A Three-Dimensional Thermal Model for Hydraulic Fracturing

Abstract Distributed Temperature Sensing (DTS) can provide the wellbore temperature profile during the hydraulic fracturing treatment. This temperature profile is a complex function of many parameters including leakoff coefficient, thermal conductivities of the rock and the injected fluid, minimum stress, porosity, etc. Because of these complexities analytical solutions are not capable of adequately determining the effect of these various parameters on the temperature profile. Moreover, these parameters may vary from one layer to another. Therefore, a three-dimensional temperature model is needed to estimate the fracture parameters by matching the wellbore temperature profile with simulation results. A three-dimensional temperature model was developed to determine the temperature profile in and around the fracture based on a pseudo three-dimensional (P3D) fracture propagation model. The propagation model, the wellbore thermal model, and the fracture thermal model were solved simultaneously to consider the effect of temperature and pressure on various parameters, such as specific volume. Moreover, the results of the fracture propagation simulation of five cases were compared with the results of full 3D simulators, obtained from literature. The fracture half-length, fluid efficiency and the net pressure at the entrance of the fracture simulated by this model were in good agreement with the results of full 3D simulation. The minifrac propagation, closure and its temperature were also simulated by this model. The pressure decline curve was predicted by simulator while the effect of temperature and pressure on other variables, such as fracturing fluid density and viscosity, was considered. Additionally, it was observed that the location of optical fiber cable was very important in DTS temperature measurement. Accordingly, a method is provided to consider the effect of the distance of the fiber optics cable from the fracture. The development of this hydraulic fracturing 3D thermal model is another step for the interpretation of the wellbore thermal profile, measured by the DTS technology during hydraulic fracturing treatment. This model is also capable of being used for more accurate hydraulic fracturing design and analysis.