Improved and More Rapid History Matching With a Nonlinear Proxy and Global Optimization
- A. Stan Cullick (Landmark Graphics Corporation) | William Douglas Johnson (Pavilion Energy Solutions) | Genbao Shi
- Document ID
- Society of Petroleum Engineers
- SPE Annual Technical Conference and Exhibition, 24-27 September, San Antonio, Texas, USA
- Publication Date
- Document Type
- Conference Paper
- 2006. Society of Petroleum Engineers
- 6.5.2 Water use, produced water discharge and disposal, 5.5.8 History Matching, 5.5.5 Evaluation of uncertainties, 5.5.7 Streamline Simulation, 2.3 Completion Monitoring Systems/Intelligent Wells, 6.1.5 Human Resources, Competence and Training, 5.6.9 Production Forecasting, 5.6.3 Deterministic Methods, 4.3.4 Scale, 5.1.5 Geologic Modeling, 5.5 Reservoir Simulation, 5.1.2 Faults and Fracture Characterisation
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The generation of reservoir simulation models that match field production data has been a long-time industry challenge. This paper presents two workflows for assisted history match. One workflow minimizes the misfit between simulated versus history data with a global optimizer, by adjusting reservoir and well unknown parameters in the simulation model. An alternative workflow is used to reduce the number of numerical simulations. The workflow trains a comprehensive nonlinear proxy model with a small set of numerical simulations from experimental design. The nonlinear proxy neural network is used to characterize parameter sensitivities to reservoir parameters and to generate solution sets of the parameters that match history. The neural network solution sets can be validated with the simulator or used as initial solutions for a full optimization. The paper demonstrates that the neural network is an excellent proxy for the numerical simulator over the trained parameter space. A field example from a water injection project illustrates the approach with excellent matches for individual well fluid rates, using a number of reservoir and well parameters. The use of the proxy yields excellent matches for well production profiles.
Reservoir simulation history match to observed production data has been a long-time challenge in the industry. History matching is by its nature an ill-posed optimization problem with many unknown reservoir parameters that could be adjusted to achieve a match against a relatively small amount of measured data at wells. The most common method of history match is to execute many simulations one-at-a-time, changing a few parameters in a trial-and-error fashion. Often, a reservoir simulation history match might require months of effort and many simulations to achieve a single model that neglects model non-uniqueness and often may not be a good predictor of future field performance1.
Automated history match algorithms have been tried virtually since the inception of finite-difference simulation several decades ago. A review is beyond the scope of this paper, but the Monograph by Wen et al2 provides an extensive review. Early in the development of assisted history match, the emphasis was on deterministic, gradient optimization algorithms that require complete derivatives of the production response with respect to reservoir parameters. Subsequently, the emphasis evolved to faster methods to compute the sensitivity coefficients, such as streamline simulation, with emphasis on preserving uncertainty2,3 through the integration of geostatistics. Recent developments with adjoint models4 have renewed interest in sensitivity-based algorithms. Other recent work utilizes Kalman filters5 to better quantify uncertainty. However, none of these methods have been taken up widely by practioners.
The approach proposed by Williams et al6 and implemented by Kromah et al7 within a "top-down reservoir modeling?? context has promise for practical application. The approach uses a genetic algorithm as a "black-box?? global optimizer in conjunction with the numerical simulator to achieve a flexible and scaleable history match, along with uncertainty quantification. Schulze-Riegert et al8,9, have a similar black-box global optimization approach, using an evolutionary algorithm.8,9. With black-box optimization, the number of required simulations to achieve a match can be very large, numbered in the hundreds of simulations6,8,9. If a single simulation model takes many hours to execute, there is good incentive to reduce the number of simulations for the optimization, even when utilizing a distributed computing system6.
|File Size||16 MB||Number of Pages||13|