Wave dominant transport in gas drainage flow from a narrow conduit

Drainage of a viscous gas from a semi-sealed narrow capillary to a large container is a pore-scale problem of fundamental interest to macroscopic level modeling of gas production from subsurface porous rocks. When the container is infinitely wide, the low Mach number, low Reynolds number flow gives rise to a diffusive drainage rate fundamentally different from the classical creeping flow theory. The current work considers a finite size container, and the study shows that the drainage process is now dominated by acoustic wave transmission at the capillary-container junction. The drainage rate is found to be controlled by the decay of the wave caused by such wave transmission in the acoustic time scale and modulated by slow wave damping over the diffusive long-time scale. A formula based on the simulation results for the drainage rate in terms of the reflection coefficient at the capillary-container junction, the wave period, and the self-diffusion coefficient is provided. Wave transmission (convective) and damping (diffusive) work concurrently, and these two effects cannot be separated as a linear superposition for the drainage rate.