( ) ( ) ξ = v,v. T r T s. X surf

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1 T r T s v,v r X X surf z α δ z = Temperatur reservoir, o F = Temperatur kondensasi uap pada tekanan injeksi di dasar sumur, o F = Koreksi temperatur terhadap arah radial dan vertikal seara berurutan, tak berdimensi = kualitas rata-rata uap pada kondisi lubang sumur selama periode injeksi uap, lb vapor/lb liquid+vapor = Kualitas uap di kepala sumur, lb vapor/lb liquid+vapor = Ketebalan hipotetik, ft = difusivitas panas batuan, sqft/d = Kuantitas, definisi pada pers. 8, tak berdimensi eerf τ τ + 2 τ / π 1, tak berdimensi ξ = s ( ) ( ) ( ρc ) = Kapasitas panas volumetrik dari R+F reservoir termasuk fluida didalamnya,btu/ft 3 - o F ρ o, ρ w = densitas minyak dan air pada kondisi stok tank, seara berurutan, lb/ft 3 τ = ˆ2 = 4 / ( ), dimensionless τ Kt h ρ + h i VIII. DAFTAR PUSTAKA 1. Ashat, Ali dan Nenny Saptadji, Korelasi untuk Penentuan Sifat Termodinamika air murni pada kondisi saturasi, Laboratorium Geothermal, Jurusan Teknik Perminyakan ITB, Bandung, R F 2. Boberg, Thomas C., Thermal Methods of Oil Reovery, An Exxon Monograph, John Wiley & Sons In., Toronto, Canada, Boberg, Thomas C. dan Lantz R.B., Calulation of the Prodution Rate of Thermally Stimulated Well, Trans. AIME, 237, I-1613, Fudiansyah, M., Reporting Pilot Projet Huff & Puff, JOB Pertamina-Bumi Siak Pusako, Siak, Riau, Hong, K.C, Steamflooding Reservoir Management: Thermal Enhaned Oil Reovery, PennWell Publishing Co., Tulsa, Oklahoma, Mandala, Wirawan Widya, Prediksi Kinerja Sumur Injeksi Uap Huff & Puff Dengan Metode Analitik dan Simulasi, Program Studi Teknik Perminyakan ITB, Bandung, Prats, Mihael, Thermal Reovery, 2 nd Printing, Amerian Institute of Mining, Metallurgial, and Petroleum Engineers In., New York, United State of Ameria Tortike, W.S. and Farouq Ali S.M., Saturated-Steam Property Funtional Correlations for fully Impliit Thermal Reservoir Simulation, SPE Paper 17094, SPE, Houston, Texas, Djabaruddin, Sem1 2007/

2 LAMPIRAN A Tabel 3. Data-data Masukan Software Sumur-sumur di lapangan X Input Sumur ADA#22 Input Sumur ADA#32 Input Sumur ADA#35 SPM 1,199,800 SPM 1,160,600 SPM 2,709,350 PIC PIC PIC UOCOLD UOCOLD UOCOLD TI 11 TI 9 TI 26 H 48 H 104 H 92 X 0.8 X 0.8 X 0.8 PINJ PINJ PINJ RHOO RHOO RHOO RHOW 62.4 RHOW 62.4 RHOW 62.4 SGO SGO SGO CPO CPO CPO CPG 0.01 CPG 0.01 CPG 0.01 RHOCR RHOCR RHOCR THCOND 38.4 THCOND 38.4 THCOND 38.4 ALFA ALFA ALFA RW 0.33 RW RW RE RE 24 RE PW 210 PW 210 PW 200 PE 260 PE 260 PE 260 GOR 200 GOR 200 GOR 200 WOR 7.9 WOR WOR TR 120 TR 120 TR 120 DT 1 DT 1 DT 1 TTIME 79 TTIME 49 TTIME 80 NUO 11 NUO 11 NUO Djabaruddin, Sem1 2007/

