Estimating permeability in shales and other heterogeneous porous media: Deterministic vs. stochastic investigations

With increasing global energy demands, unconventional formations, such as shale rocks, are becoming an important source of natural gas. Extensive efforts focus on understanding the complex behavior of fluids (including their transport in the sub-surface) to maximize natural gas yields. Shale rocks are mudstones made up of organic and inorganic constituents of varying pore sizes (1-500 nm). With cutting-edge imaging technologies, detailed structural and chemical description of shale rocks can be obtained at different length scales. Using this knowledge to assess macroscopic properties, such as fluid permeability, remains challenging. Direct experimental measurements of permeability supply answers, but at elevated costs of time and resources. To complement these, computer simulations are widely available; however, they employ significant approximations, and a reliable methodology to estimate permeability in heterogeneous pore networks remains elusive. For this study, permeability predictions obtained by implementing two deterministic methods and one stochastic approach, using a kinetic Monte Carlo algorithm, are compared. This analysis focuses on the effects resulting from pore size distribution, the impact of micro- and macropores, and the effects of anisotropy (induced or naturally occurring) on the predicted matrix permeability. While considering multiple case studies, recommendations are provided on the optimal conditions under which each method can be used. Finally, a stochastic analysis is performed to estimate the permeability of an Eagle Ford shale sample using the kinetic Monte Carlo algorithm. Successful comparisons against experimental data demonstrate the appeal of the stochastic approach proposed.