General Thermodynamics for Process Simulation. Dr. Jungho Cho, Professor Department of Chemical Engineering Dong Yang University

Transcription

1 General Thermodynamcs for Process Smulaton Dr. Jungho Cho, Professor Department of Chemcal Engneerng Dong Yang Unversty

2 Four Crtera for Equlbra μ = μ v Stuaton α T = T β α β P = P l μ = μ l1 l 2 Thermal Equlbrum Mechancal Equlbrum Condton, Phase Equlbra (VLE, LLE) G ξ T, P = 0 Chemcal Equlbrum Fugacty (or chemcal potental) s defned as an escapng tendency of a component n a certan phase nto another phase. Thermodynamc Models bult n Smulator

3 Basc Phase Equlbra Relatons Vapor-lqud equlbrum calculatons The basc relatonshp for every component n vapor-lqud equlbrum s: v ( T P y ) f l ( T P x ) where : the fugacty of component n the vapor phase v fˆ l fˆ f ˆ,, = ˆ,, : the fugacty of component n the lqud phase (1) Thermodynamc Models bult n Smulator

4 Basc Phase Equlbra Relatons There are two methods for representng lqud fugactes. - Equaton of state method - Lqud actvty coeffcent method Thermodynamc Models bult n Smulator

5 Equaton of State Method The equaton of state method defnes fugactes as: f ˆ v v = φˆ y P (2) f ˆ l l = φˆ x P (3) where: φ v φ l y x P s the vapor phase fugacty coeffcent s the lqud phase fugacty coeffcent s the mole fracton of n the vapor s the mole fracton of n the lqud s the system pressure Thermodynamc Models bult n Smulator

6 Equaton of State Method We can then rewrte equaton 1 as: ˆ φ y = ˆ φ x v l (4) Ths s the standard equaton used to represent vaporlqud equlbrum usng the equaton-of-state method. φ v and φ l are both calculated by the equaton-of-state. Note that K-values are defned as: y K = (5) x Thermodynamc Models bult n Smulator

7 Lqud Actvty Coeffcent Method (VLE) The actvty coeffcent method defnes lqud fugactes as: fˆ l The vapor fugacty s the same as the EOS approach: v f ˆ = φˆ = γ x f (6) v y 0 P (7) where: γ s the lqud actvty coeffcent of component 0 f v φˆ s the standard lqud fugacty of component s calculated from an equaton-of-state model We can then rewrte equaton 1 as: ˆv φ y P = x γ f 0 (8) Thermodynamc Models bult n Smulator

8 Lqud Actvty Coeffcent Method (LLE) For Lqud-Lqud Equlbrum (LLE) the relatonshp s: f ˆ = l1 fˆ l 2 (9) where the desgnators 1 and 2 represent the two separate lqud phases. Usng the actvty coeffcent defnton of fugacty, ths can be rewrtten and smplfed as: x l1 l1 x l 2 γ l 2 γ = (10) Thermodynamc Models bult n Smulator

9 K-values The k-values can be calculated from: K = y x = γ l φ sat P sat l V exp RT ˆv φ P ( sat P P ) (11) Or K = y x = ˆ φ ˆ φ l v (12) Thermodynamc Models bult n Smulator

10 Example 2: Ideal Raoult s Law The precedng equaton reduces to the followng deal Raoult s law: y P = x P vap Example : Pxy plot at constant T(75 o C). (P n kpa, T n o C) lnp vap 1 = , lnp vap 2 = t t Soluton At 75 o C, P vap 1 = kPa and P vap 1 = kPa The total pressure Vapor phase composton, vap vap P x1 P1 + x2p2 P= P 2 + P P x = vap ( vap vap, ) y x P vap 1 = = vap P x P vap vap ( P P ) x P vap Thermodynamc Models bult n Smulator

11 Pxy Dagram at Constant Temperature a vap P 1 vap P 2 Pressure (kpa) Lqud P x 1 c b c b P y 1 Vapor d x 1, y 1 Thermodynamc Models bult n Smulator

