An Improved Reservoir Model Calibration through Sparsity Promoting ES-MDA

The reconstruction of subsurface geological features from production data defines an inverse problem related to data assimilation, which has long been a challenge in the reservoir engineering community due to the small number of observations available. Recently the Ensemble Smoother with Multiple Data Assimilation (ES-MDA) method has become popular for this task. However, the conventional ES-MDA framework fails to accurately capture non-Gaussian spatial distributions, for example in channelized reservoirs. In those cases, novel image processing techniques based on sparsity representations provide an interesting tool for enabling us to incorporate prior information in the assimilation task and thereby improve final results. In the work presented here we will reformulate this inverse problem as a sparse field recovery task which will then be solved, in contrast to previous work, by using a combination of ES-MDA and sparsity enhancing techniques, in particular K-SVD (an acronym for K-means and Singular Value Decomposition) and Orthogonal Matching Pursuit (OMP).