Nanoscale simulation of shale transport properties using the lattice Boltzmann method: permeability and diffusivity

Abstract

Porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsic permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. For the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.

Channel-width dependent pressure-driven flow characteristics of shale gas in nanopores

“…The results indicated that Knudsen diffusion occupies an important proportion in the shale gas transport. 24 Zhang et al developed a pore network model to simulate the gas flow regimes. They found that slip flow and Knudsen diffusion are strengthened while viscous flow is weakened with the decrease of pressure.…”

Parameter Determination Using 3D FIB-SEM Images for Development of Effective Model of Shale Gas Flow in Nanoscale Pore Clusters

“…Models of the first category used in previous studies only considered the Darcy and partial non-Darcy effects Chen et al 2015). Pore-scale modelling of shale gas flow with LBM is still conducted in a capillary (Zhang et al 2014) and is incipient when applied to 3D complex porous spaces.…”

“…Ma et al (2014) extracted pore networks from reconstructed 3D images and, together with the similar non-Darcy flux formula, used them to examine the effect of TMAC (a parameter relates to slip effect) and the overall scaling of the throat size on the apparent permeability. Chen et al (2015) performed LBM simulations using reconstructed 3D images of several shale samples and only calculated the absolute permeability and diffusivity on the pore scale. On the sample scale, a modified dusty gas model (DGM) that combines the effects of slippage and Knudsen diffusion were used to derive the correlation factor of the apparent permeability.…”

“…The 3D binary images are obtained by FIB-SEM imaging or reconstruction of a 2D SEM image (Chen et al 2013(Chen et al , 2015Ma et al 2014;Tahmasebi et al 2015), and the PNs can be extracted from the 3D images or artificially generated using constraints. Mehmani et al (2013) used local shrink and adjustment of the pore networks extracted from sandstone to approximate the micro-and nano-pore networks in shale and investigated the effect of the ratio of the nano-pores to the micro-pores on the apparent permeability using Javadpour (2009)'s flow flux formula.…”

Using BIB-SEM Imaging for Permeability Prediction in Heterogeneous Shales

“…However, building a pore network model for 3D flow simulations in heterogeneous fine-grained rocks is an unresolved issue. Some approaches extract 3D pore data directly from FIB-SEM [31] or use the Markov chain Monte Carlo (MCMC) reconstruction method on 2D images [32,33]. Whether these complex pore network models are representative for the sample is another uncertainty [17,31,34].…”