Journal
INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH
Volume 57, Issue 11, Pages 3977-3989Publisher
AMER CHEMICAL SOC
DOI: 10.1021/acs.iecr.7b04927
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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, parametrization is performed to reduce the dimensionality of spatially varying Youngs 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 a process model with updated spatially varying geological parameters, which is able to make an accurate prediction of the fracture propagation dynamics in hydraulic fracturing. Next, we use the updated high-fidelity process model in a model predictive control framework to construct a closed-loop system of hydraulic fracturing to achieve uniform proppant concentration at the end of pumping.
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