Archive of SID ! "#$ (SAGD) %$ + KI +A R+9 %$ + %$ *+ 6,/ % FG 9 $ (SAGD) "#$ % &'( ) * % %$ +!

(SAGD)! "#$ + *! " #$ %! &"' #( )* 7 8 (SAGD) 2 -. + 345 6 "1 0+,! -. +&1 + * 7 Coats 7 >?@. #! < * MATLAB )9 Coats " F& A 0 0+,! "E. C D +< A (" B5 "1 LM. #! JK SAGD "1 @"! GH <I - &. #! #& )2 0 N! AA +. " ) +K&.! 0+,! * AA. A A B 7 O +" 4 - "E.! AA IMPES (SAGD) 2 -. + 345 6 0 +,! KEY WORDS Simulation, Steam-assisted gravity drainage (SAGD), IMPES, Preheating. %$ + KI +A 4@ R+9 %$ + %$ *+ 6, % FG 9 $ %! + KI '9 0 R+9 4 6 4@ %$,<+9 2 " % " < 8 =., +1S % #9 T+ 9, #P9 4. %, *= #6 % 41 UV.[],+ X-,<+9 2 %!+ +A %,<2 W@ Saskatchewan Alberta SAGD, G9 '+ 6"P9 19, *P!J %. $,$9 ] ^!O +FJ JI,<+9 [ \G9 G3 6<@ SAGD, 6%F _&` FO K9 6%F R+9-60, *K.+ + % %. + CMG (STARS) + E-mail pishvaie@sharif.edu ( Q) Steam flooding () (SAGD) "#$ % &'( ) * % %$ +! ' 2 SAGD 0+#1, "., %!- 9 8 2.,+ 3 4 56 7+ % 4$ *= +> %.+,<+9 2 DBC9 %$ +A % + 9 4@ =?6$ % % FG!H <2 &E % %!? J 2 # % $3,.,! 4I % %$ +C % 5!G %,6 = K?= ( 03 %3 %$ LM + F'9,$ $3,6 PH9 ( "O9) NF,. ( P) 3A "#$ % &'( ), %1+9 Q,6 B,*$ #* $

% &'(,&$ 6!,19 %,E 0, G3 j#6., %J [e] 4P#6 Barillas akkg 0 +I 4@ #6 J9 %$ #6 4 " 9.,@ (c) % CMG (STARS) *! + \* G (d9 +#E 9 %$,, %I+! 64@!H T 5$ k v k h FG %$ 6. 2 (d9 = ' 9 > 6!.,,6+- 4 l ( j#6 64@., %J.,$ MATLAB * "#$ % %F " l3 $., %!-, %F 71<M % UV,,<+9., @ >? %S- +A %,! 3 )., I? =? 4, SAGD,,! T9 FG > 4 9&#E 6! G3 <@ T2 +#E %&S T 9 H T = *,$ 6 m9 6(., *K %!+ _l 2 N1., nc 6! NF % 4, 9,+9 SAGD, %$ K@ J 6! o$ m9 T,$,<+9,#O T03 p.,p6+- +I GP p 4p (h) G $ % FG 4 4+2 G3 p<@. G ^!O,' #E p$ qc< %p$ p9,$ "#$ p %p,p!g6 SAGD,p p p!j p6%p= ^!O.5$ 0? =?, *K $ J9 9,#E SAGD, " Kovscek Elliot R+9 bbb +6? =? +.[g], *K %62 "9.!H 6 71<M % %62 0+#1 SAGD, P&#E %G' K., *K? =? 4,? =?.,6 4H? =? 7&#E *K 7l %G'? =? 7! 7, % FG, P&#E j#6., Oil reservoi Steam injection well Steam flows to interface and.sagd -., "! bbc [a] 4P#6 Kamath = > 4 #6 %$,E,1 0, <@., *K SAGD, G3 <@ " %< W@ NF T&M 9 T&9 6! FG (d9 () T $ T T4 D 9 TBC! (a) & \ T,<+9 9 2 %&S T' 2 0+A.,K % <3 " % FG 62 FI %&S 6! % FG,S %1<M D 9 SAGD, P&#E.,+,, 8 FG T& \ +F T BC! %< W@ NF T8 62 %J +#E %&S ' % +#E 9,<+9 62 FI %&S., +FJ #H2 +A %. D=(9 ] #E %< 64 JH %1<M bbe [c] Yeung Kisman FG ( %$ % <3,1,E 0, "! T = T4I \+ T =, 6+!$., *K $ fh 2 4P 0+&C = TFG 9 '#E %1<M [h] 4P#6 Nasr bbg 0,E 6H @! SAGD, <@ JI SAGD 2%#H2 %F 9 (d9 64@., *K D= `@ %&3 #6 %1<M.,$.,6 4H, %$,? `@, 4 7, 9?6$. &'( ), $ 9 #6,6 4H ( Q) injectivity ( S) Barrier ( T) Shale barrier ( U) SOR (Steam Oil Ratoi) *+ Heated oil flows to well Production well oil and condensate era drained )

