Monte Carlo simulations of flow and transport in heterogeneous porous media: An evaluation of first- and second-order theories and the importance of porosity variability

Ahmed Emam Ahmed Hassan, Purdue University

Abstract

Monte Carlo simulations are employed to study flow and transport in randomly heterogeneous porous media. The aquifer heterogeneity is represented by random conductivity, porosity and geochemistry (distribution coefficient and reaction rate) fields. These aquifer properties are generated from fractional Brownian and other distributions, and are used with the flow and transport equations in two-dimensional settings. An implicit finite difference scheme is used to solve the flow equation, whereas a random-walk, particle-tracking approach is employed to simulate the transport equation. A Monte Carlo simulation is used to test the predictions of an Eulerian nonlocal transport theory and to examine the extent to which the theory, with the underlying assumptions, hold. Theoretical predictions are found to be in close agreement with the Monte Carlo simulations when the fluctuating log-conductivity variance is small and the integral scale is short. Localization errors are also addressed and found to increase as the log-conductivity variance or its integral scale increases. The Monte Carlo method is also used to test the first-order solution to the flow equation. When the variance of the fluctuating log-conductivity, $\sigma\sbsp{f}{2},$ is small, the first-order solution is adequate, however, as $\sigma\sbsp{f}{2}$ grows so does the error. This result suggest a second-order correction is needed and such a correction is tested and found to be in good agreement with the Monte Carlo results for conductivity variances on the order of unity. The importance of including local-scale dispersion in the transport process is investigated. It is found that purely convective models agree with the convective-dispersive model when local dispersivity is small. However, as local dispersivity grows, the purely convective models gradually break down. Monte Carlo simulations are also used to explore the significance of porosity variability to flow and transport processes in heterogeneous systems. Porosity variability has a significant influence on the evolution of contaminant plumes when it is correlated to the conductivity field. The results reveal that the combination of geochemistry variability and porosity variability leads to results that are markedly different than if only one variability is considered. Further, porosity variability may be much more important than higher-order head and velocity corrections to the velocity covariance function. The movement and dispersion of the lithium plume at the Cape Cod site is simulated using the Monte Carlo method. A random porosity that is negatively correlated to the hydraulic conductivity yields better results than deterministic porosity. The geochemistry is represented by a spatially varying distribution coefficient negatively correlated to the conductivity. A linear nonequilibrium sorption isotherm with a slow reaction rate may be used to reproduce the observed spatial moments.

Degree

Ph.D.

Advisors

Cushman, Purdue University.

Subject Area

Civil engineering|Hydrology

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