A FRACTAL-MONTE CARLO APPROACH TO SIMULATE KOZENY–CARMAN CONSTANT OF ROUGHENED FIBROUS POROUS MEDIA

Abstract

The Kozeny–Carman (KC) equation is a well-known semi-empirical formula, which is used to calculate the permeability of porous media in the seepage field. The KC constant is an empirical constant in the KC equation. In this paper, based on the fractal theory, the Fractal-Monte Carlo technique is used to simulate the KC constant of the roughened fibrous porous media (RFPM) with micro-scale effects. There is no empirical constants in the proposed model, and each parameter has its physical meaning. The KC constant model of RFPM can be expressed as a function of structural parameters, including relative roughness ([Formula: see text]), porosity ([Formula: see text]), pore area fractal dimension ([Formula: see text]), tortuosity fractal dimension ([Formula: see text]), capillary diameter ([Formula: see text]) and Knudsen number ([Formula: see text]). The result shows that the KC constant increases with increases in [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. On the contrary, with increases in [Formula: see text] and [Formula: see text], the KC constant decreases. In addition, the KC constant model constructed in the paper agrees well with the existing experimental data and the model. According to the proposed Fractal-Monte Carlo technique, it is possible to better clarify the transmission physical mechanism in RFPM with micro-scale effects.