History matching with an ensemble Kalman filter and discrete cosine parameterization

History matching of large hydrocarbon reservoirs is challenging because of several reasons including: (1) scarcity of available measurements relative to the number of unknowns, leading to an ill-posed inverse problem, (2) computational effort required for large reservoir problems, and (3) the need to insure that solutions are geologically realistic. All of these problems can be helped by using algorithms that rely on efficient and parsimonious descriptions (or parameterizations) of reservoir properties. This paper demonstrates the use of a novel parameterization approach, the discrete cosine transform, for history matching with a recently introduced sequential estimation technique, i.e., the ensemble Kalman filter. The proposed approach exploits the structure of the estimation and parameterization algorithms to reduce the size of reservoir states (pressures and saturations) as well as parameters (e.g., intrinsic permeability) with a marginal loss in accuracy. The introduced methodology eliminates redundancy in posing the estimation problem and results in additional computational savings. Application and generality of this approach are demonstrated using two waterflooding experiments characterized by different types of geological variability.

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