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In this dissertation, we illustrate the problem of using the standard ensemble Kalman filter (EnKF) with a compositional model in which the updated CO 2 molar density in some regions of the model space is observed to take negative values while molar densities of the remaining components are increased. The results can include a spurious increase in reservoir pressure with a subsequent inability to maintain injection. In this dissertation, we present two different methods for incorporating the inequality constraints into the EnKF methodology.