Nandi Formentin, Helena (Durham University and University of Campinas) | Vernon, Ian (Durham University) | Avansi, Guilherme Daniel (University of Campinas) | Caiado, Camila (Durham University) | Maschio, Célio (University of Campinas) | Goldstein, Michael (Durham University) | Schiozer, Denis José (University of Campinas)
Reservoir simulation models incorporate physical laws and reservoir characteristics. They represent our understanding of sub-surface structures based on the available information. Emulators are statistical representations of simulation models, offering fast evaluations of a sufficiently large number of reservoir scenarios, to enable a full uncertainty analysis. Bayesian History Matching (BHM) aims to find the range of reservoir scenarios that are consistent with the historical data, in order to provide comprehensive evaluation of reservoir performance and consistent, unbiased predictions incorporating realistic levels of uncertainty, required for full asset management. We describe a systematic approach for uncertainty quantification that combines reservoir simulation and emulation techniques within a coherent Bayesian framework for uncertainty quantification.
Our systematic procedure is an alternative and more rigorous tool for reservoir studies dealing with probabilistic uncertainty reduction. It comprises the design of sets of simulation scenarios to facilitate the construction of emulators, capable of accurately mimicking the simulator with known levels of uncertainty. Emulators can be used to accelerate the steps requiring large numbers of evaluations of the input space in order to be valid from a statistical perspective. Via implausibility measures, we compare emulated outputs with historical data incorporating major process uncertainties. Then, we iteratively identify regions of input parameter space unlikely to provide acceptable matches, performing more runs and reconstructing more accurate emulators at each wave, an approach that benefits from several efficiency improvements. We provide a workflow covering each stage of this procedure.
The procedure was applied to reduce uncertainty in a complex reservoir case study with 25 injection and production wells. The case study contains 26 uncertain attributes representing petrophysical, rock-fluid and fluid properties. We selected phases of evaluation considering specific events during the reservoir management, improving the efficiency of simulation resources use. We identified and addressed data patterns untracked in previous studies: simulator targets,
We advance the applicability of Bayesian History Matching for reservoir studies with four deliveries: (a) a general workflow for systematic BHM, (b) the use of phases to progressively evaluate the historical data; and (c) the integration of two-class emulators in the BHM formulation. Finally, we demonstrate the internal discrepancy as a source of error in the reservoir model.
La Rosa Almeida, Forlan (University of Campinas) | Nandi Formentin, Helena (University of Campinas) | Maschio, Célio (University of Campinas) | Davolio, Alessandra (University of Campinas) | José Schiozer, Denis (University of Campinas)
This paper proposes new objective functions to assimilate dynamic data for history matching, and evaluates their influence on the uncertainty conditioning. Representative events are observed and evaluated separately for the available dynamic data. The proposed objective functions evaluate two specific events: (1) the production transition behavior between the historical and forecasting period, and (2) the water breakthrough time. To assess production transition behavior, the deviation between the latest available historical data is compared with the forecast value, at a specific moment, under forecasting conditions. To assess water breakthrough, the irruption time error is measured in addition to the water-rate objective function. The new objective functions are normalized using the Normalized Quadratic Deviation with Sign, for comparison with conventional objective functions (