Efficient and Robust Reservoir Model Updating Using Ensemble Kalman Filter With Sensitivity-Based Covariance Localization

Abstract

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractRecently Ensemble Kalman Filtering (EnKF) has gained increasing attention for history matching and continuous reservoir model updating using data from permanent downhole sensors. It is a sequential Monte-Carlo approach that works with an ensemble of reservoir models. Specifically, the method utilizes cross-covariances between measurements and model parameters estimated from the ensemble. For practical field applications, the ensemble size needs to be kept small for computational efficiency. However, this leads to poor approximations of the cross-covariance matrix, resulting in loss of geologic realism. Specifically, the updated parameter field tends to become scattered 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 this limitation of the EnKF through a 'covariance localization' method that utilizes sensitivities that quantify the influence of model parameters on the observed data. These sensitivities are used in the EnKF to modify the cross-covariance matrix in order to reduce unwanted influences of distant observation points on model parameter updates. In particular, streamline-based analytic sensitivities are easy to compute, require very little extra computational effort and can be obtained using either a finite difference or streamline-based flow simulator.We show that the effect of the covariance localization is to increase the effective ensemble size. But key to the success of the sensitivity-based covariance-localization is its close link to the underlying physics of flow compared to a simple distance-dependent covariance function as used in the past. This flow-relevant conditioning leads to an efficient and robust approach for history matching and continuous reservoir model updating, avoiding much of the problems in traditional EnKF associated with instabilities, parameter overshoots and loss of geologic continuity. We illustrate the power and utility of our approach using both synthetic and field applications.

On the efficiency of the hybrid and the exact second-order sampling formulations of the EnKF: a reality-inspired 3-D test case for estimating biodegradation rates of chlorinated hydrocarbons at the port of Rotterdam

“…They further do not introduce any new directions to diversify the ensemble, limiting the filter update to a small-dimensional ensemble subspace (Song et al, 2010(Song et al, , 2013. Moreover, global model parameters are not local quantities and therefore localization techniques might not be as straightforward (Devegowda et al, 2007). In addition, the parameters are dynamically constant quantities (static in time), and thus large ensembles are usually needed to well approximate the parameter distributions (Hendricks Franssen and Kinzelbach, 2008;Zhou et al, 2012).…”

Ensemble-based conditioning of reservoir models to seismic data

“…While the function C typically depends only on distance, alternative approaches are available for model simulators which support streamlines. Streamlinebased localization for production data was discussed by Devegowda et al [6]. This approach limits updates to model grid regions which are connected to a particular well by streamlines.…”

Reservoir Multiscale Data Assimilation Using the Ensemble Kalman Filter

“…and state variables such as pressure, water saturation (two-phase flow) and production data at well locations using the EnKF as discussed in [5,7,13]. Following these previous works, in this paper we assume that the only dynamic data available is water cut data, and that porosity is known.…”