4 : 1423 laterologfirstlyaccordingtoboreholesizeanddrilingfluidpropertiestheduallaterolog resistivityresponsesarecalculatedwiththreedimensionalfinitee

55 4 2012 4 CHINESE JOURNAL OF GEOPHYSICS Vol55No4 Apr2012 201255(4):1422-1432doi: 106038/jissn0001-5733201204038 Tan MJGaoJZouY LetalEnvironmentcorrectionmethodofduallaterologindirectionalwelChineseJGeophys(in Chinese)201255(4):1422-1432doi:106038/jissn0001-5733201204038 12 3 1 4 5 1 100083 2 ( ) 100083 3 ( ) 102249 4 ( ) 257096 5 100027 ; - / - / (3DFEM) doi:106038/jissn0001-5733201204038 P631 2011-10-092012-03-16 Environmentcorrectionmethodofduallaterologindirectionalwel TAN Mao-Jin 12 GAOJie 3 ZOU You-Long 2 XIE Guan-Bao 4 QIAO Yue-Dong 5 1Key Laboratoryof Geo-detection (China Universityof GeosciencesBeijing)Ministryof EducationBeijing100083China 2Schoolof Geophysicsand Information TechnologyChina Universityof GeosciencesBeijing100083China 3Colegeof Geophysicsand Information EngineeringChina Universityof PetroleumBeijing102249China 4Colegeof Geosciencesand TechnologyChina Universityof PetroleumDongying257096China 5ResearchInstituteof China NationalOffshore OilCorpBeijing100027China Abstract In directional welssuchasdeviated welsand horizontal welsduallaterolog of resistivityisusualynotaccurateenoughduetosomeenvironmentalfactorssuchasborehole surroundingbedweldeviationradialinvasionzoneandso onsoitis dificultforfluid identificationandquantitativeevaluationofthereservoirsa newcombination methodofchart correctionandinvasioninversionisproposedtostudyapparentresistivitycorrection ofdual (41172130) (2010ZY28) (2011ZX05014-001) (2011D-5006-0305) 1973 E-mail:tanmj@cugbeducn

4 : 1423 laterologfirstlyaccordingtoboreholesizeanddrilingfluidpropertiestheduallaterolog resistivityresponsesarecalculatedwiththreedimensionalfiniteelementmethod (3D FEM)and theboreholecorrectionchartsareconstructedthenaccordingtoalkindsofformationmodels withdiferentdeviationanglesandbedthicknesstheresistivityresponsesarecomputedandthe weldeviationandsurroundingbedorthicknesscorrectionchartsarebuiltthenaccordingto thelaw ilustratedin thecorrection chartsthe boreholeweldeviation surrounding bed/ thicknesscorrectionsoftheloggingresistivityarerealizedfastfinalywithrespecttotheefect ofdrilingfluidinvasiontheinvasionradiusandtrueresistivityoftheformationarecalculated usingtheinversion methodand the environmentcorrection for duallaterologis achieved completelyafterthetheoryisappliedtoduallaterologdatain marinedeviated welthedual laterologresistivitycorrectionresultscanenhancetheaccuracyofqualitativeidentificationand quantitativeevaluationofthereservoirs Keywords DirectionalwelsDuallateralogThreedimensionalfiniteelementmethod (FEM) Environmentcorrection 1 / ( ) (2DFEM) [1-4] ; - / (3DFEM) / - / - / 30 [5-10] 2 21 [11] (FEM) [12] (2D FEM ) [617-18 ] ( 1) [13-16] : (R m ) / / 10Ωm 6in(1in=254cm ) 2in 22in (R ld ) (R ld /R m

