Mesh-Free Numerical Simulation of Pressure-Driven Fractures in Brittle Rocks

Abstract

A better understanding of failure in heterogeneous rock materials can benefit a wide range of areas, from earthquake engineering to petroleum engineering. Study of such failure is of particular interest in the field of hydraulic fracturing. The prediction of this breakage phenomenon is a big challenge for the scientific community. Traditional continuum modeling techniques have the advantage of using classical nonlinear material models, however they often fail to accurately capture the complexity of the fractured geometry and path of multiple intersecting fractures. In particular, mesh dependence of the fracture path, 3D representation of natural fractures and their intersections, closing of an opened fracture, or shear in fractures, are difficult to accurately capture using these techniques. The use of the smoothed particle hydrodynamics (SPH) method for simulation of fracture in solids is relatively recent, where mesh free methods like SPH have the potential to overcome the previously mentioned limitations of mesh based methods. Simulation of the initiation and propagation of pressuredriven fractures in brittle rocks is presented in this study. By exploiting techniques commonly used in traditional continuum methods, we have implemented an elasto-plastic SPH model, which is based on the Drucker-Prager yield criterion, and the Grady-Kipp damage model. Results show that SPH is able to correctly predict the evolution of fracture in brittle rocks. The SPH method has been applied to the solution of crack propagation in a variety of test cases, including a pressurized borehole, 2D line crack, and 3D penny shaped crack. The influence of initial in-situ stresses was also accounted for. Comparison of SPH results for these cases to analytical solutions shows that SPH may be applied to accurately simulate the evolution of fluid-driven fractures in brittle rocks. Such model is a vital tool in correctly predicting fracture propagation in highly heterogeneous formations, for instance, shale formations.

Numerical methods for hydraulic fracture propagation: A review of recent trends

“…It has been used to address some geological problems (Gray and Monaghan, 2004;Das and Cleary, 2010). Applications to hydraulic fracturing (Douillet-Grellier et al, 2016) are preliminary in nature, i.e. they are limited to uniform pressure cases for which the fluid coupling vanishes except for the global volume balance.…”

Comparison of multiphase SPH and LBM approaches for the simulation of intermittent flows

“…A. 28 show that LBM has a smoother density field compared with SPH. As expected, due to the choice to use the weakly compressible approach, SPH presents a noisy density field.…”

“…Since there is no connectivity between particles, a neighbor searching procedure has to be carried for every particle at every time step, which is a serious bottleneck for code efficiency. Among the numerous applications of SPH, we can mention astrophysics [24], hydrodynamics [25], geophysics [26,27,28,29] and computer graphics [30]. Some extensive reviews have been published [31,32,33].…”

Optimization of Non-Uniform Perforation Parameters for Multi-Cluster Fracturing

“…These methods possess the advantage of requiring no additional criterion for the determination of fracture propagation behavior, which makes it convenient for complex fracture problems with fracture branching and joining. Furthermore, other approaches have been proposed, such as the numerical manifold method [29,30], the lattice method [31], the meshless method [32,33], and the discretized virtual internal bond method [34]. Though so many methods have been proposed, most of them face the challenges of high computational cost for field application.…”