An Analytical Model of Apparent Gas Permeability for Tight Porous Media

Real Gas Effect and Bulk Diffusion Characteristics of Shale Mixed Gas Transport in Microscale Fractures

Shale gas reservoirs are rich in microscale fractures. In this paper, the characteristics of gas percolation in microscale fractures are taken as the research object. By coupling the actual gas equation, the multi-component gas equation, and the bulk gas diffusion equation, analytical solutions of the comprehensive percolation equation are obtained. Through mathematical model research, the following conclusions are obtained: (a) after considering the slip flow of the solid surface, the mass flow rate of multi-component gas under different pressure conditions increases by about 20-10,000%. (b) Different from continuous flow and slip flow, the mass flow rate of bulk gas diffusion decreases with pressure increase. (c) The intersection pressure is 31 MPa. When the pressure increases from 0.5 MPa to the pressure at the intersection point, the mass flow rate of integrated flow increases with decrease of the methane content. (d) When the pressure continues to increase from the intersection point pressure, the mass flow rate of integrated flow decreases with decrease of the methane content.

Numerical Study of Gas Flow in Super Nanoporous Materials Using the Direct Simulation Monte-Carlo Method

The direct simulation Monte Carlo (DSMC) method, which is a probabilistic particle-based gas kinetic simulation approach, is employed in the present work to describe the physics of rarefied gas flow in super nanoporous materials (also known as mesoporous). The simulations are performed for different material porosities (0.5≤ϕ≤0.9), Knudsen numbers (0.05≤Kn≤1.0), and thermal boundary conditions (constant wall temperature and constant wall heat flux) at an inlet-to-outlet pressure ratio of 2. The present computational model captures the structure of heat and fluid flow in porous materials with various pore morphologies under rarefied gas flow regime and is applied to evaluate hydraulic tortuosity, permeability, and skin friction factor of gas (argon) flow in super nanoporous materials. The skin friction factors and permeabilities obtained from the present DSMC simulations are compared with the theoretical and numerical models available in the literature. The results show that the ratio of apparent to intrinsic permeability, hydraulic tortuosity, and skin friction factor increase with decreasing the material porosity. The hydraulic tortuosity and skin friction factor decrease with increasing the Knudsen number, leading to an increase in the apparent permeability. The results also show that the skin friction factor and apparent permeability increase with increasing the wall heat flux at a specific Knudsen number.

An Apparent Gas Permeability Model for Real Gas Flow in Fractured Porous Media with Roughened Surfaces

The investigation of gas transport in fractured porous media is essential in most petroleum and chemical engineering. In this paper, an apparent gas permeability model for real gas flow in fractured porous media is derived with adequate consideration of real gas effect, the roughness of fracture surface, and Knudsen diffusion based on the fractal theory. The fractal apparent gas permeability model is obtained to be a function of micro-structural parameters of fractured porous media, relative roughness, the pressure, the temperature, and the properties of gas. The predictions from the apparent gas permeability model based on the fractal theory match well with the published permeability model and experimental data, which verifies the rationality of the present fractal apparent gas permeability model.