Prediction of Hydraulic Fractured Well Performance using Empirical Correlation and Machine Learning

Prediction of Hydraulic Fractured Well Performance using Empirical Correlation and Machine Learning

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ABSTRACT - +\GUDXOLFIUDFWXULQJKDVEHHQHVWDEOLVKHGDVRQHRISURGXFWLRQHQKDQFHPHQWPHWKRGVLQWKHSHWUROHXP LQGXVWU\7KLVPHWKRGLVSURYHQWRLQFUHDVHSURGXFWLYLW\DQGUHVHUYHVLQORZSHUPHDELOLW\UHVHUYRLUVZKLOHLQPHGLXP SHUPHDELOLW\LWDFFHOHUDWHVSURGXFWLRQZLWKRXWDIIHFWLQJZHOOUHVHUYHV+RZHYHUSURGXFWLRQUHVXOWORRNVVFDWWHUHGDQG appears to have no direct correlation to individual parameters. It also tend to have a decreasing trend, hence the success UDWLRQHHGVWREHLQFUHDVHG+\GUDXOLFIUDFWXULQJLQWKH6RXWK6XPDWUDDUHDKDVEHHQLPSOHPHQWHGVLQFHDQGWKHUH LVSOHQW\RIGDWDWKDWFDQEHDQDO\]HGWRUHVROYHWKHUHODWLRQVKLSEHWZHHQDFWXDOSURGXFWLRQZLWKUHVHUYRLUSDUDPHWHUV DQGIUDFWXULQJWUHDWPHQW(PSLULFDOFRUUHODWLRQDSSURDFKDQGPDFKLQHOHDUQLQJ0/PHWKRGVDUHERWKXVHGWRHYDOXDWH WKLVUHODWLRQVKLS&RQFHSWRI'DUF\¶VHTXDWLRQLVXWLOL]HGDVEDVLVIRUWKHHPSLULFDOFRUUHODWLRQRQWKHDFWXDOGDWD7KH 0/PHWKRGLVWKHQDSSOLHGWRSURYLGHEHWWHUSUHGLFWLRQVERWKIRUSURGXFWLRQUDWHDQGZDWHUFXW7KLVPHWKRGKDVDOVR EHHQGHYHORSHGWRVROYHGDWDOLPLWDWLRQVVRWKDWWKHSUHGLFWLRQPHWKRGFDQEHXVHGIRUDOOZHOOV(PSLULFDOFRUUHODWLRQ FDQJLYHVDQ5²RIZKLOH0/FDQJLYHDEHWWHU5²WKDWLVFORVHWR)XUWKHUPRUHWKLVSUHGLFWLRQPHWKRGFDQEH XVHGIRUZHOOFDQGLGDWHVHOHFWLRQPHDQV

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INTRODUCTION

+\GUDXOLFIUDFWXULQJLVDVWLPXODWLRQWUHDWPHQW to enhance well productivity and improves the HFRQRPLFYDOXHRIZHOOUHVHUYHV,WKDYHEHHQZLGHO\

applied to both low and moderate permeability reservoirs. In low permeability reservoir, it greatly contributes both to well productivity and to well reserves, while in moderate permeability reservoirs, it accelerates production without impacting the ZHOOUHVHUYHV+ROGLWFK 0D7KHSURGXFWLRQ

improvePHQWDQGDGGLWLRQDOUHVHUYHLIDQ\KDYHWREH MXVWL¿HGHFRQRPLFDOO\EHFDXVHK\GUDXOLFIUDFWXULQJ jobs requires high cost and involve large scale equipment.

0HDQZKLOHK\GUDXOLFIUDFWXULQJLQVRPH¿HOGV in South Sumatra has been implemented on more WKDQZHOOVVLQFH<HDUE\\HDULWEHFRPHV more challenging due to increasingly limited well candidates with good reservoir properties and GHFUHDVLQJ WUHQG LQ SURGXFWLRQ UHVXOWV 7KXV K\GUDXOLFIUDFWXULQJRSWLPL]DWLRQERWKLQSODQQLQJ Reserach and Development Centre for Oil & Gas Technology

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,661H,661 VOL. 44 NO. 2, AUGUST 2021

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7KH¿UVWPHWKRGLVHPSLULFDOFRUUHODWLRQHTXDWLRQ It contains a mathematical equation based on some SDUDPHWHUVIURPDJLYHQVHWRIHPSLULFDOGDWDWKDWZLOO EHXVHGIRUSUHGLFWLQJRWKHUGDWD5LEDULþ âXãWHUãLþ ,Q WKLV SDSHU WKH HPSLULFDO FRUUHODWLRQ HTXDWLRQLVXVHGWRSUHGLFWWKHK\GUDXOLFIUDFWXULQJ UHVXOW EDVHG RQ FRPELQHG SDUDPHWHUV RI UHVHUYRLU pressure, transmissibility data and dimensionless SURGXFWLYLW\ LQGH[ IURP K\GUDXOLF IUDFWXULQJ treatment.

