0
Research Papers: Petroleum Engineering

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 S4S 0A2, Canada

Daoyong Yang

Department of Petroleum Systems Engineering,
University of Regina,
Regina, SK S4S 0A2, Canada

Di Chai

Department of Chemical
and Petroleum Engineering,
University of Kansas,
Lawrence, KS 66045

Xiaoli Li

Department of Chemical and
Petroleum Engineering,
University of Kansas,
Lawrence, KS 66045
e-mail: li.xiaoli@ku.edu

1Corresponding author.

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received March 20, 2018; final manuscript received August 27, 2018; published online September 26, 2018. Editor: Hameed Metghalchi.

J. Energy Resour. Technol 141(2), 022901 (Sep 26, 2018) (9 pages) Paper No: JERT-18-1218; doi: 10.1115/1.4041406 History: Received March 20, 2018; Revised August 27, 2018

The iterative ensemble smoother (IES) algorithm has been extensively used to implicitly and inversely determine model parameters by assimilating measured/reference production profiles. The performance of the IES algorithms is usually challenged due to the simultaneous assimilation of all production data and the multiple iterations required for handling the inherent nonlinearity between production profiles and model parameters. In this paper, a modified IES algorithm has been proposed and validated to improve the efficiency and accuracy of the IES algorithm with the standard test model (i.e., 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 (i.e., well bottomhole pressure (WBHP), gas-oil ratio, and water cut) 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 the estimated relative permeability and capillary pressure in comparison to those obtained from the original IES algorithm. Consequently, the modified IES algorithm integrated with the recursive approach and normalization method has been substantiated to be robust and pragmatic for improving the performance of the IES algorithms in terms of reducing the computational expenses and improving the accuracy.

FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Evensen, G. , 1994, “ Sequential Data Assimilation With a Nonlinear Quasi-Geostrophic Model Using Monte Carlo Methods to Forecast Error Statistics,” J. Geophys. Res., 99(C5), pp. 10,143–10,162. [CrossRef]
Houtekamer, P. L. , and Mitchell, H. L. , 1998, “ Data Assimilation Using an Ensemble Kalman Filter Technique,” Mon. Weather Rev., 126(3), pp. 796–811. [CrossRef]
Reichle, R. H. , Mclaughlin, D. B. , and Entekhabi, D. , 2002, “ Hydrologic Data Assimilation With the Ensemble Kalman Filter,” Mon. Weather Rev., 130(1), pp. 103–114. [CrossRef]
Evensen, G. , 2003, “ The Ensemble Kalman Filter: Theoretical Formulation and Practical Implementation,” Ocean Dyn., 53(4), pp. 343–367. [CrossRef]
Gu, Y. , and Oliver, D. S. , 2005, “ History Matching of the PUNQS3 Reservoir Model Using the Ensemble Kalman Filter,” SPE J., 10(2), pp. 51–65. [CrossRef]
Gu, Y. , and Oliver, D. S. , 2005, “ The Ensemble Kalman Filter for Continuous Updating of Reservoir Simulation Model,” ASME J. Energy Resour. Technol., 128(1), pp. 79–87. [CrossRef]
Liu, N. , and Oliver, D. S. , 2005, “ Critical Evaluation of the Ensemble Kalman Filter on History Matching of Geologic Facies,” SPE Reservoir Eval. Eng., 8(6), pp. 470–477. [CrossRef]
Lorentzen, R. J. , Nævdal, G. , Vàlles, B. , Berg, A. M. , and Grimstad, A.-A. , 2005, “ Analysis of the Ensemble Kalman Filter for Estimation of Permeability and Porosity in Reservoir Models,” SPE Annual Technical Conference and Exhibition, Dallas, TX, Oct. 9–12, SPE Paper No. SPE 96375.
Nævdal, G. , Johnsen, L. M. , Aanonsen, S. I. , and Vefring, E. H. , 2005, “ Reservoir Monitoring and Continuous Model Updating Using Ensemble Kalman Filter,” SPE J., 10(1), pp. 66–74. [CrossRef]
Zhang, Y. , and Yang, D. , 2013, “ Simultaneous Estimation of Relative Permeability and Capillary Pressure for Tight Formations Using Ensemble-Based History Matching Method,” Comput. Fluids, 71(1), pp. 446–460. [CrossRef]
Zhang, Y. , Fan, Z. , Yang, D. , Li, H. , and Patil, S. , 2017, “ Simultaneous Estimation of Relative Permeability and Capillary Pressure for PUNQ-S3 Model With a Damped Iterative-Ensemble-Kalman-Filter Technique,” SPE J., 22(3), pp. 971–984. [CrossRef]
Kang, B. , and Choe, J. , 2017, “ Regeneration of Initial Ensembles With Facies Analysis for Efficient History Matching,” ASME J. Energy Resour. Technol., 139(4), p. 042903. [CrossRef]
Anderson, J. L. , and Anderson, S. L. , 1999, “ A Monte Carlo Implementation of the Nonlinear Filtering Problem to Produce Ensemble Assimilations and Forecasts,” Mon. Weather Rev., 127(12), pp. 2741–2758. [CrossRef]
Hamill, T. M. , Snyder, C. , Baumhefner, D. P. , Toth, Z. , and Mullen, S. L. , 2000, “ Ensemble Forecasting in the Short to Medium Range: Report From a Workshop,” Bull. Am. Meteorol. Soc., 81(11), pp. 2653–2664. [CrossRef]
Wen, X. H. , and Chen, W. H. , 2007, “ Some Practical Issues on Real-Time Reservoir Model Updating Using Ensemble Kalman Filter,” SPE J., 12(2), pp. 156–166. [CrossRef]
Oliver, D. S. , and Chen, Y. , 2011, “ Recent Progress on Reservoir History Matching: A Review,” Comput. Geosci., 15(1), pp. 185–221. [CrossRef]
Panwar, A. , Trivedi, J. J. , and Nejadi, S. , 2015, “ Importance of Distributed Temperature Sensor Data for Steam Assisted Gravity Drainage Reservoir Characterization and History Matching Within Ensemble Kalman Filter Framework,” ASME J. Energy Resour. Technol., 137(4), p. 042902. [CrossRef]
Zhang, Y. , and Yang, D. , 2014, “ Estimation of Relative Permeability and Capillary Pressure for Tight Formations by Assimilating Field Production Data,” Inverse Probl. Sci. Eng., 22(7), pp. 1150–1175. [CrossRef]
Zhang, Y. , Yang, D. , and Song, C. , 2016, “ A Damped Iterative EnKF Method to Estimate Relative Permeability and Capillary Pressure for Tight Formations From Displacement Experiments,” Fuel, 167(5), pp. 306–315. [CrossRef]
Zhang, Y. , Li, H. , and Yang, D. , 2012, “ Simultaneous Estimation of Relative Permeability and Capillary Pressure Using Ensemble-Based History Matching Techniques,” Transp. Porous Media, 94(1), pp. 259–276. [CrossRef]
Zhang, Y. , Song, C. , Zheng, S. , and Yang, D. , 2012, “ Simultaneous Estimation of Relative Permeability and Capillary Pressure for Tight Formations From Displacement Experiments,” SPE Canadian Unconventional Resources Conference, Calgary, AB, Canada, Oct. 30–Nov. 1, SPE Paper No. SPE-162663.
Jung, H. , Jo, H. , Lee, K. , and Choe, J. , 2017, “ Characterization of Various Channel Fields Using An Initial Ensemble Selection Scheme and Covariance Localization,” ASME J. Energy Resour. Technol., 139(6), p. 062906. [CrossRef]
Fan, Z. , Zhang, Y. , and Yang, D. , 2016, “ Estimation of Three-Phase Relative Permeabilities for a Water-Alternating-Gas Process by Use of an Improved Ensemble Randomized Maximum-Likelihood Algorithm,” SPE Reservoir Eval. Eng., 19(4), pp. 683–693. [CrossRef]
Fan, Z. , Zhang, Y. , and Yang, D. , 2017, “ Estimation of Three-Phase Relative Permeabilities for a WAG Process Using An Improved Ensemble Randomized Maximum Likelihood Algorithm,” SPE Reservoir Characterisation and Simulation Conference, Abu Dhabi, UAE, May 8–10, SPE Paper No. SPE 186012.
Burgers, G. , Van Leeuwen, P. , and Evensen, G. , 1998, “ Analysis Scheme in the Ensemble Kalman Filter,” Mon. Weather Rev., 126(6), pp. 1719–1724. [CrossRef]
Kang, B. , Yang, H. , Lee, K. , and Choe, J. , 2017, “ Ensemble Kalman Filter With Principal Component Analysis Assisted Sampling for Channelized Reservoir Characterization,” ASME J. Energy Resour. Technol., 139(3), p. 032907. [CrossRef]
Gu, Y. , and Oliver, D. S. , 2007, “ An Iterative Ensemble Kalman Filter for Multiphase Fluid Flow Data Assimilation,” SPE J., 12(4), pp. 438–446. [CrossRef]
Rommelse, J. , 2009, “ Data Assimilation in Reservoir Management,” Ph.D. dissertation, Technical University of Delft, Delft, The Netherlands.
Van Leeuwen, P. J. , and Evensen, G. , 1996, “ Data Assimilation and Inverse Methods in Terms of a Probabilistic Formulation,” Mon. Weather Rev., 124(12), pp. 2898–2913. [CrossRef]
Skjervheim, J. , and Evensen, G. , 2011, “ An Ensemble Smoother for Assisted History Matching,” SPE Reservoir Simulation Symposium, The Woodlands, TX, Feb. 21–23, SPE Paper No. SPE 141929.
Lee, K. , Jung, S. , Lee, T. , and Choe, J. , 2017, “ Use of Clustered Covariance and Selective Measurement Data in Ensemble Smoother for Three-Dimensional Reservoir Characterization,” ASME J. Energy Resour. Technol., 139(2), p. 022905. [CrossRef]
Li, R. , Reynolds, A. C. , and Oliver, D. S. , 2003, “ History Matching of Three-Phase Flow Production Data,” SPE J., 8(4), pp. 328–340. [CrossRef]
Evensen, G. , 2004, “ Sampling Strategies and Square Root Analysis Schemes for the EnKF,” Ocean Dyn., 54(6), pp. 539–560. [CrossRef]
Li, H. , Chen, S. , Yang, D. , and Tontiwachwuthikul, P. , 2010, “ Ensemble-Based Relative Permeability Estimation Using B-Spline Model,” Transp. Porous Media, 85(3), pp. 703–721. [CrossRef]
Li, H. , Chen, S. , Yang, D. , and Tontiwachwuthikul, P. , 2012, “ Estimation of Relative Permeability by Assisted History Matching Using the Ensemble Kalman Filter Method,” J. Can. Pet. Technol., 51(3), pp. 205–214. [CrossRef]
Chen, Y. , and Oliver, D. S. , 2012, “ Ensemble Randomized Maximum Likelihood Method as an Iterative Ensemble Smoother,” Math. Geosci., 44(1), pp. 1–26. [CrossRef]
Li, H. , and Yang, D. , 2012, “ Estimation of Multiple Petrophysical Parameters for Hydrocarbon Reservoirs With the Ensemble-Based Technique,” Adv. Pet. Explor. Dev., 4(2), pp. 1–17.
Fan, Z. , Yang, D. , and Li, X. , 2017, “ Determination of Three-Phase Relative Permeability in CHOPS Processes by Use of An Improved Ensemble Smoother,” SPE Reservoir Characterisation and Simulation Conference, Abu Dhabi, UAE, May 8–10, SPE Paper No. SPE 186080.
Wang, Y. , Li, G. , and Reynolds, A. C. , 2010, “ Estimation of Depths of Fluid Contacts by History Matching Using Iterative Ensemble-Kalman Smoothers,” SPE J., 15(2), pp. 509–525. [CrossRef]
Zhao, Y. , Reynolds, A. C. , and Li, G. , 2008, “ Generating Facies Maps by Assimilating Production Data and Seismic Data With the Ensemble Kalman Filter,” SPE/DOE Symposium on Improved Oil Recovery, Tulsa, OK, Apr. 20–23, SPE Paper No. SPE 113990.
Reynolds, A. C. , Li, R. , and Oliver, D. S. , 2004, “ Simultaneous Estimation of Absolute and Relative Permeability by Automatic History Matching of Three-Phase Flow Production Data,” J. Can. Pet. Technol., 43(3), pp. 37–46. [CrossRef]
Floris, F. J. T. , Bush, M. D. , Cuypers, M. , Roggero, F. , and Syversveen, A. R. , 2001, “ Methods for Quantifying the Uncertainty of Production Forecasts: A Comparative Study,” Pet. Geosci., 7(S), pp. S87–S96. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

