Identification of spatially varying geological properties in a heterogeneous reservoir using EnKF and POD based parameterization

Parameter estimation problems in large-scale non-linear systems such as hydraulic fracturing processes are inherently ill-posed owing to the large number of unknown parameters. Moreover, the estimation of parameters is paramount in such processes due to its consequences on the final fracture geometry which directly influences the productivity of fractured wells. Reduced order modeling can play a pivotal role in redefining these problems to alleviate its ill-posed nature by increasing the identifiability of the parameters. Within this context, in this paper, we apply proper orthogonal decomposition (POD) to parameterize the heterogeneous Young's modulus and use the ensemble kalman filter (EnKF) to estimate the reduced parameters. We perform several forward simulations with different realizations and assimilate the available measurement data. Through a series of simulation results, we demonstrate that the integrated order-reduction and data assimilation techniques provide a model with updated spatially varying geological parameters, which has good predictive capabilities of the fracture propagation dynamics in hydraulic fracturing.