Nonlinear Seepage Behaviors of Pore-Fracture Sandstone under Hydro-Mechanical Coupling

Ying Zhang,Qifeng Guo,Zhaohong Zhang,Meifeng Cai,Xu Wu

doi:10.3390/cryst12030373

Abstract

This work focused on the nonlinear seepage behaviors of flow in pore-fracture media. Natural sandstones were selected to prefabricate single-fracture specimens with different inclinations (0–90°). Seepage tests of combined media were performed under different confining pressures (8–10 MPa) and different water pressures (3–7 MPa) in a triaxial pressure chamber. The fitting analysis of experimental data showed that Forchheimer’s law described the nonlinear characteristics of flow in the pore-fracture media. Linear term coefficient a and nonlinear term coefficient b of the sandstone samples with different inclinations changed more obviously with the increased inclination. When the fracture inclination was greater than 30°, a and b values had a sudden jump. The nonlinear inertial-parameter equation of fluid flow in pore-fracture media was proposed based on non-Darcy flow coefficient β and inherent permeability k. The applicability of the following methods to evaluate Darcy’s law was discussed, including normalized hydraulic conductivity, pressure gradient ratio, and discharge ratio. The three methods were able to determine critical parameters and distinguish linear and nonlinear flow. Furthermore, it was specified for the first time that when β was negative, critical nonlinear effect E was −0.1, and Forchheimer’s coefficient F0 was −0.091. In the −∇P-Q relationship, the fitting curve was convex to the −∇P axis, and the increase of Q was higher than the linear increase, presenting the nonlinearity of overflow. On the one hand, the fractures and pores were compressed under the confining pressure due to the prefabricated fractures of different shapes and different inclinations. A higher seepage water pressure was needed to stabilize the seepage system with the excessive flow rate. On the other hand, the barrier effect of the fluid inside the rock was completely lost because the fluid expanded the seepage channel. Its permeability was changed, leading to seepage instability.

Highlights

Relationship, the fitting curve was convex to the −∇P axis, and the increase of Q was higher than the linear increase, presenting the nonlinearity of overflow
Numerical calculations quantitatively prove that the micro-inertia phenomenon is the root cause of the nonlinear effect [11]
The Forchheimer equation was used to analyze the influences of single fractures with different inclinations on the nonlinear flow in pore-fracture media

Summary

Introduction

The seepage of fluids in rock pores and fractions often occurs in the mining of mineral resources, underground tunnel excavation, geological storage of greenhouse gases, deep disposal of nuclear wastes, geothermal energy extraction, natural gas and oil extraction, and other processes. The seepage characteristics of fluids in porous and fractured rock masses under hydro-mechanical coupling are of great significance to the engineering safety of underground rock masses. Many scholars have conducted extensive studies on the flow behaviors of fluids in pores and fractures based on Darcy’s law [1–8]. Linear Darcy’s law is not sufficient to describe the seepage behaviors in pores and fractures with an increased flow rate, which exhibit significant nonlinear seepage characteristics. The increase in microscopic viscous force (resistance) causes nonlinear effects at high flow rates [10]. Numerical calculations quantitatively prove that the micro-inertia phenomenon is the root cause of the nonlinear effect [11]

Methods

Discussion

Conclusion