A numerical method of moments for solute transport in a porous medium with multiscale physical and chemical heterogeneity

In this study, geostatistical and stochastic methods are used to study groundwater flow and solute transport in a multiscale heterogeneous formation. The formation is composed of various materials, and distributions of conductivity and chemical sorption coefficient within each material are heterogeneous. The random distributions of materials in the formation are characterized by an indicator function. The conductivity and chemical sorption coefficient fields in each material are assumed to be statistically stationary. On the basis of these assumptions a general expression is derived for the covariance function of the composite field in terms of the covariance of the indicator variable and the properties of the composite materials. Darcy's law and perturbation method are applied to develop the covariance of the retarded velocity. The numerical method of moments [Zhang et al., 2000; Wu et al., 2003a, 2003b] is used to study the effects of various uncertain parameters on flow and transport predictions. Case studies have been conducted to investigate the influences of a medium's physical and chemical heterogeneity and nonstationarity on solute flux prediction. The study results indicate that the large-scale heterogeneity dominates the effects on flow and solute transport processes, and the effect of small-scale heterogeneity is secondary. It is also shown from the case studies that the numerical method of moments is applicable to studying flow and solute transport in complex subsurface environments, especially for the uncertainty analysis. Monte Carlo simulation is also conducted, and the results are compared with those obtained through method of moment. The calculation results of the mean total solute flux by the two methods match very well, but the variance of total solute flux obtained by the method of moments is smaller than that by the Monte Carlo method, especially for the cases with large total variances of the conductivity and sorption coefficient. In comparison with the Monte Carlo simulation, the method of moments is much more efficient in calculation.