Flow-Relevant Covariance Localization During History Matching Using Ensemble Kalman Filters

Author: Akhil Datta-Gupta. Texas Engineering Experiment Station (TEES), Texas A&M University, College Station, TX.

Venue: Norwegian Research Council/University of Bergen Workshop about Ensemble Kalman Filter for Updating of Reservoir Simulation Models, June 18–20, Hotel Edvard Grieg, Bergen, Norway (http://qp.rf.no/QuickPlace/enkfseminar/Main.nsf [external site]).

Abstract: Recently, Ensemble Kalman Filters (EnKF) have gained increasing popularity for history matching and continuous reservoir model updating using data from permanent downhole sensors. 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. 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 and loss of geologic realism through parameter overshoots, specifically by introducing localized patches of low and high permeabilities. This difficulty is compounded by the strong non-linearity of the multiphase history matching problem. As a result, 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. The project performer proposes a novel approach to overcome the limitations of the EnKF through a “covariance localization” method that utilizes streamline-based analytic sensitivities that are easy to compute and require very little extra computational effort. The sensitivities quantify the influence of the model parameters on the observed data and can be obtained using a single finite difference or streamline-based flow simulation. These sensitivities are then used in conjunction with the EnKF to modify the cross-covariance matrix and to reduce the influence of distant observation points on model parameter updates. It can be shown that the effect of such covariance localization is to increase the effective ensemble size, leading to an efficient and robust approach for history matching and continuous reservoir model updating. This approach is general, suitable for non-Gaussian distribution, and avoids much of the problems in traditional EnKF associated with instabilities, overshooting, and loss of geologic continuity during model updating. Researchers illustrate the power and utility of their approach using both synthetic and field applications.

Related NETL Projects: The goal of the related NETL project DE-FC26-05NT15457, “Rapid Calibration of High-Resolution Geologic Models to Dynamic Data Using Inverse Modeling: Field Application and Validation,” is to develop a systematic procedure and workflow for dynamic data integration for improved reservoir characterization. The overall goal is additional oil recovery by locating critical reservoir features such as flow channels, barriers, and reservoir compartmentalization that result in bypassed oil.

NETL Project Contacts
NETL – Purna Halder (purna.halder@netl.doe.gov or 918-699-2084)
TEES – Akhil Datta-Gupta (data-gupta@spindletop.tamu.edu or 979-847-9030)