Lecture 8. Chapter 7. - Thermodynamic Web - Departure Functions - Review Equations of state (chapter 4, briefly)
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1 Lecture 8 Chapter 5 - Thermodynamc Web - Departure Functons - Revew Equatons of state (chapter 4, brefly) Chapter 6 - Equlbrum (chemcal potental) * Pure Component * Mxtures Chapter 7 - Fugacty (chemcal potental fugacty equlbrum calculatons) * Vapor (overvew), lqud, solds - ctvty Coeffcents [Fugacty Coeffcents (overvew)] Chapter 8 - Phase Equlbrum * Dagrams * Vapor Lqud (VLE) * Lqud Lqud (LLE) * Sold Lqud (SLE) Chapter 9 - Reacton Equlbra
2 Fugacty Coeffcent (methods to calculate) ˆ. Data. Equatons of State 3. Generalzed correlatons a. Pure Flud 3. Generalzed correlatons b. Multcomponent system: ˆ a. Pure Flud. Data ln P ln P 0 dp P P dp RT P CO at 38 o C, 3.79 bar P [bar] P data ln CO dp RT P 0
3 Fugacty Coeffcent (methods to calculate) a. Pure Flud. Equatons of State 3 See handout on webste from Kyle for Peng-Robnson EOS 3 ( ) ( 3 ) ( 3 ) 0 ln ln( ) ln CO at 38 o C, 3.79 bar PREOS CO 0.935
4 Fugacty Coeffcent (methods to calculate) 4 ˆ. Data a. Pure Flud. Equatons of State 3. Generalzed correlatons b. Multcomponent system: ˆ vdw EOS RT a a y a y b b RT b P P y f b a b a a mx a mx v a a v a ln ˆ ln ˆ ln c Peng Robnson EOS (see Kyle handout on web) j j j ln ˆ ln ln
5 Fugacty Coeffcent (Contnued) 5
6 Fugacty Coeffcent (Contnued) 6
7 Fugacty Coeffcent (PREOS) 7 c j j j ln ln ˆ ln T P r r P r T r r T c c c j j j k j j j j k 0 ) ( ) 3 ( ) ( ) ( ) 3 ( ) (
8 Fugacty Coeffcent (spenplus Examples) 8. for ethylene at 5 o C and 40 bar ˆ CO. for CO n 50:50 (mole) mxture wth toluene at 45 o C and 40 bar
9 Fugacty Coeffcent (multcomponent approxmaton) 9 Lews fugacty approxmaton (rule) ˆ Vald near deal soluton condtons,.e. y n excess ( >0.9)
10 ) y Fugacty / Equlbrum (SUMMRY) V L f ˆ ˆ f P ˆ V x P ˆ L Vapor phase: good; lqud phase: good for HC or moderate hgh pressures (compressble lqud phase) 0 ˆ Typcally used for lqud phase V sat sat ) y P x P P. C. fugacty calculatons y Pˆ V x H 3) Used for specal cases (lke gases dssolvng nto lqud phase)
11 L fˆ f. Compressble lquds. Ideal and real solutons 3. Dssolved gases Fugacty (Lqud Phase). Compressble lquds (mod hgh P, and hydrocarbons) f ˆ L L x Pˆ L Use EOS for: ˆ & or L L. Ideal lqud soluton f ˆ L f ˆ deal x f deal x f o o f Pure speces fugacty real soluton fˆ L fˆ deal x f ctvty coeffcent o fˆ fˆ Lews/Randall bass L deal fˆ x L o f
12 real soluton o L Fugacty (Lqud Phase) fˆ x f Lews/Randall bass s o o f P L sat sat P exp dp at system T and P sat RT P fˆ L x P sat sat P exp P sat L RT dp
13 Fugacty (Typcal Lqud Phase Models) fˆ real soluton o L sat sat Lews/Randall bass s x P P.C. 3? real soluton behaves deally n the lqud phase then: fˆ L x P sat real soluton behaves non-deally n the lqud phase then: fˆ L x P sat
14 G E G G ctvty Coeffcent (ways to calculate) deal u RT ln fˆ deal u deal fˆ but : fˆ ˆ L f deal 4 G E RT ln G E nt g n E T, P, n j RT ln nt g n E T, P, n j E Now, need models for calculatng g and then can fnd. -suffx Margules (smple, symmetrc) [bnary] g E x x RT ln RT ln x x x x p RT ln exp x ln ln lm 0 0 x x 0 RT exp
15 ctvty Coeffcent ( suffx Margules model). -suffx Margules agues (smple, symmetrc) [bnary] g E x x x x 5 Fnd : take data y P x P sat Example: bnary mx of cyclohexane (a) and dodecane (b) at o C cycloc C lm x 0 RT exp
16 ctvty Coeffcent (Models). -suffx Margules agues (smple, symmetrc) [bnary] g E x x x x 6 symmetrc models:. Three-suffx Margules: (addtonal parameter) 3. Van Laar: (older model but stll good and easy to work wth) 4. Wlson: (not good for lqud-lqud-equlbra) 5. NRTL: (Non-Random-Two-Lqud; R T d good dfrst choce, usually) 6. UNIQUC: (UNIversal QUs-Chemcal; also good) 7. UNIFC: (only predctve model)
17 ctvty Coeffcent (nary Models) 7 Koretsky, 004
18 ctvty Coeffcent (nary Models) 8
19 ctvty Coeffcent (nary Models) 9 Prausntz, et.al., 999
20 ctvty Coeffcent (nary Models) 0 Prausntz, et.al., 999
21 ctvty Coeffcent (nary Models) Prausntz, et.al., 999
22 ctvty Coeffcent (nary Models) Prausntz, et.al., 999
23 ctvty Coeffcent (nary Models) 3 Prausntz, et.al., 999
24 ctvty Coeffcent (nary Models) 4 Prausntz, et.al., 999
25 ctvty Coeffcent (nary Models) 5 r and q depend on molecular sze (volume) and external surface areas of pure components. Prausntz, et.al., 999
26 ctvty Coeffcent (nary Models) 6 Prausntz, et.al., 999
27 ctvty Coeffcent (Example) 7 Temperature-composton dagram at.03 bar ( atm) pressure for system: formc acd () and acetc acd () Prausntz, et.al., 999
28 Lecture 8 Chapter 5 - Thermodynamc Web - Departure Functons - Revew Equatons of state (chapter 4, brefly) Chapter 6 - Equlbrum (chemcal potental) * Pure Component * Mxtures Chapter 7 - Fugacty (chemcal potental fugacty equlbrum calculatons) * Vapor (overvew), lqud, solds - ctvty Coeffcents [Fugacty Coeffcents (overvew)] Chapter 8 - Phase Equlbrum * Dagrams * Vapor Lqud (VLE) * Lqud Lqud (LLE) * Sold Lqud (SLE) Chapter 9 - Reacton Equlbra 8
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