A mathematical model for hydraulic fracture propagation in three dimensional poroelastic medium

Currently hydraulic fracturing (HF) is a stimulation technique which is most widely used during industrial development of gas and oil reservoirs. At the same time widely used mathematical models of hydraulic fracturing are often oversimplified, as fracture geometry is assumed to be planar and predefined, a comprehensive treatment of geomechanical effects is seldom considered, and the fracture growth is often assumed using empirical criteria. Despite their successful applications, their possibilities are not sufficient for solving a number of important problems of reservoir development. This paper considers a complete three dimensional self-consistent mathematical model for large scale hydraulic fracture development. The model consist of several groups of equations including non-isothermal Biot poroelastic model to describe reservoir behavior, Reynold’s lubrication equations to describe flow inside fracture and corresponding “reservoir”/”fracture” interface conditions. The fracture’s geometric model assumes that it is an arbitrary smooth surface with a boundary. The fracture’s surface evolution is governed by the physically-sound criteria based on J-integral of Rice and Cherepanov in the vector from. The model is suitable for describing hydraulic fracture development as well as for the analysis of flow and geomechanical effects induced by normal operations of a fractured well. The main purpose of the suggested model is a consistent description of hydraulic fracture development in a general setting with a minimal number of a-priory assumptions and, at the same time, useful for solution of applied reservoir development problems using advanced numerical simulation techniques. Thus, we have also given a short review of the computational algorithms suitable for the model’s implementation.