A Comparison Study between Batch and Continuous Process Simulation for the Separation of Carbon-13 Isotope by Cryogenic Distillation

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1 Korean Chem. Eng. Res., Vol. 45, No. 1, February, 2007, pp Methanel C lk l i nj r o i p Çm Çmm Ç s ne t 3 26 ( o 15p r, o 19p }ˆ) A Comparison Study between Batch and Continuous Process Simulation for the Separation of Carbon- Isotope by Cryogenic Distillation Jong Hwan Kim, Doug Hyung Lee, Euy Soo Lee and Sang Jin Park Department of Chemical Engineering, Dongguk University, 26, 3-ga Pil-dong, Chung-gu, Seoul , Korea (Received 15 November 2006; accepted 19 December 2006) k p rp }l d p 12 C l p ˆ oo C p k 1.1Í l p. Cp kr oo f p, k, p kl p v n tn o p. d p ˆ C p r p pp, n ˆ q lp p l p. krrp C oo rm v p rp v p p ~ w }l d oo p p CH 4 m H 2 Op pp l ll v CO v p. l l LNG NG C oo o l n r n l Rigorous rm v r Š m. m 12 CH 4 p p p n qk r Cp rp qlp r Feasibility Study n. SRK ˆ rep Acentric factor v k p l Acentric factor p l r Feasibility Studyl r r s p rm v Cp p p m pl. e l e rm v rp l v nr r p l rp rk m. l l Cp rm p rp nr p re pl. h Abstract Natural gases generally consist of mainly 12 C and about 1.1 of C. It is well known that a stable carbon isotope, C, has been widely used for the applications of medical, pharmaceutical, and agricultural tracers. As a result, the development of the separation and concentrating technology of C can cause of high value-added products and the possibility of the generation of new carbon materials. In general, there are two kinds of approaches to obtain a stable C isotope by the separation of cryogenic distillation. One is to obtain a concentrated isotope from natural gas. Another approach is to get concentrated CO by distillation followed by a chemical reaction of CH 4 and H 2 O. In this study, rigorous process simulations of the cryogenic distillation have been performed and analyzed for the concentrated separation of C isotopes from LNG and NG by using commercial process simulator. Due to the very small differences of relative volatilities and separabilities of 12 C and C, the process design and operation of effective separation and concentration of C need special strategies and feasibility studies. Utilization of vapor pressure data to acentric factor in SRK equation of state and optimized process conditions have been able to predict for the effective of the separation yield and concentration of C for the cryogenic distillation. The various operation strategies for both batch and continuous cryogenic distillation are also studied and suggested for the basic design of the process. Development of this study can provide a tool for the effective design and operation of the cryogenic separation of C. Key words: Carbon Isotopes, Cryogenic Distillation, Process Simulation, Carbon- To whom correspondence should be addressed. sjpark@dongguk.edu 57

