Phase Equilibriain Reactive Distillation Processes...
46
2006/6/21 NTUST 1 Phase Equilibria in Reactive Distillation Processes- Theories and Experiments Ming-Jer Lee Department of Chemical Engineering National Taiwan University of Science and Technology
Transcript of Phase Equilibriain Reactive Distillation Processes...
2006/6/21 NTUST 1
Phase Equilibria in Reactive Distillation Processes- Theories and Experiments
Ming-Jer LeeDepartment of Chemical Engineering
National Taiwan University of Science and Technology
2006/6/21 NTUST 2
Outline
n Introductionn Phase Equilibrium Criterian Thermodynamic Models
u Equations of Stateu Activity Coefficient Models
n Parameter Determinationsn Thermodynamic Properties from Literaturen Experiments
u VLE, LLE, VLLEn Concluding Remarks
2006/6/21 NTUST 3
Reactive Distillation Processes
n Reactionsu Esterification, hydrolysis,
transesterification,….u Kinetic models (ai = xi γi)
« Pseudo-homogeneous« Langmuir-Hinshelwood« Eley-Rideal
n Phase equilibriau VLE, VLLEu Thermodynamic models
« φ−φ (Equations of state)« γ−φ (Activity coefficient models)
A
B
C
D
Reaction + VLE
VLE
VLE
VLLE
2006/6/21 NTUST 4
Phase Behavior in an Esterification, Hydrolysis, or Transesterification Reactive Distillation Column
n Components: Alcohol/Acid/Ester/Water
n Partially miscible: (two liquid phases)u Water + Alcohols (C4 or higher)u Water + Estersu Water + Alcohols + Estersu Water + Alcohols + Esters + Acids
n One liquid phase: Vapor-liquid equilibrium (VLE)n Two liquid phases: Vapor-liquid-liquid equilibrium (VLLE)
2006/6/21 NTUST 5
Phase Equilibrium Criterian At phase equilibria:
u TI = TII = TIII = … = Tu PI = PII = PIII = … = Pu fiI (T, P, xi
I) = fiII (T, P, xiII) = fiIII (T, P, xi
Iii) = .. for i = 1, 2,.., c
n Criteria for systems at VLE:
u fiv = fiL for i = 1, 2,…, c
u φ-φ method:PxfPyf i
Li
Lii
Vi
Vi φφ ===
Both the vapor phase and liquid phase fugacities are calculated from an equation of state.
u γ-φ method:oL
iiiL
iiVi
Vi fxfPyf γφ ===
Vapor phase fugacity is calculated from an equation of state and liquid phase fugacity from an activity coefficient model.
2006/6/21 NTUST 6
Phase Equilibrium Criterian Criteria for systems at LLE
u fiLI = fiLII for i = 1, 2,…, cu Using EOS
IIi
LIIi
Ii
LIi
IIi
LIIi
Ii
LIi xxPxPx φφφφ =⇒=
IIi
IIi
Ii
Ii
oLi
IIi
IIi
oLi
Ii
Ii xxfxfx γγγγ =⇒=
n Criteria for systems at VLLE u fiv = fiLI = fiLII for i = 1, 2,…, c
u φ-φ method
u Using activity coefficient model
u γ-φ method
PxPxPy IIi
LIIi
Ii
LIii
Vi φφφ ==
oLi
IIi
IIi
oLi
Ii
Iii
Vi fxfxPy γγφ ==
2006/6/21 NTUST 7
Fugacity and Fugacity Coefficient
n Definition of fugacity (fi)
−=
RT)y,P,T(G)y,P,T(Gexp)Py(f i
IGMiii
ii
−==
RT)y,P,T(G)y,P,T(Gexp
)Py(f i
IGMiii
i
iiφ
n Definition of fugacity coefficient (φi)
( )
−= ∫ dPVV
RTexp
P IGMii
0
1
EOS
ZlnVdNPN
VRT
RTln
P/ZRTV
VN,V,Ti
i
ij
−
∂∂
−= ∫=
∞=≠
1φ
2006/6/21 NTUST 8
Fugacity Coefficient in Vapor Phase
n fiV = φiV P yi
n Gases at very low pressures:u EOS: Ideal gas lawu φi
V = 1, fiV = P yi = Pi
n Gases at low to moderate pressures (up to 10 –20 bar):u EOS: Two-term virial equation
∑∑==+=i j
ijjiimixmiximix )T(Byy)y,T(Bwhere,Z
V)y,T(B
RTVP 1
++=−= ∑
= RTPBZwhere,Zln)T(By
Vln mix
mixmix
c
jijj
Vi
411212
1φ
u B(T): Second virial coefficientu Non-association: Tsonopoulos (1974, 1975), Lee and Chen (1998)u Association: Hayden and O’Connell (1975)u Input variables: critical properties, ω, µ, Rg, association parameters,.
