Experimental Investigation on Nonlinear Flow Anisotropy Behavior in Fracture Media

Chun Zhu,Zhigang Tao,Xiuting Wang,Xiaoding Xu,Jing Chen,Feng Xiong,Yun Lin

doi:10.1155/2019/5874849

Chun Zhu, Zhigang Tao + Show 5 more

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https://doi.org/10.1155/2019/5874849

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Abstract

A series of flow experiments were performed on matched fractures to study the problem of non-Darcy flow in fractured media. Five rock fractures of different roughness were generated using indirect tensile tests, and their surface topographies were measured using a stereo topometric scanning system. The fracture was assumed to be a self-affine surface, and its roughness and anisotropy were quantified by the fractal dimension. According to the flow tortuosity effect, the nonlinear flow was characterized by hydraulic tortuosity and surface tortuosity power law relationships based on Forchheimer’s law. Fracture seepage experiments conducted with two injection directions (0° and 90°) showed that Forchheimer’s law described the nonlinear flow well. Both the proposed model and Chen’s double-parameter model gave similar results to the experiment, but the match was closer with the proposed model. On this basis, a new formula for the critical Reynolds number is proposed, which serves to distinguish linear flow and Forchheimer flow.

Highlights

A long history of geological and human activities has caused most rock masses to be cut by a large number of faults and fractures [1,2,3,4,5]
These results indicate that Forchheimer’s law (equation (1)) is able to quantitatively describe the nonlinear flow behavior, which is consistent with Zimmerman et al [17]
Equation (25) shows that the critical Reynolds number is closely related to hydraulic aperture, the fractal dimension of the fracture surface, and the flow direction

Summary

Introduction

A long history of geological and human activities has caused most rock masses to be cut by a large number of faults and fractures [1,2,3,4,5]. Some engineering projects involve a high hydraulic gradient, for example, dam construction in the deep weak overburden of a river valley, exploitation of low-permeability oil and gas wells, and coal mine gas outbursts [12,13,14,15,16]. Under this condition, fluid flow through fractures is not linear, and the use of the cubic law or related modified models would cause large deviations. The well-known Forchheimer law is used to describe this flow behavior:

Methods

Discussion

Conclusion