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

Abstract

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 (1-500nm). 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.

Quantifying Pore Width Effects on Diffusivity via a Novel 3D Stochastic Approach with Input from Atomistic Molecular Dynamics Simulations

“…29,30 Apostolopoulou et al recently implemented stochastic kinetic Monte Carlo (KMC) simulations to study fluid transport across pore networks. 31 KMC methods can access long time scales (up to ms and, in some cases, hours) and large spatial scales (nm to μm) at comparatively low computational expense. 32,33 For example, in a bottom-up 1D approach, Apostolopoulou et al 1) used previously reported MD data to inform the KMC model, 2) simplified a 3D, 2-phase system consisting of confined liquid water and methane into a 1D problem, and 3) obtained KMC transport data in quantitative agreement with atomistic MD simulations at a fraction of the computational cost.…”

Evidence of Facilitated Transport in Crowded Nanopores

“…A comprehensive understanding of the fundamental mechanisms responsible for carbon bearing-fluid migration in the presence of CO 2 /H 2 S is crucial for risk assessment and site selection for geologic CCS, monitoring H 2 S emissions, and perhaps identifying innovative enhanced oil recovery (EOR) processes that use CO 2 and H 2 S. , Because a thorough quantification of the phenomena that govern fluid transport in the complex heterogeneous pore networks found in organic-rich shale caprocks, which consist of crowded nanopores that provide poor connections between dispersed pockets of organic matter, remains elusive, because of practical difficulties in observing fluid transport in such complicated systems, computational approaches could be helpful. − …”

A Novel Modeling Approach to Stochastically Evaluate the Impact of Pore Network Geometry, Chemistry and Topology on Fluid Transport

“…Our KMC approach, applied to 1D, 2D and 3D pore networks, is described by Apostolopoulou et al (2017Apostolopoulou et al ( , 2019a. The underlying model of the KMC simulation is the Master equation (Eq.…”