Current 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. This is particularly the case for the Bayesian approach that utilizes a prior covariance matrix that can be large and full. To date, no systematic study has been carried out to examine the scaling properties and relative merits of the methods. The main purpose of this work is twofold. First, 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. Second, we 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. This can lead to orders of magnitude savings in computation time for model sizes greater than 100,000 grid blocks. 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. The use of the new efficient Bayesian formulation along with the Randomized Maximum Likelihood method allows straightforward assessment of uncertainty. The former provides computational efficiency and the latter avoids rejection of expensive conditioned realizations.

Current 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. This is particularly the case for the Bayesian approach that utilizes a prior covariance matrix that can be large and full. To date, no systematic study has been carried out to examine the scaling properties and relative merits of the methods. The main purpose of this work is twofold. First, 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. Second, we 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. This can lead to orders of magnitude savings in computation time for model sizes greater than 100,000 grid blocks. 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. The use of the new efficient Bayesian formulation along with the Randomized Maximum Likelihood method allows straightforward assessment of uncertainty. The former provides computational efficiency and the latter avoids rejection of expensive conditioned realizations.

Integration of dynamic data is critical for reliable reservoir description and has been an outstanding challenge for the petroleum industry. This work develops practical dynamic data integration techniques using streamline approaches to condition static geological models to various kinds of dynamic data, including two-phase production history, interference pressure observations and primary production data. The proposed techniques are computationally efficient and robust, and thus well-suited for large-scale field applications. We can account for realistic field conditions, such as gravity, and changing field conditions, arising from infill drilling, pattern conversion, and recompletion, etc., during the integration of two-phase production data. Our approach is fast and exhibits rapid convergence even when the initial model is far from the solution. The power and practical applicability of the proposed techniques are demonstrated with a variety of field examples. To integrate two-phase production data, a travel-time inversion analogous to seismic inversion is adopted. We extend the method via a 'generalized travel-time' inversion to ensure matching of the entire production response rather than just a single time point while retaining most of the quasi-linear property of travel-time inversion. To integrate the interference pressure data, we propose an alternating procedure of travel-time inversion and peak amplitude inversion or pressure inversion to improve the overall matching of the pressure response. A key component of the proposed techniques is the efficient computation of the sensitivities of dynamic responses with respect to reservoir parameters. These sensitivities are calculated analytically using a single forward simulation. Thus, our methods can be orders of magnitude faster than finite-difference based numerical approaches that require multiple forward simulations. Streamline approach has also been extended to identify reservoir compartmentalization and flow barriers using primary production data in conjunction with decline type-curve analysis. The streamline 'diffusive' time of flight provides an effective way to calculate the drainage volume in 3D heterogeneous reservoirs. The flow barriers and reservoir compartmentalization are inferred based on the matching of drainage volumes from streamline-based calculation and decline type-curve analysis. The proposed approach is well-suited for application in the early stages of field development with limited well data and has been illustrated using a field example from the Gulf of Mexico.

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