An analytical model for shale gas transport in circular tube pores

Abstract

An analytical model for gas transport in shale media is proposed on the basis of the weighted superposition of slip flow, bulk diffusion and Knudsen diffusion. The model takes account of slip effect and real gas effect, and is successfully validated by experimental data and Lattice Boltzmann simulation results. The contribution of each transport mechanism to the total flow is investigated. The effect of porosity, diameter and pressure on the apparent permeability is studied and a sensitivity analysis is performed to evaluate the significance of the parameters for gas transport. The results show: (1) the present model can reasonably describe the process of the mass transform of all different gas transport mechanisms; (2) As pressure and pore diameter decrease, the number of molecule-wall collisions gradually predominates over the number of intermolecular collisions, Knudsen diffusion contributes more to the total flow; and (3) the apparent permeability increases with porosity, pore diameter, and decreases with pressure. It is more sensitive to pressure in rarefied gas flow regime, and pore diameter has a significant impact under high pressure. The present model can provide some theoretical support in numerical simulation of shale gas production.