2006/6/21 NTUST 9
Fugacity Coefficient in Vapor Phase
where kij: binary interaction parameter
( )( )( )
−+
++
−−
−−−=
∑
RTbPZRTbPZ
lnbb
a
ay
bRTa
RTbPZlnZ
bbln
V
V
ijijj
VViVi
21
212
221φ
)bV(b)bV(V)T(a
bVRTP
−++−
−=
( ) i
c
ji
c
i
c
jjjiiijji
c
i
c
jijji byb;aakyyayya ∑∑∑∑∑
== == =
=−==11 11 1
1
n Gases at high pressures:u EOS: e.g., Peng-Robinson EOS
Mixing Rules:
n Input variables: Tc,i, Pc,i, ωi
n Parameters: kij’s
2006/6/21 NTUST 10
Fugacity Coefficient in Liquid Phase
( )( )( )
−+
++
−−
−−−=
∑
RTbPZRTbPZ
lnbb
a
ax
bRTa
RTbPZlnZ
bbln
L
L
ijijj
LLiLi
21
212
221φ
)bV(b)bV(V)T(a
bVRTP
−++−
−=
( )
i
c
ji
c
i
c
jjjiiijji
c
i
c
jijji
bxb
aakxxaxxa
∑
∑∑∑∑
=
= == =
=
−==
1
1 11 1
1
n fiL = φiL P xi
n Fugacity coefficient calculated from an EOS: Peng-Robinson EOS
Mixing rules:
2006/6/21 NTUST 11
Fugacity in Liquid Phase
n If pressures are sufficiently low (no greater than a few bars),
)T(Px)x,T()x,P,T(f satiiiii
Li γ=
oLiii
Li fxf γ=
= ∫
P
P
Li
sati
sati
oLi sat
i
dPVRT
exp)T()T(P)P,T(f 1φ
n Fugacity calculated from an activity coefficient model
fioL: fuagcity of liquid i at the defined standard state; pure liquid i at system T & P, as usual.
)T(P)P,T(f sati
oLi ≈
then,
Poynting pressure correction factor
2006/6/21 NTUST 12
Correlative Activity Coefficient Models
u Margules modelu van Laar modelu Redlich-Kister model
n Example: Margules model for binary systems:
n Random mixing assumption (Wohl’s expansion):
.....zzzazzaxqRT
Gkji
i j kijk
i jjiij
iii
ex
++= ∑∑∑∑∑∑
RT/Glnexii =γ ∑=
iii
ex lnxRT/G γ
( )[ ] ( )[ ]22112212121122112
221 22 xAAAxln;xAAAxln −+=−+= γγ
Parameters: A12, A21
2006/6/21 NTUST 13
Correlative Activity Coefficient Modelsn Non-random mixing assumption (Wilson’s local composition)
u Wilson model (Wilson, 1964)« For binary systems:
u Input variables: V1L, V2
L
u Parameters: (λ12 – λ11 ), (λ21 – λ22)u Note:
• Good for a variety of miscible mixtures containing polar or association components
• Only require binary parameters for multi-component systems• Invalid to LLE systems
( )
+
−+
−+−=2211
21
1221
12121122 xxxx
xxxlnlnΛ
ΛΛ
ΛΛγ
( )
+
−+
++−=2211
21
1221
12212211 xxxx
xxxlnlnΛ
ΛΛ
ΛΛγ
−−=
−−=
RTexp
VV;
RTexp
VVwhere L
L
L
L2221
2
121
1112
1
212
λλΛ
λλΛ
2006/6/21 NTUST 14
Correlative Activity Coefficient Modelsu NRTL model (Non-Random Two-Liquid; Renon and Prausnitz, 1968)
« For binary systems:
( )
++
+
= 21212
1212
2
2121
2121
221 Gxx
GGxx
Gxln ττγ
( )
++
+
= 22121
2121
2
1212
1212
212 Gxx
GGxx
Gxln ττγ
−
−=
−
−=RT
ggexpG;RT
ggexpGwhere 11211221
22121212 αα
u Parameters: (g12 - g22), (g21 - g11), α12
u Note: • Good for both miscible and partially miscible systems• Only require binary parameters for multi-component
systems
2006/6/21 NTUST 15
Correlative Activity Coefficient Modelsu UNIQUAC (Abrams and Prausnitz, 1975)
« For binary systems:
( )++−
−++= 212112
2
112
1
11
1
11 2
τθθΦΦθΦ
γ '''**
*
lnqlrrllnqz
xlnln
+
−+ 1212
12
2121
2112 τθθ
ττθθ
τθ ''''
'' q
( )++−