... -.50.'34 50 12 = J %I _G3 4@ %$ [] Tikhomirov R+9 %<1. Btu hr.ft. F _G3., JH [a] Farouq Ali R+9 %, 7+S % H % W@ <2!G ρ ρ i i,ref 1 = + ζ (p p ) β (T T ) i ref i ref (rr) 0,I 6 V<!@ <2 %FC,! 1 9279 10 00255 53 14 201 96 4 s exp( T) T ρ = < 0 5 10 201 96 11 4 2694 ρ = T T s 9469 85 87 2545 0 299668 2 H = + T T + s 5 4361 10 5 46484 10 2 88759 10 6 28068 10 4 3 7 4 T T + 10 5 14 6 T T (rs) (c) (rv)., P %I _G3 T Btu lbm _G3 H.,%!= > M- 19 ] % FG 9 %FC [c] Stone I 0,.,! 6 %M % 5!G,#O NF S om.,! [h] Matthews Fayers R+9, %} %$, 4H,$ %? @ 6 64@ Stone II 0, 8 ), %FC S om Stone I 0, 6 V<!@ %FC.[e h] CI! V<!@ ] P + 9 %M W@ 7+S % H 7m9 % &9!G.,.[g], %!= > φ = φ exp[c (p p )] φ [ + c (p p )] 0 R 0 0 R 0 1 (e) T % &9 TH % 78 =!G ()!G6 ( 2 56 H % FG 9!G., > QS NF %M T 0,I 6!., #9 H _G3 36 87 112 21 008854 25 T = ln(p) + p < ( Q) Hysteresis (g) &' %! ( *I %+ 781,9FE % 5$3 6%<1 0 E.((a) %<1 ) ] %+ ( %<1 ) 6.+ I ((c) %<1 ) %<1 %<1 J2 ( φρ is i ).( ρ iu i ) ρ iq = i t.(ak H T) +.( ρ whwuw + ρ ohouo + ρ ghgu g ) + qh + ql = Vb t [( 1 φ) ρ U + φ(s ρ U + S ρ U + S ρ U )] u i kk = µ R R w w w o o o g g g i ri o w g.[p ρ g] i,+ S + S + S =1 p = p p = f (s ) cow o w w p = p p = f (s ) cog g o g i 0! FI 781 j#6 P#$ 781 8 &S 6 %<1 E %<1.+! 0 y z+- 19!= >.,! = %FC [{] Walther log[log( µ o + a)] = b + c log(t + 460) ({) _G3 = J %I _G3 %$ I., cp.[ Tb], % Yao R+9 W@ = (T ) 1 562 µ = 0 6612 229 0 ( ) w [k] + %FC %M = 0 546807 3 83050 10 104938 10 1 42291 10 9 49798 10 2 49747 10 3 s T 5 2 8 3 T + T 12 4 15 5 T + T µ = +., cp _G3 = R _G3 4@ %$, = _l #9 JI %M.+! 8 788 0 6 62 4 0 6 460 k = exp ( ρ + S )(T + ) 055 H R w (r) (s) (t) (v) (w) (x) (b) (k)

