This article focuses on single phase compressible gas flow in porous media, especially hydrogen \(H_2\) or other gases like air. It includes a comprehensive literature review on analytical approaches to gas flow, Klinkenberg effect, and other effects like gravitational acceleration (super-gravity cases). The review investigates previous findings for ideal gas flow under isothermal conditions under various conditions – including one-dimensional (1D) permeametric flow conditions – taking into account perfect gas compressibility and the Klinkenberg effect due to gas slippage in fine pores. Usually, gravitational acceleration is neglected in the gas flow literature: this classical assumption is assessed quantitatively, and a new 1D analytical solution is developed at steady state for the case of strong gravitational acceleration, as may arise under centrifugal conditions. On the other hand, new 1D analytical solutions are developed for space-time gas pressure profiles and for mass flux density profiles in the porous column, with or without Klinkenberg effect. These analytical solutions are tested and compared to numerical simulations, both Finite Volume and Finite Element. Both the gas pressure profiles and the mass flux density profiles approach the exact steady state at large times. Furthermore, it is is demonstrated that the proposed analytical solution for gas pressure is a fair approximation over a broad range of time scales, from early times up to large times approaching steady state.
