Pump-stopping pressure drop model considering transient leak-off of fracture network

Abstract

By introducing the coupling flow expressions of main fracture-matrix, secondary fracture-matrix and main fracture-secondary fracture into the traditional main fracture material balance equation, the “main fracture—secondary fracture—matrix” leak-off coupling flow model is established. The pressure-dependent fracture width equation and the wellbore injection volume equation are coupled to solve the pressure-rate continuity problem. The simulation and calculation of the bottomhole pressure drop and fracture network closure after the pump stopping in slickwater volumetric fracturing treatment are realized. The research results show that the log-log curve of pump-stopping bottomhole pressure drop derivative presents five characteristic slope segments, reflecting four dominant stages, i.e. inter-fracture crossflow, fracture network leak-off, fracture network closure and residual leak-off, after pump shutdown. At the initial time of pump shutdown for volumetric fracturing treatment of horizontal well, the crossflow between main and secondary fractures is obvious, and then the leak-off becomes dominant. The leak-off of main and secondary fractures shows a non-uniform decreasing trend. Specifically, the leak-off of main fractures is slow, while that of secondary fractures is fast; the fracture network as a whole presents the leak-off law of fast first, then slow, until close to zero. The influence of fracture network conductivity on the shape of pressure decline curve is relatively weaker than that of fracture network size. The fracture network conductivity is positively correlated with leak-off volume and fracture closure. The secondary fracture size is positively correlated with leakoff volume and closure of the secondary fracture, but negatively correlated with closure of the main fracture. Field data validation proves that the proposed model and simulation results can effectively reflect the closure characteristics of the fracture network, and the interpretation results are reliable and can reflect the non-uniform stimulation performance of each fracturing stage of an actual horizontal well.