−++= 121221
1
221
2
22
2
22 2
τθθΦΦθΦ
γ '''**
*
lnqlrrllnqz
xlnln
+
−+ 2121
21
1212
1221 τθθ
ττθθ
τθ ''''
'' q
102121
1212 =
−=
−= z;
RTuexp;
RTuexpwhere ∆τ∆τ
u Input variables: molecular structure (constituent groups)u Parameters: (∆u12), (∆u21)u Note:
• Good for both miscible and partially miscible systems• Only require binary parameters for multi-component
systems
2006/6/21 NTUST 16
Predictive Activity Coefficient Modelsn Regular solution model
u For binary systems:
u Input variables: solubility parameter (δi), liquid molar volume (Vi
L)u Note: γi always greater than 1 (positive deviation)
( )221
22
11 δδΦγ −=
RTVln
L
( )221
21
22 δδΦγ −=
RTVln
L
)fractionvolume(Vx
Vxwhere c
j
Ljj
Lii
i
∑=
=
1
Φ
2006/6/21 NTUST 17
Predictive Activity Coefficient Modelsn Group-contribution approach：
u ASOG (Analytic Solutions of Groups, Wilson and Deal, 1962)
u UNIFAC (UNIQUAC Functional Group Activity Coefficients, Fredenslund et al., 1975)
u Input variables: molecular structure (constituent groups)
CH3-C-CH2-CH-CH3
CH3
CH3 CH3
CH3-OH
Mixtures of 2,2,4-trimethyl pentane + methanol
u - CH3 group: 1u -OH group: 1
u -CH3 group: 5u -C- group: 1u -CH2 group: 1u -CH group: 1
2006/6/21 NTUST 18
Parameter Determination (Data Reduction)n VLE data reduction (γ-φ method)
u Bubble-P calculation« Given T, xi => Calculate P, yi from fiV = fiL
c....,,i,fxPy oLiiii
Vi 1== γφ
Vi
oLiii
iifxPyP
φγ
==
∑∑==
==c
iVi
oLiii
c
ii
calc fxPP11 φ
γ
( ) ( ) ( )∑=
−+
−=
N
kky
texpi
calci
P
texpcalc
i
yyPPparametersbinarymin1
2
2
2
2
σσπ
where N: number of data points.σ: standard deviation of measurement.
Objective function π defined on the basis of themaximum-likelihood principle:
Activity coefficient model
Vapor pressure
Two-term virial equation
2006/6/21 NTUST 19
Parameter Determination (Data Reduction)n LLE data reduction
u Flash calculation:Given T, zi (feed composition) => Calculate xi
I, xiII from
fiLI = fiLII and material balance equations
c....,,i,xx IIii
Iii 1== γγ
( )( ) 0111
11
=+−
− ∑=
N
i i
i
K/z:equationFlash
β
IIi
Ii
IIi
IIii /x/xKwith γγ==
where β : fraction of phase I
( ) ( ) cn/xxparametersbinaryminn
k j
c
i
texp,jk,i
calc,jk,i 2
1
2
1 1
2
−= ∑∑∑
= = =
π
where n: number of tie-lines; c: number of components.
Activity coefficient model
( ) ( )( )i
icalc,IIi
i
icalc,Ii K/
zx;K
zx1111 +−
=−+
=βββ
2006/6/21 NTUST 20
Parameter Determination (Data Reduction)n VLLE data reduction via a flash calculation:
Given T, zi (feed composition) => Calculate xiI, xi
II, yi, P from fiV= fiLI = fiLII
and material balance equations
c....,,i,fxfxPy oLi
IIii
Li
Iiii
Vi 10 === γγφ
( )( ) ( )[ ] 0
1111
1
=−+−+
−∑=
N
iIIi
Ii
Ii
iIi
K/KKzK:equationFlash
ββαα
Vi
oLi
IIi
IIii
IIi
Vi
oLi
Ii
Iii
Ii P/fx/yK,P/fx/yKwith φγφγ ====
Activity coefficient model
( )( )[ ] 0
1112
1=
−+−+−∑
=
N
iIi
IIi
IIi
iIIi
K/KKzK:equationFlash
ββαα
Solve α (fraction of vapor phase) and β (fraction of liquid phase I) from flash eqs. 1 and 2, simultaneously.
