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.

Analysis of gas transport behavior in organic and inorganic nanopores based on a unified apparent gas permeability model

Different from the conventional gas reservoirs, gas transport in nanoporous shales is complicated due to multiple transport mechanisms and reservoir characteristics. In this work, we presented a unified apparent gas permeability model for real gas transport in organic and inorganic nanopores, considering real gas effect, organic matter (OM) porosity, Knudsen diffusion, surface diffusion, and stress dependence. Meanwhile, the effects of monolayer and multilayer adsorption on gas transport are included. Then, we validated the model by experimental results. The influences of pore radius, pore pressure, OM porosity, temperature, and stress dependence on gas transport behavior and their contributions to the total apparent gas permeability (AGP) were analyzed. The results show that the adsorption effect causes Kn(OM) > Kn(IM) when the pore pressure is larger than 1 MPa and the pore radius is less than 100 nm. The ratio of the AGP over the intrinsic permeability decreases with an increase in pore radius or pore pressure. For nanopores with a radius of less than 10 nm, the effects of the OM porosity, surface diffusion coefficient, and temperature on gas transport cannot be negligible. Moreover, the surface diffusion almost dominates in nanopores with a radius less than 2 nm under high OM porosity conditions. For the small-radius and low-pressure conditions, gas transport is governed by the Knudsen diffusion in nanopores. This study focuses on revealing gas transport behavior in nanoporous shales.

Rapid Evaluation of the Permeability of Organic-Rich Shale Using the 3D Intermingled-Fractal Model

Summary Shale possesses abundant micro/nanopores. Most micro/nanopores that exist in organic-rich shale are organic pores and mainly developed in organic matter. The pore distribution in matrix space significantly affects gas percolation and diffusion. Pore-size distribution possesses a self-similar, or fractal, property. The pore space and gas permeability of shale can be easily rebuilt and evaluated, respectively, using fractal theory. In this work, a 3D intermingled-fractal model (3D-IFM) is successfully built using scalable scanning-electron-microscopy (SEM) images of shale samples. 3D-IFM is made up of several components, including organic pores in organic matter and in pyrites, inorganic pores, slits, and matrix. An improved pore-connective-calculation method is also introduced to evaluate the apparent gas permeability of the shale model. The proposed 3D-IFM rapid-permeability-evaluation method for organic-rich shale is valid and useful and considers the main components of shale. This method can rapidly evaluate apparent gas permeability and simplify the apparent-gas-permeability-calculation process. Thus, the method provides a promising means of rapidly evaluating apparent gas permeability.