Asymptotic Analysis of Unsteady Ideal Gas Flow Through Layered Porous Media

• Published in: Transport in porous media Vol. 139; no. 2; pp. 397 - 417
• Main Authors: Keenan, Seth, Nec, Yana
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.09.2021; Springer Nature B.V
• Subjects: Asymptotic methods; Boundary conditions; Civil Engineering; Classical and Continuum Physics; Compressibility; Dirichlet problem; Domains; Earth and Environmental Science; Earth Sciences; Flow control; Fluid dynamics; Fluid flow; Gas flow; Geotechnical Engineering & Applied Earth Sciences; Hydrogeology; Hydrology/Water Resources; Ideal gas; Industrial Chemistry/Chemical Engineering; Landfill gas; Natural gas; Nonlinear differential equations; Partial differential equations; Porous media; Porous media flow; Pressure dependence; Pressure distribution; Similarity solutions; Sparging; Suction; Time dependence; Asymptotic expansions; 35G20; 35G31; 35A35; 35Q35; Time-dependent non-linear problem; Flow control; 35C20; Multiple layer porous media; 76S05; Weakly compressible gas flow
• ISSN: 0169-3913; 1573-1634
• DOI: 10.1007/s11242-021-01672-5

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. Article Highlights In most realistic cases the slow asymptotic regime governs the flow response to time dependent boundary conditions. With a sealed outer boundary the spatio-temporal variation is decoupled, enabling full control of the pressure field. Pressure time dependence obeys a similarity law throughout the domain with generic unsteady boundary conditions.