Use of Clustered Covariance and Selective Measurement Data in Ensemble Smoother for Three-Dimensional Reservoir Characterization

Abstract

History matching is essential for estimating reservoir performances and decision makings. Ensemble Kalman filter (EnKF) has been researched for inverse modeling due to lots of advantages such as uncertainty quantification, real-time updating, and easy coupling with any forward simulator. However, it requires lots of forward simulations due to recursive update. Although ensemble smoother (ES) is much faster than EnKF, it is more vulnerable to overshooting and filter divergence problems. In this research, ES is coupled with both clustered covariance and selective measurement data to manage the two typical problems mentioned. As preprocessing work of clustered covariance, reservoir models are grouped by the distance-based method, which consists of Minkowski distance, multidimensional scaling, and K-means clustering. Also, meaningless measurement data are excluded from assimilation such as shut-in bottomhole pressures, which are too similar on every well. For a benchmark model, PUNQ-S3, a standard ES with 100 ensembles, shows severe over- and undershooting problem with log-permeability values from 36.5 to −17.3. The concept of the selective use of observed data partially mitigates the problem, but it cannot match the true production. However, the proposed method, ES with clustered covariance and selective measurement data together, manages the overshooting problem and follows histogram of the permeability in the reference field. Uncertainty quantifications on future field productions give reliable prediction, containing the true performances. Therefore, this research extends the applicatory of ES to 3D reservoirs by improving reliability issues.

Characterization of three-dimensional channel reservoirs using ensemble Kalman filter assisted by principal component analysis

“…Some researchers used multi-dimensional scaling (MDS) to reduce the data's dimensions. Each distance is required to construct a distance matrix for using MDS so that there are many proposed methods to define and measure difference between the data (Scheidt and Caers 2009;Chiotoroiu et al 2017;Lee et al 2017).…”

“…For this reason, ES is faster than EnKF in updating the ensemble, but ES tends to give unstable results in highly complex problems. Thus, many researchers have attempted to improve Kalman gain estimations for stable convergence in ES (Kang et al 2016;Lee et al 2016Lee et al , 2017.…”

Efficient Assessment of Reservoir Uncertainty Using Distance-Based Clustering: A Review

“…While building static models, reservoir properties, such as permeability, facies, porosity, and water saturation, are assigned for each grid. Permeability is the most common reservoir property for distance definition [4][5][6][7]. It is highly correlated with future production because it is an important parameter that affects flow rate in Darcy's law.…”

“…However, dynamic distances can provide more reliable DBC results since it is directly connected with the reservoir performance [36,37]. Many researchers utilized time-series production data, such as oil production rate, cumulative oil production, bottomhole pressure (BHP), and gas-oil ratio (GOR), as criteria of dissimilarity [7,15,38,39]. These data are easily obtained by commercial reservoir simulators.…”

“…If more than three datasets exist, an exact solution in 2D space does not exist but we numerically approximate the position. Since MDS is a simple but very powerful algorithm to manage the data, many studies used MDS to reduce the data dimension [2][3][4][6][7][8][9]14,15,18,20,21,26,[36][37][38][39][40][43][44][45]51,53]. MDS can maintain the distance information while reducing the dimension in a lower space.…”