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

Abstract

a b s t r a c tShale formations consist of numerous nanoscale pores within a range of 2 nme50 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.

Simulation of Shale Gas Transport in 3D Complex Nanoscale-Pore Structures Using the Lattice Boltzmann Method

“…Therefore, the impact of this accommodation coefficient has been investigated in our previous work (Ning et al, 2015). It has been found that ϭ1.0 is a reasonable choice and it will be continuously used in this work.…”

“…The multiple-relaxation-time (generalized) LBM proposed by d' Humieres (1992) has been proved to be an effective LBM model for high Knudsen flows (Guo et al, 2008;Li et al, 2011;Ning et al, 2014;Ning et al, 2015). The generalized LBM relaxes various moments (i.e., density, energy, momentum, heat flux, viscous stress tensor, etc.)…”

“…Shale gas transport can be dominated by the release of absorbed gas from the nano-pores. The adsorption in LBM can be modeled by introducing the intermolecular forces among gas molecules and between gas molecule and solid walls (Sukop and Or, 2004;Ning et al, 2014;Ning et al, 2015). Since intermolecular forces are incorporated into LBM, the equation of state (EOS) needs to be modified accordingly (He and Doolen, 2002;Sukop and Thorne Jr., 2006) in order to include the non-ideality effect.…”

A non-equilibrium molecular dynamics study of methane transport in clay nano-pores

“…One of the distinctive characteristics of shale rock formations is that typically more than 60 % of their porosity can be attributed to small nano-pores less than 30 nm in diameter [1][2][3][4][5][6][7][8][9][10]. As a result, these formations have extremely low permeability, typically of the order of magnitude of one hundred nanodarcies [11].…”

Multiple-relaxation-time lattice Boltzmann simulation for flow, mass transfer, and adsorption in porous media

“…At the microscopic pore scale, the geometric structure of porous media is described in detail; while, at the mesoscopic REV scale, the geometric structure is simplified by an elementary cell using the volume-averaging method. Due to the briefness of boundary schemes to handle the complex morphology of porous matrix, a series of pore scale LB models have been proposed to study the adsorbate's mass transport and adsorption behaviors in the pore structures of porous media, which were constructed by the regular particles or the stochastic irregular solid matrix [21][22][23][24][25][26][27][28]. By using these LB simulations at the pore scale, the transient fluid velocity and the adsorbate concentration profiles in the pore structures were presented in detail, and the effect mechanism of pore structure characteristics on the dynamic adsorption performance was elaborated to provide a guidance for the design and optimization of adsorption systems in the micro-scale.…”