DERIVATION OF PERMEABILITY-PORE RELATIONSHIP FOR FRACTAL POROUS RESERVOIRS USING SERIES-PARALLEL FLOW RESISTANCE MODEL AND LATTICE BOLTZMANN METHOD

Permeability of porous reservoirs plays a significant role in engineering and scientific applications. In this study, we investigated the relationship between pore size fractal dimension (D-f) and its porosity, as well as that between D-f and the pore structure parameters, and consequentially developed an algorithm to generate pore spaces with arbitrary fractal dimension characterizing the pore size distribution. Using the series-parallel flow resistance model and lattice Boltzmann method (LBM) in combination, we then systematically analyzed the effects of physical properties on the fluid flows in two-dimensional (2D) context, and quantitatively derived a permeability-pore relationship for fractal porous media. The new relationship shows that: (i) the permeability of a fractal porous medium is proportional to the square of its maximum pore size lambda(max); (ii) the larger the fractal dimension D-f of a pore space, the smaller the flow resistance of the porous medium; (iii) porosity phi to the power of (4 - D-f)/(2 - D-f) is proportional to the permeability of a porous medium; (iv) similar to the Kozeny-Carman (KC) equation, the tortuosity tau has its square inversely proportional to the permeability; more importantly, it is found to be a function of porosity approximately satisfying the relationship tau = phi(Df-2) in a fractal porous medium. Moreover, we demonstrated that the newly derived fractal permeability-pore relationship is equivalent to KC equation and Poiseuille's law respectively, at D-f = 1 and D-f = 2.