The use of discrete Markov random fields in reservoir characterization

In this work, we discuss relevant aspects concerning the use of discrete Markov random fields (MRF) in the simulation of rock properties in petroleum reservoirs. The Strauss multi-color model is useful to describe complex image configurations, by handling with parameters of repulsion between the different rock facies, symbolized in this case, by the different colors. The transition between the facies and the porous medium anisotropy are imposed to the system, and it is possible to generate various types of arrangement of the facies on the image, in contrast to Gaussian stochastic process, that can only simulate diffusion-type images. Another point focused is the behavior of the spatial correlation in discrete Markov random fields, here studied by the calculus of the practical semivariogram function in the binary Markov images, generated by using the Metropolis algorithm. These images have a correspondence to Gaussian images with Gaussian-type correlation, after truncated in binary facies. This similarity is validated by analysis in the behavior of the semivariogram function of the discrete Gaussian processes.