Evaluation of EnKF and Variants on the PUNQ-S3 Case

R Valestrand,G Nævdal,A.S Stordal

doi:10.2516/ogst/2012044

Abstract

Over the last decade the ensemble Kalman filter (EnKF) has attracted attention as a promising method for solving the reservoir history matching problem: updating model parameters so that the model output matches the measured production data. The method possesses unique qualities, such as; it provides real-time updates and uncertainty quantification of the estimate, it can estimate any physical property at hand and it is easy to implement. The method does, however, have its limitations; in particular, it is derived based on an assumption of a Gaussian distribution of variables and measurement errors. Several refinements have been proposed to overcome the shortcomings of the EnKF. These refinements are, however, mainly tested on synthetic cases addressing one shortcoming at a time, not containing or combining the complexity and the high nonlinearity of a real field case. In this paper, we investigate some of the refined methods on a nonlinear reservoir, the 3D, three-phase, PUNQ-S3 model. We compare the performance of the original EnKF with the performance of the ensemble square root filter (EnSRF), an EnKF method with localization, which is named the hierarchical ensemble Kalman filter (HEnKF) and the newly proposed Adaptive Gaussian Mixture filter (AGM). To the best of our knowledge, this is the first time the EnKF and the EnSRF have been compared on a high-dimensional nonlinear field case. Overall, we see that the AGM and HEnKF work better than the EnSRF and EnKF. The EnSRF seems to have a slightly better performance than the EnKF. However, the introduction of a localization procedure (as in the HEnKF) seems to be much more influential than replacing the EnKF with the EnSRF. Comparing the top two methods, the AGM is preferable over the HEnKF, both when it comes to preserving the initial geology of the ensemble and to the consistency of the predictions.

Highlights

We investigate some of the refined methods on a nonlinear reservoir, the 3D, three-phase, PUNQ-S3 model
To the best of our knowledge, this is the first time the ensemble Kalman filter (EnKF) and the ensemble square root filter (EnSRF) have been compared on a high-dimensional nonlinear field case
Petroleum production is a challenging task in many ways

Summary

Introduction

To be able to optimize petroleum production, when it comes to both the economic and environmental aspects, it is important to know as much as possible about the reservoir at hand. History matching of reservoir properties from well data has been an important tool in the petroleum industry for decades, improving production decision-making when it comes to, e.g., quantifying remaining oil volumes, determining their location in the reservoir, and optimal placement of wells and well trajectories. Its first use in petroleum science was in Lorentzen et al [2], where a fluid-flow well model was tuned, and shortly after, in Nævdal et al [3], it was used to tune the permeability field of a near-well reservoir model. For a review on the use of EnKF in reservoir engineering see Aanonsen et al [7], and for more recent developments and applications see Seiler et al [8], Chen and Oliver [9] and Lorentzen et al [10]

Methods

Results

Conclusion