Streamline Assisted Ensemble Kalman Filter for Rapid and Continuous Reservoir Model Updating

Abstract

Abstract The use of the ensemble Kalman filter (EnKF) appears to be a promising approach for data assimilation and assessment of uncertainties during reservoir characterization and performance forecasting. It provides a relatively straightforward approach to incorporating diverse data types including production and/or time-lapse seismic data. Unlike traditional sensitivity-based history matching methods, the EnKF relies on a cross-covariance matrix computed from an ensemble of reservoir models to relate reservoir properties to production data. For practical field applications, we need to keep the ensemble size small for computational efficiency. However, this leads to poor approximations of the cross-covariance matrix and loss of geologic realism through parameter overshoots, in particular by introducing localized patches of low and high permeabilities. This difficulty is compounded by the strong non-linearity of the multiphase history matching problem. Specifically, the updated parameter distribution tends to become Gaussian with a loss of connectivities of extreme values such as high permeability channels and low permeability barriers which are of special significance during reservoir characterization. We propose a novel approach to overcome these limitations by conditioning the cross-covariance matrix using information gleaned from streamline trajectories. Our streamline-assisted EnKF is analogous to the conventional assisted history matching whereby the streamline trajectories are used to identify grid blocks contributing to the production response of a specific well. We then use these grid blocks only to compute the cross-covariance matrix and eliminate the influence of unrelated or distant observations and noisy calculations. We show that the streamline-assisted EnKF is an efficient and robust approach for history matching and continuous reservoir model updating. Our approach is general, suitable for non-Gaussian distribution and avoids much of the problems in traditional EnKF associated with instabilities, overshooting and the loss of geologic continuity during model updating. We illustrate the power and utility of our approach using both synthetic and field applications. Introduction Proper characterization of the reservoir and the assessment of uncertainty are crucial aspects of any optimal reservoir development plan and management strategy. To achieve this goal, it is necessary to reconcile geological models to the dynamic response of the reservoir through history matching. The topic of history matching has been of great interest and an area of active research in the oil industry.1–3 The past decade has seen some significant developments in assisted and automatic history matching of high-resolution reservoir models and associated uncertainty quantification. Many of these techniques involve computation of sensitivities that relate changes in production response at a well to a change in reservoir parameters. Techniques of automatic history matching that typically do not use parameter sensitivities or gradient of the misfit function are stochastic algorithms such as Markov Chain Monte Carlo (MCMC), simulated annealing and genetic algorithms. A relatively recent and promising addition to this class of techniques is the use of ensemble Kalman Filters(EnKF) for data assimilation. It is a Monte-Carlo approach that works with an ensemble of reservoir models. Specifically, the method utilizes cross-covariances between measurements and model parameters computed directly from the ensemble members to sequentially update the reservoir models. A major advantage of the EnKF is that it can be readily linked to any existing reservoir simulator. The ability to assimilate diverse data types and the ease of implementation have resulted in considerable interest in the approach. Moreover, EnKF uses a sequential updating technique, that is, the reservoir data is assimilated as and when it becomes available. The EnKF can assimilate the latest production data without re-running the simulator from the initial conditions. These characteristic makes it particularly well-suited for continuous model updating and a natural choice for reservoir characterization from production data. The increased application of downhole monitors, intelligent well systems and permanent sensors to continuously record pressure, well rates and temperature has provided a further boost to the sequential model updating via EnKF.4–9