A methodology for predicting choked compressible gas flow in pores using dimensional analysis

High-velocity compressible gas flow in porous media has been reported in several subsurface geological environments. As gases migrate through pore throats under high pressure gradient conditions, the velocity can increase to sonic levels and choked flow can occur, which affects the flow behaviors. In this study, pore-scale numerical simulations and dimensional analysis of the results have been carried out to describe the choking conditions. Two different numerical simulators have been prepared for two-dimensional (2D) and three-dimensional (3D) geometries, and relevant simulations have been designed, performed, and post-processed. It has been proved that both simulators can capture the unique behaviors of the process, and their result's accuracy has been validated using the available analytical solutions. A detailed dimensional analysis using the Buckingham π theorem has been performed to investigate the physics of the choking process. Quantification of different mechanisms has produced several dimensionless groups describing the interplay of various driving forces. Accordingly, different equations have been developed to determine the critical pressure ratio that choked flow occurs, and the maximum mass flow rates that pass through choked capillaries. The accuracy of the equations has been tested against the results of the 2D and 3D numerical simulations with satisfactory agreement.