Characterization of non-Gaussian hydraulic conductivity fields using multiple-point geostatistics and ensemble smoother with multiple data assimilation method

In alluvial aquifers, hydraulic conductivity usually follows non-Gaussian distribution due to litho-facies heterogeneity. It is still a great challenge to characterize the non-Gaussian aquifers. The ensemble smoother with multiple data assimilation (ESMDA) is an effective and low-cost inversion method, but only works for the Gaussian fields. The multiple-point geostatistics methods (MPS) are widely used to estimate the non-Gaussian fields, but cannot integrate dynamic data (e.g., piezometric head and concentration) for highly parameterized inversion. In this work, we developed a new data assimilation framework, ESMDA-DS, by coupling the Direct Sampling method (DS, one of Multiple-point geostatistics method) and ESMDA method. The performance of the ESMDA-DS is demonstrated by three synthetic cases. The influence of different observation data types on parameter estimation are also discussed. For Case 1, only piezometric head data are assimilated. For Case 2, both piezometric head and concentration data are assimilated simultaneously. For Case 3, the piezometric head, concentration and hydraulic conductivity observation data are assimilated together. The results show that the ESMDA-DS method can not only preserve the non-Gaussian pattern, but also incorporate the dynamic data to identify the non-Gaussian aquifers with a high resolution. Case 3 has the highest accuracy to estimate the non-Gaussian field and predict the evolution of piezometric head and concentration, Case 2, the second, and Case 1 the worst, which demonstrate that integration of multiple data can improve the accuracy of parameter estimation and has a better performance for model prediction.