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The standard formulation of the ensemble Kalman filter (EnKF) does not take into account the physical constraints on state variables during the data assimilation step so constraint violations are often handled heuristically. The physical constraints often contain valuable information about the system which are critical for the valid initialization and forecast. A successful enforcing of these constraints during the data assimilation step of the EnKF is necessary for valid estimation of reservoir properties.

A number of solutions to the problem of constraint violation have been proposed in the past including the constrained EnKF (CEnKF), iterative EnKF, transformation of state variables, reparameterization, and truncation. In this paper, we present an interior-point method for incorporating the inequality constraints into the EnKF methodology (IPCEnKF). In this approach, the objective function for data assimilation is …