Modeling and Control of Proppant Distribution of Multistage Hydraulic Fracturing in Horizontal Shale Wells
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2019 American Chemical Society. In shale rock formations, multistage hydraulically fractured horizontal wells with slick water are generally used to enhance the production of shale gas and oil. However, slick water proppant transport in simultaneously growing multiple fractures has not been well studied. Motivated by these considerations, we initially focus on the development of a new high-fidelity model for simultaneously growing multiple fractures to describe the fracture propagation by explicitly accounting for stress shadow effects as well as the proppant transport. The hydrocarbon production rate through these multiple fractures is strongly dependent on the proppant distribution within the fractures. To regulate the distribution of proppant at the end of pumping in simultaneously growing multiple fractures, we propose a model-based pumping schedule. Specifically, we develop a reduced-order model utilizing the simulation data from the above-developed high-fidelity model, which is then used to design a Kalman filter and a model predictive controller (MPC) to estimate unmeasurable states and compute online fracturing fluid pumping schedules, respectively. By utilizing the proposed MPC, we show that the proppant bank height at the end of pumping is uniform across multiple fractures.