7KHVHFRQGPHWKRGLVPDFKLQHOHDUQLQJDSSURDFK 0DFKLQHOHDUQLQJLVWKHVWXG\RIFRPSXWHUDOJRULWKPV that can improve automatically through experience by discovering general rules in large data sets to PHHW WKH XVHU¶V LQWHUHVW 0LWFKHOO 7HPL]HO et al. KDV GHVFULEHG WKH DSSOLFDWLRQV RI PDFKLQHOHDUQLQJLQRLO JDVLQGXVWU\DQGSURYLGHLWV capability and limitations in unconventional reservoir engineering and well completion calculations. In many cases, machine learning was proven able to predict the output that has problem in data limitation DQGGDWDTXDOLW\0DNKRWLQet al.

)LQDOO\ ERWK WZR DSSURDFKHV DUH H[SHFWHG to yield a robust prediction tool that can be easily

applied to all wells using common primary data as LQSXWSDUDPHWHUV7KHSUHGLFWLRQWRROLVWKHQXWLOL]HG in well candidate selection to determine the good ZHOO FDQGLGDWHV DQG HOLPLQDWH QRQSRWHQWLDO ZHOO FDQGLGDWHV LQ WKH IXWXUH K\GUDXOLF IUDFWXULQJ MRE FDPSDLJQ ,W¶V DOVR H[SHFWHG WR HQVXUH DQG JXLGH WKH IUDFWXULQJ WUHDWPHQW RSWLPL]DWLRQ WR PD[LPL]H the production result.

DATA AND METHODS

7KHZRUNÀRZLQGHYHORSLQJWKLVVWXG\FRQVLVW RIPDMRUSKDVHVWKDWUHSUHVHQWVWKHZKROHSURFHVV DQG GHWDLOV RI ZRUNLQJ SURFHGXUH ,W LV VKRZQ RQ )LJ WKDW FRQVLVWV RI GDWD SUHSDUDWLRQ HPSLULFDO correlation approach, machine learning approach to predict production and water cut, and its application RQZHOOFDQGLGDWHVHOHFWLRQ$FWXDOGDWD¿HOGZLOOEH LQFRUSRUDWHGLQWKHGLVFXVVLRQRIHDFKVWHSWRHQVXUH that this methodology is applicable.

A. Data Preparation

'DWDIURPDFWXDOK\GUDXOLFIUDFWXULQJMREZHUH collected and tabulated that including input and output GDWD7KHRXWSXWGDWDLVWKHSURGXFWLRQSHUIRUPDQFH whereas input data covers well data including well FRPSOHWLRQ GDWD VXFK DV SHUIRUDWLQJ OHQJWK DQG ZHOOERUHVL]HDQGUHVHUYRLUGDWDLQFOXGLQJVHYHUDO SDUDPHWHUVVXFKDVUHVHUYRLUSUHVVXUHRSHQKROHORJDQG SHWURSK\VLFDOGDWD+\GUDXOLFIUDFWXULQJSDUDPHWHUV also covers actual treatment data and calculated IUDFWXUHJHRPHWU\

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B. Empirical Correlation Approach

7KH HPSLULFDO FRUUHODWLRQ DSSURDFK XWLOL]HV WKH'DUF\HTXDWLRQLQUDGLDOFRQGLWLRQDVVKRZQLQ HTXDWLRQ7KLVHTXDWLRQQHHGUHVHUYRLUSURSHUWLHV that are represented by transmissibility and reservoir SUHVVXUH DQG IUDFWXUH SDUDPHWHUV 7UDQVPLVVLELOLW\

FDQEHGH¿QHGIURPSHWURSK\VLFDODQDO\VLVDQGZHOO WHVWLQJ 7KH ODWWHU PHWKRG LV SUHIHUUHG EHFDXVH LW represents the reservoir quality at certain radius.

7KLV PHWKRG XWLOL]HV WKH SUHIUDF GDWD REWDLQHG LQ PLQLIDOORII WHVW DQG DQDO\]HG XVLQJ VKRUW

impulse injection test to obtain reservoir permeability

$ERXVOHLPDQet al7KURXJKWKLVPHWKRGZH can also estiamte the reservoir pressure.

