CHDS: conflict handling in direct sampling for stochastic simulation of spatial variables

Abstract

In recent years, multiple-point geostatistical (MPS) approaches have gained significant popularity for modeling subsurface heterogeneity in hydrogeological systems by employing a training image for describing the features of the target field. The most important challenges of MPS simulation methods include appropriate pattern reproduction and connectivity preservation, handling conditional data, and appropriately modeling the variability of real fields. Preserving connectivity of the patterns is of paramount importance, particularly in fluid flow modeling problems. During sequential simulation, if the algorithm produces a value (or patch) inconsistently with previously synthesized data, such conflicts will propagate in the realization and lead to poor pattern reproduction. Here, we have introduced a two-step simulation algorithm, where in the first phase, the coarse structure of the realization is synthesized with minimum conflicts by rejecting inconsistent patterns and allowing removing previously synthesized data, and in the second phase, the fine grid is simulated by ignoring the conflicts. Ignoring short-range inconsistencies in the fine simulation phase not only improves the algorithm’s convergence but also leads to higher variabilities without sacrificing the quality of the realizations. Convergence problems of traditional conflict-handling methods are further alleviated by a new distance reweighting strategy, which prevents cyclic deletions and resimulations. We have employed different statistical descriptors to evaluate our method in comparison with existing pixel and patch-based methods in conditional and unconditional modes. The proposed method shows outstanding results in terms of connectivity preservation, conditional data handling, and pattern innovation. Compared to traditional conflict-handling methods, the proposed method shows good convergence and histogram preservation.