4 : 1423 laterologfirstlyaccordingtoboreholesizeanddrilingfluidpropertiestheduallaterolog resistivityresponsesarecalculatedwiththreedimensionalfinitee

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1 CHINESE JOURNAL OF GEOPHYSICS Vol55No4 Apr (4): doi: /jissn Tan MJGaoJZouY LetalEnvironmentcorrectionmethodofduallaterologindirectionalwelChineseJGeophys(in Chinese)201255(4): doi:106038/jissn ( ) ( ) ( ) ; - / - / (3DFEM) doi:106038/jissn P 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 ( ) (2010ZY28) (2011ZX ) (2011D ) tanmj@cugbeducn

2 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 ) [ ] ( 1) [13-16] : (R m ) / / 10Ωm 6in(1in=254cm ) 2in 22in (R ld ) (R ld /R m

3 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 Rld Table1 BoreholecorrectionformulacoeficientsforRld (in) B B B B : 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 Rls Table2 BoreholecorrectionformulacoeficientsforRls (in) B B B B / (R s ) - / ) : (3D FEM)

4 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 ; / : m( R ldc /R ld 10~19 ) (R s ) 30Ωm 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 Rld / (H=06~192m) Table3 Bed-thicknescorrectionformulacoeficientsforRld with45 deviationangle(h=06~192m) Rld/Rs B B B B (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 Rld / (H=192~150m) Table4 Bed-thicknescorrectionformulacoeficientsforRld with45 deviationangle(h=192~150m) Rld/Rs B B B B B c 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 / :

5 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 B B B B (SP) (GR) / ; 23 ;

6 4 : Rls / (H=272~150m) Table6 Bed-thicknescorrectionformulacoeficientsforRlswith45 deviationangle(h=272~150m) Rls/Rs B B B B / (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) :

7 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 ) 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@ Ωm@57 ; n (9) A CCLT DLL/MSFL Tikhonov 33 Arsenin - / (Regularization Method) [1920] ( ) (RLDB) (RLSB);

8 4 : (a) ;(b) ;(c) ;(d) Fig4 Forwardmodelingandinversiontestsofduallaterolog (a)formationresistivitymodel;(b)invasionmodelandinvasionradiusinverted; (c)duallaterologmodelingresults;(d)comparisonsofinversionresultsandmodel RLDB RLSB - / RLDP RLSP; RLDP 10 - / RLSP ~2330m ) (R xo ) (R in ) ~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 m 3 03m 3 33 C B C 01381Ωm@ Ωm@84 ; ;

9 1430 (ChineseJGeophys) 55 5 A Fig5 DuallaterologenvironmentcorrectionresultsforWelA ~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

10 4 : B Fig6 DualLaterologenvironmentcorrectionresultsforWelB [3] ; (3) ; 05~15m China (inchinese)199620(1):24-30 ( ) - (References) [1] ChemaliRGianzeroSSu S MThe DualLaterologIn CommonComplexSituationsSPWLA29thAnnualLogging SymposiumJune [2] deconvolution of laterologs by direct inverse filtering (6): SPWLA32ndannualloggingsymposiumJune Wang H MZhang G JThedualLaterologresponsein dippingbedswellogging Technology(inChinese) (6): (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 SPWLA37thannualloggingsymposiumJune [6] WangH MFiniteElementAnalysisofResistivityLogging DissertationofUniversityofHouston1999 [7] WangH MShenLCZhangGJDuallaterologResponse in3-denvironmentspetrophysics200041(3): [8] Cosmo C Spalburg M R Looyestijn W J Fast [9] Maurer H Antonov Y Corley B et al Advanced processingforanew arraylaterologtoolspwla Fiftieth AnnualLoggingSymposiumJune

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