Development of a Fractal-Theory-Based Gas-Flow Model for Porous Media

To address the complex pore structure of porous media and the overprediction of flow rate by the baseline fractal viscous-flow model under high pressure differences, a gas mass-flow-rate model was developed for gas-permeable steel. The pore fractal dimension and tortuosity fractal dimension were determined from CT-derived pore-size statistics and a porosity constraint. Pore-size distribution, flow-path tortuosity, and gas compressibility were incorporated into the model, while the nonlinear resistance correction coefficient was introduced through an assumed structure-informed closure based on the relative contribution of pore-structure characteristics. For the four back-pressure conditions investigated, the correction reduced the mean relative error from 13.0–14.4% to 2.3–7.0%. Without relying on experimental fitting of pressure-difference–flow-rate data, the proposed model effectively improves the prediction of non-Darcy gas flow under high pressure differences.