Application of Spectral Clustering Algorithm to ES-MDA with DCT for History Matching of Gas Channel Reservoirs

Sungil Kim,Kyungbook Lee

doi:10.3390/en12224394

Abstract

History matching is a calibration of reservoir models according to their production history. Although ensemble-based methods (EBMs) have been researched as promising history matching methods, reservoir parameters updated using EBMs do not have ideal geological features because of a Gaussian assumption. This study proposes an application of spectral clustering algorithm (SCA) on ensemble smoother with multiple data assimilation (ES-MDA) as a parameterization technique for non-Gaussian model parameters. The proposed method combines discrete cosine transform (DCT), SCA, and ES-MDA. After DCT is used to parameterize reservoir facies to conserve their connectivity and geometry, ES-MDA updates the coefficients of DCT. Then, SCA conducts a post-process of rock facies assignment to let the updated model have discrete values. The proposed ES-MDA with SCA and DCT gives a more trustworthy history matching performance than the preservation of facies ratio (PFR), which was utilized in previous studies. The SCA considers a trend of assimilated facies index fields, although the PFR classifies facies through a cut-off with a pre-determined facies ratio. The SCA properly decreases uncertainty of the dynamic prediction. The error rate of ES-MDA with SCA was reduced by 42% compared to the ES-MDA with PFR, although it required an extra computational cost of about 9 min for each calibration of an ensemble. Consequently, the SCA can be proposed as a reliable post-process method for ES-MDA with DCT instead of PFR.

Highlights

IntroductionVarious clues regarding target reservoirs, e.g., satellite images, geological surveys, seismic exploration, and core sampling, can be used for geostatistical algorithms to generate prior reservoir models
Reservoir characterization consists of the integration of static and dynamic data
Water comes into the reservoir from four sides of the aquifer

Summary

Introduction

Various clues regarding target reservoirs, e.g., satellite images, geological surveys, seismic exploration, and core sampling, can be used for geostatistical algorithms to generate prior reservoir models. Unconventional resources such as shale gas and shale oil are difficult to provide an accurate reservoir simulation for in the first place, which is why careful calibration of reservoir models has been becoming a more critical issue in recent years [1,2]. For this reason, we need a trustworthy method to conduct a history matching. After Evensen [3] first proposed the use of EnKF in ocean dynamics, Nævdal et al used it for reservoir characterization in petroleum engineering for the very first time [4]

Methods

Results

Conclusion