2 58 s Ëp Ëpp Ë v 1. v p ql l sq ˆ p 8 p ˆ oo ( 9 C~ C) l p p ˆ C(carbon-twelve) sq p. p n ˆ oo p p p C (carbon-thirteen) p v ql l k 1.1Í r l pp lrp tn vp p. C 12 C m p kr oo,, kl, v, p, k,, l on n p (tracer, vp r j oo ) v n. n (urea), (glucose), (fructose), m p(triolein) p s t ˆ p C eˆ l s pn l k e~ svp p r v s l on pn p. p n, p m p p qp pp Œk p p qn p qp ~n CO 2 v l oo l p p r v p. v, v e p C Cp 12 r l svp ˆ d p p. m l, C urea pn l Žp (Helicobacter Pylori, oq r l p k) p p o ~ o kp opp p o kp kp okp v p p. CO 2, CH 3 OH, CF 3 Br p p ˆ oo C eˆ vp n d pr pn p. ql p ˆ l ˆ oo C l Cp p 12 p. m l, C 99Í eˆ rp C 99.99Íp p 12 v. C q r pn l n ep 12 p. p 12 C p pk rp lr p 1.1Íp C ql pk 50Í p p p. pm p q pn l p rq p l l m q(heat sink) n p, NMR l C 12 nr rn p. C p v n eqp l ˆ p q p. C p q q p l p p k p p ˆ l sq CO/ 12 CO oo rm v (cryogenic distillation) ~ p [1, 2]. p ˆ 99Í eˆ Cp p q e ˆ tl p. pnl k p ˆ(CH 4 )p rm v rp pn l oo rp n k r p. l p ˆ (CO 2 )l sq oo o e r l p ˆ d(ch 4 ) p oo l (thermal diffusion)p pn l p l pp, l ˆ d l rn p qn Ž qn p rp o l oo p p [3-5]. l p p d(carbon source) C l r q }l d rp. l p }l d LNG(liquified natural gas, t ˆ(CH 4 )) ˆ p l rn rn l n p. LNG o45 o k l o l p C / rp n n LNGp p p pp kn n q eqp } pp p. LNG C/ Cp oo rp l r 12 l n q Œq n. p pm p s n q lrp r nm p pv k p. p rp LNG NG oo p rmp s l f v p p. v k ˆp rm v ( v ) l p l rm l l p l p. v m 12 CH 4 p l p t (v k ) (separability, α)p p n qp rp ƒ r. p n rp p o bench scale p pilot scale e l pl q p (dimension) m m (m, wall effect, end effect, hydraulic effect ) e l ƒ m p. p e er m r o r(methodology) r p n, p m o p rp r p m kp re p [1-2, 6]. v l m p LNGp r p ˆ oo p rl t m p rp l l r q p ( e q )m p p o e p Š rp pl r l rp lk [7]. l l LNG / 12 CH 4 rm v r q o q m q p e l v l p / 12 CH 4 p e p q m. kn l l Cp r l r p v m pl rp rs p l rm v r l p Commercial Process Simulator pn l q m. 2. m n y 2-1. Methane lk m r h ˆp oo n o vp p rp t. l l Raoultp p /k p m. p o l v kp kkk l ˆ q pn m. ˆp v k p Antoineep p [6]. v ln P (P v L = L in kpa and T in K) (1) T p v kp pp ep. v log P L = (T in K) (2) v T P H T 2 q op e (2)m p ˆ oo ~ p v kp 12 CH 4 ˆ p v k m, p p v kp p p p.

3 Methanep C oo o e l e rm v r l 59 Table 1. Comparison between α Eqn and α SRK for optimized acentric factor of α Eqn α SRK ω CH4 α SRK α Eqn α SRK α Eqn Fig. 1. Comparison of vapor pressure between 12 CH 4 & -I. Table 2. Relative volatility and K-value of 12 CH 4 / 12 CH 4 (Mole Fraction) K-value ( 12 CH 4 ) K-value ( ) Relative volatility b = RT c P c (6) Fig. 2. Comparison of vapor pressure between 12 CH 4 & - II. v P H T = exp T T 2 (T in K) (3) e (1) e (3)l v v P L P H 12 CH 4 m p v kp ˆ. el k( kpa)l 12 CH 4 p rp Kp, p rp K p pp r p Kp. v, r p n p k p. op Fig. 1l 12 CH 4 m p m l v k p ˆ l 100 K p v k p Fig. 2l ˆ l SRK o l mk r h v k p r o SRK ˆ rep n l q m. SRK ˆ rep e (1)~ (4)m. RT at ( ) P = ( v b) vv ( + b) 2 at ( ) R2 T = c α ( T) P c (4) (5) α( T) 1 ( ω 0.156ω = [ + )( 1 T r )] 2 op e l p b l p m m p k p p, T c, P c p p a(t) T c, P c m Reduced Temperature T r Acentric factorp p. l l p m l v kp r o 12 CH 4 m p T c, P c p p r, Acentric factor ω p Acentric factor rel v kp qkv Acentric factor v v ƒv 100 Kl e (2) α Eqn = P L P H = p 100 Kl Commercial Process Simulatorl SRK v v ˆ rep pn l α SRK = K L K H m l m q q Acentric factor ω p m. p rp Table 1l ˆ l p s p Acentric factor ω p e. 12 CH 4 p Acentric factor ω p p. Table 2l 100 kpal 12 CH 4 p l 12 CH 4 m p K-value ˆ l. 100 kpal 12 CH 4 / p k pp k p Short-cut i m m l l p ˆ oo ~ p p 12 CH 4 m qnp p p lp ~p v qlp ˆ o pp p k~ (Ideal liquid mixture) r l r l. Shortcut p p n FUG(fenske-underwood-gilliland) p rn l v l n p m p q FUG(fenske-underwood-gilliland) FUG p pn p p v ˆp p pn l p p. p Korean Chem. Eng. Res., Vol. 45, No. 1, February, 2007 (7)

