Nowadays, the only economic and effective way to exploit shale reservoirs is multi-stage fracturing of horizontal wells. The backflow after fracturing affects the damage degree of a fracturing fluid to a formation and fracture conductivity, and directly influences a fracturing outcome. At present, the backflow control of the fracturing fluid mostly adopts empirical methods, lacking a reliable theoretical basis. Therefore, it is of positively practical significance to reasonably optimize a flowback process and control the flowback velocity and flowback process of a fracturing fluid. On the other hand, the previous research on the productivity of multi-stage fracturing horizontal wells after fracturing is limited, and an equation derivation process has been simplified and approximated to a certain extent, so its accuracy is significantly affected. Based on previous studies, this paper established a new mathematical model. This model optimizes the flowback velocity after fracturing by dynamically adjusting a choke size and analyzes and predicts the production performance after fracturing. To maximize fracture clean-up efficiency, this work builds the model for a dynamic adjustment of choke sizes as wellhead pressure changes over time. It uses a two-phase (gas and liquid) flow model along the horizontal, slanted and vertical sections. The forces acting on proppant particles, filtration loss of water, the compressibility of a fracturing fluid, wellbore friction, a gas slippage effect, water absorption and adsorption are simultaneously considered. With the theories of mass conservation, we build a mathematical model for predicting production performance from multi-fractured horizontal wells with a dynamic two-phase model considering dual-porosity, stress-sensitivity, wellbore friction, gas adsorption and desorption. In this model, the gas production mechanisms from stimulated reservoir volume and gas and water relative permeabilities are employed. Based on shale reservoir parameters, wellhead pressure, a choke size, a gas/liquid rate, cumulative gas/liquid production, cumulative filtration loss and a flowback rate are simulated. In the simulations, the influential factors, such as shut-in soak time of the fracturing fluid, forced flowback velocity, fracturing stages and fracture half-length after fracturing, are studied. It is found by comparison that in the block studied, when a well is shut in four days after fracturing, the dynamic choke size is adjusted with wellhead pressure changing over time, the fracturing stage is 11, and the fracture half-length is 350 meters, the fracture conductivity after flowback is the largest, and the productivity of the horizontal well is the highest.

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