PARAMETERIZATION TECHNIQUES TO IMPROVE MASS CONSERVATION AND DATA ASSIMILATION FOR ENSEMBLE KALMAN FILTER

The ensemble Kalman filter (EnKF) has shown great potential for becoming a useful tool for assisted or automatic history matching. In particular, it has been shown to be possible to efficiently integrate many types of data and to history match many types of model variables, including gridblock permeabilities and porosities, facies locations and relative permeability curves. At each analysis step of EnKF, model and state variables are updated using a linear combination of the forward models to honor the production history and prior knowledge of the reservoir description. The analysis step, however, could result in updates that are beyond their plausible range, violation of mass conservation and loss of geological realism. Proper selection of the model and state variables to be updated in EnKF is critically important to achieve good data match, retain geological realism of the updated realizations and satisfy nonlinear constraints that may apply. In this paper, we discuss parameterization techniques for these three purposes. We revisit the updating formulation of EnKF and investigate the constraint on the weighting coefficients at the analysis step. We show that by reparameterization of the state vector nonlinear constraints, for example conservation of mass or volume, can be satisfied without complicating the updating process. The presence of geological trends or channels induces strong non‑Gaussianity that violates the Gaussian assumption of the EnKF analysis step, and appropriate parameterization is necessary to constrain the EnKF solution. Finally, the choice of model variables also depends on available observations. Including model variables that are highly sensitive to certain types of data provides improved data match and more realistic updates. A large scale reservoir model is used to illustrate the parameterization techniques. By using these techniques multiple realistic history matched models were obtained that provide reliable basis for accessing uncertainty and design of reservoir management strategy.