Enhancing multiple-point geostatistical modeling: 2. Iterative simulation and multiple distance function

Abstract

This series addresses a fundamental issue in multiple-point statistical (MPS) simulation for generation of realizations of large-scale porous media. Past methods suffer from the fact that they generate discontinuities and patchiness in the realizations that, in turn, affect their flow and transport properties. Part I of this series addressed certain aspects of this fundamental issue, and proposed two ways of improving of one such MPS method, namely, the cross correlation-based simulation (CCSIM) method that was proposed by the authors. In the present paper, a new algorithm is proposed to further improve the quality of the realizations. The method utilizes the realizations generated by the algorithm introduced in Part I, iteratively removes any possible remaining discontinuities in them, and addresses the problem with honoring hard (quantitative) data, using an error map. The map represents the differences between the patterns in the training image (TI) and the current iteration of a realization. The resulting iterative CCSIM - the iCCSIM algorithm - utilizes a random path and the error map to identify the locations in the current realization in the iteration process that need further "repairing;" that is, those locations at which discontinuities may still exist. The computational time of the new iterative algorithm is considerably lower than one in which every cell of the simulation grid is visited in order to repair the discontinuities. Furthermore, several efficient distance functions are introduced by which one extracts effectively key information from the TIs. To increase the quality of the realizations and extracting the maximum amount of information from the TIs, the distance functions can be used simultaneously. The performance of the iCCSIM algorithm is studied using very complex 2-D and 3-D examples, including those that are process-based. Comparison is made between the quality and accuracy of the results with those generated by the original CCSIM algorithm, which demonstrates the superior performance of the iCCSIM.