Coupling of high Knudsen number and non-ideal gas effects in microporous media

Abstract

High Knudsen number non-ideal gas flows in porous media are important and fundamental in various applications including shale gas exploitation and carbon dioxide sequestration. Because of the small pore size in tight rocks, the Knudsen number (Kn) may be high (i.e. much higher than 0.01) even though the gas is really dense. In fact, due to the high pressure and temperature underground, the gas usually manifests a strong non-ideal gas effect. Understanding the coupling mechanism of the high Kn effect and non-ideal gas effect is a premise to accurately model deep-seated underground gas exploitation or carbon dioxide sequestration. In this work, we theoretically analyse the high Kn non-ideal gas flows in microporous media. Based on the relative importance of the non-ideal gas effect and high Kn effect, the coupling is divided into four types. The analysis is subsequently validated by multiscale numerical simulations, in which the four types of coupling are clearly demonstrated. After applying the analysis to laboratory measurements, we propose a characteristic pressure model to calculate the gas permeability of tight rocks with better precision. The new model incorporates the non-ideal gas effect with the high Kn effect accurately and better bridges the laboratory measurements with the reservoir engineering.

Analytical Solution of Gas Flow in Rough‐Walled Microfracture at In Situ Conditions

“…The first case is CH 4 flow with in situ conditions similar to deep coal seam and shale gas reservoirs, and the second is CO 2 flow with in situ conditions similar to CO 2 sequestration. The main parameters for these two cases collected from the literature (Wang et al, ) are listed in Table . The corresponding Kn for CH 4 and CO 2 are shown in Figure , which indicate both flows are in the slip flow regime.…”

“…Additionally, the ideal gas law, PV = nRT , has been applied to estimate the mean free path and to study rarefied gas flow behavior for a variety of problems at early times (Kang et al, ; Ko et al, ; Moghadam & Chalaturnyk, ; Zhang et al, ). However, this basic assumption for gas flow in microfractures at in situ conditions may be questionable, because gas behavior is often nonideal at high pressure and elevated temperature subsurface conditions, indicating that the observed relationships between pressure, volume, and temperature might not be accurately described by the ideal gas law (Ma et al, ; Wang et al, , ). Hypothetical ideal gas molecules have no significant volume and do not attract or repel each other, and real gases show this behavior only at relatively low pressures and high temperatures.…”

“…However, most of the previous studies mainly focus on microporous media or simplified structures such as tubes or channels (Wang et al, ; Wu, Li, et al, ), which ignore the roughed inner surface. By solving the generalized Enskog equation (Wu, Liu, et al, ), deriving an empirical correlation (Wang et al, ; Wu et al, ; Song et al, ), or applying the lattice Boltzmann method (Shi et al, ), molecular dynamics simulation (Barisik & Beskok, ; Oulebsir et al, ) and direct simulation Monte Carlo (Wang & Li, ), nonideal gas flow in simplified microstructures has been widely studied in detail. Additionally, the nonideal gas law is applied along with the lattice Boltzmann method (Landry et al, ) or pore network modeling techniques (Ma et al, ; Song et al, ), to estimate the gas flow in complex tight porous media such as shale or coal at in situ conditions.…”

An improved immersed moving boundary for hydrodynamic force calculation in lattice Boltzmann method

“…Lattice Boltzmann method (LBM) is an efficient numerical method for solving the partial differential equations especially with complicated boundary condition such as porous media and particle suspensions. [38][39][40][41][42][43][44] Different from the traditional computational fluid dynamics (CFD), where the macroscopic governing equations (such as Navier-Stokes equations) are solved directly, LBM solves Boltzmann equation in the finite discrete velocities space, while according to the Chapman-Enskog expansion the Navier-Stokes equations can be recovered. 45 Thus, the basic variables in LBM is the particle distribution function, f i .…”

Patch‐Based Multiscale Algorithm for Flow and Reactive Transport in Fracture‐Microcrack Systems in Shales

“…Small sampling regions (i.e., patches) are defined in the latter simulation domain and solved by fine-scale simulations, while the gaps between sampling regions are evaluated by interpolation. Since the fine-scale simulations are only performed in the sampling regions, which only occupy a small portion of the entire computational domain, the computational burden of solving fine-scale problems over macroscopic length scales can be controlled (Wang et al, 2016(Wang et al, , 2018. Differently from the original adoption of patch-based interpolation in the context of equation free methods where the coupling between the macroscales and microscales is bottom-up (Gear et al, 2003;Kevrekidis et al, 2004), the proposed algorithm is based on a bottom-up top-down coupling where the boundary condition between the two simulation domains is updated iteratively.…”