슬라이드 1

hapter 4 Sngle Equlbrum Stages Youn-Woo Lee School o hemcal and Bologcal Engneerng Seoul Natonal Unversty

4.0 INSTRUTIONAL OBJETIVES Ater completng ths chapter, you should be able to: Eplan what an equlbrum stage s Eplan why t may not be sucent to acheve a desred separaton. Etend Gbbs phase rule to nclude etensve varables so that the number o degrees o reedom number o varables mnus the number o ndependent relatons among the varables) can be determned. Use T y and y dagrams o bnary mtures, wth the q-lne, to determne equlbrum compostons. Understand the derence between mnmum- and mamum-bolng azeotropes and how they orm. alculate bubble-pont, dew-pont, and equlbrum-lash condtons. Use trangular phase dagrams or ternary systems wth component materal balances to determne equlbrum compostons o lqud lqud mtures. Use dstrbuton partton) coecents, rom actvty coecents, wth component materal-balance equatons to calculate lqud lqud phase equlbra or multcomponent systems. Use equlbrum dagrams wth materal balances to determne amounts and compostons or sold lud systems leachng, crystallzaton, sublmaton, desublmaton, adsorpton) and gas absorpton n lquds. Seoul Natonal Unversty

4. Introducton The smplest separaton process s one n whch two phases n contact are brought to physcal equlbrum, ollowed by phase separaton. I the separaton actor s very large, a sngle contactng stage may be sucent to acheve a desred separaton between them; not, multple stages are requred. or eample, a vapor phase s brought to equlbrum wth a lqud phase, the separaton actor s the relatve volatlty,, o a volatle component called the lght key, L, wth respect to a less-volatle component called the heavy key, H, where L, H L / H. I the separaton actor s 0,000, a near-perect separaton s acheved n a sngle equlbrum stage. I the separaton actor s only.0, an almost perect separaton requres hundreds o equlbrum stages. Relatve volatlty o A separaton actor) Seoul Natonal Unversty

4. Gbbs Phase Rule and Degrees o reedom Equlbrum calculatons nvolve ntensve varables and etensve varables. Phase-equlbrum equatons and mass and energy balances provde dependences among the ntensve and etensve varables. When a certan number o the ndependent varables are speced, all other dependent varables become ed. The number o ndependent varables s called the varance, or the number o degrees o reedom,. Intensve varables Intensve property s a physcal property o a system that does not depend on the system sze or the amount o materal n the system. Temperature, pressure, and mole or mass ractons are ntensve. Etensve varables Etensve property s one that s addtve or ndependent, nonnteractng subsystems. It s drectly proportonal to the amount o materal n the system. Etensve varables nclude mass or moles and energy or a batch system, and mass or molar low rates and energy-transer rates or a low system. Seoul Natonal Unversty

4. Gbbs Phase Rule Proposed by Josah Wllard Gbbs n the 870s The number o varables The number o equatons 2 : Temperature and Pressure : ompostons at each phases I ntensve varables are speced, the remanng ntensve varables are determned rom equatons. : requrement that mole ractons sum to one n each phase : number o ndependent phase-equlbrum eqn. mole racton o n phase ) mole racton o n phase 2) y Seoul Natonal Unversty

4. Degrees o reedom Bolng water Vapor-Lqud equlbra Vapor-Lqud equlbra P 2 2 P 2 bnary) 3 P 2 tertary) P 2 P 2 P 2 2 2 2 2 2 2 3 2 2 3 T P T P y T P y z Seoul Natonal Unversty

4. Degrees o reedom Vapor-Lqud Equlbrum Seoul Natonal Unversty

4. Degrees o reedom Type a) Varables T, P : 2 varables,... : varables, 2, y, y 2 ) y Equatons P y y /,... : equatons : equatons P Degree o reedom = 2 + P) P - P - ) = P + 2 e) or bnary V-L system =2) : gven T, P calculate and y P Seoul Natonal Unversty

