Studying the Effect of Correlation and Finite-Domain Size on Spatial Continuity of Permeable Sediments

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The percolation of high-permeability cells in geo-reservoir models is affected by cluster correlation and by lattice size. These affects are studied using an analytical methodology, presented as a useful augmentation to Monte Carlo approaches. The analytical method compares Euclidean cluster size distributions between random and correlated lattices. It shows that correlation affects both high-permeability (sand) and low-permeability (clay) clusters equally, and thus correlation does not likely affect the percolation threshold for infinite lattices. On finite lattices, the analysis shows that the effect of correlation on lowering the percolation threshold can be understood through the truncation of clay cluster-size distributions, without the need for Monte Carlo simulations.