The non-stationary temperature field of the fracturing fluid during the propagation of planar 3D hydraulic crack

Under the influence of temperature the viscosity of the fracturing fluid changes that in its turn affects the final shape of the fracture. Therefore, there is a need for a model that allows calculating the temperature of the liquid in the planar 3D hydraulic crack propagating in a layered medium. The resulting code has to consume minimum computational resources and use the available data for the thermal properties of the rock and fluid. The key features of the model developing in the present work are the reduction of the system of partial differential equations to a system of ordinary differential equations, as well as adopting the method of universal asymptotes for determining the position of the crack front.