4. Degrees o reedom o a low system Etenson o Gbbs Phase Rule to Etensve Varables Varables P+2) - T, P : 2 varables -,... : varables y P Type b) Addtonal varables - V L 3 varables - z varables - 3 varables P T Q 6 addtonal varables) Equatons - equatons P z yv L,2,..., h Q Vh Lh Addtonal equatons - V L equatons) M-balances) E-balance) I the +5 degrees o reedom are used to specy all z and the ve varables, T, P, T, and P, the remanng varables are ound usng equatons n g.4.. Seoul Natonal Unversty

4.2 Zeotropc Vapor-Lqud System Resources Epermental vapor-lqud equlbrum data or systems contanng two components are wdely avalable. Perry s chemcal engneers handbook Perry, Green, 2007) Vapor-Lqud Equlbrum Data ollecton Gmehlng, Onken, 977) Seoul Natonal Unversty

4.2 Epermental vapor-lqud equlbrum system Seoul Natonal Unversty

4.2 Zeotropc Vapor-Lqud System Types o Data Isobarc T - y Isothermal P y Table 4. Vapor-Lqud Equlbrum Data or Three ommon Bnary Systems at atm Pressure Table 4.2 Vapor-Lqud Equlbrum Data or the Methanol- Water system at Temperatures o 50, 50, and 250 Seoul Natonal Unversty

4.2 methanol-water system: Isobarc T - y Table 4. Vapor-Lqud Equlbrum Data or Three ommon Bnary Systems at atm Pressure Water A) Glycerol B) System Methanol A) Water B) System bp = 90, AB =hgh, No. o Trays ~ evaporator produces a nearly pure water vapor and a glycerol-rch lqud.) bp = 35.5, AB =medum, No. o Trays ~ 30 99 mol% o A n dstllate and a 98 mol% o B n bottoms) Para-ylene A) Meta-ylene B) System bp = 0.8, AB ~, No. o Trays ~ 000, rystallzaton or adsorpton Seoul Natonal Unversty

4.2 methanol-water system: Isothermal P y Table 4.2 Vapor-Lqud Equlbrum Data or the Methanol-Water at Temperatures o 50, 50, and 250 T = 50 T = 50 At 50, AB averages 4.94. At 50, the average AB s only 3.22; and at 250, t s.75. Thus, as temperature and pressure ncrease, AB decreases. T = 250 Dstllaton columns must operate at pressures well below the crtcal pressure o the mture to avod relatve volatltes that approach. At a pont reached near,29 psa methanol mole racton o 0.772), where the relatve volatlty s.0, dstllaton s mpossble because the vapor and lqud compostons are dentcal and the two phases become one. Ths s the crtcal pont or the mture. Seoul Natonal Unversty

4.2 methanol-water system Types o Plots T - y - plot y - plot P - plot dew-pont bubble-pont atm atm 50 o a) b) c) gure 4.2 Vapor-lqud equlbrum condtons or the methanol-water system: a) T-y- dagram or atm pressure; b) y- dagram or atm pressure; c) p- dagram or 50 o Seoul Natonal Unversty

4.2 n-heane n-octane system at atm. Pont H : superheated vapor 275 ), y H = 0.3 Pont G : dew pont 245 ), y H = 0.3 Pont E : 기상과액상의상대몰수는 nverse lever-arm rule 로정해짐 V L DE V, E DE DE Pont A : subcooled lqud 50 ), H = 0.3 DE at 255 o H = 0.7, y H = 0.55) 증기 =dew pont, 액 =bubble pont, 총괄조성은 H 30mole% 유지 Pont B : bubble pont 20 ) lne B : te lne H = 0.3, y H = 0.7) 0.3 kpa, heaneh) 30mole%- octane O) 70 mole%

4.2 Equlbrum Bnary mture) T T 2 Equlbrum Bnary mture) Equlbrum value: 2 y y 2 Equlbrum or bnary dstllaton Relatve Volatlty:, 2 Equlbrum urve: 2 y / y / 2 2 y / y /