4 60 s Ëp Ëpp Ë v e (8)p Fenske ep pn l p. N min x D ( 1 x) ln D ( 1 x B ) x B lnsf = = lnα lnα (8) l l SF(separating factor) e (9)m p rp. x DLK SF , xbhk, = x DHK, x BLK, (9) e (10)p Underwood ep pn l p. N α R j x Dj, min = α j θ j = 1 (10) l l θ e (11) p. N α j x Fj, = 1 q α j θ j = 1 (11) e (8) e (9)l p m pn l Gilliand el p p p. Gilliand ep e (12). N N m ψ ψ 1 = exp N ψ R R m ψ = R+ 1 ψ 0.5 (12) () e (8)~(11)p pn l / 12 CH 4 rm rl n p 1Íl 10Í rl N min = R min = p 10Íl 80Í rl N min =967.3 R min = p. 3. r o lp q lp p. ll p r p nn p tl s r p p o l n rp v rp. v r p v p p pn v p k~ p sqp o rp, rl p v pn p. sq k l kv, kv, rkv v v sq el e v, l e v. e v rp r nnl ol p v pl l e v r l s p r p v ˆl pp k s p o } p qrp v p. v l e v rl l v r p v p. Short-Cut Simulation Š SRK ˆ rep pn l Rigorous e v rp l p nr r p m. e v r p r Fig. 3l ˆ l r o Short-Cut Simulationp pn l }l d ˆ ˆˆp o45 o k Fig. 3. Schematic flow diagram for batch distillation. rm v rp }l d tl l p k 1.000Íp p 1.967Í v Batch Distillation Columnl eˆ rp m. r pn l r p 1,000 p tp, rp p m. p r l CH 4 Feed 1 kmol n r ˆrr p p moleí m, ˆrr p p kp 0.5 kmol m. ˆ p k p 24 kpa, ˆrp k p 38 kpa l m. R/R min l, Heat Duty Table 3m. R/R min p 100r po Rp o l rp 100p p l Short-Cut Simulationp e m. e v r p o nr s p Table 4m. LNG t ˆp rn ~ ˆ p Table 3. Fenske/underwood calculation results of batch distillation R/R min N/N min Tarys (N) Reflux Duty (Mkcal/h) ratio Condenser Reboiler ,003 12, ,000 18, , , , Minimum reflux ratio (R min ) : , Minimum theoretical No. of trays (N min ) : Table 4. Basic specification of batch distillation column Number of plate Top pressure Column pressure drop Vapor flow rate Feed Charge amount Composition 12 CH 4 Condenser temperature G[kPa] 14G[kPa] 20G[kgmol/h] 1G[kgmol] 0.99G[mol ] 0.01G[mol ] BubbleGTemperature

5 Methanep C oo o e l e rm v r l 61 Fig. 6. Batch distillation process operation strategy - Case 1. Fig. 4. composition vs. batch cycle time. Fig. 7. Batch distillation process operation strategy - Case 2. Fig. 5. composition vs. no. of stages. d. l p e l e v r l r} rp ˆ p ~ o n m. Feed Charge Table 4p nr s l Condenserp Holdupp Feed 50Í sr l nr e l Stillpotl Fig. 4l ˆ l. Fig. 4l nr e p 24e p p Í p p p v k p k p. p e v r p nr e p 24e p r l m. p p Condenserp m Cp o Heat Duty Mkcal/hp Stillpotp m Cp o Heat Duty Condenserp Heat Dutym. Fig. 5l e v rp l r p. k 1,000 p p rlv p lt. p p p o Cp Condenser Holdupi r o p o e v r l p p Table 4p nr s l 1,000, nr e p 24e p s p l Condenserp Holdupp e r m. pl e rp r p Fig. 6 Fig. 7l ˆ l. Case 1(Fig. 6)l Condenserp Holdupp Feedp kp 50Í, Case 2(Fig. 7)l Condenserp Holdupp Feedp Í, Case 3, 4, 5l Condenserp Holdupp Feedp 65Í, 75Í, 80Í sr pr o veˆ o Distillate Flow Rate 0p p l r l Stillpotl k kk k. Fig. 8l Case 1l p nr e l tn p ˆ l. Fig. 8. composition of each stage vs. batch operation time. Korean Chem. Eng. Res., Vol. 45, No. 1, February, 2007

