Hydraulic fracturing is a technique for enhancing the extraction of oil and gas from deep underground sources. Two important goals during this process are to achieve a final fracture with a predefined geometry and to have a proper distribution of proppant material within the fracture to keep the fracture walls open and allow oil and gas to flow to the surface. The hydraulic fracturing system contains limited real-time measurements of the actual fracture conditions largely due to the remote

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... rranean location where the fracture propagates. The fracturing process is characterized by multiphase transport, proppant settling, and coupling of fluid and fracture growth mechanics, all occurring within a time-varying spatial domain. These features present a challenge for the implementation of online feedback control of the fracture growth and proppant placement, and there are very few accounts of attempting this goal in the open literature. To address these issues, the current work proposes a control strategy that allows for closed-loop model-based control of the hydraulic fracturing process. Previous work introduced a dynamic fracture model capable of describing the fracture propagation, fluid and particle transport, proppant bank formation, and fracture closure processes necessary to determine the fracture state evolution and predict the fracture's final performance. The QDMC (quadratic-dynamic matrix control) form of model-based control is studied. A particle filter provides a means for effective state estimation due to limited real-time measurements. Controlling the fracture geometry and proppant distribution within a hydraulic fracture is a novel application for real-time model-based control. Results of a numerical study are provided to demonstrate the performance of the closed-loop system.