4.2 n-heane n-octane system at atm. Vy L q- Lne y ) where V / 헥산몰수지식 : z H Vy H L H 전체몰수지식 : V L the q-lne equaton slope V / V / z z H H 0. 6 H y H y H Slope = 0, V/)= - all vapor large q ) / H zh V / V / V Slope = nnte, V/)=0 - all lqud small q)

4.2 n-heane n-octane system at atm. z z H H q-lne : Vy V y y H H q-lne slope no vapor no lash H y L H / H V / V / V H L ) 0 : H H H where z H 0 0 V z H 0.6 no lqud all lash no vapor no lash 0 y ), y ) Z H = 0.6 의 중 60% 가 V 로들어감 점선 ). no lqud all lash : 0 0. 6 60% vapor A-B lne 0. 6 : 0. 6 3 2 pont B y H = 0.76, H =0.37 g 4.3 에서는 tral & error 로계산 )

4.2 Azeotropc Vapor-Lqud System azeotrope 은 mamum 또는 mnmum bolng pont 를보이는액체혼합물에의해형성되며, Raoult s law 에서음의압력편차또는양의압력편차를보임. 공비점 Azeotrope) 는통상의증류에서성취할수있는분리한계이다. 충분한압력변화를주면기 - 액평형이동으로공비를 깰 break the azeotrope) 수있다. 예로 ethanol-water 는 78.5 & 0.3 kpa 에서 95.6wt% EtOH 의 homogeneous mnmum bolng azeotrope 을형성하지만, 9.3kPa 이하의 vacuum 에서는 azeotrope 이형성되지않는다.

most common Mnmum-bolng Homogeneous azeotrope Three types o azeotropes Mamum-bolng Homogeneous azeotrope Mnmum-bolng Heterogeneous azeotrope sopropyl ether sopropyl alcohol acetone chloroorm water/n-butanol 0 kpa 00

=78 mol% 4.2 a) Mnmum-bolng homogeneous azeotropc sopropyl ether-sopropyl alcohol system 23 kpa 923 torr), b) y =78 mol% 활동도계수 actvty coecents) 들이 보다크기때문에, 총압력의최대값이순수한성분의증기압보다높다. c) azeotrope bols at mnmum bolng pont 66. 증류탑에서는최소공비점 66) 혼합물은탑정제품으로회수된다.

=39 mol% 4.3 a) 86 kpa 630 torr), Mamum-bolng homogeneous azeotropc aceton-chloroorm System Mtures o close-bolng speces o derent chemcal types whose lqud solutons are non-deal b) y =39 mol% 활동도계수 actvty coecents) 들이 보다작기때문에, 총압력의최소값이순수한성분의증기압보다낮다. c) 증류탑에서는최대공비점 66) 혼합물은탑저제품으로회수된다. azeotrope bols at mnmum bolng pont.

4.3 Mnmum-bolng heterogeneous azeotropc water-n-butanol system Heterogeneous azeotropes are mnmum-bolng because actvty coecents must be sgncantly greater than to orm two lqud phases. 2 regon 상변화량이변할수록총압력과부분압력은일정하게유지된다. 그러나각조성은변한다. 2 phase regon = Immscble regon

4.2 Azeotropc Vapor-Lqud System

4.2 Azeotropc Vapor-Lqud System

4.2 Azeotropc Vapor-Lqud System

4.3 Azeotropc Dstllaton Etractve Dstllaton 24% E 54% B 22% W 83% E % W 20% E 72% B 8% W eed 89% E % W Make up Benzene 35% E 6% B 59% W 49% E 5% W Ethanol ~00% E Water ~00% W Azeotropc Dstllaton Benzene Recovery Water Removal

4.3 Heterogeneous azeotropc dstllaton o n-butanol and water Organc Aqueous eed Butanol Water

4.3 Azeotropc dstllaton

4.4 Sngle-stage lash calculaton lash separaton ndcates the order o volatltes: The lghter or more volatle components tend to be gaseous. The heavy or less volatle components tend to be lqud. Only a non-sharp separaton s avalable.

