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

Ailian Chang (State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, China)
Le Huang (School of Mechanical Engineering and Rail Transit, Changzhou University, Changzhou, China)
Qian-Qian Li (School of Mechanical Engineering and Rail Transit, Changzhou University, Changzhou, China)
Kambiz Vafai (Department of Mechanical Engineering, University of California Riverside, Riverside, California, USA)
Minglu Shao (School of Petroleum and Natural Gas Engineering, School of Energy, Changzhou University, Changzhou, China)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 28 June 2023

Issue publication date: 17 August 2023

77

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.

Keywords

Acknowledgements

The work was partially supported by the Natural Science Foundation of Jiangsu Province under Grant No. BK20220615, the Natural Science Foundation of Jiangsu Higher Education Insititution of China under Grant No. 22KJB130001, Jiangsu Province Engineering Research Center of High-Level Energy and Power Equipment under Grant No. JSNYDL-202208, the Research Initiation fund of Changzhou University under Grant No. ZMF21020352.

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

Publisher

:

Emerald Publishing Limited

Copyright © 2023, Emerald Publishing Limited

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