On Conjectures for the Higher-Order Transverse Macrodispersion Coefficient in Randomly Heterogeneous Porous Media
Abstract
The existing stochastic analyses of solute transport are mostly only valid for the mild heterogeneous porous media although the field data often show strong heterogeneity. There is a need to evaluate the effect of strong heterogeneity on the solute transport. Based on the existing results of perturbation theory in the literature, we proposed two conjectures for the higher-order transverse velocity covariance and their associated macrodispersion coefficients. The first conjecture is in an exponential form as used in approximating the saturated and unsaturated effective hydraulic conductivity in the literature. The second conjecture is of an algebraic form with a power of 3/4 and leads to a better fit for the results of Monte Carlo simulation found in the literature. Theoretical macrodispersion coefficients are investigated for the first-order advective transport associated with different forms of velocity covariance including first-order (in variance of log hydraulic conductivity), second order, and two possible conjectured higher-order forms. Both conjectures show a peak transverse macrodispersion coefficient growing with the variance of log-conductivity. The first conjecture shows that it will lead to a longer non-Fickian stage in reaching the asymptotic macrodispersion coefficient than the second conjecture. The proposed two high-order velocity covariances will generate plumes which both grow faster than the first-order approximation. The first conjecture of velocity covariance generates a larger transversal macrodispersion coefficient than the second one.
- Publication:
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AGU Spring Meeting Abstracts
- Pub Date:
- May 2004
- Bibcode:
- 2004AGUSM.H41D..01H
- Keywords:
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- 1829 Groundwater hydrology;
- 1832 Groundwater transport;
- 1869 Stochastic processes