Generalized lattice Boltzmann model for flow through tight porous media with Klinkenberg's effect

Abstract

Gas slippage occurs when the mean free path of the gas molecules is in the order of the characteristic pore size of a porous medium. This phenomenon leads to Klinkenberg's effect where the measured permeability of a gas (apparent permeability) is higher than that of the liquid (intrinsic permeability). A generalized lattice Boltzmann model is proposed for flow through porous media that includes Klinkenberg's effect, which is based on the model of Guo et al. [Phys. Rev. E 65, 046308 (2002)]. The second-order Beskok and Karniadakis-Civan's correlation [A. Beskok and G. Karniadakis, Microscale Thermophys. Eng. 3, 43 (1999) and F. Civan, Transp. Porous Med. 82, 375 (2010)] is adopted to calculate the apparent permeability based on intrinsic permeability and the Knudsen number. Fluid flow between two parallel plates filled with porous media is simulated to validate the model. Simulations performed in a heterogeneous porous medium with components of different porosity and permeability indicate that Klinkenberg's effect plays a significant role on fluid flow in low-permeability porous media, and it is more pronounced as the Knudsen number increases. Fluid flow in a shale matrix with and without fractures is also studied, and it is found that the fractures greatly enhance the fluid flow and Klinkenberg's effect leads to higher global permeability of the shale matrix.

Multicomponent Lattice Boltzmann Simulations of Gas Transport in a Coal Reservoir with Dynamic Adsorption

“…When the porosity is relatively high (ε = 0 4 on the right), the streamline almost appears along with a straight path. The results are consistent with the simulation results in [8], further suggesting the validity of our model. Figure 9 summarizes the effect of the matrix porosity and the Langmuir pressure on the adsorbed amount magnitude distribution.…”

“…Guo and Zhao [9] developed an LB model which can be used to solve the generalized Navier-Stokes equations. Then, Chen et al [8] employed the generalized Lattice Boltzmann (GLB) model with the Klinkenberg effect in shale gas for studying the gas slippage and its effect on apparent permeability. Ning et al [12] and Wang et al [11] used a similar model for studying the impact of surface adsorbed gas on apparent permeability based on 2D and 3D reconstructed shale, respectively.…”

“…The adsorption processes of methane in the reservoir can be divided into two parts: Enter the irregular macropore-microfractures system by advection-diffusion; diffuse in the nanopore network of a matrix, then adsorbed on the interior surface of pores. The heterogeneity of geometric shapes, the difference of pore size/distribution, and the involved multiple transport mechanism of fluid causing the difficulty of the research and causing the fluid flow and transport in the reservoir are usually treated at the representative elementary volume (REV) scale in experiments and numerical simulation [8][9][10][11][12]. Recently, the Lattice Boltzmann method (LBM) has been widely used in the field relevant to fluid flow and gas transport at the mesoscale because of its efficiency and effectiveness in the implementation of multiple interparticle interactions and complex geometry boundary conditions [13][14][15].…”

Novel molecular simulation process design of adsorption in realistic shale kerogen spherical pores

“…Compared with organic pores of simplified geometry and solid components, the reconstructed organic molecular-based pore can provide more reliable data of the fluids confined within. Such data, including adsorption isotherms and diffusion coefficients, is essential information for mesoscopic and marcoscopic descriptions of fluid transport in shale [6]. However, in realistic shale samples a large quantity of shale gas molecules preferentially reside in 2-50 nm kerogen pores rather than the natural kerogen subnano pores [23,10].…”

Pore-scale prediction of transport properties in reconstructed nanostructures of organic matter in shales

“…We also developed a representative elementary volume (REV)-scale generalized LB model for fluid flow through tight porous media with slippage [19]. In the present study, we further apply the LB model developed in [18] to study Knudsen diffusion and gas flow in the organic matter.…”