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ABSTRACT: The study presents an analysis of the back-stress effect on precise determination of in-situ stresses in a model samples in laboratory experiments on hydraulic fracturing. Main stage of this study included the determination of the fracture closure pressure using standard methods and comparing this pressure with the minimum loads applied to the sample. The comparison showed the inequality of these values. To eliminate the identified discrepancy, it was proposed to take into account the back-stress effect. This stress occurs due to an increase in pore pressure when fluid is filtrated into the reservoir from a hydraulic fracture. It affects the walls of the fracture, contributing to its closure. The second part of the study was devoted to analysis of back-stress effect impact on estimation of maximum horizontal stress. In this work, we evaluated the influence of this effect on the determination of the minimum and maximum stresses in the medium in laboratory experiments on hydraulic fracturing. Some assumptions about how to account for back-stress in the calculation of minimum stresses were considered. It was found that taking into account the back-stress when calculating the horizontal stresses significantly reduces the difference between the calculated values and experimental data. 1. INTRODUCTION The problem of boundary conditions estimation emerges often when dealing with reservoir geomechanics problems (Zoback, 2007). First of all, contrary to the classical problems of mathematical physics, determination of stress-strain state of rock masses cannot be carried out with boundary conditions postulated at real boundaries of the rock mass, as there are no distinct boundaries constraining the rock mass within a single domain (Mukhamediev, 2015). Information necessary for stress estimation can be obtained only at discrete points – from seismic events analysis or wellbore data. This paper is focused on the latter – the problem of using wellbore data to understand the in-situ stresses at rock mass via estimating stresses existing in the well vicinity.

Numerous laboratory and field experiments on hydraulic fracturing show that often classical elastic models are not able to accurately predict the values of breakdown pressure. In this work, computer simulation of the sample was carried out based on experiments conducted at the Institute of Geospheres Dynamics of the Russian Academy of Sciences (IDG RAS) and the Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences (IPE RAS). The geometry of the computational domain, the applied boundary conditions, and nonlinear properties were set based on the conditions of hydraulic fracturing experiments and the results of uniaxial compression tests. As a result of the simulation, it was revealed that the fractured fluid injected under pressure causes plastic deformation in the vicinity of the well, which, in turn, is the cause of the increased breakdown pressure.

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.