Scalability of the deterministic and Bayesian approaches to production-data integration into reservoir models
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SummaryCurrent techniques for production-data integration into reservoir models can be broadly grouped into two categories: deterministic and Bayesian. The deterministic approach relies on imposing parameter-smoothness constraints using spatial derivatives to ensure large-scale changes consistent with the low resolution of the production data. The Bayesian approach is based on prior estimates of model statistics such as parameter covariance and data errors and attempts to generate posterior models consistent with the static and dynamic data. Both approaches have been successful for field-scale applications, although the computational costs associated with the two methods can vary widely. To date, no systematic study has been carried out to examine the scaling properties and relative merits of the methods.We systematically investigate the scaling of the computational costs for the deterministic and the Bayesian approaches for realistic field-scale applications. Our results indicate that the deterministic approach exhibits a linear increase in the CPU time with model size compared to a quadratic increase for the Bayesian approach. We also propose a fast and robust adaptation of the Bayesian formulation that preserves the statistical foundation of the Bayesian method and at the same time has a scaling property similar to that of the deterministic approach. We demonstrate the power and utility of our proposed method using synthetic examples and a field example from the Goldsmith field, a carbonate reservoir in west Texas.
