(σv4) (or second order in terms of σv2) is explicitly expressed in spatial-Fourier and temporal-Laplace space and numerically inverted to real space via FFT. The second-order transport solution is combined with a first-order solution to the flow equation and used to calculate the mean concentration as well as the spatial moments. The calculated second-order and first-order results are compared with Monte Carlo simulated results. The results demonstrate that the first-order solution is equivalent to a non-local reactive transport theory. The second-order correction to the reactive transport solution slightly decreases the second longitudinal moment, but significantly increases the second transverse moment and decreases the skewness of the plume. The comparison among the first-order, second-order and Monte Carlo simulated results also reveals that the Monte Carlo simulated second longitudinal moment is closer to the second-order corrected longitudinal moment, but the Monte Carlo simulated second transverse moment is much closer to the first-order solution. Moreover, the second-order correction significantly increases the fourth moments, especially in the transverse direction.