Flow and solute transport in strongly heterogeneous porous media

The stochastic analysis of flow and solute transport provides the required probabilistic information for the risk assessment of hazard and radioactive waste management. Only low-order approximations of the velocity covariance based on the perturbation theory exit in literature. The high-order stochastic theory is needed to describe the flow and solute transport in strongly heterogeneous porous media. A conjecture on the high-order transverse velocity covariance is proposed in this study. It is based on the analytical results of first- and second-order velocity covariances from the perturbation theory. The conjecture is of an algebraic form with a power of 3/4. It leads to a good fit with the results of Monte Carlo simulations found in literature. Theoretical transverse macrodispersion coefficients are investigated for the first-order advection transport associated with different forms of velocity covariances including first-order (in variance of log-hydraulic conductivity), second-order, and the conjectured high-order forms. The conjecture shows a peak transverse macrodispersion coefficient growing with the variance of log conductivity. The proposed high-order velocity covariance will generate plumes that grow faster than the first-order but slower than the second-order approximation. The validity of the conjecture requires further investigation.