Data assimilation for transient flow in geologic formations via ensemble Kalman filter

Formation properties are one of the key factors in numerical modeling of flow and transport in geologic formations in spite of the fact that they may not be completely characterized. The incomplete knowledge or uncertainty in the description of the formation properties leads to uncertainty in simulation results. In this study, the ensemble Kalman filter (EnKF) approach is used for continuously updating model parameters such as hydraulic conductivity and model variables such as pressure head while simultaneously providing an estimate of the uncertainty through assimilating dynamic and static measurements, without resorting to the explicit computation of the covariance or the Jacobian of the state variables. A two-dimensional example is built to demonstrate the capability of EnKF and to analyze its sensitivity with respect to different factors such as the number of realizations, measurement timings, and initial guesses. An additional example is given to illustrate the applicability of EnKF to three-dimensional problems and to examine the model predictability after dynamic data assimilation. It is found from these examples that EnKF provides an efficient approach for obtaining satisfactory estimation of the hydraulic conductivity field with dynamic measurements. After data assimilation the conductivity field matches the reference field very well, and different kinds of incorrect prior knowledge of the formation properties may also be rectified to a certain extent.

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