3 DATA LAMPIRAN B Tabel 4. Data Sumur & Perhitungan Lapangan "X" Proposed Huff & Puff/ Cyli steam Injetion Lapangan "X" Well ADA-32 ADA-22 ADA-33 Total Initial Water Saturation, % 30% 30% 30% Initial Oil Saturation, % 70% 70% 70% Oil Gravity, API WHT, F Reservoir Temp, F Reservoir Pressure, psi Oil Prodution, BOPD Water ut, % Gross Pay Thikness, ft Net Pay Thikness, ft Porosity, % 26% 26% 26% Top Sand Depth, ft Opened interval Oil Spesifi Heat, Btu/lb-F Volumetri Heat Capaity, Btu/Cuft-F Estimate Radius, ft Estimate Temperatur, F CALCULATION Bulk Volume Gross, Cuft 188, , ,386 Bulk Volume Nett, Cuft 188, , ,359 Heat Required in Oil Zone, Btu 1,028,288, ,803,491 1,964,527,051 Heat Required in Shale Zone, Btu - 482,021, ,596,202 Total Heat Required, Bbtu Barrel Cold Water Equivalent, BCWE, bbls 3,316 3,428 7,741 14,485 Injetion Capaity, BCWEPD Estimated Injetion Days, Days Estimated Fuel Consumtion, bbls (diesel) ,323 Lt (diesel) 45,851 60, , ,414 bbls (rude oil as fuel) ,693 Djabaruddin, Sem1 2007/

4 LAMPIRAN C Soure ode Program Metode Modifikasi Boberg-Lantz Program for a Cyle Steam Preditive Model By Boberg-Lantz - Main Soure Boberg, T.C. and Lantz, R.B. "Calulation of the Prodution Rate of a Thermally Stimulated Well", JPT De. 1966, pp An Error Funtion Complimentary Program (Numerial Re.) - Steam and Vapor Correlation from : Tortike and Farouq Ali (Paper SPE#17094) in Metri Units: p in kpa(1./6.894 psi), T in K - Data Test:- paper SPE Comparative No. 4 - their paper (JPT De. 1966) Hf dan Hg menggunakan korelasi W.S Tortike dan SM. Farouq Ali Tutuka Ariadji ( ) Wirawan Widya Mandala ( ) Djabaruddin ( ) COMMON/SINGL1/X,THCOND,TS,TR,TI,NS,TIME,ALFA,RHOCR,RW,RE,H,STM COMMON/SINGL2/SGO,CPO,GOR,CPG,RHOW,WOR,QOHB,DT,PW,PE,PIC,DTIME COMMON/VISCO/NUO,TEMP(11),UO(11),UOCOLD COMMON/PARAM/ESFUNC,RH,HFT,HFS,HFR,HFG C Input Data NS = 16 CALL FILEDATA(STM,PIC,UOCOLD,TI,H,X,PINJ,RHOO,RHOW,SGO,CPO, &CPG,RHOCR,THCOND,ALFA,RW,RE,PW,PE,GOR,WOR,TR,DT,TTIME) P=PINJ* /100. A1= A2= A3= A4= A5= A6= A7= TSC=A1+A2*ALOG(P)+A3*(ALOG(P))**2+A4*(ALOG(P))**3+A5*(ALOG(P))**4 &+A6*(ALOG(P))**5+A7*(ALOG(P))**6 TS=(9./5.)*TSC+32 CALL TIMED(TAU,TI,H,THCOND,RHOCR,NS) ESFUNC=ES(TAU) TIME=0. TOL= TAVG=TS NTIME=INT(TTIME/DT) QOHB=0. TIME=TI DO 100 I=1,NTIME TIME=TIME+DT DTIME=I*DT HFT=HW(TAVG) HFS=HW(TS) HFR=HW(TR) HFG=HLATENT(TAVG) CALL HEATRAD(RH,H,STM,X,HFG,HFS,HFR,ESFUNC,THCOND,TS,TR,TI,NS) TEMPAVG=FUNCTEMP(TAVG) TAVG=TEMPAVG CALL VISCRATIO(UOR,UOCOLD,TAVG) CALL CONSTANTS(C1,C2,RH,RE,RW,RC,S) CALL PIRATIO(PIR,UOR,C1,C2) CALL OILRATE(QOH,PE,PW,PIR,PIC,TI,STM,DTIME) QOHB=QOH WRITE(*,*)TIME,QOH WRITE(6,1)TIME,QOH Djabaruddin, Sem1 2007/