% &'( % +H e? P9,19 %$ 9+S j#6, ^ %&3 4#6 *=,,H #6 +6 ) %$ K@.+ %FC %&3 4@ 0#E % %,, 6m9 %$ T, IMPES G 6*= % X!3 +, % + %>C< <,<+9 `@ 8+#1,, 6m9.5 "2+.+,6H,@ +I % % %$ = 9,<+9,? 6.,! [ ] Coats R+9, %} #l,! 0, F!E,9 [b] m.+,6h c P M9., @ % +- M9 +I *,E +I P %$ $, 79, m 4, _I+ = Q9., = Q9 c P.+ *K 9 %K! %! > = Q9 %$ %F 6%K!.,$?!H,- + )*' +#E = k,1 0, " p 4 0, %F R+9 cft ft B+&, ' = e, @ 0,I 4 7S+^-., I 0 " 60,I, )= FG 9 6 j#6. 4 D= "O9, +C.,! c a., 4H a P 4 2! +*1 0 '. k 9 m9. {ge x k y %< FG 6m9 (.+, a %,' +#E +#E 9?., 4H e h 6P 9,<+9 2 ƒf9 JI *8 4?6$ ne N 9,<+9, *= 9\ %K!.+!H 94@ +#E ƒf9 &E % j#6.+.+ % FG? ne %$,,<+9 NF. ce{ae cp %< = k e % =,' m9., g c cp %,'., I % T,' e ( Q) Tolerance 185 48 2 7005 00198 8 10 7 4 1 10 p 25 p 195 T = + p p + p T = ln(p) < p < 2 5 3 94 472 12016 195 600 5 2 404 44 01562 2 10 600 T = + p p p ({) ( ) (b) H J %I _G3 6%<1., psi _G3 2 0, ' 2 0, =,j?6$ 6+C %$ %+= %,! Peaceman +#E \O., ' 2 # 9 +,-2 %I bk.[{],+ KI z y 6+C [ ] 4P#6 Coats ) %,! 3 ) T 1O % 0,p p!h P JI 03 p., %<1 +?= 7FE Coats 0, Q-, _l j#6,, qc< ] %+ %!= > W@ NF Ty <2 19 4+E % p(,',p? Coats %p$ <p3., ),<+9 &S *P %$,$ %I+9. %!= > ' %<1?= 4+9# T?= SAGD 3 ) +!H 7EA.$ >QS ] ) *= 0!$.,$ %1I [b] \I %., %} %&3 6 *8 P9,19 % 0!$ 6%F o$, %!= $ % 0+#1 ) m! " 7m9 o$,3,c 0#E T *= = %$ +A %., *= 6 (NF %I 8+#1 ) %!?6$ *= T$ m9 K 7m9? m! ).[{] + I %!#$ *=,! 4 6= *#9 NF %I Q!- 4$ "2 %! 7+S %$ J,. *= 6 4 9FC 4 % %F ~ ) %$ 9+S. *= W! 19 4, JI *8 P9,19 %G' % J9, %} () U<+9, 7+S % ). #6 % #6 JI P9 c 9 a % H, W! + c? #6 JI *8 P9,19 =..+ I ^ *=,1 %&3 T, #6 W+I %

