Hydraulic fracturing plays an important role in extracting unconventional resources such as shale gas/oil, tight gas and coal seam gas by increasing the conductivity of intact low-permeability reservoirs. It is important to know the performance of hydraulic fracturing treatment, such as the fracture geometries and their propagation behaviors. In this study, a numerical model, in the framework of linear elastic fracture mechanics (LEFM) and combing the dual boundary element method (DBEM) and the finite volume method (FVM), is developed to study the hydraulic fracture initiation and propagation from a circular wellbore. The displacement boundary integral equations are applied to one of the crack surfaces and the traction boundary integral equations are applied to the other surface. Stress and displacement fields in the rock matrix are interconnected by the kernel functions and solved by the DBEM while the fluid pressure in the fracture is described via the lubrication equation and solved by the FVM. The solutions for the responses of solid and fluid are obtained simultaneously in a fully coupled way. The stress intensity factors are determined by the discontinuous displacement near the crack tip. The present model is verified against the existing analytical solutions for some simple cases and shows excellent agreements. In the end, the initiation and propagation behaviors from a circular wellbore are also analyzed for a series of scenarios, such as different fluid viscosities and inclination angles of initial flaws.

1. Introduction

Hydraulic fracturing by fluid injection is extensively used in unconventional resources exploitation. The viscous fluid is pumped into a wellbore under high pressure to initiate and propagate one or multiple fractures, which are expected to enhance the conductivity of the reservoir. The prediction of the fracture geometry as well as the pressure along the fracture and wellbore during the fracture propagation is essential in the design of a hydraulic fracturing treatment. In addition to experimental study, numerical method is a powerful tool for analyzing the propagation mechanics of fluid-driven fractures with complex geometries. Comparing with other numerical methods, the boundary element method (BEM) can handle the fracture propagation problem in a more efficient way since it only requires the discretization of the boundaries, which significantly reduces the size of the problem (Lecampion, Bunger, and Zhang 2018). Indirect BEM such as displacement discontinuity method(Crouch 1976) has been used in studying hydraulic fracturing widely in two and three dimension cases (Vandamme and Curran 1989; Lecampion and Detournay 2007; Napier and Detournay 2013; Kumar and Ghassemi 2016; Zhang and Jeffrey 2014). The ability of detecting the influence of the contact and friction makes it more realistic when simulating the interaction between hydraulic fracture and natural fracture (Lecampion, Bunger, and Zhang 2018; Zhang and Jeffrey 2014).

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