5 100 CONTINUE CLOSE(6) 1 FORMAT(F30.10,F30.10) STOP SUBROUTINE FILEDATA(STM,PIC,UOCOLD,TI,H,X,PINJ,RHOO,RHOW,SGO,CPO, &CPG,RHOCR,THCOND,ALFA,RW,RE,PW,PE,GOR,WOR,TR,DT,TTIME) CHARACTER*10 BUFF CHARACTER*20 FILENAME,OUTNAME REAL VALUE(24) COMMON/VISCO/NUO,TEMP(11),UO(11) WRITE(*,*)'INPUT FILENAME:?' READ(*,1)FILENAME OPEN(UNIT=5,FILE=FILENAME,STATUS='OLD') 1 FORMAT(A12) WRITE(*,*)'OUTPUT FILENAME:?' READ(*,2) OUTNAME OPEN(UNIT=6,FILE=OUTNAME,STATUS='REPLACE') 2 FORMAT(A12) WRITE(*,*)'INPUT FILE NAME:',FILENAME WRITE(*,*)'OUTPUT FILE NAME:',OUTNAME I=0 NDAT=24 DO 30 I=1,NDAT READ(5,15)BUFF,VALUE(I) 30 CONTINUE STM = VALUE(1) PIC = VALUE(2) UOCOLD = VALUE(3) TI = VALUE(4) H = VALUE(5) X = VALUE(6) PINJ = VALUE(7) RHOO = VALUE(8) RHOW = VALUE(9) SGO = VALUE(10) CPO = VALUE(11) CPG = VALUE(12) RHOCR = VALUE(13) THCOND = VALUE(14) ALFA = VALUE(15) RW = VALUE(16) RE = VALUE(17) PW = VALUE(18) PE = VALUE(19) GOR = VALUE(20) WOR = VALUE(21) TR = VALUE(22) DT = VALUE(23) TTIME = VALUE(24) READ(5,16)BUFF,NUO DO 40 I=1,NUO READ(5,*)TEMP(I),UO(I) 40 CONTINUE CLOSE(5) 15 FORMAT(A7,F30.10) 16 FORMAT(A7,I3) SUBROUTINE TIMED(TAU,TI,H,THCOND,RHOCR,NS) TAU=4*THCOND*TI/((H/NS)*(H/NS)*RHOCR) Djabaruddin, Sem1 2007/

6 FUNCTION ES(TAU).Dimensionless Time for Fig.3 PI= RTTAU=SQRT(TAU) RTPI=SQRT(PI) ES=EXP(TAU)*ERFC(RTTAU)+(2/RTPI)*RTTAU-1. FUNCTION HW(TINPUT) T=TINPUT T= (T-32.)*5./9. A1= A2= A3= A4= A5= A6= A7= HW=A1+A2*T+A3*T**2.+A4*T**3.+A5*T**4.+A6*T**5.+A7*T**6. HW = HW / K<=T<=645K FUNCTION HLATENT(TINPUT) T=TINPUT T= (T-32.)*5./9. A1= A2= A3= A4= A5= HFGT=(A1+A2*T+A3*T**2.+A4*T**3.+A5*T**4.)**0.5 HLATENT=HFGT / K<=T<=645K SUBROUTINE HEATRAD(RH,H,STM,X,HFG,HFS,HFR,ESF,THCOND,TS,TR,TI,NS).Radius of region originally heated,ft PI= RH1=(H/NS)*STM*((X*HFG)+HFS-HFR)*ESF RH2=4*THCOND*PI*(TS-TR)*TI*NS RH=(RH1/RH2)**0.5 FUNCTION FUNCTEMP(TAVG) COMMON/SINGL1/X,THCOND,TS,TR,TI,NS,TIME,ALFA,RHOCR,RW,RE,H,STM COMMON/SINGL2/SGO,CPO,GOR,CPG,RHOW,WOR,QOHB,DT,PW,PE,PIC COMMON/PARAM/ESFUNC,RH,HFT,HFS,HFR,HFG & PI= CALL HYPOTHICK(Z,STM,X,HFG,HFS,HFR,PI,RH,RHOCR,TS,TR,NS,H) CALL THETA(THETAR,THETAZ,ALFA,TIME,TI,RH,Z) CALL VRVZMULT(VR,VZ,THETAR,THETAZ) CALL DELTA(TAVG,WOR,CPO,RHOW,SGO,GOR,CPG,TR,HFT,HFR,HFG,QOHB, RHOCR,TS,NS,TI,TIME,DT,PW,Z,RH,DLT,H,DLTA,STM,PIC,PE) FUNCTEMP = TR+(TS-TR)*(VR*VZ*(1.-DLT)-DLT) DLTA=DLT SUBROUTINE HYPOTHICK(Z,STM,X,HFG,HFS,HFR,PI,RH,RHOCR,TS,TR,NS,H) PI= Z=(STM*(X*HFG+HFS-HFR)/(PI*RH*RH*RHOCR*(TS-TR)*NS))-(H/NS) SUBROUTINE THETA(THETAR,THETAZ,ALFA,TIME,TI,RH,Z) Djabaruddin, Sem1 2007/

