Theoretical Generalization of Markov Chain Random Field in Reservoir Lithofacies Stochastic Simulation

This paper mainly focuses on the theoretical generalization of Markov chain random field (MCRF) model and discusses its application in reservoir lithofacies stochastic simulation. We first introduce the fully independent and conditional independent assumptions of multidimensional Markov chain models. The Equivalence of Markov property and conditional independence is derived explicitly based on the Bayes’ theorem, which completes the theoretical foundation of MCRF. The MCRF model is then applied to the lithofacies identification of a region in China, and the results are compared with those by fully independent assumption. Analyses show that conditional independent-based MCRF model performs better in maintaining the percentage composition of each lithofacies and reproducing the geological continuity of lithofacies distribution.