6 62 s Ëp Ëpp Ë v Table 5. Condenser : stillpot = 50 : 50 (binary system) - Case 1 Feed Stage 1 Stage 2 Stage 3 Stage 4 Product yield ( ) purity ( ) Table 6. Condenser : stillpot = : (binary system) - Case 2 Feed Stage 1 Stage 2 Stage 3 Stage 4 Product yield ( ) purity ( ) Table 5l p Case 1(Fig. 6)p l p 1 Í r l ee r Í Product p 6.25Í. p p Condenser p m , Reboiler(Stillpot)p m l. e v rp nrp Fig. 6 p 4 (stage)p rp r p. 1 (8 ), 2 (4 ), 3 (2 ), 4 (1 ) rp 15, v 15dayp nr e p 1.000Íp Feed s p v l Íp 0.5 kmolp s Product lp p. Table 6l p Case 2(Fig. 7)l p p 1.000Í r l r Í Product p Feedp k 0.093Í. Fig. 7 p =233 p, v 233dayp nr e p kmolp lp p p p Í. v Case 3, 4, 5l Condenser Holdupp Case 1 Case 2p t vrp 65Í, 75Í, 85Í l Feedp p 1.000Í r l r Í, Í, Í Product p 1.346Í, 0.391Í, 0.160Í. Case 3, 4, 5p l p Product Yield p Table 7~9l ˆ l r p Fig. 9~11l ˆ l. l v Condenser Holdupl r nkp Table 10 Fig. 9. Batch distillation process operation strategy - Case 3. Fig. 10. Batch distillation process operation strategy - Case 4. Table 7. Condenser : stillpot = 65:35 (binary system) - Case 3 Feed Stage 1 Stage 2 Stage 3 Stage 4 Product yield ( ) purity ( ) Table 8. Condenser : stillpot = 75:25 (binary system) - Case 4 Feed Stage 1 Stage 2 Stage 3 Stage 4 Product yield ( ) purity ( ) Table 9. Condenser : stillpot = 80:20 (binary system) - Case 5 Feed Stage 1 Stage 2 Stage 3 Stage 4 Product yield ( ) purity ( ) o45 o k Fig. 11. Batch distillation process operation strategy - Case 5. l ˆ l Product Yield, r, nr e p l Condenser Holdupp rr sr l nr lk p. v p n n Condenser Holdupp r k rp nr e p n, r p pk Product n n Condenser Holdupp q k p. 4. i r o Short-Cut Simulation Š SRK ˆ rep pn l Rigorous l e v rp

7 Methanep C oo o e l e rm v r l 63 Table 10. Results of batch process simulation for various condenser holdup Condenser holdup ( ) TotalGfeed (kmol) Final product (kmol) comp. of final product (mol ) Product yield ( ) (Feed/Product) Total No. of batch operation (Operation time, day) = = = = = 233 nr r m p r p p kk k i r o Short-Cut Simulationp pn l }l d ˆ ˆˆp rm v rp }l d tl l p k 1.000Íp p Í v Column 1l eˆ rp m. r pn l r p 1,000 p tp, rp p m. p r l CH 4 Feed 1 kmol/h n r ˆ r p p moleí m, ˆrr p p Í m. ˆ p k p 24 kpa, ˆrp k p 38 kpa l m. R/R min l, Heat Duty Table 11. Column 2 l k Íp p Í v eˆ rp m. r pn l r p 1,000 p tp, rp p r m. p r l 10Í Feed 0.05 kmol/h n r ˆ r p p moleí m, ˆrr p p Í m. ˆ p k p 24 kpa, ˆrp k p 38 kpa l m. R/R min l, Heat Duty Table 11. Fenske/underwood calculation results of column 1 Tarys Reflux Duty (Mkcal/h) R/R min N/N min (N) Ratio Condenser Reboiler , , , Minimum reflux ratio (R min ) : , Minimum theoretical No. of trays (N min ) : Table 12m. Table 11 Table 12l lt p Column 1l k 1Íp p 10Í rp R/R min 2 r N/N min k nr 1,000, Reflux Ratio 300p Column 2l k 10Íp p 80Í rp R/R min 15 r N/N min k 1,035 nr 1,000, Reflux Ratio 1,500p m. Column 2p Reflux Ratio 1,500 p po Feed Rate o qp kp Columnp Sizingl r (80Í p )p o p i r o ~ w l e v r o nr s p Table Table. Specification of continuous distillation column Column 1 Number of trays Feed tray Top pressure Prssure drop Feed Rate Composition 12 CH 4 Condenser Reflux ratio [Mol Basis] Column 2 Number of trays Feed tray Top pressure Prssure drop Condenser Reflux ratio [Mol Basis] 1, G[kPa] 14G[kPa] 1G[kgmol/h] 99.00G[mol ] 1.00G[mol ] 300 1, G[kPa] 14G[kPa] 1,500 Table 12. Fenske/underwood calculation results of column 2 R/R min N/N min Tarys (N) Reflux Duty (Mkcal/h) Ratio Condenser Reboiler , ,012 1, ,001 1, , , Minimum reflux ratio (R min ) : 87.16, Minimum theoretical No. of trays (N min ) : Fig. 12. Schematic flow diagram for continuous distillation. Korean Chem. Eng. Res., Vol. 45, No. 1, February, 2007