7 THETAR=ALFA*(TIME-TI)/(RH*RH) THETAZ=ALFA*(TIME-TI)/(Z*Z) SUBROUTINE VRVZMULT(VR,VZ,THETAR,THETAZ) DIMENSION THETADAT(31),VRDAT(31),VZDAT(31) DATA THETADAT/0.0,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09, &0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.,2.,3.,4.,5.,6.,7.,8.,9., &10.,20.,30./ DATA VRDAT/1.,0.92,0.88,0.835,0.8,0.77,0.74,0.71,0.69,0.66,0.64, &0.51,0.425,0.375,0.31,0.28,0.25,0.22,0.2,0.19,0.09,0.06,0.04, &0.03,0.025,0.02,0.015,0.012,0.01,0.007,0.005/ DATA VZDAT/1.,0.95,0.925,0.9,0.88,0.87,0.86,0.85,0.84,0.83,0.82, &0.75,0.69,0.65,0.61,0.575,0.55,0.525,0.5,0.48,0.355,0.3,0.26, &0.23,0.22,0.2,0.19,0.18,0.17,0.12,0.08/ NDAT = 31 CALL LININT1(NDAT,THETADAT,VRDAT,THETAR,VR) CALL LININT1(NDAT,THETADAT,VZDAT,THETAZ,VZ) WRITE(6,*)vr,vz SUBROUTINE LININT1(NDAT,THETADAT,VDAT,THETA,V) For Asending Order of X-Data DIMENSION THETADAT(500),VDAT(500) DO 50 I=1,NDAT-1 IF((THETADAT(I+1)-THETA).GE.0)THEN V=VDAT(I)+((THETA-THETADAT(I))/(THETADAT(I+1)-THETADAT(I))) & *(VDAT(I+1)-VDAT(I)) GOTO 110 IF 50 CONTINUE 110 CONTINUE SUBROUTINE DELTA(TAVG,WOR,CPO,RHOW,SGO,GOR,CPG,TR,HFT,HFR,HFG,QOHB, & RHOCR,TS,NS,TI,TIME,DT,PW,Z,RH,DLT,H,DLTA,STM,PIC,PE) PI= TIMEO=TI+DT TIMER=TIME A1= A2= A3= A4= A5= E-08 A6= E-11 TAVG=((TAVG-32.)*5./9.) PSAT=A1+A2*TAVG+A3*TAVG**2.+A4*TAVG**3.+A5*TAVG**4.+A6*TAVG**5. PWV=(PSAT**2.)/ RWA=WOR RWVS= *(PWV/(PW-PWV))*GOR IF (TIMER.EQ.TIMEO)THEN RWV=RWA RWV1=RWVS IF IF (RWVS<RWA.AND.PWV>=PW)THEN RWV=RWA RWV=RWV1 IF HOG=(5.61*CPO*RHOW*SGO+GOR*CPG)*(TAVG-TR) HOW=5.61*RHOW*(WOR*(HFT-HFR)+RWV*HFG) Djabaruddin, Sem1 2007/

8 HFSTAR=QOHB*(HOG+HOW) DNUMER=2*PI*RH*RH*RHOCR*(TS-TR)*(H+(NS*Z)) DLTE = DT*HFSTAR/DNUMER DLT=DLTA+DLTE SUBROUTINE LININT2(NUO,TEMP,UO,TEMPINP,UOH) DIMENSION TEMP(11),UO(11) DO 50 I=1,NUO IF (TEMPINP.GE.TEMP(I).AND.TEMPINP.LE.TEMP(I+1))THEN UOH=(TEMPINP-TEMP(I))*(UO(I+1)-UO(I))/(TEMP(I+1)-TEMP(I))+UO(I) GOTO 110 IF 50 CONTINUE 110 CONTINUE SUBROUTINE VISCRATIO(UOR,UOCOLD,TAVG) COMMON/VISCO/NUO,TEMP(11),UO(11) CALL LININT2(NUO,TEMP,UO,TAVG,UOH) UOR=UOH/UOCOLD SUBROUTINE CONSTANTS(C1,C2,RH,RE,RW,RC,S).Constants C1 and C2 from Table 1:.for pe deline S=5.1 RWA=RW*EXP(-S) C1=(ALOG(RH/RWA)-RH**2./(2*RE**2.))/(ALOG(RE/RWA)-0.5) C2=(ALOG(RE/RH)-0.5+RH**2./(2*RE**2.))/(ALOG(RE/RWA)-0.5) --for onstant pe C1=(S+ALOG(RH/RWA))/(S+ALOG(RE/RWA)) C2=ALOG(RE/RH)/(S+ALOG(RE/RWA)) SUBROUTINE PIRATIO(PIR,UOR,C1,C2) PIR=1./(UOR*C1+C2) SUBROUTINE OILRATE(QOH,PE,PW,PIR,PIC,TI,STM,DTIME) A= *ALOG( EXP(-( /STM))) B= /STM C= *TI TPEAK= C-B-A IF (DTIME.LE.TPEAK) THEN QOH=(DTIME/TPEAK)*(PIR*PIC*(PE-PW)) QOH=PIR*PIC*(PE-PW) IF FUNCTION ERF(X) REAL ERF,X USES GAMMP REAL GAMMP IF(X.LT.0.)THEN ERF=-GAMMP(.5,X**2) ERF=GAMMP(.5,X**2) IF Djabaruddin, Sem1 2007/

