Subsurface characterization using a cellular automaton approach

In this paper, a random Cellular Automaton model is developed to characterise heterogeneity of geological formations. The CA-model is multilateral and can be easily applied in both two and three dimensions. We demonstrate that conditioning on well data is possible and the method is numerically efficient. To construct the model, the subsurface is subdivided into N cells, with an initial lithology assigned to each cell. Rules to update the current cell states are chosen from a set of rules, independently for each cell. The model converges typically in less than 50 iterations to a steady state or periodic solution. Within one period the realisations exhibit similar statistical properties. The final fraction of the various lithologies can be tuned by choosing the proper initial fractions. In this way, geological knowledge of those fractions can be satisfied.