4.4 Sngle-stage lash calculaton lash vaporzaton Varables 3 0 varables) - T, P, TV, PV, TL, PL : 6 -,,,... : y z 2 -, V, L : 3 - : Q Equatons 2 5 equatons) Partal ondensaton Degree o reedom, ) 5 Assumng that +3 eed varables, T, P, and values o z are known, two addtonal varables can be speced or a lash calculaton.

4.4 Sngle-stage lash calculaton Isothermal lash :, Two addtonal Varables: ommon Types o Speccaton Bubble Pont Temperature :, Dew Pont Temperature :, Bubble Pont Pressure :, Dew Pont Pressure :, T V PV V / 0 P L z V / z y V / 0 T L P V z V / z y T V Q 0 Adabatc lash :, Q Nonadabatc lash :, P V PV V / Percent Vaporzaton lash :, P V

Sngle-stage lash calculaton 4.4 ) y, V ) y L y V z L Vy z 0 z A nonlnear equaton n the unknowns V, L, y, and. 0 0 z y y z y z

4.4 Rachord-Rce Algorthm Rachord, H.H., Jr., and J.D. Rce, J. Pet. Tech., 40), Secton, p. 9, and Secton 2, p. 3 Oct.952). Isothermal-lash calculatons are not straghtorward because Eq. 4) n Table 4.3 s a nonlnear equaton n the unknowns V, L, y, and. Equatons contanng only a sngle unknown are solved rst. Thus, Eqs. ) and 2) n Table 4.3 are solved, respectvely, or P L and T L. The unknown Q appears only n 6), so Q s computed ater all other equatons have been solved. Ths leaves Eqs. 3), 4), 5), and 7) n Table 4.3 to be solved or V, L, and all values o y and.

Newton-Raphson Method - nd to )=0 - Taylor seres epanson o ) 0 2 2 0 0 0 0 0... ''! ' 0 0 0 ' Multcomponent lash, Bubble-Pont, and Dew-Pont alculatons 4.4 rst order appromaton ' ontnue teraton untl converges 2 3 4 ) ) ndng soluton Newton-Raphson method 0 z 0 k k z 0 ' 2 2 k k z k k k k '

Start Gven,,,,,, End Yes No c z z,..., T P V T P V L T L P L T V T V L P P 0 k k z 0 ' 2 2 k k z k k k k ' V z z y V L h L h V h Q L V -value subroutne Rachord-Rce Algorthm or Isothermal lash alculaton 4.4 k k k k ' 0 ' 2 2 k k z 0 k k z 0 z Newton-Raphson method

4.4 Eample 4.: Phase ondtons o a Process Stream A 00-kmol/h eed consstng o 0, 20, 30, and 40 mol% o propane 3), n-butane 4), n-pentane 5), and n-heane 6), respectvely, enters a dstllaton column at 00 psa 689.5 kpa) and 200 366.5). Assumng equlbrum, what racton o the eed enters as lqud, and what are the lqud and vapor compostons? = 00 kmol/h z = 0. propane) z 2 = 0.2 n-butane) z 3 = 0.3 n-pentane) z 4 = 0.4 n-heane) T = 366.5 P = 689.5 kpa V =? kmol/h y =? propane) y 2 =? n-butane) y 3 =? n-pentane) y 4 =? n-heane) T V = 366.5 P V = 689.5 kpa P=00 psa 689.5 kpa) T= 200 366.5). L =? kmol/h =? propane) 2 =? n-butane) 3 =? n-pentane) 4 =? n-heane) T L = 366.5 P L = 689.5 kpa

4.4 Eample 4.: Phase ondtons o a Process Stream g 2.4 로부터 값을찾는다. lash condton 에서의 3 =4.2, 4 =.75, 5 =0.74, 6 =0.34 은조성에무관하다. -value 들이일부는 보다크고일부는 보다작아서, Table 4.4 식 3) 의 {0} 와 {} 를계산할필요가있다. 0.720-0.28 {0}=-0.28 < 0 above the bubble pont. {} =0.720 > 0 below the dew pont 0.29 z 0 혼합물은일부가 vapor 임 0.29 V /

