Fast History Matching of Finite-Difference Models Using Streamline-Derived Sensitivities
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AbstractWe propose a novel approach to history matching finite-difference models that combines the advantage of the 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 efficiently 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 utilize 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 utilized in an inversion algorithm to update the reservoir model during finite-difference simulation.The use of 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 efficiency of the approach. For history matching, we use a generalized travel-time inversion that is shown to be extremely robust because of its quasi-linear properties and converges in only a few iterations. The approach is very fast and avoids much of the subjective judgments and time-consuming trial-and-errors associated with manual history matching. We demonstrate the power and utility of our approach using a synthetic example and two field examples. The first one is from a CO2 pilot area in the Goldsmith San Andreas Unit, a dolomite formation in west Texas with over 20 years of waterflood production history. The second example is from a giant 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.
