Optimization of the finite element mesh in modeling of hydrofracturing crack growth

The effect of mesh geometry on the accuracy of solution of linear fracture mechanics problems by the finite element methods is considered. Guidelines on determination of an optimal mesh for several routine problems using elements with the linear and quadratic approximation of displacements have been formulated. The accuracy of finite-element solutions is estimated as the difference of a calculated stress intensity factor (SIF) from that obtained in analytical solution. In problems of oil-bearing formation hydrofracturing, the pump-in pressure of injected water produces a distributed load on crack flanks as opposed to standard problems of fracture mechanics having analytical solutions, where a load is applied to the external boundaries of a computational region, while cracks themselves are kept free from stresses. Some model pressure profiles, as well as pressure profiles taken from real hydrodynamic computations, have been considered. Computer models of cracks with regard to the pre-stressed state, fracture toughness, and elastic material properties have been developed in the batch system of finite-element analysis MSC.Marc.2012. The Irwin force criterion is used as a criterion of brittle fracture and SIFs are computed using the Cherepanov-Rice invariant J-integral. The process of crack propagation in a linear isotropic elastic body is described in terms of elastic energy release rate G and the VCCT (Virtual Crack Closure Technique) approach is used for modeling the crack propagation. It has been found that the accuracy of solution is sensitive to the mesh configuration. Several parameters, which are dominant factors in constructing effective meshes of finite elements, that is, the minimum element size, the distance between mesh nodes in the vicinity of a crack tip, and the ratio of the height of an element to its length, have been established. It has been shown that using only small elements does not necessarily improve the accuracy of solutions.