American Society of Civil Engineers

Flow and Solute Transport in Strongly Heterogeneous Porous Media

by Kuo-chin Hsu, (corresponding author), (Assistant Professor, Dept. of Resources Engineering, National Cheng-Kung Univ., Tainan, Taiwan E-mail:

Practice Periodical of Hazardous, Toxic, and Radioactive Waste Management, Vol. 8, No. 3, July 2004, pp. 148-154, (doi:

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Document type: Journal Paper
Abstract: 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.

ASCE Subject Headings:
Stochastic processes
Radioactive wastes