The recursive approach for optimizing the damping factor [21]

Grahic Jump Location
Fig. 9

(a) Relative permeability and (b) capillary pressure curves for the water-oil system

Grahic Jump Location
Fig. 10

(a) Relative permeability and (b) capillary pressure curves for the oil-gas system

Grahic Jump Location
Fig. 2

Map of geological structure and well locations [11]

Grahic Jump Location
Fig. 3

Production data of a production well (PRO-1) in the PUNQ-S3 model [11]

Grahic Jump Location
Fig. 4

Objective functions of scenario #1 using the original IES algorithm, scenario #2 using the modified IES algorithm solely with the recursive approach, and scenario #3 adopting the modified IES algorithm with both the recursive approach and normalization methods

Grahic Jump Location
Fig. 5

Well bottomhole pressures of the exemplified production well PRO-1: (a) the reference and initial ensemble of WBHP; (b) the estimated ensembles of WBHP by using the original IES algorithm; and (c) the estimated ensemble of WBHP with the modified IES algorithm

Grahic Jump Location
Fig. 6

Well bottomhole pressures of the exemplified production well PRO-5: (a) the reference and initial ensemble of WBHP; (b) the estimated ensembles of WBHP by using the original IES algorithm; and (c) the estimated ensemble of WBHP with the modified IES algorithm

Grahic Jump Location
Fig. 7

Well bottomhole pressures of the exemplified production well PRO-15: (a) the reference and initial ensemble of WBHP; (b) the estimated ensembles of WBHP by using the original IES algorithm; and (c) the estimated ensemble of WBHP with the modified IES algorithm

Grahic Jump Location
Fig. 8

(a) Initial distribution, (b) estimated distribution using the original IES algorithm, and (c) estimated distribution using the modified IES algorithm of the exemplified model parameter nrw, and (d) presents the variance evolution of three coefficients of the power-law model, i.e., Swi, nrw, and aow

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In