PD[LPL]HWKHZHOOSURGXFWLYLW\)RUDJLYHQSURSSDQW volume, square well drainage area, and values IRU ERWK SURSSDQW DQG UHVHUYRLU SHUPHDELOLW\ WKH GLPHQVLRQOHVVSURSSDQWQXPEHU1SLVGH¿QHGDV

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C. Machine Learning Approach

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DSSURDFKLVGLYLGHGLQWRWZRSKDVHV,QSKDVHWKH input data is limited to pressure, transmissibility DQG3,GLPHQVLRQOHVVGDWDVLPLODUWRWKHHPSLULFDO correlation approach. It aims to compare the result RI HPSLULFDO FRUUHODWLRQ DQG 0/ PHWKRGV DQG WR HYDOXDWH WKH LPSRUWDQFH RI HDFK SDUDPHWHU LQ machine learning. In phase 2, the input used in phase LVUHSODFHGE\SULPDU\GDWDVXFKDVRSHQKROHORJ SHWURSK\VLFDOSDUDPHWHUVDQGIUDFWXULQJWUHDWPHQW 7KLV SKDVH LV SURSRVHG WR PDNH WKH 0/ PRGHO usable practically by using parameters that almost all wells have.

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D. Application on Well Candidate Selection 7KHEHVW0/PRGHORQSURGXFWLRQUDWHDQGZDWHU cut predictions are implemented in well candidate VHOHFWLRQIRUIXWXUHK\GUDXOLFIUDFWXULQJMRE(FRQRPLF YDOXHLVGHWHUPLQHGIRUHDFKZHOOEDVHGRQWKHQHW RLOSUHGLFWLRQ7KLVPHWKRGFDQHOLPLQDWHZHOOVZLWK low oil production potential that yields low economic value.

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RESULTS AND DISCUSSION

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A. Empirical Correlation Approach

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the equivalent wellbore radius whereas the second PHWKRG LV XQL¿HG IUDFWXUH GHVLJQ XVLQJ SURSSDQW QXPEHU7KHHPSLULFDOFRUUHODWLRQUHVXOWVIRUHDFK PHWKRGDUHVKRZQRQ)LJXUH

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B. Machine Learning Approach

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7KH REMHFWLYH WR GHYHORS WKH SUHGLFWLRQ WRRO WKDWFDQEHDSSOLHGIRUDQ\ZHOOVFDQEHDFKLHYHG,W enable quantitative comparison on estimated hydraulic IUDFWXULQJUHVXOWVRWKDWSRWHQWLDOZHOOFDQGLGDWHFDQ EHHDVLO\VHOHFWHG7KLVWRRODOVRFDQEHXWLOL]HGWR HQVXUHDQGJXLGHWKHIUDFWXULQJWUHDWPHQWRSWLPL]DWLRQ WRPD[LPL]HWKHSURGXFWLRQUHVXOW

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CONCLUSIONS

6RPH FRQFOXVLRQV FDQ EH LQIHUUHG IURP WKH DERYHGLVFXVVLRQDERXWWKHSUHGLFWLRQRIK\GUDXOLF IUDFWXULQJMREUHVXOWXVLQJHPSLULFDOFRUUHODWLRQDQG machine learning model. Several points that can be LQIHUUHGLVEHORZ

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using coordinate and altitude well. It can give a VDWLVI\LQJUHVXOWZLWK5²YDOXHRILQWKHWHVWLQJ data set.

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Economides, M. J., Hill, A. D., Ehlig-Economides, C.

Up, D. ZPetroleum Production System. 2nd HG0DVVFDFKXVHWWV3UHQWLFH+DOO

Economides, M. J. Nolte, K. G Reservoir Stimulation. UGHG1HZ-HUVH\3UHQWLFH+DOO Friedman., J. H*UHHG\IXQFWLRQDSSUR[LPDWLRQD

gradient boosting machine. Annals of Statistics, SS

Holditch, S. A. Ma, Y. Z. Unconventional Oil and Gas Resources Handbook: Evaluation and Development(OVHYLHU*XOI3URIHVVLRQDO3XEOLVKLQJ Kang, S.N1HDUHVW1HLJKERU/HDUQLQJZLWKJUDSK

neural networks. Mathematics, S

Makhotin, I., Koroteev,, D. Burnaev, E.,

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Mutalova, R. F., Mozorov, A.D., Osiptsov, A.A., Vainshtein, A.L., Burnaev, E.V., Shel, E.V., Paderin, G.V.,0DFKLQHOHDUQLQJRQ¿HOGGDWD

IRUK\GUDXOLFIUDFWXULQJGHVLJQRSWLPL]DWLRQJournal of Petroleum Science & Engineering. Special Issue:

Petroleum Data Science, SS

Pearson, K.1RWHVRQWKHKLVWRU\RIFRUUHODWLRQ Biometrika, SS

5LEDULþ0 âXãWHUãLþ/Empirical formulas for prediction of experimental data & appendix, 6ORYHQLD -RåHI6WHIDQ,QVWLWXWH/MXEOMDQD

Smola, A. Viswanathan, S. V. N.Introduction to machine learning. &DPEULGJH&DPEULGJH8QLYHUVLW\

3UHVV

Temizel, C., Canbaz, C.H., Palabiyik, Y., Aydin, H., Tran, M., Ozyurtkan, M.H., Yurukcu, M., Johnson, P., A thorough review of machine learning applications in oil and gas industry. Virtual, 63(,$70,

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