Direct numerical simulation of supercritical gas flow in complex nanoporous media: Elucidating the relationship between permeability and pore space geometry

Abstract:

Mudrocks and shales are currently a significant source of natural gas and understanding the basic transport properties of these formations is critical to predicting long-term production, however, the nanoporous nature of mudrocks presents a unique challenge. Mudrock pores are predominantly in the range of 1-100 nm, and within this size range the flow of gas at reservoir conditions will fall within the slip-flow and early transition-flow regime (0.001 < Kn < 1.0). Therefore, flow-rates will significantly deviate from Navier-Stokes predictions. Currently, the study of slip-flows is mostly limited to simple tube and channel geometries, but the geometry of mudrock pores is often sponge-like (organic matter) and/or platy (clays). Here we present a local effective viscosity lattice Boltzmann model (LEV-LBM) constructed for flow simulation in the slip- and early-transition flow regimes, adapted here for complex geometries. At the macroscopic scale the LEV-LBM is parameterized with local effective viscosities at each node to capture the variance of the mean free path of gas molecules in a bounded system. The LEV-LBM is first validated in simple tube geometries, where excellent agreement with linearized Boltzmann solutions is found for Knudsen numbers up to 1.0. The LEV-LBM is then employed to quantify the length effect on the apparent permeability of tubes, which suggests pore network modeling of flow in the slip and early-transition regime will result in overestimation unless the length effect is considered. Furthermore, the LEV-LBM is used to evaluate the predictive value of commonly measured pore geometry characteristics such as porosity, pore size distribution, and specific solid surface area for the calculation of permeability. We show that bundle of tubes models grossly overestimate apparent permeability, as well as underestimate the increase in apparent permeability with decreasing pressure as a result of excluding topology and pore shape from calculations.