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A mathematical model of water-induced hydraulic fracture propagation is introduced in the paper. The main point of the proposed model being compared to the existing ones is the correct asymptotic behavior: the classical models of hydraulic fracture propagation being implemented for solving the problem of water-induced hydraulic fracture lead to infinite fracture growth. We use a special method of taking the leak off into account to get around this issue. It includes the analysis of poroelastic effects in the vicinity of the fracture. Applying this method to solve the problem of water-induced hydraulic fracture propagation a following result can be obtained: the fracture continues to grow as long as the leaks are less than the amount of fluid injected. Nevertheless, there is a moment when the leaks become equal to injection and thus the fracture growth stops. So the fracture length becomes a bounded function of time and the upper limit of it may be calculated and used in reservoir development as a final length of water-induced hydraulic fracture.

The study is concentrated on the analysis of the interaction between oil wells and water-induced hydraulic fractures. The problem is considered in terms of theory of poroelasticity, hydrodynamics and fracture mechanics. The hydrodynamic aspect of the problem is divided into two types: oil displacement by water injected and the study of water behaviour inside the fracture itself. Numerical modelling was used for solving the problems. A two dimensional problem of Perkins-Kern fracture propagation in a permeable medium is considered. The basic equation of piezoconductivity is used to describe the process of filtration outside the fracture with the boundary conditions defined by “well-formation” system. The proper pressure distribution in the fracture is determined from the solution of continuity equation and Navier-Stokes equation in one-dimensional form. Fracture is considered to be propagating perpendicular to the direction of the lowest principal stress which is determined by several factors analysed in the research. The paper suggests a method for considering the dynamic process of fracture propagation. This result can be further used to predict the water-induced hydraulic fracture geometry while planning the development of an oil field.