Semiphenomenological Model of Hydraulic Fracturing in Granular Media

Abstract

Abstract Petroleum engineers have faced the problem of hydraulic fracturing in soft rock formations for many years. However, existing programs used with soft rock formations often do not provide satisfactory treatment designs. Difficulties emerge because hydraulic fracturing in soft rock involves development of a plastic zone near the fracture surface, where rocks partly lose their cohesion. This study has developed a more appropriate model for fracture design, which takes into account processes in the plastic zone for the special case of soft rock that is a cohesionless granular impermeable medium. The real problem of hydraulic fracturing in an elastoplastic medium has been represented in the model as brittle hydraulic fracture growth in a quasielastic medium. The medium resistance to fracture development is determined by variable apparent fracture toughness, which is a function of the fracture length and is found from the analysis of energy dissipation in the plastic zone. The dependence of the apparent fracture toughness on input parameters and fracture width at the fracturing fluid front has been established. It reflects the specific feature of the granular medium deforming and closes the equation set of the problem. Semianalytic solutions are obtained. First, there is the area of input parameters, where the effect of plasticity on fracture geometry is significant. Secondly, fracture behavior depends on the typical magnitude of friction forces on fracture sides, but it depends also on the fracturing fluid rheology. This new model of hydraulic fracturing in a granular medium is an improvement over existing models because traditional brittle fracture models do not take into account the specific rheology of soft rocks and poorly predict fracture geometry. Newer elastoplastic models are unclosed because the size of the plastic zone is undefined. Also, they usually are finite element models and cannot be used for the calculation of practical fracture designs because of time limitations. This work is only the first step toward practical hydraulic fracturing design in soft rock formations. The model is supposed to be developed and validated against experimental results or field data.