Pattern formation in sedimentary rocks: Connectivity, permeability, and spatial correlations

Sedimentary rocks have complicated permeability patterns arising from the geological processes that formed them. We concentrate on pattern formation in one particular geological process, avalanches (grain flow) in wind-blown or fluvial sands. We present a simple experiment and numerical model of how these avalanches cause segregation in particle size that lead to characteristic laminated patterns. We also address the longstanding question of how such patterns are generated. We analyze data on two sandstone samples from different, but similar, geological environments, and find that the permeability fluctuations display long-range power-law correlations characterized by an exponent H. For both samples, we find H ≈ 0.82-0.90. These permeability fluctuations significantly affect the flow of fluids through the rocks. We demonstrate this by investigating the influence of long-range correlation on percolation properties, like cluster morphology. We relate these properties to characteristics important for hydrocarbon recovery such as breakthrough time for injected fluids and recovery efficiency.