... -.50.'34 50 12 Y Y < = >? @ A B C <? < = >? @ A B C <??? > > Gas Saturation after h{ days > Gas Saturation after ee days > = x >. J %I hea hcc _99 % 6H =., 4H b 6P 6%K! &E % 5$ H 9 T, %!, #6 2 %$,6 4H b P 0o. CI SOR?6$ 6H,<+9 4,S hk. cek psi H e a _99 % hck psi c k psi 98!H T,!H 9 H %26 &E %!H >!.+ 4 %! +I?!H =!H?6$. G 98 9 H T,J W+&M +I., 4, 56 (b P) 56+-!H SOR 56. *8!H ] +V#$ R+9 98 H % %J ^!O 0, " % %J 9 H fh9. ^!O Q,6 \9 = = = x < < < < > = = < <? > > = = < < < = >? @ A B C <?. SAGD - 9! 78.6, *+ Y Y < = >? @ A B C <? Gas Saturation after ek days = = x Gas Saturation after gk days?6$.,, 4H { g 6P 6%K! %K! + DBC9? ne = %$,6 4H { P.+!H 9\,<+9!H T ^H,'?6$.+,<+9!H = %$ 9 %K! T+,<+9 9\ 9 3 T=.+ K "O9 PH9 JI!H %K!,# 4!H + ne 6 SOR 6,' Q!-.,?6$,<+9 SOR.!#$ 79 %< 64 %$ <3 T!H 8?? > > > > = = x 4#3 +*1 0 '. %F. c k psi % <3 9 H., I hck psi cek psi 9 6H <3 < < < <? > > = = < <? > > = = < < "

% &'( <? SOR vs Time A Comparison between Experimental and Simulated Results <= @ SOR (lbmlbm) < B @?? > = = < < = = >..3 9! N. 10L M, *% A @? > = < < vs Time < = =.1& 1!. 1&.O M, @ *% Kxky = < Kxky = < <A@ Kxky = >?,!#$ %&S %2 6 T,? N+#K SOR 2.+ J 2 9\ 6%K!, m9 k ac ft k e ft % k cc ft 2 N1,!H 2 N1 %2 6.,, 4H a P S3,+9!H +!H #9 LM.+ 4.+,6+-!H,<+9!= N1,<+9 2 j#6 03. 4H N+l+ %F 6%K! SOR %>3 O m9 2 N1 m9., }I G <3 % 79, =,_@ 4, 2 4 %F T% <3 = Viscosity = (base case) Viscosity = base case Viscosity = < (base case) > >? < < Pore Volume Produced.JK I( ( G5H. E! F!4,> *%..50.1& 1!. 10L M,? *% %&S DP g ft 9,<+9 2 % <3 6%K!., I { ft h ft ' %F., 2 %&S %2 6.,, 4H k 6P %K! + O 9\ 2 ƒf9,!#$ %$,6 4H k P.+ N 9,<+9 4 H3 Q!-, `@ %$ +A4#6 03. +I 2 7! 6%&S J T <3 % 6, Ll+9?.,@ % 4 J,' GP F'9 64 4+9,<+9 % FG 2 %&S ( %&S?6$ p %$,p6 4H p!., P < A @? > = < < vs Time < = = Simulated Exprimental > = Kxky = = Kxky = < <A@ Kxky = > =? $

... -.50.'34 50 12 A @? > = vs Time Wells interval =? ft Wells interval = @ ft Wells interval = A ft SOR (lbmlbm) <= < B @? vs Time Viscosity = (base case) Viscosity = base case Viscosity = < (base case) < = SOR (lbmlbm) < < = = >.1& 1!. T.U.RS- M, <B <@ <? <= < B @? =.9! 3 N. T.URS- M, A @? > = < < Produced SOR vs Wells interval = Wells interval =? ft h Wells interval = @ ft Wells interval = Wells interval = A ft g = rw = => ft rw = >> ft rw = ft < >? vs Time < > ) *+ @ *+ A?.9! 3 N. 1&.O M,Q *+.1& 1!. 9! FN - M, # *+ = = > >? SOR (lbmlbm) A @? > = < = <B <@ <? <= < B @? = < < = Pinj = > psi Pinj = >B psi Pinj =?> psi Pinj = > Pinj = >B Pinj =?> < = >? vs Time < = = SOR vs >? > @ > @ A? A.1& 1!. T V' M, *+.9! 3 N. 9! FN - M, *+