4.4 Eample 4.: Phase ondtons o a Process Stream ntal guess ψ=0.5 k k ) k) { } k) `{ } k) 0.5000 0.255 0.6259 0.0982 0.8037 2 0.0982-0.0209 0.9 0.2 0.2335 3 0.2-0.0007 0.8539 0.29 0.0065 4 0.29 0.0000 0.852 0.29 0.0000 k ) k ) k ) 0.720 z 0-0.28 0.29 V / 0.29

4.4 Eample 4.: Phase ondtons o a Process Stream Soluton g. 2-4 =4.20 2 =.75 3 =0.74 4 =0.34 0.29 V / y = 00 kmol/h z = 0. propane) z 2 = 0.2 n-butane) z 3 = 0.3 n-pentane) z 4 = 0.4 n-heane) T = 366.5 P = 689.5 kpa z z V = 2.9 kmol/h y = 0.302 propane) y 2 = 0.3207 n-butane) y 3 = 0.2293 n-pentane) y 4 = 0.479 n-heane) T V = 366.5 P V = 689.5 kpa P=00 psa 689.5 kpa) T= 200 366.5). L = 87.8 kmol/h = 0.079 propane) 2 = 0.833 n-butane) 3 = 0.3098 n-pentane) 4 = 0.4350 n-heane) T L = 366.5 P L = 689.5 kpa

T= 200 =4.2 propane P=00 psa

Seoul Natonal Unversty 열역학 액 - 액추출에서의열역학 - VLE 에서의이상용액과같은단순한이론이존재하지않음 E) R) - 많은경우에, actvty-coecent correlaton 에기본을둔예측보다는실험적평형자료가이용 E ) E) E ) - 실제로는이러한자료를기반으로 NRTL이나 UNIQUA 식과같은 semtheoretcal actvty-coecent equaton에의한상관관계를활용 - 착한용매를찾는데에도상당한실험적노력이요구 D R ) E ) R ) R) R ) R ) E )

열역학 액 - 액시스템에서의평형 Physcal Equlbrum o two lqud phases Etract & Ranate) μ E) μ R) partal ugacty : E) ep R) 0 RT E ) R ) E ) R ) E) R) E) R) E ) E ) 0 E ) R ) R ) 0 R ) 0 E ) 0 R )

열역학 3 성분액 - 액시스템에서의분배계수의정의 분배계수 = -value = D = E) / R) E ) E ) R ) R ) Mole racton epresson ' D D X X X E ) R ) E ) R ) D R ) E ) Mole rato epresson R ) E ) E ) R ) E) E ) R) R ) 값들이작으면 D 는 D 에접근한다.

Mole racton epresson 2) ) 2) 2) 2) ) ) ) ) ) ) ) D 2 2 X ) ) D ) ) ) ) ) ) ' D X X 2 2 2 2 Tertary Lqud-Lqud Systems 4.5 When A and are mutually nsoluble Mole rato epresson Dstrbuton coecent approach 값들이작으면 D 는 D 에접근한다.

추출 3 성분액 - 액시스템 低밀도 ) A carrer) B solute) solvent) Etract 추출액 ): 용매 S) 와추출된용질 B) 을함유하는액상 高밀도 ) Ranate 잔사액 ): 원료의 carrera) 와추출되지않고남은용질 B) 의일부가남아있는액상 3 성분계에서는 A 와 서로용해하지않을경우의狀분리행태

추출 3 성분액 - 액시스템에서의추출인자 Dstrbuton coecent approach - Materal balance X X S X X ) B A - Equlbrum E) B X E) ' R) B D B B A 와 가서로용해하지않을경우 R) B A ) 2) X R) B B ) X B ' ' D A E S / B X R) B / X ) B A D B A S - Etracton actor E B ) E B X X E ) B R ) B B 3) 4) 5) A = eed rate o carrer A S = low rate o solvent massmoles) o solute B X B massmoles) o other component n eed) E B 값이크면클수록더많은용질 B) 이추출된다. E B 값이크면클수록추출안된용질 B) 의분율이작다. 큰 E B 값은 DB 가크거나 S/ A 가크면된다.