12 Example 3: Slghtly Non-deal System For systems whch the lqud phase behaves nondeally: y P = γ x P vap Relaton between actvty coeffcent and excess Gbbs energy s as: lnγ = ex ( ng / RT ) n T, P, n j As an example, excess Gbbs energy expresson s as: G ex = RT Ax 1 x 2 Therefore, 1 γ and γ 2 becomes. 2 2 γ = ( ) γ = ( ) 1 exp Ax 2 So, = A( 1 x ) 2 exp Ax 1 [ ] 2 vap ( 2 ) vap x P Ax x P P exp exp y 1 exp = 2 [ A( 1 x ) ] P 1 x 1 P vap 1 Thermodynamc Models bult n Smulator

13 Predcton wth Margules Equatons 160 Unstable Pressure (kpa) A = 0.0 A = 0.5 A = 1.0 A = 2.0 A = x 1, y 1 Thermodynamc Models bult n Smulator

14 Devatons from Raoult s Law (1 of 2) In general, you can expect non-dealty of unlke molecules. Ether the sze and shape or the ntermolecular nteractons between components may be dssmlar. For short, these are called sze and energy asymmetry. Energy asymmetry occurs between polar and non-polar molecules and also between dfferent polar molecules. In the majorty of mxtures, actvty coeffcents s greater than unty. The result s a hgher fugacty than deal. The fugacty can be nterpreted as the tendency to vaporze. If compounds vaporze mere than n an deal soluton, then they ncrease ther average dstance. So actvty coeffcents s greater than unty ndcate repulson between unlke molecules. If the repulson s strong, lqud-lqud separaton occurs. Ths s another mechansm that decreases close contact between unlke molecules. If the actvty coeffcent s larger than unty, the system s sad to show postve devatons from Raoult s law. Negatve devatons from Raoult s law occur when the actvty coeffcent s smaller than unty. Thermodynamc Models bult n Smulator

15 Devatons from Raoult s Law (2 of 2) Sub-cooled Lqud Pressure (kpa) postve negatve deal 40 Super-heated Vapor x 1, y 1 Thermodynamc Models bult n Smulator

16 Isothermal Flash Calculatons Lqud feed T,P,F z T & P Flash Drum Heater Valve L, x Thermodynamc Models bult n Smulator

17 Equlbrum Flash Vaporzaton The equlbrum flash separator s the smplest equlbrum-stage process wth whch the desgner must deal. Despte the fact that only one stage s nvolved, the calculaton of the compostons and the relatve amount of the vapor and lqud phases at any gven pressure and temperature usually nvolves a tedous traland-error soluton. Buford D. Smth, 1963 Thermodynamc Models bult n Smulator

18 Flash Calculaton (1 of 4) MESH Equaton Materal Balance Equlbrum Relatons Summaton of Compostons Enthalpy(H) Balance Thermodynamc Models bult n Smulator

19 Flash Calculaton (2 of 4) Overall Materal Balance F = V + L (1) Component Materal Balance Fz = Vy + Lx (2) Equlbrum Relatons y = K x (3) Thermodynamc Models bult n Smulator

20 Flash Calculaton (3 of 4) Summaton of Compostons x = 1 Defnng (4a) y = 1 (4b) φ =V F (5) Combnng (1) through (5), we obtan: ( 1 K ) ( K 1) ( ) z F φ = + = 0 1 φ (6) Thermodynamc Models bult n Smulator

21 Flash Calculaton (4 of 4) From deal Raoult s law y P = x vap K-value can be rewrtten as: From Antone equaton y K = = x log P vap ( kpa) P P = vap P A t B ( o C) + C (7) (8) (9) Thermodynamc Models bult n Smulator

22 Antone Coeffcents log P vap ( kpa) = A t B ( o C) + C Benzene Toluene A B C Thermodynamc Models bult n Smulator

23 Rachford-Rce Functon φ = F(φ) ( 1 K ) ( K 1) ( ) z F φ = + = 0 1 φ φ Thermodynamc Models bult n Smulator

24 Flash Calculaton Results (1 of 3) Vapor Flowrate (K-mole/hr) V = Fφ = ( 100 ) (0.707) = (1) Lqud Flowrate (K-mole/hr) L = F V = = 29.3 (2) Thermodynamc Models bult n Smulator