% &'( SOR (lbmlbm) <= < B @? Produced SOR vs skin factor = > no damage skin factor = > A @? > = skin factor = > no damage skin factor = > vs Time = < < = >? @ A.9! 3 N. K XY M, $ *%.1& 1!. K XY M,,'! &S &E (g P) 4 % '9,' kc c %!+ _l %F 4#6 UV., *K 0+A?? =? 3.,6 4H %J 6P 6%K!.+ 2 QA _@ (d9 9, I %2 6. 8 4 H,9 %? =? 7,,<+9 62 QA _@ K., @ h c %&3 +,6+- 98 H +!H 0+A.+ N 9 %K!.,?6$ 9 H % 4@ 4, H?6$!H 4,<+9.+,<+9 J 2!H?. SAGD, JI _ 9&#E!H < 7+S %? =? 7, 0+A 2 6 %5%1 =,',6 4H g P %$ +A 4#6.+# 4,C 7, %!+ +A %? = p?? e 9? =? 4? 4 % '9.+ O 2 ƒf9 9 + 9 4 % 2 6.,?6$ 4@,1 SAGD, 4@,1 T,?,3 9 H ˆ#&G.+, 9&#E H 4#6 % H,9 % 5 )*'? =? %&3 4 PH9 H? < % SAGD, P&#E? JI = %F " #6 SAGD,.,? T G P# %,! 3 )., %!- MATLAB *? =? 7! 64 %!+? =? 1O %!H P JI 9m9 0#E Coats 0,!P2+$, c < 60,I S+^-?= + ( 4$ qc< 7m9.,., %G',P 6%K!, I (7+ k ae)., m! =?! ] %<1 e 9? =? 4? %$,6 4H e P O 4 %$,6 4H Willman 0, %G' J +# 4@ U., +FJ J., 9, +-!FG? % 0+A T 7FE %.,! &FO 6+# 9 %$,6 4H %F R+9, *K G3 <@., %J,' " J? =?!J ƒf9 ne,$!h DBC9 %$ & E 6 A %$, > % #!C %$ %< %I+9? 4 + 9,<+9 2 9\ +!#$ = + 4!H = %2 6 9 FG?6p$ SAGD, J p.,6 0+A %26 A,,6+-!H,<+9 %K! T 9 H? T=?6$ T+#E % ' +#.+ `@ 9 4,!H < < = = > >? " *% W

... -.50.'34 50 12 k cc ek kkk cc g c k ce{ ae gk g e k k kkkh c k g k kkkhb a b{ k e ckk k k ag k {h c e k k cc g chk c k hh kb.n9 [S\2,< Z( %< &9 mdarcy T+#E 9 mdarcy T' 9 c Btuft. F Ty = psi T4 y ƒgf _l T %< =.5O, 1& G -.5-0L.," Z( So kg Krog Pcog t r w Š Š t v ršw Šr Š s w Šw Šv Š sr x Šr rsw Š rx ŠŠr Š t Š rs t Š Š Š rr ft cp c bmft T %< <2 psi T D 5$9 F T H 56 ƒgf _l psi TW@ D 5$9 F TW@ H 56 ƒgf _l API %I Btulbm. F T = Btulbm. F TW@ = x y psi F T%< H T%< W@ %< NF %< NF x, ft y, ft! =,19! =,19 ft T2 N1 T9,<+9 2 +#E %&S psi psi F c lbmft T,<+9 2 H T9 2 H T9 Ty <2.]H, 1& G -.5-0L., Z( Sw kw Krow Pcow rsx Š Š s s t ŠŠr v w r v Šrw Š rœw Š w Šw rss Š ws x rrw Š w Š t sšw Š Š st Q

