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RESTUDY ENKF ON E-SEGMENT NORNE RESERVOIR WITH INITIAL ENSEMBLE USING PETREL

Ria Amelia SusantoJune-July 2010

OUTLINE Objectives Introduction to E-segment Norne Reservoir Ensemble Kalman Filter (EnKF) Theory Initial Ensemble using PETREL Eclipse Input File Modifications setUpCase.m Shellscript describingWorkFlow.m Discussions

OBJECTIVES Make 100 realizations porosity and permeability

x-direction using PETREL : done Run EnKF-IRIS on E-segment Norne Reservoir :

partially done Eclipse Input File Modifications : Done setUpCase.m : Done Shellscript : Done describingWorkFlow.m : Done Debug : not yet finished

Use seismic for verification : not done(The limitation is time)

INTRODUCTION TO E-SEGMENT NORNE RESERVOIR

The first benchmark case based on real field data.

From top to base: Garn, Ile, Tofte and Tilje

INTRODUCTION TO E-SEGMENT NORNE RESERVOIR (CONT’D) C, D, E and G segments E segments: 3 producer wells, 2 injector wells and

2 side track wells (7 wells in ECLIPSE)

ENSEMBLE KALMAN FILTER (ENKF) EnKF is one of data assimilation technique Data assimilation aims at merging the

information from observation into a numerical model

Ensemble Kalman Filter (EnKF) is an estimation method which performs continuously statistical updating of parameters and dynamical states, and estimates the model uncertainty by using an ensemble of model representations.

FROM KALMAN FILTER TO ENSEMBLE KALMAN FILTERKalman Filter Model Equation : Forward Step

Observation Equation : Analysis Step

FROM KALMAN FILTER TO ENSEMBLE KALMAN FILTER (CONT’D)Extended Kalman Filter Use linearization of the model equation and

observation equation

Shortcomings : highly nonlinier model Storage problem when updating covariance Cy

Change to be

FROM KALMAN FILTER TO ENSEMBLE KALMAN FILTER (CONT’D)Ensemble Kalman Filter Cy is partially propagated by modification on

analysis step based on mean and covariance matrix

Nonlinier problems are written to be (2.9) so the relation become linier

Goal EnKF to solve 2.10 using integration Monte Carlo in time

INITIAL ENSEMBLE USING PETREL PORO and PERMX are chosen as updated static

variables, because of poorly known parameters their distribution are normal/lognormal (Gaussian)

distribution which is required for EnKF Min, Max, Mean and Standard deviation are

extracted from Norne Geomodel using PETREL

INITIAL ENSEMBLE USING PETREL (CONT’D)Assumptions: Use Min, Max, Mean, Std from zone 1-22 Norne

Coarse Model with Sequential Gaussian Method* Variogram: Exponential type (random realization

produced is easier to get the original min,max,mean,std values (T&E)) Sill=1, nugget =0.1, azimuth =0, dip =0

* Sequential Gaussian Simulation honors well data, input distributions, variograms and trends. Source: Petrel.

POROSITY NORNE STATISTIC

Zone Min Max Delta N Mean Std Var Sum1 0.1466 0.35 0.2034 4792 0.2594 0.0441 0.0019 1242.86572 0.1938 0.2822 0.0883 5151 0.2424 0.017 0.0003 1248.49353 0.1554 0.274 0.1186 5152 0.2089 0.0198 0.0004 1076.18334 0 0 0 5152 0 0 0 05 0.1908 0.2814 0.0906 5152 0.2281 0.0149 0.0002 1174.95776 0.1908 0.2814 0.0906 5152 0.2281 0.0149 0.0002 1174.967 0.1974 0.271 0.0736 5151 0.2368 0.0137 0.0002 1219.74358 0.1974 0.271 0.0736 5151 0.2368 0.0137 0.0002 1219.74579 0.1353 0.2988 0.1635 3707 0.2394 0.0289 0.0008 887.5729

10 0.2058 0.2865 0.0807 4369 0.2495 0.0161 0.0003 1089.923611 0.1752 0.2818 0.1066 4404 0.2314 0.019 0.0004 1019.126912 0.1727 0.2834 0.1107 4843 0.2192 0.0234 0.0005 1061.594113 0.2517 0.3473 0.0956 5151 0.281 0.0169 0.0003 1447.178214 0.2201 0.3059 0.0858 5151 0.2571 0.0153 0.0002 1324.285215 0.2034 0.2995 0.0961 5151 0.2342 0.0151 0.0002 1206.552516 0.17 0.2776 0.1076 5151 0.2205 0.0251 0.0006 1136.040717 0.0862 0.2701 0.1839 5151 0.1873 0.0363 0.0013 964.68818 0.1611 0.306 0.1449 5151 0.2368 0.0356 0.0013 1219.550219 0.1342 0.2184 0.0843 2878 0.1866 0.0187 0.0003 537.172720 0.1679 0.265 0.0971 3603 0.2294 0.0191 0.0004 826.598521 0.1517 0.2193 0.0676 4255 0.1834 0.0128 0.0002 780.39722 0.2235 0.2844 0.0608 5152 0.2525 0.0135 0.0002 1300.8384

