Numerical simulation of non-isothermal drainage flow of a viscous gas from a narrow channel

Drainage of a compressed viscous gas from a semi-sealed narrow conduit to a large container is a model problem of fundamental interest to fluid production from subsurface porous rocks. The low Mach number drainage flow exhibits behaviors contrary to predictions from conventional incompressible flow approximations. This work employs direct numerical simulation to study non-isothermal drainage flow from a semi-sealed narrow channel to a laterally bounded large container. The Navier-Stokes characteristic boundary conditions are implemented at the open boundary downstream in the computational domain to avoid spurious wave reflection. For a laterally bounded container, wave transport dominates the drainage process. It is shown that in the absence of an imposed temperature drop, thermal effect slows down the drainage process with adiabatic walls. With large enough temperature drop, thermal effect speeds up the drainage, and it also produces excess mass beyond that of the isothermal model. These thermal effects are consistent with the previous results for a laterally unbounded container in a linear theory.