Fast History Matching of Finite-Difference Models Using Streamline-Derived Sensitivities

Abstract

Summary We propose a novel approach to history matching finite-difference models that combines the advantages of streamline models with the versatility of finite-difference simulation. Current streamline models are limited in their ability to incorporate complex physical processes and cross-streamline mechanisms in a computationally efficient manner. A unique feature of streamline models is their ability to analytically compute the sensitivity of the production data with respect to reservoir parameters using a single flow simulation. These sensitivities define the relationship between changes in production response because of small changes in reservoir parameters and, thus, form the basis for many history-matching algorithms. In our approach, we use the streamline-derived sensitivities to facilitate history matching during finite-difference simulation. First, the velocity field from the finite-difference model is used to compute streamline trajectories, time of flight, and parameter sensitivities. The sensitivities are then used in an inversion algorithm to update the reservoir model during finite-difference simulation. The use of a finite-difference model allows us to account for detailed process physics and compressibility effects. Although the streamline-derived sensitivities are only approximate, they do not seem to noticeably impact the quality of the match or the efficiency of the approach. For history matching, we use a generalized travel-time inversion (GTTI) that is shown to be robust because of its quasilinear properties and that converges in only a few iterations. The approach is very fast and avoids many of the subjective judgments and time-consuming trial-and-error steps associated with manual history matching. We demonstrate the power and utility of our approach with a synthetic example and two field examples. The first one is from a CO2 pilot area in the Goldsmith San Andreas Unit (GSAU), a dolomite formation in west Texas with more than 20 years of waterflood production history. The second example is from a Middle Eastern reservoir and involves history matching a multimillion-cell geologic model with 16 injectors and 70 producers. The final model preserved all of the prior geologic constraints while matching 30 years of production history.