Changming He

Stochastic study on groundwater flow and solute transport in a porous medium with multi-scale heterogeneity

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.

On stochastic modeling of groundwater flow and solute transport in multi-scale heterogeneous formations

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, a general expression is derived for the covariance function of the composite field in terms of the covariance of the indicator variables and the statistical properties of the composite materials. 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 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. This study also shows that the NMM can be used to study flow and transport in complex subsurface environments. Therefore, the method may be applicable to complex environmental projects.

Using sequential self-calibration and genetic algorithm methods to optimally design tracer test for estimation of conductivity distribution

Limiting the quantity of field test data needed to obtain an accurate estimate of a hydraulic conductivity field is a continuing challenge for hydrogeologists. A gradientbased inverse method, the sequential self-calibration (SSC) method, conditioned using tracer test data is presented as a means for estimation of hydraulic conductivity fields. To improve the calculation efficiency of sensitivity coefficients, a fast streamline-based approach was applied to compute the derivative of concentration with respect to the changes of hydraulic conductivity. The performance of SSC method was tested using a synthetic aquifer with a sandwich-like geologic structure, in which hypothetical tracer tests were conducted. The SSC method was also used to assess the impact of sampling well locations and the number of sampling wells on the estimation accuracy of the hydraulic conductivity field. A genetic algorithm, combined with the SSC method, was applied to estimate the optimal tracer test design plan. We found that the estimation accuracy of the hydraulic conductivity field increased with an increase in the number of the sampling wells, but the rate of increase in the estimation accuracy decreased as the number of sampling wells increased. The estimation accuracy was also significantly influenced by the locations of the sampling wells. The optimal sampling well locations were dependent on the geologic structure.