9 (C) Copr Numerial Reipes Software i]. FUNCTION ERFC(X) REAL ERFC,X USES GAMMP,GAMMQ REAL GAMMP,GAMMQ IF(X.LT.0.)THEN ERFC=1.+GAMMP(.5,X**2) ERFC=GAMMQ(.5,X**2) IF (C) Copr Numerial Reipes Software i]. FUNCTION GAMMP(A,X) REAL A,GAMMP,X USES GCF,GSER REAL GAMMCF,GAMSER,GLN IF(X.LT.0..OR.A.LE.0.)PAUSE 'Bad argument in GAMMP' IF(X.LT.A+1.)THEN CALL GSER(GAMSER,A,X,GLN) GAMMP=GAMSER CALL GCF(GAMMCF,A,X,GLN) GAMMP=1.-GAMMCF IF (C) Copr Numerial Reipes Software i]. FUNCTION GAMMQ(A,X) REAL A,GAMMQ,X USES GCF,GSER REAL GAMMCF,GAMSER,GLN IF(X.LT.0..OR.A.LE.0.)PAUSE 'Bad argument in GAMMQ' IF(X.LT.A+1.)THEN CALL GSER(GAMSER,A,X,GLN) GAMMQ=1.-GAMSER CALL GCF(GAMMCF,A,X,GLN) GAMMQ=GAMMCF IF (C) Copr Numerial Reipes Software i]. FUNCTION GAMMLN(XX) REAL GAMMLN,XX INTEGER J DOUBLE PRECISION SER,STP,TMP,X,Y,COF(6) SAVE COF,STP DATA COF,STP/ D0, D0, & D0, D0, D-2, & D-5, D0/ X=XX Y=X TMP=X+5.5D0 TMP=(X+0.5D0)*LOG(TMP)-TMP SER= D0 DO 11 J=1,6 Y=Y+1.D0 SER=SER+COF(J)/Y 11 CONTINUE GAMMLN=TMP+LOG(STP*SER/X) (C) Copr Numerial Reipes Software i]. Djabaruddin, Sem1 2007/

10 SUBROUTINE GCF(GAMMCF,A,X,GLN) INTEGER ITMAX REAL A,GAMMCF,GLN,X,EPS,FPMIN PARAMETER (ITMAX=100,EPS=3.E-7,FPMIN=1.E-30) USES GAMMLN INTEGER I REAL AN,B,C,D,DEL,H,GAMMLN GLN=GAMMLN(A) B=X+1.-A C=1./FPMIN D=1./B H=D DO 11 I=1,ITMAX AN=-I*(I-A) B=B+2. D=AN*D+B IF(ABS(D).LT.FPMIN)D=FPMIN C=B+AN/C IF(ABS(C).LT.FPMIN)C=FPMIN D=1./D DEL=D*C H=H*DEL IF(ABS(DEL-1.).LT.EPS)GOTO 1 11 CONTINUE PAUSE 'A too large, ITMAX too small in GCF' 1 GAMMCF=EXP(-X+A*LOG(X)-GLN)*H (C) Copr Numerial Reipes Software i]. SUBROUTINE GSER(GAMSER,A,X,GLN) INTEGER ITMAX REAL A,GAMSER,GLN,X,EPS PARAMETER (ITMAX=100,EPS=3.E-7) USES GAMMLN INTEGER N REAL AP,DEL,SUM,GAMMLN GLN=GAMMLN(A) IF(X.LE.0.)THEN IF(X.LT.0.)PAUSE 'X<0 in GSER' GAMSER=0. IF AP=A SUM=1./A DEL=SUM DO 11 N=1,ITMAX AP=AP+1. DEL=DEL*X/AP SUM=SUM+DEL IF(ABS(DEL).LT.ABS(SUM)*EPS)GOTO 1 11 CONTINUE PAUSE 'A too large, ITMAX too small in GSER' 1 GAMSER=SUM*EXP(-X+A*LOG(X)-GLN) (C) Copr Numerial Reipes Software i]. Djabaruddin, Sem1 2007/

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