Numerical model of crack growth in hydraulic re-fracturing

Abstract

Crack propagation simulations with FEM employ remeshing to provide more accurate results. This raises a question about the direction and criterion of mesh modification. In the case of general-purpose CAE-packages, we have to deal with a stationary mesh, and the crack trajectory is usually represented as a chain of elements with degraded properties. The accuracy of the solution is heavily dependent on the choice of mesh topology, the degree of mesh refinement in the unpredictable crack propagation zone, and correct crack surface loading in this case is impossible. The algorithm proposed in this paper is based on the ANSYS Mechanical APDL language for stepwise geometry reconstruction and mesh modification in accordance with the current configuration of a growing crack and assures a more accurate description of its shape. The crack propagation process is divided into stages. Each subsequent stage differs from the previous one by the crack shape modified due to the crack length increment in the calculated direction, and the linear stationary boundary value problem of elasticity is solved under the assumption of small deformations. To check the adequacy of the model, an experiment on crack propagation in glass samples with an initial cutoff under uniaxial compression has been performed. Samples of size 200×100 mm with a 2.5×40 mm central cutout at an angle of 30 ° to the horizontal axis are made from 4 mm thick window glass. Vertical loading is increased until the crack passes through the sample. The relative difference between the calculated and experimental crack paths does not exceed 5%. The numerical model developed is used to solve the problem of secondary crack growth for different values of stress field anisotropy in the oil ground layer. The factors of crack propagation re-fracturing along the normal to the crack primary gap are defined: 1) stress anisotropy ratio> 0.8; 2) growth of discharge pressure; 3) increase of primary crack disclosure.