https://doi.org/10.1140/epjp/s13360-022-03499-5
Regular Article
Influence of fracture roughness and void space morphology on nonlinear fluid flow through rock fractures
1
State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, 400044, Chongqing, China
2
Geofluids, Geomechanics and Geoenergy (3G) Research Group, Chongqing University, 400044, Chongqing, China
3
School of Mines, China University of Mining and Technology, 221116, Xuzhou, China
Received:
30
August
2022
Accepted:
15
November
2022
Published online:
29
November
2022
The effects of fracture roughness and geometric morphology of void space between two fracture walls on nonlinear fluid flow through rock fractures were investigated by performing fluid dynamic computation on mated and non-mated rock fractures. The fractal dimension D was used to characterize to the morphology of fracture void space, and it shows a positive correlation with either the root mean square of the height of the fracture void space morphology or the standard deviation of roughness angle. Forchheimer equation describes the nonlinear flow behavior through rock fractures well. Compared to mated rock fractures, the unmatched morphology of fracture void space of non-mated rock fractures increased the flow heterogeneities, producing prominent preferential flow and obvious eddy flow in non-mated rock fractures. This renders the nonlinear coefficient in the Forchheimer equation of non-mated rock fractures is generally greater than that of mated rock fractures of identical fracture aperture and roughness. For mated rock fractures, a power-law relationship was proposed to quantify the nonlinear coefficient b in terms of fracture peak asperity Rz, the first derivative of the profile Z2 and fracture aperture eh, and then, the critical Reynolds number for the onset of nonlinear fluid flow was derived. To further describe the influence of fracture void space morphology on the nonlinear fluid flow through non-mated rock fractures, an extended power-law model was proposed by quantifying b in terms of fracture surface roughness parameters Rz, Z2, aperture eh and fractal dimension D, and the critical Reynolds number to demark the onset of nonlinear flow was subsequently derived. The predicted critical Reynolds number agrees well with that of fluid dynamic computation for both mated and non-mated rock fractures, validating the proposed power-law and extended power-law relationships. Our research also shows that the critical Reynolds number generally decreased with the increase in fractal dimension.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
