Ensemble Kalman filter (EnKF) is one of the widely used optimization methods in petroleum engineering. It uses multiple reservoir models, known as ensemble, for quantifying uncertainty ranges, and model parameters are updated using observation data repetitively. However, it requires a large number of ensemble members to get stable results, causing huge simulation time. In this study, we propose a sampling method using principal component analysis (PCA) and K-means clustering. It excludes poor ensemble with different geological trends to the reference so we can improve both speed and reliability of future predictions. A representative model, which is selected from candidate models of each cluster, has a role to choose proper ensemble for EnKF. For applying EnKF to channelized reservoirs, we compare cases with using 400, randomly picked 100, sampled 100 using Hausdorff distance, and sampled 100 by the proposed method. The proposed method shows improvements over the other cases compared. It gives stable uncertainty ranges and well-updated reservoir parameters after the assimilations. Randomly selected 100 ensemble members predict wrong reservoir performances, and 400 ensemble members exhibit too large uncertainty ranges with long simulation times. Even though more ensemble members are utilized, they provide worse results due to disturbance by improperly designed models. We confirm our sampling strategy in a real field case, PUNQ-S3, and it reduces simulation time as well as improves the future predictions for efficient and reliable history matching.

References

References
1.
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.
10143
10162
.
2.
Nævdal
,
G.
,
Manneseth
,
T.
, and
Vefring
,
E. H.
,
2002
, “
Near-Well Reservoir Monitoring Through Ensemble Kalman Filter
,”
SPE/DOE Improved Oil Recovery Symposium
, Tulsa, OK, Apr. 13–17,
Paper No. SPE 75235
.
3.
Houtekamer
,
P. L.
, and
Mitchell
,
H. L.
,
1998
, “
Data Assimilation Using an Ensemble Kalman Filter Technique
,”
Mon. Weather Rev.
,
126
(
3
), pp.
796
811
.
4.
Jafarpour
,
B.
, and
McLaughlin
,
D. B.
,
2009
, “
Estimating Channelized-Reservoir Permeabilities With the Ensemble Kalman Filter: The Importance of Ensemble Design
,”
SPE J.
,
14
(
2
), pp.
374
388
.
5.
Lee
,
K.
,
Jeong
,
H.
,
Jung
,
S. P.
, and
Choe
,
J.
,
2013
, “
Characterization of Channelized Reservoir Using Ensemble Kalman Filter With Clustered Covariance
,”
Energy Explor. Exploit.
,
31
(
1
), pp.
17
29
.
6.
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
.
7.
Kang
,
B.
,
Lee
,
K.
, and
Choe
,
J.
,
2016
, “
Improvement of Ensemble Smoother With SVD-Assisted Sampling Scheme
,”
J. Pet. Sci. Eng.
,
141
, pp.
114
124
.
8.
Oliver
,
D. S.
, and
Chen
,
Y.
,
2011
, “
Recent Progress on Reservoir History Matching: A Review
,”
Comput. Geosci.
,
15
(
1
), pp.
185
221
.
9.
Jung
,
S. P.
, and
Choe
,
J.
,
2012
, “
Reservoir Characterization Using a Streamline-Assisted Ensemble Kalman Filter With Covariance Localization
,”
Energy Explor. Exploit.
,
30
(
4
), pp.
645
660
.
10.
Shin
,
Y.
,
Jeong
,
H.
, and
Choe
,
J.
,
2010
, “
Reservoir Characterization Using and EnKF and a Non-Parametric Approach for Highly Non-Gaussian Permeability Fields
,”
Energy Sources, Part A
,
32
(
16
), pp.
1569
1578
.
11.
Wang
,
Y.
, and
Li
,
M.
,
2011
, “
Reservoir History Matching and Inversion Using an Iterative Ensemble Kalman Filter With Covariance Localization
,”
Pet. Sci.
,
8
(
3
), pp.
316
327
.
12.
Lorentzen
,
R. J.
,
Flornes
,
K. M.
, and
Nævdal
,
G.
,
2012
, “
History Matching Channelized Reservoirs Using the Ensemble Kalman Filter
,”
SPE J.
,
17
(
1
), pp.
137
151
.
13.
Lee
,
K.
,
Jeong
,
H.
,
Jung
,
S. P.
, and
Choe
,
J.
,
2013
, “
Improvement of Ensemble Smoother With Clustered Covariance for Channelized Reservoirs
,”
Energy Explor. Exploit.
,
31
(
5
), pp.
713
726
.
14.
Evensen
,
G.
,
2004
, “
Sampling Strategies and Square Root Analysis Schemes for the EnKF
,”
Ocean Dyn.
,
54
(
6
), pp.
539
560
.
15.
Aanonsen
,
S. I.
,
Nævdal
,
G.
,
Oliver
,
D. S.
,
Reynolds
,
A. C.
, and
Vallès
,
B.
,
2009
, “
The Ensemble Kalman Filter in Reservoir Engineering—A Review
,”
SPE J.
,
14
(
3
), pp.
393
412
.
16.
Haugen
,
V. E. J.
,
Nævdal
,
G.
,
Natvik
,
L. J.
,
Evensen
,
G.
,
Berg
,
A. M.
, and
Flornes
,
K. M.
,
2008
, “
History Matching Using the Ensemble Kalman Filter on a North Sea Field Case
,”
SPE J.
,
13
(
4
), pp.
382
391
.
17.
Scheidt
,
C.
, and
Caers
,
J.
,
2009
, “
Uncertainty Quantification in Reservoir Performance Using Distances and Kernel Methods—Application to a West Africa Deepwater Turbidite Reservoir
,”
SPE J.
,
14
(
4
), pp.
680
692
.
18.
Chen
,
C.
,
Gao
,
G.
,
Ramirez
,
B. A.
,
Vink
,
J. C.
, and
Girardi
,
A. M.
,
2016
, “
Assisted History Matching of Channelized Models Using Pluri-Principal Component Analysis
,”
SPE J.
,
21
(
5
), pp.
1793
1812
.
19.
Scheevel
,
J. R.
, and
Payrazyan
,
K.
,
2001
, “
Principal Component Analysis Applied to 3D Seismic Data for Reservoir Property Estimation
,”
SPE Reservoir Eval. Eng.
,
4
(
1
), pp.
64
72
.
20.
Park
,
J.
,
Jin
,
J.
, and
Choe
,
J.
,
2016
, “
Uncertainty Quantification Using Streamline Based Inversion and Distance Based Clustering
,”
ASME J. Energy Resour. Technol.
,
138
(1), p.
012906
.
21.
Lee
,
H.
,
Jin
,
J.
,
Shin
,
H.
, and
Choe
,
J.
,
2015
, “
Efficient Prediction of SAGD Productions Using Static Factor Clustering
,”
ASME J. Energy Resour. Technol.
,
137
(
3
), p.
032907
.
22.
Suzuki
,
S.
,
Caumon
,
G.
, and
Caers
,
J.
,
2008
, “
Dynamic Data Integration for Structural Modeling: Model Screening Approach Using a Distance-Based Model Parameterization
,”
Comput. Geosci.
,
12
(
1
), pp.
105
119
.
23.
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
.
24.
Gu
,
Y.
, and
Oliver
,
D. S.
,
2005
, “
History Matching of the PUNQ-S3 Reservoir Model Using the Ensemble Kalman Filter
,”
SPE J.
,
10
(
2
), pp.
217
224
.
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