% &'( Cumulative Steam Injection (lbm) Cumulative Gas Injection Comparison various Preheating Periods < <? < > < = < < < < b< < < = = > ark9.5.,! 'J,^N 9!,^, W *%.`O ` T %!+ 9? =? 9 4 7, T7,?., %J,' ".+ 4!H? =? 4p J9 9 H 4,= %! 8 4 H 7, P# T *8 p!h 4p 9&#E H %p p!#$ p J!? =? p!h 4p 7, p.+ 4 QSZZ S QZ 6\ V* QSZ[ QY QU 1 V* > No Preheating Q )???? > > = = < < Comparison for various Preheating Periods = = > SAGD,- _ N9 5 1! N.L^, *%.`O ` [&.5.! %<? T9,<+9 2 +#E %&S?6$,<+9,'.,? %!+ _l?6$ 4 T=? T+#E % ' 9 FG?6$,,<+9 2 +#E %&S?6$ T 9 H? (d9 2 N1.,? %!+ _l?6$ 9.,<+9 % FG 4 2 SAGD,pp pp&#e %p$ p6 pj#6 7p&#E %p$,6 4pH,p *pk? =?. 4 E #H2 (d9? =? [1] Butler R.M., "Thermal of Oil and Bitumen", Prentice-Hall 529, New Jersey, (1991). [2] Kamath V.A., Sandeep Sinha and Hatzignatiou, D.G., Simulation Study of Steam-Assisted Gravity Drainage Process in Ugnu Tar Sand Reservoir, SPE 26075, (1993). [3] Kisman K.E., Yeung K.C., Numerical Study of SAGD Process in the Burnt Lake Oil Sands Lease, SPE 30276, (1995). [4] Nasr T.N., Golbeck H., Lorimer S., Analysis of the Steam Assisted Gravity Drainage (SAGD) Process Using ExperimentalNumerical Tools, SPE 37116, (1996). [5] Barillas J.L.M., Dutra Jr. T.V. and Mata W., Reservoir and Operational Parameters Influence in SAGD Process, J. of Petroleum Science and Engineering, 54, (2006). [6] Elliot K.T., Kovscek A.R., A Numerical Analysis of Single-Well Steam Assisted Gravity Drainage Process (SW-SAGD), 20 th Annual Workshop and Symposium on Enhanced Oil International Energy Agency, (1999). No Preheating Q ) < < >?? 78 #

... -.50.'34 50 12 [7] Farouq Ali S.M., "Practical Heavy Oil ", Draft of a Book Under Finalization, (2007). [8] Yao S.C., "Fluid Mechanics and Heat Transfer in Steam Injection Wells, M.S. Thesis, The University of Tulsa, (1986). [9] Partha Sarathi, "Thermal Numerical Simulator for Laboratory Evaluation of Steamflood Oil ", Prepared as a Report to National Institute for Petroleum and Energy Research, (1991). [10] Tortike W.S. and Farouq Ali S. M., Saturated Steam Property Functional Correlations for Fully Implicit Thermal Reservoir Simulation, SPE Reservoir Eng., 4 (4), p. 471 (1989). [11] Tikhomirov V.M., Thermal Conductivity of Rock Samples and Its Relation to Liquid Saturation, Density, and Temperature, (In Russian), Neftyanoe Khozaistvo, 46 (4), (1968). [12] Farouq Ali S.M., Oil by Steam Injection, Producers Publishing Company, Bradford, PA, p. 34 (1970). [13] Stone H. L., Probability Model for Estimating Three-Phase Relative Permeability, Journal of Petroleum Technology, 22, p. 214 (1970). [14] Fayers F.J. and Matthews J. D., Evaluation of Normalized Stone s Methods for Estimating Three-phase Relative Permeabilities, SPE Journal, 20, p. 224 (1984). [15] Martin J. Blunt, An Empirical Model for Three-Phase Relative Permeability, SPE 56474, (1999). [16] CMG User Guide, Version (2006). [17] Turgay Ertekin, Abou-Kassem J.H., King G.R., Basic Applied Reservoir Simulation, Society of Petroleum Engineers, Richardson, Texas, (2001). [18] Coats K.H., George W.D., Marcum B.E., Three-Dimensional Simulation of Steamflooding, SPE paper 4500, (1974). [19] Mahshid Jafarpour, Simulator Development for Thermal Operation (Pre-Heating) of SAGD, Ms Thesis, Sharif University of Technology, Dec (2008). [20] Coats K.H., A Highly Implicit Steamflood Model, SPE paper 6105, (1978).