Empirical prediction of hydraulic aperture of 2D rough fractures: a systematic numerical study

Abstract

This study aims to propose an empirical prediction model of hydraulic aperture of 2D rough fractures through numerical simulations by considering the influences of fracture length, average mechanical aperture, minimum mechanical aperture, joint roughness coefficient (JRC) and hydraulic gradient. We generate 600 numerical models using successive random additions (SRA) algorithm and for each model, seven hydraulic gradients spanning from 2.5 × 10⁻⁷ to 1 are considered to fully cover both linear and nonlinear flow regimes. As a result, a total of 4200 fluid flow cases are simulated, which can provide sufficient data for the prediction of hydraulic aperture. The results show that as the ratio of average mechanical aperture to fracture length increases from 0.01 to 0.2, the hydraulic aperture increases following logarithm functions. As the hydraulic gradient increases from 2.5 × 10⁻⁷ to 1, the hydraulic aperture decreases following logarithm functions. When a relatively low hydraulic gradient (i.e., 5 × 10⁻⁷) is applied between the inlet and the outlet boundaries, the streamlines are of parallel distribution within the fractures. However, when a relatively large hydraulic gradient (i.e., 0.5) is applied between the inlet and the outlet boundaries, the streamlines are disturbed and a number of eddies are formed. The hydraulic aperture predicted using the proposed empirical functions agree well with the calculated results and is more reliable than those available in the preceding literature. In practice, the hydraulic aperture can be calculated as a first-order estimation using the proposed prediction model when the associated parameters are given.

Graphical abstract

Keywords

fluid flow / rough fracture surface / mechanical aperture / hydraulic aperture / predictive model

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Acknowledgments

This study has been partially funded by National Key R&D Program of China (No. 2022YFE0128300), National Natural Science Foundation of China (Grant Nos. 52379114 and 52379113), Natural Science Foundation of Jiangsu Province, China (No. BK20211584), the Assistance Program for Future Outstanding Talents of the China University of Mining and Technology (No. 2023WLKXJ187) and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX23_2746). These supports are gratefully acknowledged.

Conflict of Interest

The authors declare that they have no conflict of interest.

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