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research-article

Estimation of Relative Permeability and Capillary Pressure for PUNQ-S3 Model Using a Modified Iterative Ensemble Smoother

[+] Author and Article Information
Zhaoqi Fan

Department of Chemical and Petroleum Engineering, University of Kansas, Lawrence, KS, 66045; Department of Petroleum Systems Engineering, University of Regina, Regina, SK, Canada, S4S 0A2
fan240@uregina.ca

Daoyong (Tony) Yang

Department of Petroleum Systems Engineering, University of Regina, Regina, SK, Canada, S4S 0A2
tony.yang@uregina.ca

Di Chai

Department of Chemical and Petroleum Engineering, University of Kansas, Lawrence, KS, 66045
krischa90@gmail.com

Xiaoli Li

Department of Chemical and Petroleum Engineering, University of Kansas, Lawrence, KS, 66045
xiaoli.laura@gmail.com

1Corresponding author.

ASME doi:10.1115/1.4041406 History: Received March 20, 2018; Revised August 27, 2018

Abstract

A modified IES algorithm has been proposed and validated to improve the efficiency and accuracy of the IES algorithm with the PUNQ-S3 model. More specifically, a recursive approach is utilized to optimize the screening process of damping factor for improving the efficiency of the IES algorithm without compromising of history matching performance because an inappropriate damping factor potentially yields more iterations and significantly increased computational expenses. In addition, a normalization method is proposed to revamp the sensitivity matrix by minimizing the data heterogeneity associated with the model parameter matrix and production data matrix in updating processes of the IES algorithm. The coefficients of relative permeability and capillary pressure are included in the model parameter matrix that is to be iteratively estimated by assimilating the reference production data of five production wells. Three scenarios are designed to separately demonstrate the competence of the modified IES algorithm by comparing the objective function reduction, history-matched production profile convergence, model parameters variance reduction, and the relative permeability and capillary pressure of each scenario. It has been found from the PUNQ-S3 model that the computational expenses can be reduced by 50% while comparing the modified and original IES algorithm. Also, the enlarged objective function reduction, improved history-matched production profile, and decreased model parameter variance have been achieved by using the modified IES algorithm, resulting in a further reduced deviation between the reference and estimated relative permeability and capillary pressure in comparison to those obtained from the original IES algorithm.

Copyright (c) 2018 by ASME
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