1424 (ChineseJGeophys) 55 1 (a) ;(b) Fig1 Boreholecorrectionchartsforduallaterolog (a)deeplaterolog;(b)shalowlaterolog (R ldc /R ld ) (D) 1a R ld /R m R ldc /R ld ; R ld /R m R ldc /R ld R ls /R m ( 1b): 8in R ldc = (B 0 +B 1*x+B 2*x 2 +B 3*x 3 )*R ld R lsc /R ls ; 8in 1 : x =log10(r ld /R m ) (1) R lsc /R ls B 0 B 3 1 1 Rld Table1 BoreholecorrectionformulacoeficientsforRld (in) 6 8 10 12 14 16 18 20 22 B0 100684 100648 100859 101032 101049 100917 100639 100267 099752 B1-008643 -003544 001918 00717 012056 016477 020621 024614 028971 B2 000212-002007 -004721-007446 -010052-012472 -01485-017258 -020053 B3-420 10-4 000206 000558 000925 001286 001634 002007 002433 003004 : x =log10(r ls /R m ) (2) R lsc = (B 0 +B 1*x+B 2*x 2 +B 3*x 3 )*R ls B 0 B 3 2 2 Rls Table2 BoreholecorrectionformulacoeficientsforRls (in) 6 8 10 12 14 16 18 20 22 B0 101426 101111 101047 100119 095163 095492 095691 095639 095617 B1-011367 -004256 003664 015101 043324 051637 058363 064707 069525 B2 002912 001037-001745 -00782-029008 -037542-044848 -051561-055692 B3-000216 -551 10-4 000278 001372 006068 009295 013003 017365 021679 22 - / (R s ) - / ) : (3D FEM)

4 : 1425 [247 ] (H) R ldc /R ld 1 R ld R ls ; (H) R ld /R s ( R ls /R s ) R ld /R ls / 20m R ld /R ls ; 1 2 3 15 30 45 60 75 90 / : 60 0045m( R ldc /R ld 10~19 ) (R s ) 30Ωm 75 90 R ldc /R ld (H) (R ldc /R ld ) (R lsc /R ls ) (R ld /R s 3 2 R ls /R s ) 30 R ldc /R ld 10~13 ; R lsc /R ls 2 (R ldc /R ld ) 2c 45 (H) R ld /R s (H) 06~192m R ldc /R ld 1 R ldc = (B 0+B 1*H+B 2*H 2 +B 3*H 3 )*R ld (3) ; B 0 B 3 3 3 45 Rld / (H=06~192m) Table3 Bed-thicknescorrectionformulacoeficientsforRld with45 deviationangle(h=06~192m) Rld/Rs 02 05 1 2 5 10 20 50 100 B0 004499 035942 099872 363914 28858 338682 185052 376569 229454 B1 188502 130156 00-521337 -376993-471993 -172892-561659 -229707 B2-152512 -101531 00 386668 279872 348463 130375 427687 187252 B3 039732 025702 00-094281 -068164-08458 -032126-106419 -050052 (H) 192~150m +B 3*H 3 +B 4*H 4 )*R ld (4) R ldc = (B 0 +B 1*H +B 2*H 2 B 0 B 3 B 4 4 4 45 Rld / (H=192~150m) Table4 Bed-thicknescorrectionformulacoeficientsforRld with45 deviationangle(h=192~150m) Rld/Rs 02 05 1 2 5 10 20 50 100 B0 101785 10062 099872 11288 105619 109411 101113 11697 119914 B1-010583 -004478 00 002663 003815 003494 002822 000947-000745 B2 001352 000468 00 000517 836 10-4 000303-000129 000797 001015 B3-501 10-4 -638 10-5 00-121 10-3 -686 10-4 -987 10-4 -209 10-4 -141 10-3 -152 10-3 B4 238 10-6 -432 10-6 00 495 10-5 314 10-5 423 10-5 120 10-5 548 10-5 566 10-5 3c R ls R ldc = (B 0+B 1*H+B 2*H 2 +B 3*H 3 )*R ld (6) (H) 06~272m R lsc = (B 0+B 1*H +B 2*H 2 +B 3*H 3 )*R ls (5) B 0 B 3 5 (H) 272~150m B 0 B 3 6 - / :