E 4.6 Sngle-Stage Etracton o Acetc Acd 3,500kg/h 의원료중에 92wt% 의물 A) 과 8wt% 초산 B) 이들어있다. 증류로는너무많은양의물을증발시켜야하므로물에서초산을제거하기위해서 Methyl sobutyl ketone MIB) 을용매로사용하여액 - 액추출한다. 단일단을사용하면서 ranate 에단지 wt% 초산이포함되도록하기위해필요한용매의유량 kg/h) 을구하여라. 해답 carrer 물 ) 와용매가서로녹지않는다고가정하자. Perry 의화학공학자핸드북에의하면이계에대한 D =0.657 중량단위 ) 이다. 그런데여기서는초산의농도가낮기때문에 D = D 라고할수있다. A = 0.92)3,500) = 2,420 kg/h 물의유량 ) X B ) = 3,500-2,420)/2,420 = 0.087 Ranate 는 wt% B 만있어야하므로 X B R) = 0.0/-0.0) = 0.00 Eq 4-25) 로부터 E B 에대해풀면 X X ) E B B R ) B S E E B 'D A 44, 000kg Eq 4-24) 로부터 0. 087 7. 6 0. 00 7. 6 2, 420 / 0. 657 ) / h S 44000 2420. 6 S/ rato o solvent to eed) 는.6 으로매우크다. S/ 를줄이기위해다단공정을사용하거나더큰분배계수를갖는용매를사용해야한다.

열역학 Equlateral Trangular LLE Dagram Above bubble pont - No vapor phase est. M pont beore separaton) - Ethylene glycol : 20% - urural : 6% - Water : 9% B solute) mscblty boundary = saturaton curve cloud-pont ttraton: 50% 의 glycol-urural mture clear) 에 water 를첨가하기시작하여, 2nd phase 가생김으로써 cloudness 가생기는조성 0% water, 45% urural, 45% glycol) 을구한다. Etract = urural-rch phase Ranate = water-rch phase solvent) 부분혼합 A carrer)

열역학 Equlateral Trangular LLE Dagram B solute) Sngle phase regon Plat pont: Two lquds have dentcal compostons degree o reedom =-P+2 =3-2+2 =3 Gbbs phase rule Mscblty lmt or water-urural 5.2wt% solvent) Two lquds phase regon Mscblty lmt or water-urural 7.9wt% A carrer)

열역학 Tertary Lqud-Lqud Systems 25 와 0kPa 에서 00g 의공급용액 ) 이 200g 의용매 urural) 과평형으로접촉된후만들어진抽出상과抽殘상의양과조성을구하라. S 00 200 300g E R A 55g, B 45g, 200g A 00 55 / 300 ) 8. 3% B 00 45 / 300 ) 5. 0% 00 200 / 300 ) 66. 7% urural R=80g E=220g S E R M A=water B=EG =urural Seoul Natonal Unversty

열역학 Equlateral Trangular LLE Dagram Phase Splttng o Ternary Mtures B solute) M pont beore separaton) - Ethylene glycol : 20% - urural : 6% - Water : 9% Ranate Ethylene Glycol : % urural : % Water : % Etract Ethylene Glycol : % urural : % Water : % solvent) A carrer)

Seoul Natonal Unversty 열역학 Tertary Lqud-Lqud Systems step : 삼각도표에점 와 S 를찍는다. step 2 : M 의물질수지 : M = + S =E + R Step 3: 용매 urural) 에대한수지식 S) w M ) w Sw S ) S w w S ) M ) w w M ) ) 공급용액 ) 45 wt% EG 55 wt% water S SM M 2 M 의조성 : A=8.3 wt% B=5.0 wt% =66.7 wt% S M

열역학 Tertary Lqud-Lqud Systems step 4 : M 이 two phase regon 내에있기때문에이혼합물은 te lne 을따라 2 상으로분리된다. E 추출상 ) A=04.5 wt% B=08.5 wt% =87.0 wt% R 추잔상 ) A=56.0 wt% B=34.0 wt% =0.0 wt% step 5 : E, M, R 의선에 nverse lever rule 이적용되어 E = MRM/ER) M = 00+200 = 300g 이고 lne segment 의측정에의해 E=30047/200)=220g, R=M-E=300-220=80g 이다. R E M S Seoul Natonal Unversty

