A mathematical model of fracturing fluid leak-off based on dynamic discrete grid system

Abstract

Based on the classical PKN two-dimensional fracture propagation mathematical model, the two-dimensional leak-off model of fracturing fluid of fractured dual-medium reservoir is established by considering the time-varying non-Newtonian fracturing fluid leak-off coefficient in the stretching process of fractures. Using the finite element difference method, a dynamic discrete grid system is established and solved by Newton-Raphson iterative method. At the same time, the effect on fracturing fluid leak-off of the fractured reservoir stress sensitivity coefficient, the pumping rate, and the propagating length of the fractures is analyzed. As it is analyzed, under the combined effect of the formation pressure, the fracture pressure, the edge effect, and the fracture permeability, the greater the stress sensitivity coefficient is, the smaller the leak-off rate and coefficient are. However, the greater pumping rate is, the larger leak-off rate and coefficient are. If both of them increase to a certain value, the leak-off coefficient firstly decreases , and then increases; the longer the fracture is, in the same position, the larger fracturing fluid leak-off coefficient is; and the greater boundary effect is, the larger fracturing fluid leak-off coefficient near the pinch point is.