sum 104970

***Extract from Coarse Norne Model using Petrel

Zone Min Max Delta N Mean Std Var Sum1 0.1466 0.3458 0.1992 4792 0.2486 0.044 0.0019 1191.1822 0.1938 0.282 0.0882 5151 0.2394 0.0176 0.0003 1232.89913 0.1572 0.2685 0.1113 5152 0.2085 0.0193 0.0004 1074.29474 0 0.001 0.001 5152 0.0004 0.0003 0 2.2015 0.1943 0.2787 0.0845 5152 0.2356 0.0148 0.0002 1213.68086 0.1943 0.2787 0.0845 5152 0.2356 0.0148 0.0002 1213.68087 0.1974 0.2679 0.0705 5151 0.23 0.013 0.0002 1184.58798 0.1974 0.2679 0.0705 5151 0.23 0.013 0.0002 1184.58799 0.1375 0.2985 0.161 3707 0.2363 0.0302 0.0009 875.9032

10 0.2058 0.285 0.0792 4369 0.2392 0.0167 0.0003 1044.936311 0.1797 0.2808 0.1011 4404 0.2308 0.0182 0.0003 1016.52212 0.1727 0.2831 0.1104 4843 0.2207 0.0227 0.0005 1068.86513 0.2517 0.3379 0.0862 5151 0.2821 0.0163 0.0003 1453.150214 0.2201 0.3038 0.0837 5151 0.2514 0.0151 0.0002 1294.968815 0.2034 0.282 0.0786 5151 0.2365 0.0157 0.0002 1218.316916 0.17 0.2755 0.1055 5151 0.2135 0.0239 0.0006 1099.796717 0.0862 0.2697 0.1835 5151 0.1881 0.0394 0.0016 968.909318 0.1611 0.3059 0.1448 5151 0.2304 0.0344 0.0012 1186.893219 0.1342 0.2184 0.0842 2878 0.1836 0.0203 0.0004 528.300420 0.1697 0.265 0.0953 3603 0.2275 0.0203 0.0004 819.595921 0.1518 0.2143 0.0625 4255 0.183 0.0118 0.0001 778.6822 0.2235 0.2829 0.0594 5152 0.2522 0.0125 0.0002 1299.5081

sum 104970

***Extract from Coarse Norne Model using Petrel

Original Model Realization 1 Model

DIFFERENCE BETWEEN ORIG. AND R1

Porosity Difference between Original and R1

0%

2%

4%

6%

8%

10%

12%

14%

0 5 10 15 20 25

Zones No.

Poro

sity

Diff

eren

ce

MinMaxMeanStd

Less than 9 %

PORO DISTRIBUTION OF R1:

PERMEABILITY NORNE STATISTICOriginal Model Realization 1 Model

Zone Min Max Delta N Mean Std ln (Std) distribution1 35 1376 1341 4792 401 199 5.29330482 0 829 829 5151 159 189 5.241747 log3 1 795 795 5152 83 132 4.8828019 log4 0 0 0 5152 0 05 8 1207 1199 5152 129 133 4.8903491 log6 8 1207 1199 5152 129 133 4.8903491 log7 31 435 404 5151 117 63 4.1431347 log8 31 435 404 5151 117 63 4.1431347 log9 9 2019 2010 3707 375 381 5.9427994 log

10 132 1934 1802 4369 610 288 5.662960511 27 580 553 4404 203 114 4.736198412 2 390 387 4843 82 68 4.219507713 67 2577 2510 5151 860 531 6.27476214 30 1688 1658 5151 258 210 5.3471075 log15 1 1970 1969 5151 151 210 5.3471075 log16 33 2522 2489 5151 489 472 6.156979 log17 0 2437 2437 5151 207 278 5.6276211 log18 76 3997 3920 5151 1011 1001 6.9087548 log19 1 387 386 2878 95 95 4.5538769 log20 34 957 923 3603 337 203 5.31320621 11 454 443 4255 106 70 4.248495222 173 2106 1933 5152 900 363 5.8944028

sum 104970

***Extract from Coarse Norne Model using Petrel

Zone Min Max Delta N Mean Std Var Sum ln (Std) distribution1 35 1113 1078 4792 381 196 38530 1825874 5.27811472 0 828 828 5151 116 216 46653 596545 5.3752784 log3 1 794 793 5152 99 170 28947 508299 5.1357984 log4 0 0 0 5152 0 0 0 25 8 1174 1166 5152 107 161 25878 549158 5.0814044 log6 8 1174 1166 5152 107 161 25878 549158 5.0814044 log7 31 425 394 5151 97 74 5459 498254 4.3040651 log8 31 425 394 5151 97 74 5459 498254 4.3040651 log9 9 1996 1987 3707 357 433 187272 1323360 6.0707377 log

