Streamline-based three-phase history matching

Geologic models derived from static data alone typically fail to reproduce the production history of a reservoir, thus the importance of reconciling simulation models to the dynamic response of the reservoir. This necessity has been the motivation behind the active research work in history matching. Traditionally, history matching is performed manually by applying local and regional changes to reservoir properties. While this is still in general practice, the subjective overtone of this approach, the time and manpower requirements, and the potential loss of geologic consistency have led to the development of a variety of alternative workflows for assisted and automatic history matching. Automatic history matching requires the solution of an inverse problem by minimizing an appropriately defined misfit function. Recent advances in geostatistics have led to the building of high-resolution geologic models consisting of millions of cells. Most of these are scaled up to the submillion size for reservoir simulation purposes. History matching even the scaled up models is computationally prohibitive. The associated cost in terms of time and manpower has led to increased interest in efficient history matching techniques and in particular, to sensitivity-based algorithms because of their rapid convergence. Furthermore, of the sensitivity-based methods, streamline-based production data integration has proven to be extremely efficient computationally. In this work, we extend the history matching capability of the streamline-based technique to three-phase production while addressing in general, pertinent issues associated with history matching. We deviate from the typical approach of formulating the inverse problem in terms of derived quantities such as GOR and Watercut, or measured phase rates, but concentrate on the fundamental variables that characterize such quantities. The presented formulation is in terms of well node saturations and pressures. Production data is transformed to composite saturation quantities, the time variation of which is matched in the calibration exercise. The dependence of the transformation on pressure highlights its importance and thus a need for pressure match. To address this need, we follow a low frequency asymptotic formulation for the pressure equation. We propose a simultaneous inversion of the saturation and pressure components to account for the interdependence and thus, high non-linearity of three phase inversion. We also account for global parameters through experimental design methodology and response surface modeling. The validity of the proposed history matching technique is demonstrated through application to both synthetic and field cases.