In this study, a numerical moment method (NMM) is applied to study groundwater flow and solute transport in a multiple-scale heterogeneous formation. The formation is composed of various materials and conductivity distribution within each material is heterogeneous. The distribution of materials in the domain under study is characterized by an indicator function and the conductivity field within each material is assumed to be statistically stationary. Based on this assumption, a general expression is derived for the covariance function of the composite field in terms of the covariance of the indicator variables and the properties of the composite materials. The NMM is used to investigate the effects of various uncertain parameters on flow and transport predictions in the case study. It is shown from the study results that the two-scale stochastic processes of heterogeneity will both significantly influence the flow and transport predictions, especially for the variances of hydraulic head and solute fluxes.
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