Lattice Boltzmann simulation of fluid flow through coal reservoir’s fractal pore structure

Abstract

The influences of fractal pore structure in coal reservoir on coalbed methane (CBM) migration were analyzed in detail by coupling theoretical models and numerical methods. Different types of fractals were generated based on the construction thought of the standard Menger Sponge to model the 3D nonlinear coal pore structures. Then a correlation model between the permeability of fractal porous medium and its pore-size-distribution characteristics was derived using the parallel and serial modes and verified by Lattice Boltzmann Method (LBM). Based on the coupled method, porosity (φ), fractal dimension of pore structure (D b ), pore size range (r min, r max) and other parameters were systematically analyzed for their influences on the permeability (κ) of fractal porous medium. The results indicate that: ① the channels connected by pores with the maximum size (r max) dominate the permeability κ, approximating in the quadratic law; ② the greater the ratio of r max and r min is, the higher κ is; ③ the relationship between D b and κ follows a negative power law model, and breaks into two segments at the position where D b ≌2.5. Based on the results above, a predicting model of fractal porous medium permeability was proposed, formulated as κ=Cfr max , where C and n (approximately equal to 2) are constants and f is an expression only containing parameters of fractal pore structure. In addition, the equivalence of the new proposed model for porous medium and the Kozeny-Carman model κ=Cr n was verified at D b =2.0.