Study on the REV Size of Fractured Rock in the Non-Darcy Flow Based on the Dual-Porosity Model

Yuan Wang,Yu-Long Niu,Qiang Feng

doi:10.1155/2018/7535927

Abstract

For the problem of whether the representative elementary volume (REV) obtained in the Darcy flow is also applicable to the case of the non-Darcy flow, the study on the REV size within the non-Darcy flow is proposed tentatively. The concept of the REV in the non-Darcy flow is based on the definition of the REV. According to the determination of the REV in the Darcy flow, the intrinsic permeability k and non-Darcy coefficient β are used simultaneously for the determination of the REV in the non-Darcy flow. The pore pressure cohesive element (PPCE) is developed with the subroutine in ABAQUS. Then the simulation method of the Darcy and non-Darcy flow in the fractured rock mass is built using the PPCE. The proposed plan is examined through the comparison with existing research results. It is validated that this technic is efficient and accurate in simulating the Darcy and non-Darcy flow in the fractured rock mass. Combined with fracture networks generated by Monte Carlo Simulation technique, the PPCE is applied to the study on the REV size. Both conditions of the Darcy and non-Darcy flow are simulated for comparison. The simulation results of this model show that the REV of the non-Darcy flow is inconsistent with the REV of the Darcy flow, and the REV of the non-Darcy flow is more significant than the REV of the Darcy flow. The intrinsic permeability k tensors obtained in the Darcy flow and the non-Darcy flow are basically the same.

Highlights

Hydraulic property of the fractured rock mass plays a vital role in on-site engineering, like the underground basement, oil storage, CO2 storage, and giant dams
The representative elementary volume (REV) is defined as the minimum volume of the sampling domain, beyond which the intrinsic permeability of the sampling domain remains essentially constant [1]
The stress ratio was mainly considered for the study, and the results showed that it became more difficult to establish an equivalent tensor and the REV with increasing stress ratios

Summary

Introduction

Hydraulic property of the fractured rock mass plays a vital role in on-site engineering, like the underground basement, oil storage, CO2 storage, and giant dams. The 2D models, based on the dual-porosity model and mathematic analysis, are established by taking the fracture as interfaces within the Forchheimer flow while the flow in the surrounding matrix is such that Darcy’s law is adequate [30,31,32], but those studies only set few fractures in porous media To take both the dual-porosity model and the non-Darcy flow behavior in the fracture network into consideration, the REV size should be further studied. Considering that the pressure in the matrix would affect the velocity of flow in the breach, the REV size of fractured rock based on the dual-porosity model is investigated.

Fracture

Calculation of the Equivalent Intrinsic Permeability

Determination of the REV

Discussions and Conclusions