10 132 1381 1249 4369 655 229 52595 2861730 5.43372211 27 576 549 4404 259 112 12542 1141860 4.718498912 2 287 285 4843 94 57 3291 453821 4.043051313 67 2195 2128 5151 715 429 184160 3684104 6.061456914 30 1664 1634 5151 226 282 79599 1163220 5.6419071 log15 1 1836 1835 5151 118 246 60636 609377 5.5053315 log16 33 2425 2392 5151 460 460 211873 2371266 6.1312265 log17 0 2345 2345 5151 159 318 101032 818866 5.7620514 log18 76 3973 3897 5151 1090 996 991312 5612123 6.9037473 log19 1 385 384 2878 85 106 11148 245337 4.6634391 log20 34 918 884 3603 365 184 33780 1315115 5.214935821 11 366 355 4255 131 75 5646 556859 4.317488122 173 2058 1885 5152 926 328 107629 4770349 5.7930136

sum 104970

***Extract from Coarse Norne Model using Petrel

DIFFERENCE BETWEEN ORIG. AND R1

Permeability Difference between Original and R1 model

0%

5%

10%

15%

20%

25%

30%

35%

40%

0 5 10 15 20 25

Zone No.

Diff

eren

ce (%

)

MinMaxMeanStd

Less than 35

PERMX DISTRIBUTION OF R1:

ECLIPSE INPUT FILE MODIFICATIONS RUNSPEC

TEST.DATA: NOECHO GRID

TEST.DATA: STATVAR1 and STATVAR2 SOLUTION

MATLAB.RESTARTINFO SUMMARY

WOPR, WWPR, WGPR, , WWIR, WOPRH, WWPRH, WGPRH, WWIRH

SCHEDULE RPTRST BASIC 2 SKIPREST NEXTTIME.SCH

Re-enter COMPDAT to keep Transmissibility and Kh

SETUPCASE.M Overwrite numGridBlock

Set up Matrix y, H and W (measIndexList.m)

IRIS-EnKF

overwrite

SHELLSCRIPT Run Eclipse and Run Matlab from Matlab RunEclipse

From#!/bin/sh/appl/ecl/macros/@eclipse -ver 2006.2 TEST > /dev/nullTo

#!/bin/sh/opt/ecl/macros/@eclipse -ver 2009.1 TEST fcisa f > /dev/null

Run TrueFrom #!/bin/sh/appl/ecl/macros/@eclipse -ver 2006.2 TRUE > /dev/nullTo#!/bin/sh/opt/ecl/macros/@eclipse -ver 2009.1 TRUE > /dev/null

* Linux Eclipse is installed in opt

DESCRIBINGWORKFLOW.M describingWorkFlow.m modifications

Numstep Ensemble size

DESCRIBINGWORKFLOW.M (CONT’D)

Plot True Measurements

DESCRIBINGWORKFLOW.M (CONT’D)

Plot True Measurements

DISCUSSIONSSTATVAR2.DATA Wrong set up input. Compatibility initial ensemble generated by

PETREL with IRIS-EnKF, although it has exported into Eclipse format.

Norne Model which is slightly different with Bjorke and Rorvik Norne Model.

Restart TEST.DATA

BIBLIOGRAPHY Aanonsen,S.I.,Naevdal,G.,Reynolds, A.C. and Valles, B.(2009). The Ensemble

Kalman Filter in Reservoir Enginering-a Review. Paper SPE 117274-PA. Rwechungura, R., Suwartadi, E., Dadashpour, M., Kleppe, J.,Foss,B.(2010).

The Norne Field Case-A Unique Comparative Study. Paper SPE 127538-MS-P. Statoil AS (2006). Annual reservoir development plan Norne and Urd Field

2006. Statoil AS (2001). PL 128-Norne Reservoir Management Plan. Oliver, D.S., Reynold, A.C., Liu, N. (2008). Inverse Theory for Petroleum

Reservoir Characterization and History Matching.p.347-357. Jafarpour, Benham.(2009). Data Assimilation in Reservoir ENgineering.

Summer School Romania. http://www.data-assimilation.com/ssda/presentation-ssda-2009.

Bjorke,K.,Rorvik,E.(2010). Application of the EnKF routine in history matching, and tested on the Norne field. Master Thesis NTNU.

Begum,Nasima (2009). Reservoir Parameter Estimation for Reservoir Simulation using Ensemble Kalman Filter (EnKF). Master Thesis NTNU.

Dadashpour, M., Kleppe, J., Landro, M. (2007). Porosity and Permeability Estimation by Gradient-Based History Matching Using Time-Lapse Seismic Data.

Przybysz, J.K. (2010). Hydrocarbon Reservoir Parameter estimation using production data and time lapse seismis. Phd Thesis TU Delft.

Acknowledgement Supervisor: Profesor Jon Kleppe Mentors: Eka Suwartadi & Mohsen Dadashpour NTNU and IO Center