1426 (ChineseJGeophys) 55 2 / (a)15 ;(b)30 ;(c)45 ;(d)60 ;(e)75 ;(f)90 Fig2 Bed-thicknesscorrectionchartsfordeeplaterologindiferentderivationangles (a)15 deviationangle;(b)30 deviationangle;(c)45 deviationangle; (d)60 deviationangle;(e)75 deviationangle;(f)90 deviationangle 5 45 Rls / (H=06~272m) Table5 Bed-thicknescorrectionformulacoeficientsforRlswith45 deviationangle(h=06~272m) Rls/Rs 02 05 1 2 5 10 20 50 100 B0 090583 086229 093165 105825 129882 145964 156202 162114 107483 B1-027981 -006618 00-002714 -01955-034455 -04587-058681 035888 B2 014779 003745 00 00113 009794 017652 023785 03119-023844 B3-001083 -260 10-4 00-000664 -002727-004374 -005597-006963 00322 (SP) (GR) / ; 23 ;

4 : 1427 6 45 Rls / (H=272~150m) Table6 Bed-thicknescorrectionformulacoeficientsforRlswith45 deviationangle(h=272~150m) Rls/Rs 02 05 1 2 5 10 20 50 100 B0 094563 084578 093165 107885 129237 141216 147946 149258 144985 B1 006059 006981 00-00844 -019632-025585 -028949-030201 -029045 B2-001554 -001392 00 001531 003431 004395 004908 00507 004845 B3 133 10-3 108 10-3 00-113 10-3 -000246-000312 -000345-000354 -000337 3 / (a)15 ;(b)30 ;(c)45 ;(d)60 ;(e)75 ;(f)90 Fig3 Bed-thicknesscorrectionchartsforshalowlaterologindiferentderivationangles (a)15 deviationangle;(b)30 deviationangle;(c)45 deviationangle; (d)60 deviationangle;(e)75 deviationangle;(f)90 deviationangle ( ) 231 (p ) R th (p) :

1428 (ChineseJGeophys) 55 ( R ai i= 12 m) Jacobi : A = R th1 熿 Rth1 燄 ρ 1 ρ n R thm Rthm 燀 ρ 1 ρ n 燅 a ij = Rthi (i=12 m;j=12 n) ) (R xo ) ρj (R in ) 4d Jacobi i R thi j ( ρj Frechet ) (7) h (R a ) : ε(p)= R a -R th (p) Ra -R th (p 0 )-AΔp (8) b=r a-r th (p 0 ) R a ( p 0 ) R th (p 0 ) (8) AΔp =b-ε(p) ε(p) (9) ) (R xo ) (A T A+αI)Δp =A T b (10) (R in ) Marquardt Δp (p ) Marquardt p =p 0 +Δp - / p 0 Taylor p = R xo r in ) T : 232 R th (p)= R th (p 0 )+AΔp (7) ( 4a R th (p) 4b) 4a R th (p)= h1 R th2 R thm )m ;p = ( ρ 1 ρ 2 5 0 ) ρ n) T n ;Δp = (R xo0 ) 4b (R in0 ) p-p 0 p A m n (R ld ) (R ls ) ( 4c) 3 AΔp =b (9) ) (R xo ) (R in ) Δp m n 31 A A m 0421Ωm@22 0233Ωm@57 ; n (9) A CCLT DLL/MSFL Tikhonov 33 Arsenin - / (Regularization Method) [1920] ( ) (RLDB) (RLSB);

4 : 1429 4 (a) ;(b) ;(c) ;(d) Fig4 Forwardmodelingandinversiontestsofduallaterolog (a)formationresistivitymodel;(b)invasionmodelandinvasionradiusinverted; (c)duallaterologmodelingresults;(d)comparisonsofinversionresultsandmodel RLDB RLSB - / RLDP RLSP; RLDP 10 - / RLSP 6 2230~2330m ) (R xo ) (R in ) 5 1500~1600m (R ld ) 6Ωm ) - 10Ωm 40Ωm / : (R ls ) 1~2Ωm (RLDP) (RLSP) ) (R xo 2 (1520~15310m) (R in ) 10~15 m 10 Ωm ( ) 14~15 Ωm 4~ 2~4Ωm) 5Ωm (R xo ) 6Ωm 20Ωm ) (R xo ) 2~5 ; (R in ) 05~10m 32 B 2010 10 8m 3 03m 3 33 C B C 01381Ωm@27 0063Ωm@84 ; 0421Ωm @22 0233Ωm @57 ;

