FORMATION МODEL OF A CRACK IN A ROCK WITH NON-STATIONARY SHAPE PARAMETERS DURING HYDRAULIC FRACTURING

Abstract

Currently, hydraulic fracturing (HF) is used for hard-to-recover hydrocarbon reserves. As a result of hydraulic fracturing, cracks are formed in productive formations. To select the technological parameters of hydraulic fracturing, it is necessary to be able to calculate the fracture shape parameters – length and width. In this regard, the creation of a mathematical model for calculating the parameters of the shape of a crack in a rock is an urgent task. The article presents a mathematical model for the development of a crack in a rock, taking into account the non-stationary parameters of its shape and the flow regimes of the hydraulic fracturing fluid. Also, the proposed mathematical model, unlike the existing ones, takes into account the variable nature of the coefficient of fluid leakage into the reservoir, and the criterion for opening a new rock element. The paper presents the results of a numerical experiment and compares the proposed mathematical model with the results of a numerical experiment. The scientific novelty of the work is the proposed mathematical model of a crack in the rock, taking into account the non-stationary parameters of its shape. The mathematical model, in contrast to the existing ones, is based on the differential equation of motion of the elementary rock element of the opening fracture, taking into account the leakage of hydraulic fracturing fluid into the rock formation. The recommendation for application in engineering practice of the obtained mathematical model is the obtained values of the crack shape, which are comparable with numerical experiments.