Microscopic choked flow for a highly compressible gas in porous media

Abstract

Choked flow can impact the gas flow rate from a high-pressure gas well with a vertical fracture of finite conductivity and the development of tensile stress near the wellbore. Traditionally, the choking condition of the flow of a highly compressible gas in porous media is obtained by considering the porous media to be a homogeneous porous medium at the macroscopic scale. In reality, when the average existing pressure of the porous medium decreases, if the compressible gas flow is choked in only one microscopic basic structural unit, the gas flow is choked in the macroscopic porous medium. In this paper, the choking condition of a compressible gas flow in a basic structural unit is studied. It is shown that for the given inlet pressure and temperature, the choked flow occurs first in the basic structural unit with a constant cross-section and with lower porosity and shorter flow distance. If the roughness of the basic structural unit is more complicated or its flow distance is shorter, this basic structural unit requires a lower pressure drop when the gas flow is choked. Whether the basic structural unit is a pipe with finite wall thickness or a single pore, the choking condition first occurs in the position with the smallest porosity or permeability near the exit. It is found that for microscopic choked flow, the outlet-to-inlet pressure under conditions of varying friction is substantially lower than that under the effect of constant friction.