INVESTIGATION OF THE NON-STATIONARY TEMPERATURE FIELD IN A RESERVOIR WITH A HYDRAULIC FRACTURING BASED ON AN ANALYTICAL MODEL

Abstract

Currently, well temperature studies are widely used to solve various problems of control and monitoring of hydraulic fracturing. Temperature data measured in production wells during and after hydraulic fracturing provide important information about non-stationary filtration and thermal processes that are sensitive to fracture parameters — position and orientation, geometry and filtration characteristics. Mathematical models developed for calculating non-stationary pressure and temperature fields with known geometry and filtration-capacitive properties of the fracture and reservoir, in the general case, can be numerical and analytical. In the quantitative interpretation of temperature measurements and solving inverse problems for estimating fracture parameters, the speed of calculating the temperature field is important, in this regard, the development of analytical mathematical models of non-isothermal filtration in a reservior with a hydraulic fracturing is relevant. The paper presents the results of a study of a non-stationary formation temperature field in a reservoir with a hydraulic fracture based on an analytical model. The developed analytical model takes into account convective heat transfer, heat and mass transfer between the fracture and the formation, thermodynamic (adiabatic and Joule — Thomson) effects. To control the calculation correctness and adequacy of the temperature field, the analytical solution was compared with numerical calculations in the Ansys Fluent software package. The non-stationary temperature formation features of the fluid flowing into the well in the constant withdrawal mode at various parameters of the fracture (width and permeability) are investigated. It was found that the temperature of the fluid flowing into the well increases in inverse proportion to the width and permeability of the fracture, and in the first hour after putting the well into operation, negative dynamics of the flowing liquid temperature is observed, the duration of which increases with the growth of the fracture width.