POD-based EnKF estimation of heterogeneous reservoir parameters for feedback control of hydraulic fracturing
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2018 Elsevier B.V. Accurate characterization of reservoir properties is of central importance to achieve a desired fracture geometry during a hydraulic fracturing process. However, the estimation of spatially varying geological properties in hydraulic fracturing is inherently ill-posed due to a limited number of measurements. In this work, parameterization is performed to reduce the dimensionality of spatially varying Young's modulus profiles via proper orthogonal decomposition (POD), and a data assimilation technique called Ensemble Kalman filter (EnKF) is used to estimate the parameter values in the reduced low-dimensional subspace. Through a series of simulation results, it is demonstrated that the POD-based EnKF technique provides accurate process models with updated spatially varying geological parameters. Next, we use the updated high-fidelity process model in a model predictive control framework to construct a closed-loop system that achieves uniform final proppant concentration in a hydraulic fracturing process.