Study on CO₂ transport in fractal porous media for a Hausdorff fractal derivative advection-dispersion model

Abstract

Purpose

The classical advection-dispersion equation (ADE) model cannot accurately depict the gas transport process in natural geological formations. This paper aims to study the behavior of CO₂ transport in fractal porous media by using an effective Hausdorff fractal derivative advection-dispersion equation (HFDADE) model.

Design/methodology/approach

Anomalous dispersion behaviors of CO₂ transport are effectively characterized by the investigation of time and space Hausdorff derivatives on non-Euclidean fractal metrics. The numerical simulation has been performed with different Hausdorff fractal dimensions to reveal characteristics of the developed fractal ADE in fractal porous media. Numerical experiments focus on the influence of the time and space fractal dimensions on flow velocity and dispersion coefficient.

Findings

The physical mechanisms of parameters in the Hausdorff fractal derivative model are analyzed clearly. Numerical results demonstrate that the proposed model can well fit the history of gas production data and it can be a powerful technique for depicting the early arrival and long-tailed phenomenon by incorporating a fractal dimension.

Originality/value

To the best of the authors’ knowledge, first time these results are presented.

Citation

Chang, A., Huang, L., Li, Q.-Q., Vafai, K. and Shao, M. (2023), "Study on CO₂ transport in fractal porous media for a Hausdorff fractal derivative advection-dispersion model", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 33 No. 10, pp. 3410-3424. https://doi.org/10.1108/HFF-03-2023-0158