A Fractal Permeability Model for Gas Transport in the Dual-Porosity Media of the Coalbed Methane Reservoir

In the process of coalbed methane (CBM) exploitation, permeability is a key controlling parameter for gas transport in the CBM reservoirs. The CBM reservoir contains a large number of micropores and microfractures with complex structures. In order to accurately predict the gas permeability of the micropores and microfractures in CBM reservoirs, a fractal permeability model was developed in this work. This model considers the comprehensive effects of real gas, stress dependence, multiple gas flow mechanisms (e.g., slip flow, Knudsen diffusion and surface diffusion) and fractal characteristics (e.g., pore size distribution and flow path tortuosity) of micropores and microfractures on the gas permeability. Then, this fractal permeability model was verified by the reliable experimental data and other theoretical models. Finally, the sensitivity analysis is conducted to identify key factors to the permeability of CBM reservoir. The results showed that the fractal characteristics of the micropores and microfractures have significant effects on the permeability of CBM reservoir. Higher fractal dimension of micropores diameter and microfractures aperture represents the larger number of micropores and microfractures, resulting in a higher permeability. Higher tortuosity fractal dimension of micropores and microfractures means higher gas flow resistance, leading to the lower permeability. The multiple gas transport mechanisms coexist in micropores and microfractures of CBM reservoir. The permeability of slip flow and Knudsen diffusion both increases with the decrease in pore pressure. Surface diffusion is an important gas transport mechanisms in micropores, but it can be ignored in the microfractures. Knudsen diffusion plays a more obvious role in the lower pore pressure, which controls the gas transport in microfractures. And microfractures are beneficial to improve gas transport capacity of coalbed methane reservoir.