Numerical modeling of slippage and adsorption effects on gas transport in shale formations using the lattice Boltzmann method

Shale formations consist of numerous nanoscale pores within a range of 2 nm-50 nm; the shale gas flow within this size range under typical shale reservoir pressure and temperature will fall into the slip flow or the transitional flow regime 0.001 < K-n < 10. Besides nano-pores in shale, there exist a number of mesoscopic and macroscopic pores with size larger than 50 nm, and many micrometer fractures. Natural gas, mainly methane, flows through nanoscale pores, mesoscale, and macroscopic pores or fractures during the production period. Gas slippage described by the Klinkenberg effect reduces viscous drag near the pore walls and influences permeability. In shale, the majority of gas molecules are adsorbed in kerogen that is considered to be organic source rocks. Within nano-pores and meso-pores, Darcy's law cannot effectively describe this type of transport phenomena due to its continuum assumption. Alternatively, the kinetic-based lattice Boltzmann method (LBM) becomes a strong candidate for simulating an organic-rich shale reservoir that contains a large number of nano-pores. In this paper, we present a multiple-relaxation-time (generalized) LBM, which is considered to be one of the most efficient LBM models. For gas flow in a confined system, its molecular mean free path is corrected depending on the size of the confined system and the distance of the gas molecules from the pore walls. Gas slippage on pore walls is captured with a combined bounce-back specular reflection boundary condition. In addition, adsorbed gas in shale has a significant influence on gas transport in shale gas production. Here, we propose to incorporate inter-molecular and adsorptive forces into the generalized LBM algorithm to capture gas adsorptions in organic nano-pores. Therefore, this approach is able to simulate gas flow with adsorption effect. Many factors are believed to control the flow mechanisms in these types of pores, including the pore size distribution, the specific surface area, and the adsorptive feature of the pore walls. The simulation results agree well with the existing data for high Knudsen flows between 2D parallel plates. Accounting for the adsorption and slippage effects, flow phenomena are investigated by varying different controlling factors in both simple and complex structures. The permeability of methane is also determined for complex porous geometries. (C) 2015 Elsevier B.V. All rights reserved.