8 64 s Ëp Ëpp Ë v Table 14. Feeds and products of column - Case 1 Stream name FEED OVHD1 BTMS1 OVHD2 BTMS2 Phase Liquid Liquid Liquid Liquid Liquid Temperature ( C) Pressure (kpa) Flow rate (kmol/h) Molecular weight Composition CH Table 15. Heat duty and temperature of condenser and reboiler and column diameter - Case 1 Column name Column 1 Column 2 Condenser duty (Mkcal/h) Reboiler duty (Mkcal/h) Condenser temperature ( C) Reboiler temperature ( C) Diameter (mm) 1, r Fig. 12l ˆ l. p Columnp Bottom Product Rate Columnl Total Feed Ratep 5Í m, Rebolierm Condenserp Heat Duty l Reflux Ratio 300, 1,500p seˆ ˆ p k p 24 kpa, ˆrp k p 38 kpa p l r ee m. Column Diameter Structured Packingp Sulzerp Mellapak 125.Y p m. ~ w r Table 14m Table 15l ˆ l. s Product p k 80.81Í kmol/hp Rate p k pl. p 1 nr r n 300 p 24 h = 7,200 hp 7,200 h kmol/h = kg p molí p p kg/yr p p k pl. Columnp Diameter 1,219 mmm 628 mm l. w l e v r o nr s p Table r Fig. l ˆ l. p Columnp Bottom Product Rate Columnl ~ w np Flow ratem p Rate v, kmol/h, kmol/h r m, ~ w np OVHD2 Streamp s p p k 6.829Íp p p. Feedp p 1.000Í p Fig.. Schematic flow diagram for continuous distillation with recycle stream. Recycle eˆ Rebolierm Condenserp Heat Duty l Reflux Ratio 300, 1,500p seˆ ˆ p k p 24 kpa, ˆrp k p 38 kpa p l r ee m. Column Diameter ~ w nm v Structured Packing p Sulzerp Mellapak 125.Y p m. Table 17. Heat duty and temperature of condenser and reboiler and column diameter - Case 2 Column name Column 1 Column 2 Condenser duty (Mkcal/h) Reboiler duty (Mkcal/h) Condenser temperature ( C) Reboiler temperature ( C) Diameter (mm) 1, Table 16. Feeds and products of column - Case 2 Stream name FEED OVHD1 BTMS1 OVHD2 BTMS2 Phase Liquid Liquid Liquid Liquid Liquid Temperature ( C) Pressure (kpa) Flow rate (kmol/h) Molecular weight Composition CH o45 o k

9 Methanep C oo o e l e rm v r l 65 Table 18. Feeds and products of column - Case 3 Stream name FEED OVHD1 BTMS1 OVHD2 BTMS2 Phase Liquid Liquid Liquid Liquid Liquid Temperature ( C) Pressure (kpa) Flow rate (kmol/h) Molecular weight Composition CH Table 19. Heat duty and temperature of condenser and reboiler and column diameter - Case 3 Column name Column 1 Column 2 Condenser duty (Mkcal/h) Reboiler duty (Mkcal/h) Condenser temperature ( C) Reboiler temperature ( C) Diameter (mm) 1, w r Table 16m Table 17l ˆ l. s Product p k 89.41Í kmol/hp Rate p k pl. p 1 nr r n 300 p 24 h = 7,200 hp 7,200 h kmol/h = kgp molí p p kg/yr p p k pl. Columnp Diameter 1,248 mmm 628 mm l. Recycle Flow sq Column 1p Diameter ~ w n k ƒv p k pl. w l e v r o nr s p w s r Fig. l ˆ l. p Columnp Bottom Product Rate Columnl ~ w np Productp p m d Flow rate kmol/h, kmol/h m, OVHD2 Streamp Recycle eˆ Rebolierm Condenserp Heat Duty l Reflux Ratio 300, 1,500 p seˆ ˆ p k p 24 kpa, ˆrp k p 38 kpa p l r ee m. Column Diameter ~ w nm v Structured Packingp