Control mechanisms of self-affine, rough cleat networks on flow dynamics in coal reservoir

Highlights: • Clarified the control mechanism of fractal dynamics in rough, self-affine surfaces. • Developed an algorithm to effectively characterize cleat networks in coal reservoir. • Quantified the control effects on fluid flow through cleat networks. • Established general permeability model of cleat networks with parameters well defined. -- Abstract: Cleat networks dominate the migration of coalbed methane (CBM), which is assembled by cleats of different type following special configuration and possessing rough, self-affine surfaces. Nowadays, configuration implications, scale-invariant properties, fractal control mechanisms, and their relations to flow dynamics have not yet been fully clarified. Herein we explore these issues numerically using effective modeling of cleat networks and pore-scale simulations of fluid flow through them. Firstly, the control mechanics of fractal dynamics was clarified by fractal topography theory, a new definition of Weierstrass-Mandelbrot (W-M) function was proposed to characterize the self-affine surface geometries, an algorithm was developed to effectively construct cleat networks similar in coal, and Lattice Boltzmann method (LBM) was used to reproduce the fluid flow in numerical cleat networks at the pore scale. Afterwards, the implications of spatial configuration of cleats and fractal control mechanisms of surface geometries on the permeability were systematically analyzed and quantified. Finally, an empirical model was established to predict the permeability of self-affine, rough cleat networks, rather than a rough estimation by a power-law proportionality in previous research. The performance of the proposed model was fully verified by comparative analysis and numerical simulations. Theoretical analysis denotes that our model can generalize several traditional and newly developed models from the literature.