1430 (ChineseJGeophys) 55 5 A Fig5 DuallaterologenvironmentcorrectionresultsforWelA 45 7 2260~2300 m (2260~2288m) ) (R xo (R in ) 0m (1) - / (2288~2300m) (R ld ) 50~60Ωm (R ls ) 40Ωm ; ) 80~120Ωm 30~60Ωm - / (R xo ) 20Ωm ( ) (R in ) 05~15 m - / A B C ; ; A B 20m (2) ( ) - / 4

4 : 1431 6 B Fig6 DualLaterologenvironmentcorrectionresultsforWelB [3] ; (3) ; 05~15m China (inchinese)199620(1):24-30 ( ) - (References) [1] ChemaliRGianzeroSSu S MThe DualLaterologIn CommonComplexSituationsSPWLA29thAnnualLogging SymposiumJune5-81988 [2] deconvolution of laterologs by direct inverse filtering 199418(6):408-412 SPWLA32ndannualloggingsymposiumJune16-191991 Wang H MZhang G JThedualLaterologresponsein dippingbedswellogging Technology(inChinese)1994 18(6):408-412 199422(6):30-37 NieZPChenSYThenumericalanalysisfortheresponse ofduallateralloggingtoolinacomplexenvironmentacta Electronica Sinica (inchinese)199422(6):30-37 [4] ( )199620(1):24-30 Xiao J Q Zhang G J Computation of duallaterolog responsesin highlydeviatedand horizontalwels with3-d finiteelementmethodjournalofthe Universityof Petroleum [5] Xiao JBeard D LZhou Q A practicaldipping-efect correctionfor multlarrayinductiontoolsindeviated wels SPWLA37thannualloggingsymposiumJune16-191996 [6] WangH MFiniteElementAnalysisofResistivityLogging DissertationofUniversityofHouston1999 [7] WangH MShenLCZhangGJDuallaterologResponse in3-denvironmentspetrophysics200041(3):234-241 [8] Cosmo C Spalburg M R Looyestijn W J Fast [9] Maurer H Antonov Y Corley B et al Advanced processingforanew arraylaterologtoolspwla Fiftieth AnnualLoggingSymposiumJune21-242009

1432 (ChineseJGeophys) 55 7 C Fig7 DuallaterologenvironmentcorrectionresultsforWelC [10] [14] 200750(3): 953-958 Tan MJZhangGJYun H Yetal3-Dnumericalmode- matching(nmm)methodforresistivityloggingresponsesin nonsymmetricconditionschinesejgeophys(in Chinese) 200750(3):803-810 [11] XieGBFanY RWu H YetalResearchofmudinvasion 200027(2):69-73 depthpredictionmethodinreservoirwellogging Technology GaoJXieR H3D numericalforward modelingandfast correction ofdual-laterologforhigh angledeviated wels PetrolEum Exploration And Development (in Chinese) 200027(2):69-271 [12] / invasiononlogging responses ofdualinduction and dual 200936(6):725-730 lateraltoreservoirspetroleum Explorationand Development DengSGLiZ QLiZ QResponseofduallaterologand fastcorrection for layer thickness and shoulder bed in horizontalwelspetroleum Explorationand Development (inchinese)200936(6):725-730 [13] Chinese)Beijing:PetroleumIndustryPress1980 199929(3):295-298 [18] ( ) : 1984 ChenL HLiZBEfectoftheinvadedzoneonapparent resistivityjournalof Changchun Universityof Scienceand Technology (inchinese)199929(3):295-298 200525(7):40-44 Pan H PFanZJMaYCorrectionmethodofdrilingfluid invasionofresistivityloggingnaturalgasindustry (in Chinese)200525(7):40-44 [15] 200630(3):240-243 (inchinese)200630(3):240-243 [16] 200734(5):603-608 LiCXLiCLZhouCCetalEfectsoffreshdrilingmud (inchinese)200734(5):603-608 [17] : 1980 LiD QFinite Element Methodin ElectricalLogging (in ZhangGJElectricalLogging (inchinese)beijing:petroleum IndustryPress1984 ( )