Asymptotic Analysis of Unsteady Ideal Gas Flow Through Layered Porous Media

Temporal variability of boundary conditions is a common feature of certain fluid flows through a porous matrix, encountered, for instance, in landfill gas or natural gas collection, and sparging wells. Darcy’s law subject to the weak compressibility of the fluid results in a non-linear partial differential equation for the pressure field. Slow variation admits asymptotic solutions for generic time dependence of the boundary forcing function, both as Dirichlet and Neumann conditions. Flow control strategies are suggested based on the asymptotic theory. A sealed outer domain boundary is identified as the configuration best amenable to full control of the pressure distribution via the induced well suction. Fast variation leads to a novel application of the classical compact support similarity solution in a domain with discontinuous parameters.