Numerical study of the impact of geometrical parameters on the rarefied gas transport in porous media

Abstract

To understand the transport mechanism of rarefied gas in the shale rock, the geometry of the porous media is generated based on the Voronoi tessellation, and the gas flows in continuum and rarefied flow regimes are simulated by using the Multiple-Relaxation-Time Lattice Boltzmann Method and Linearized Discrete Velocity Method, respectively. Based on explicit topological relations, porous media with diverse geometries are constructed to investigate the effect of pore-to-throat radius ratio, dead pore number and low-tortuosity throat on the rarefied flow in porous media. The relationships of the mass flow rate, apparent permeability and tortuosity versus the Knudsen number are obtained for varying pore-to-throat radius ratios. Results show that the intrinsic and apparent permeabilities of the porous media decrease as the blockage rate increases, while the reduction in intrinsic permeability is more significant than that in apparent permeability. Moreover, the phenomenon of Knudsen minimum reappears after the addition of low-tortuosity throats to porous media, in which the contribution to mass flow rate increases significantly in rarefied regimes relative to continuum regime, and it is supported by the observation that the tortuosity decreases with increasing Knudsen number. The increase in flow rate with increasing rarefaction effect in the low tortuous regions not only reveals the critical impact of fractures created by hydraulic fracturing on exploitation but also can identify the potential causes for the rapid production decay of shale gas reservoirs.