Sulzerp Mellapak 125.Y p m. w r Table 18 Table 19l ˆ l. s Product p k 80.44Í kmol/hp Rate p k pl. p 1 nr r n 300p 24h=7,200 hp 7,200 h kmol/h = kg p molí p p kg/yr p p k pl. Columnp Diameter 1,246 mmm 720 mm l. Bottom Rate w n l Column 2p Diameter w n s ƒv p k pl. ~ w n w, w nl Recycle Streamp sq l Column Diameter ƒv Duty v v w n p Product Flow Ratep ~ w n p Product lp p w nl ~ w nm d p v p v p k p. p r Table l l LNG / 12 CH 4 rm v r q o q m q p e l v l p / 12 CH 4 p e p q m. SRK ˆ rep Acentric factor l v p m p rn l e v r l r r r o Condenserp Holdupl r m. Condenser Holdupp k 82Í p p n 99Í p p p p s Product lp pl. l e v r Columnl Bottoml s k pl k 1,000 p 2 Columnp l e v rp p Product Rate rp Recycle o l k 80Íp Table 20. Results of continuos process simulation for various case Case 1 Case 2 Case 3 ColumnG1 ColumnG2 ColumnG1 ColumnG2 ColumnG1 ColumnG2 Condenser duty (Mkcal/h) Condenser temp. ( C) Reboiler duty (Mkcal/h) Reboiler temp. ( C) Column diameter (mm) 1, , , Final product composition ( ) Final product rate (kmol/h) Product amount per year (Kg/yr) Korean Chem. Eng. Res., Vol. 45, No. 1, February, 2007

10 66 s Ëp Ëpp Ë v l Recyclep lp n kg/h, Recyclep pp n kg/h p k pl. Recyclep p rl Recyclep l r p p r l n p k 89Í p k pl. CO/ 12 CO p rm v rl r l LNG pn ˆ oo rl mp e l r e np p re pl. y 1. Johns, T. F., Vapor Pressure Ratio of 12 C 16 O and C 16 O, Proc. Phys. Soc., B66, (1953). 2. McInteer, B. B., Isotope Separation by Distillation: Design of a Carbon- Plant, Sep. Sci. Tech., 15(3), (1980). 3. A Method for the Separation of Carbon Isotopes by Chemical Exchange Method, Europ. Pat (1980). 4. Vasaru, G., Ghete, P., Cocacci, I. and Atanasiu, M., Separation of Carbon- by Thermal Diffusion, Stable Isotope Life Sci. Proc. Tech. Comm. Meet Mod Trends Biol. Appl. Stable Isot., 39-52(1977). 5. Method of Centrifugal Enrichment of Carbon- Isotope in CO2 Form, RU (2000). 6. Hirose, Y., Tachibana, H. and Soh, H., Distillation Calculation Method for Isotope Separation, Kagaku Kogaku Ronbunshu, 223(3), (1996). 7. Douglas, J. M., Conceptual Design of Chemical Processes, McGraw-Hill Book Co.(1988). 8. Xopowulov, A. B., Separation of Stable Carbon Isotopes by Cryogenic Distillation, Khimicheskay Promyshlennost Moscow, 4, (1999). 9. Smith, J. M., Van Ness, H. C. and Abbott, M. M., Introduction to Chemical Engineering Thermodynamics, McGraw-Hill Book Co.(1996). 10. Prausnitz, John, M., Lichtenthaler, Rüdiger N., Edmundo Gomes de Azevedo, Molecular Thermodynamics of Fluid-Phase Equilibria, Prentice Hall(1999). 11. Tokyo Gas Report, EIT No. 32, The Utilization of LNG Cryogenic Energy(2000). 12. Alberto Bertuccon and Cristina Mio, Prediction of Vapor-liquid Equilibrium for Polymer Solution by a Group-contribution Redlich- Kwong-Soave Equation of State, Fluid Phase Equilibria, 117(1-2), 18-25(1996).. King, C. J., Separation Processes, McGraw-Hill Book. Co.(1980). 14. José O. Valderrama and Alexis Silva, Modified Soave-Redlich- Kwong Equations of State Applied to Mixtures Containing Supercritical Carbon Dioxide, Kor. J. Chem. Eng., 20(4), (2003). 15. Jungho Cho, A Study on the Simulation of Toluene Recovery Process using Sulflane as a Solvent, Kor. Chem. Eng. Res., V44(2), 129-5(2006). o45 o k