Real-Time Reservoir Model Updating Using Ensemble Kalman Filter With Confirming Option

Abstract

Summary The ensemble Kalman Filter technique (EnKF) has been reported to be very efficient for real-time updating of reservoir models to match the most current production data. Using EnKF, an ensemble of reservoir models assimilating the most current observations of production data is always available. Thus, the estimations of reservoir model parameters, and their associated uncertainty, as well as the forecasts are always up-to-date. In this paper, we apply the EnKF for continuously updating an ensemble of permeability models to match real-time multiphase production data. We improve the previous EnKF by adding a confirming option (i.e., the flow equations are re-solved from the previous assimilating step to the current step using the updated current permeability models). By doing so, we ensure that the updated static and dynamic parameters are always consistent with the flow equations at the current step. However, it also creates some inconsistency between the static and dynamic parameters at the previous step where the confirming starts. Nevertheless, we show that, with the confirming approach, the filter shows better performance for the particular example investigated. We also investigate the sensitivity of using a different number of realizations in the EnKF. Our results show that a relatively large number of realizations are needed to obtain stable results, particularly for the reliable assessment of uncertainty. The sensitivity of using different covariance functions is also investigated. The efficiency and robustness of the EnKF is demonstrated using an example. By assimilating more production data, new features of heterogeneity in the reservoir model can be revealed with reduced uncertainty, resulting in more accurate predictions of reservoir production. Introduction The reliability of reservoir models could increase as more data are included in their construction. Traditionally, static (hard and soft) data, such as geological, geophysical, and well log/core data are incorporated into reservoir geological models through conditional geostatistical simulation (Deutsch and Journel 1998). Dynamic production data, such as historical measurements of reservoir production, account for the majority of reservoir data collected during the production phase. These data are directly related to the recovery process and to the response variables that form the basis for reservoir management decisions. Incorporation of dynamic data is typically done through a history-matching process. Traditionally, history matching adjusts model variables (such as permeability, porosity, and transmissibility) so that the flow simulation results using the adjusted parameters match the observations. It usually requires repeated flow simulations. Both manual and (semi-) automatic history-matching processes are available in the industry (Chen et al. 1974; He et al. 1996; Landa and Horne 1997; Milliken and Emanuel 1998; Vasco et al. 1998; Wen et al. 1998a, 1998b; Roggero and Hu 1998; Agarwal and Blunt 2003; Caers 2003; Cheng et al. 2004). Automatic history matching is usually formulated in the form of a minimization problem in which the mismatch between measurements and computed values is minimized (Tarantola 1987; Sun 1994). Gradient-based methods are widely employed for such minimization problems, which require the computation of sensitivity coefficients (Li et al. 2003; Wen et al. 2003; Gao and Reynolds 2006). In the recent decade, automatic history matching has been a very active research area with significant progress reported (Cheng et al. 2004; Gao and Reynolds 2006; Wen et al. 1997). However, most approaches are either limited to small and simple reservoir models or are computationally too intensive for practical applications. Under the framework of traditional history matching, the assessment of uncertainty is usually through a repeated history-matching process with different initial models, which makes the process even more CPU-demanding. In addition, the traditional history-matching methods are not designed in such a fashion that allows for continuous model updating. When new production data are available and are required to be incorporated, the history-matching process has to be repeated using all measured data. These limit the efficiency and applicability of the traditional automatic history-matching techniques.

Real‐time groundwater flow modeling with the Ensemble Kalman Filter: Joint estimation of states and parameters and the filter inbreeding problem

“…The permeabilities updated after an analysis step were used again as input to recalculate the last time step and to obtain the corrected pressure solution. Wen and Chen [2006] found that their approach outperformed noniterative EnKF. Moradkhani et al [2005] handled the joint estimation of states and parameters with a dual approach.…”

“…Wen and Chen [2006] proposed a rerun option to solve these problems. The permeabilities updated after an analysis step were used again as input to recalculate the last time step and to obtain the corrected pressure solution.…”

“…In some studies in the petroleum engineering literature it was found that iterative EnKF gave a better performance than noniterative EnKF [Wen and Chen, 2006;Gu and Oliver, 2007]. Here the three different algorithms were compared for 100 and 500 realizations, and four different methods to update the log-transmissivities (a = 0.1 or a = 1.0 and updating each month or each 2 months).…”

A review of closed-loop reservoir management

“…Oliver (2004, 2005a, b) investigated a highly nonlinear problem of facies estimation using the EnKF method. When using the EnKF method, Lorentzen et al (2005) discussed the choice of initial ensemble members, while Wen and Chen (2006) focused on the effect of ensemble size. Reynolds (2012, 2013) incorporated automatic history matching in an integrated geomodeling workflow using the ensemble smoother method.…”

A Bayesian consistent dual ensemble Kalman filter for state-parameter estimation in subsurface hydrology

“…Several studies argued that the joint EnKF may suffer from important inconsistencies between the estimated state and parameters that could degrade the filter performance, especially with large-dimensional and strongly nonlinear systems (e.g., Moradkhani et al, 2005b;Chen and Zhang, 2006;Wen and Chen, 2007). One classical approach that has been proposed to tackle this issue is the so-called dual filter, which separately updates the state and parameters using two interactive EnKFs, one acting on the state and the other on the parameters (Moradkhani et al, 2005b).…”