Stochastic study on groundwater flow and solute transport in a porous medium with multi-scale heterogeneity
Hu Bill X.; Wu Jichun; Panorska Ania K.; Zhang Dongxiao; He Changming
Advances in Water Resources 26(5): 541-560
ISSN/ISBN: 0309-1708 DOI: 10.1016/s0309-1708(03)00003-4
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 study domain is characterized by an indicator function and the conductivity field within each material is assumed to be statistically stationary. Based on this assumption, the covariance function of log-hydraulic conductivity in the composite field is analytically derived and expressed in terms of the covariance of the indicator function and the statistics of log conductivity in every material. The NMM is used to investigate the effects of various uncertain parameters on flow and transport predictions in two case studies. It is shown from the case studies that the two-scale stochastic processes will both significantly influence the flow and transport predictions, especially for the variances of hydraulic head and solute fluxes. The case studies also show that the NMM can be used to study flow and transport in complex subsurface environments. In comparison with Monte Carlo simulation, NMM results are consistent with those obtained by Monte Carlo simulation method even when the total variance of log conductivity is larger than 1.