Mechanisms of viscous compressible flow in semi-sealed porous media

Viscous compressible flow in a semi-sealed porous medium is attracting increasing attention due to recent interest in gas reservoir and energy storage. Such a flow is driven by the volumetric expansion of the fluid, and Darcy's law is no longer applicable as it is fundamentally based on the incompressible flow assumption and for open systems. In the pore space, the compressible flow is governed by a damped wave equation for the density in the linear regime [Jin and Chen, “Fundamental equations for primary fluid recovery from porous media,” J. Fluid Mech. 860, 300–317 (2019)]. In this work, we study viscous compressible flow through a semi-sealed pore network generated from digital rocks, which is a representation of naturally made porous media. The mass depletion rate computed from the pore-scale simulations is then matched to that from a macroscopic effective diffusion model to extract the effective diffusion coefficient. The dependence of the macroscopic diffusion coefficient on the pore network parameters is established. The multiphase distribution during water imbibition process is further simulated by invasion percolation and the macroscopic diffusion coefficient at different water saturation process are calculated. It is shown that the macroscopic diffusion coefficient with multiphase condition is controlled by the interplay of gas-occupied pore structure parameters (pore size, connectivity) and surface wettability. For water-wet case, the macroscopic diffusion coefficient increases with the increasing water saturation and the first-order influence on macroscopic gas flux change can be attributed to the decreasing gas saturation.