25 Flash Calculaton Results (2 of 3) Mole Fracton at the lqud phase x = z 1+ φ 1 ( K ) x = = B Mole Fracton at the vapor phase y = K x = x T Kz 1+ φ 1 ( K ) y = = B y T (3) (4) (5) (6) Thermodynamc Models bult n Smulator

26 Flash Calculaton Results (3 of 3) x B = Pressure (kpa) y B = Mole Fracton of Benzene Thermodynamc Models bult n Smulator

27 PRO/II Keyword Input for Flash Calculaton TITLE PROBLEM=PRBLEM-1A,PROJECT=CLASS,USER=JHCHO DIMENSION METRIC,PRES=ATM PRINT INPUT=ALL,PERC=M,FRAC=M COMPONENT DATA LIBID 1,BENZENE/2,TOLUENE THERMODYNAMIC DATA METHOD SYSTEM=IDEAL STREAM DATA PROP STREAM=1,TEMP=25,PRES=1,RATE=100,COMP=1,60/2,40 UNIT OPERATION DATA FLASH UID=F01 FEED 1 PROD V=1V,L=1L ISO TEMP=100,PRES=1.2 END Thermodynamc Models bult n Smulator

28 PRO/II Output Summary for Flash Calculaton STREAM ID 1 1L 1V NAME PHASE LIQUID LIQUID VAPOR FLUID MOLAR FRACTIONS 1 BENZENE TOLUENE TOTAL RATE, KG-MOL/HR TEMPERATURE, C PRESSURE, ATM ENTHALPY, M*KCAL/HR MOLECULAR WEIGHT MOLE FRAC VAPOR MOLE FRAC LIQUID Thermodynamc Models bult n Smulator

29 PRO/II BVLE Analyss Thermodynamc Models bult n Smulator

30 Dew & Bubble Pont Calculaton Dew Pont s the very state at whch condensaton s about to occur. Dew Pont Temperature Calculaton at a Gven Pressure Dew Pont Pressure Calculaton at a Gven Temperature Vapor Fracton s 1 at Dew Pont Bubble Pont s the very state at whch vaporzaton s about to occur. Bubble Pont Temperature Calculaton at a Gven Pressure Bubble Pont Pressure Calculaton at a Gven Temperature Vapor Fracton s 0 at Bubble Pont Thermodynamc Models bult n Smulator

31 Ex-1: Bubble Pont Falure Case Calculate the bubble pont pressure at 85 o C of the followng stream. Dd you get a converged soluton? If not, why? Use SRK for your smulaton. Component Mole % C1 65 C2 15 C3 15 IC4 5 Save as Flename: EX-1.np Thermodynamc Models bult n Smulator

32 Dfference between Gas and Vapor For gas, T > T c For vapor, T < T c T: System temperature, T c : Crtcal temperature Methane Gas but not Methane Vapor Water Vapor but not Water Gas Thermodynamc Models bult n Smulator

33 Ex-2: C7 Plus Heavy Cut Characterzaton Calculate the bubble pressure at 45 o C and dew temperature at 1.5bar of the followng stream. Regard C6+ as NC6(1), NC7(2) and NC8(3) and compare the results. Use SRK for your smulaton. Component Mole % C1 5 C2 10 C3 15 IC4 10 NC4 20 IC5 15 NC5 20 C6+ 5 Save as Flename: EX-2A.np for NC6, EX-2B.np for NC7, EX-2C.np for NC8 Thermodynamc Models bult n Smulator

34 Results for EX-2 Characterzaton of heavycut s very mportant n the calculaton of dew pont temperature. EX-2A.np, EX-2B.np, EX-2C.np Bubble P Dew T C6 Plus at 45 o C at 1.5bar NC NC NC8 Thermodynamc Models bult n Smulator

35 Results for EX-2A (C6+ NC6) Thermodynamc Models bult n Smulator

36 Results for EX-2B (C6+ NC7) Thermodynamc Models bult n Smulator

37 Results for EX-2C (C6+ NC8) Thermodynamc Models bult n Smulator

38 The End of General Thermodynamcs The End. Thermodynamc Models bult n Smulator