4.5 Tertary Lqud-Lqud Systems 예제 4.7: 25 와 0kPa 에서 45wt% glycol B) 과 55wt% 의 watera) 로된용액이무게가 2 배인순수한 urural) 과평형접촉되고만들어진추출상과추잔상의조성을구하라. S E R

4.5 Tertary Lqud-Lqud Systems step : 삼각도표에점 와 S를찍는다. step 2 : M의물질수지 : M = + S =E + R Step 3: 용매 에대한수지식 +S)w M) = w ) + Sw S) S S w w S ) M ) SM M w w 2 M ) ) M 의조성 : A=8.3 wt% B=5.0 wt% =66.7 wt% S M

4.5 Tertary Lqud-Lqud Systems step 4 : M 이 two phase regon 내에있기때문에이혼합물은 te lne 을따라 E 추출상 ) A=04.5 wt% B=08.5 wt% =87.0 wt% R 추잔상 ) A=56.0 wt% B=34.0 wt% =0.0 wt% 으로분리된다. R E M S

4.5 Tertary Lqud-Lqud Systems step 5 : E, M, R 의선에 nverse lever rule 이적용되어 E = MRM/ER) M = 00+200 = 300g 이고 lne segment 의측정에의해 E=30047/200)=220g, R=M-E=300-220=80g 이다. R E M S

열역학 Sngle-Stage Etracton 으로초산수용액으로부터초산을추출하는데 MIB 용매가적절한가? 3,500kg/h 의원료중에 92wt% 의물 A) 과 8wt% 초산 B) 이들어있다. 증류로는너무많은양의물을증발시켜야하므로물에서초산을제거하기위해서 Methyl sobutyl ketone MIB) 을용매로사용하여액 - 액추출공정을사용하려고한다. 단 Sngle stage) 을사용하면서 ranate 에단지 wt% 초산이포함되도록하기위해필요한용매의유량 kg/h) 을구하여라. Methyl sobutyl ketone MIB) Molecular ormula : 6 H 2 O Molar mass : 00.6 g/mol Appearance : colorless lqud Densty : 0.802 g/ml Meltng pont : -84.7 Bolng pont : 7 Solublty n water :.9 g/00 ml @20 n-butyl alcohol Molecular ormula : 4 H 0 O Molar mass : 74.2 g/mol Appearance : olorless, reractve lqud Odor : harsh, alcoholc and sweet Densty : 0.8 g/ml Meltng pont : -89.8 Bolng pont : 7.7 Solublty n water : 73 g/l @ 25 Solublty very soluble n acetone mscble wth ethanol, ethyl ether

해답 물속에서의초산의용해도와 MIB 속에의초산의용해도비 D =0.657 Perry s hemcal Engneers Handbook) 이고, D = D 초산의농도가낮기때문 ) 라하면, A = A =0.92)3,500) = 2,420 kg/h 물의유량 ) X B ) = 3,500-2,420)/2,420 = 0.087 eed 중초산의분율 ) Ranate 에초산은 wt% 만있어야하므로 X B R) = 0.0/-0.0) = 0.00 Eq 5) 로부터 Etracton actor 추출인자 ) E B 에대해풀면 Eq 4) 로부터 X X ) E B B R ) B S E B A ' D 0. 087 7. 6 0. 00 7.6)2,420) 0.657 44,000 kg/h S 44, 000 0. 67 3, 500 단의경우에는 S/ rato o solvent to eed) 가 0.67로매우크다. S/ 를줄이기위해다단공정을사용하거나더큰분배계수를갖는용매를사용해야한다. 예를들어 n-butyl alcohol D =.63) 을사용하면 58,600kg/h 만사용하면된다. S/=4.34, 단물에용해력이높아 ranate 로용매의손실이크다. Trade-o)