Direct simulation of supercritical gas flow in complex nanoporous media and prediction of apparent permeability

• Developed local effective viscosity lattice Boltzmann model with non-zero slip
• Apparent permeability of finite length tubes significantly decreases for 0.02 < Kn < 1.
• Bundle of tubes models overestimate k(abs), k(app) of organic matter pore systems.
• Bundle of tubes models fail to capture k(app)/k(abs) — pressure trends.
• Pore size distribution alone insufficient predictor of apparent permeability

Mudrocks and shales contain pores within the size range of 2–100 nm. Flow of supercritical gas in these pores at reservoir pressure–temperature conditions falls within the slip-flow and early transition-flow regime (0.001 < Kn < 1.0). Currently, the description of supercritical gas flow in these flow regimes is mostly limited to simple tube and channel geometries that are of limited applicability to the sponge-like or platy nanoporous geometry in organic matter or clays. Here, we present a local-effective-viscosity multi-relaxation-time lattice Boltzmann model (LEV-LBM) designed to simulate gas flow in the slip- and early-transition-flow regimes in complex geometries. The LEV-LBM is informed with local effective viscosities at each node to capture the variance of the mean free path of gas molecules in a bounded system. The corrected mean free path for each lattice node is determined using a three-dimensional wall function adaptable to complex pore geometries. To enforce a non-zero slip velocity at solid boundaries, a combined diffusive bounce-back scheme is applied to the pore-walls. The LEV-LBM is first validated in simple tube geometries, where good agreement is found for Knudsen numbers up to 1.0. We then use the LEV-LBM to quantify the finite tube length effect and comment on the implications for pore-network models. We finally demonstrate the utility of the LEV-LBM by simulating pure methane flow in digital reconstructions of nanoporous organic matter at reservoir conditions, and compare the results to bundle of tubes models. We show that the bundle of tubes models overestimate apparent permeability by factors between 1.52 and 153, due to the non-trivial dependence of flow on pore space connectivity and shape.

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