Conditioning Geostatistical Models to Two-Phase Production Data

Wu, Zhan; Reynolds, Albert C.; Oliver, Dean S.

doi:10.2118/49003-ms

Cited by 41 publications

(52 citation statements)

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“…While there is a long history of computing sensitivities of data to model variables for automatic history matching [3,6,18,19,23,24], the sensitivity of the state variables to the model variables (F in Eq. 9) is not as well documented, so it is more difficult to choose appropriate localization functions for the updates of the state variables.…”

Section: Cross-covariance and Distance-based Localizationmentioning

confidence: 99%

Cross-covariances and localization for EnKF in multiphase flow data assimilation

2009

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The ensemble Kalman filter has been successfully applied for data assimilation in very large models, including those in reservoir simulation and weather. Two problems become critical in a standard implementation of the ensemble Kalman filter, however, when the ensemble size is small. The first is that the ensemble approximation to cross-covariances of model and state variables to data can indicate the presence of correlations that are not real. These spurious correlations give rise to model or state variable updates in regions that should not be updated. The second problem is that the number of degrees of freedom in the ensemble is only as large as the size of the ensemble, so the assimilation of large amounts of precise, independent data is impossible. Localization of the Kalman gain is almost universal in the weather community, but applications of localization for the ensemble Kalman filter in porous media flow have been somewhat rare. It has been shown, however, that localization of updates to regions of non-zero sensitivity or regions of non-zero crosscovariance improves the performance of the EnKF when the ensemble size is small. Localization is necessary for assimilation of large amounts of independent data. The problem is to define appropriate localization functions for different types of data and different types of variables. We show that the knowledge of sensitivity alone is not sufficient for determination of the region of localization. The region depends also on the prior Y. Chen (B) covariance for model variables and on the past history of data assimilation. Although the goal is to choose localization functions that are large enough to include the true region of non-zero cross-covariance, for EnKF applications, the choice of localization function needs to balance the harm done by spurious covariance resulting from small ensembles and the harm done by excluding real correlations. In this paper, we focus on the distance-based localization and provide insights for choosing suitable localization functions for data assimilation in multiphase flow problems. In practice, we conclude that it is reasonable to choose localization functions based on well patterns, that localization function should be larger than regions of non-zero sensitivity and should extend beyond a single well pattern.

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Section: Cross-covariance and Distance-based Localizationmentioning

confidence: 99%

Cross-covariances and localization for EnKF in multiphase flow data assimilation

2009

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“…The use of adjoints for history matching was pioneered by Chen et al [18] and Chavent et al [19], who applied it to single-phase problems. Since then, many other researchers have modified and improved the application of adjoint models for multiphase history matching including Wasserman et al [20], Watson et al [21], Wu et al [22], Li et al [23], Wu and Datta-Gupta [24], and Zhang et al [25]. Gavalas et al [26] introduced the use of an eigenfunction expansion for the efficient parameterization of reservoir properties, which was also used later by Oliver [27] and Reynolds et al [28].…”

Section: Introductionmentioning

confidence: 99%

Efficient real-time reservoir management using adjoint-based optimal control and model updating

et al. 2006

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The key ingredients to successful real-time reservoir management, also known as a Bclosed-loop^approach, include efficient optimization and model-updating (historymatching) algorithms, as well as techniques for efficient uncertainty propagation. This work discusses a simplified implementation of the closed-loop approach that combines efficient optimal control and model-updating algorithms for real-time production optimization. An adjoint model is applied to provide gradients of the objective function with respect to the well controls; these gradients are then used with standard optimization algorithms to determine optimum well settings. To enable efficient history matching, Bayesian inversion theory is used in combination with an optimal representation of the unknown parameter field in terms of a KarhunenYLoeve expansion. This representation allows for the direct application of adjoint techniques for the history match while assuring that the two-point geostatistics of the reservoir description are maintained. The benefits and efficiency of the overall closed-loop approach are demonstrated through real-time optimizations of net present value (NPV) for synthetic reservoirs under waterflood subject to production constraints and uncertain reservoir description. For two example cases, the closed-loop optimization methodology is shown to provide a substantial improvement in NPV over the base case, and the results are seen to be quite close to those obtained when the reservoir description is known a priori.

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“…The change in the water cut, then, is most sensitive to properties along the streamline that is currently breaking through to the producer. The location of the most sensitive streamlines typically grows away from the direct path as time increases [127,171,183]. In singlephase reservoirs, when the reservoir production rate is fixed, the bottom hole pressure is most highly sensitive to the properties in the immediate neighborhood of the well.…”

Section: Sensitivity Of Production Datamentioning

confidence: 99%

Recent progress on reservoir history matching: a review

2010

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History matching is a type of inverse problem in which observed reservoir behavior is used to estimate reservoir model variables that caused the behavior. Obtaining even a single history-matched reservoir model requires a substantial amount of effort, but the past decade has seen remarkable progress in the ability to generate reservoir simulation models that match large amounts of production data. Progress can be partially attributed to an increase in computational power, but the widespread adoption of geostatistics and Monte Carlo methods has also contributed indirectly. In this review paper, we will summarize key developments in history matching and then review many of the accomplishments of the past decade, including developments in reparameterization of the model variables, methods for computation of the sensitivity coefficients, and methods for quantifying uncertainty. An attempt has been made to compare representative procedures and to identify possible limitations of each.

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Conditioning Geostatistical Models to Two-Phase Production Data

Cited by 41 publications

References 0 publications

Cross-covariances and localization for EnKF in multiphase flow data assimilation

Cross-covariances and localization for EnKF in multiphase flow data assimilation

Efficient real-time reservoir management using adjoint-based optimal control and model updating

Recent progress on reservoir history matching: a review

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