2006/6/21 NTUST 21
Parameter Determination (Data Reduction)n VLLE data reduction via a flash calculation (continued):
( ) ( )[ ]IIi
Ii
Ii
icalc,Ii K/KK
zxββαα −+−+
=11
where α: fraction of vapor phase; β : fraction of liquid phase I
∑ ∑ ∑= = =
===c
i
c
i
c
i
oLi
IIi
IIi
oLi
Ii
Iii
calc fxfxPyP1 1 1
γγ
( )[ ]ββαα −+−+=
11 Ii
IIi
IIi
icalc,IIi K/KK
zx
( ) ( ) cn/xxparametersbinaryminn
k j
c
i
texp,jk,i
calc,jk,i 3
1
3
1 1
2
−= ∑∑∑
= = =
π
calcoLi
IIi
calc,IIi
calcoLi
Ii
calc,Ii
calc,IIIi
calci P/fxP/fxxy γγ ==≡
2006/6/21 NTUST 22
Thermodynamic Properties Needed in Phase Equilibrium Calculationsn Pure components:
u Critical properties:Tc, Pc, Vc, Zc
u Acentric factor, dipole moment,..u Vapor pressuresu Density,….
n Mixtures: (to determine binary interaction parameters, kij, Aij, α, ..)
u VLE datau LLE datau VLLE data
2006/6/21 NTUST 23
Thermodynamic Properties of Pure Fluids from Literaturen NIST Chemistry Webbook (National Institute of
Standards and Technology, USA)u http://webbook.nist.gov/chemistry/
n “TRC Thermodynamic Tables, Hydrocarbons”, Thermodynamics Research Center, The Texas A&M University System, College Station, TX.
n “TRC Thermodynamic Tables, Non-Hydrocarbons”, Thermodynamics Research Center, The Texas A&M University System, College Station, TX.
n Reid, R.C.; Prausnitz, J.M.; Poling, B.E., “The Properties of Gases and Liquids,” 4th ed., McGraw-Hill, NY (1987).
n Poling, B.E.; Prausnitz, J.M.; O’Connell, J.P., “The Properties of Gases and Liquids,” 5th ed., McGraw-Hill, NY (2001).
2006/6/21 NTUST 24
Phase Equilibrium and Other Thermodynamic Properties of Mixtures from Literature
DECHEMA-- Chemistry Data Series
Vol. I Vapor-Liquid Equilibrium Data CollectionVol. II Critical Data of Pure SubstancesVol. III Heats of Mixing Data CollectionVol. IV Recommended Data of Selected Compounds and Binary MixturesVol. V Liquid-Liquid Equilibrium Data CollectionVol. VI Vapor-Liquid Equilibria for Mixtures of Low Boiling SubstancesVol. VIII Solid-Liquid Equilibrium Data CollectionVol. IX Activity Coefficients at Infinite DilutionVol. X Thermal Conductivity and Viscosity Data of Fluid MixturesVol. XI Phase Equilibia and Phase Diagrams of ElectrolytesVol. XII Electrolyte Data CollectionVol. XIV Polymer Solution Data Collection
Thermodynamic property database: DETHERM
2006/6/21 NTUST 25
VLE Data of Mixtures from Literature
Volume 1: Vapor-Liquid Equilibrium Data CollectionJ. Gmehling, U. Onken, W. Arlt, P. Grenzhauser, U. Weidlich, B. Kolbe, J. Rarey
Part Title Published
1 Aqueous-Organic Systems 1991 1a Supplement 1 1998 1b Supplement 2 1988 2a Alcohols 1986 2b Alcohols and Phenols 1990 2c Alcohols Supplement 1 2001 2d Alcohols and Phenols Supplement 2 1982 2e Alcohols and Phenols Supplement 3 1988 2f Alcohols and Phenols Supplement 4 1990 3/4 Aldehydes, Ketones, Ethers 1979 3a Aldehydes, Supplement 1 1993 3b Ketones, Supplement 1 1993 4a Ethers, Supplement 1 1996 4b Ethers, Supplement 2 1999
2006/6/21 NTUST 26
VLE Data of Mixtures from Literature
Volume 1: Vapor-Liquid Equilibrium Data CollectionJ. Gmehling, U. Onken, W. Arlt, P. Grenzhauser, U. Weidlich, B. Kolbe, J. Rarey
5 Carboxylic Acids, Anhydrides, Esters 2001 5a Carboxylic Acids, Anhydrides, Supplement 1 2002 5b Esters, Supplement 2 2002
6a Aliphatic Hydrocarbons C4-C6 (2nd Ed. with minor changes) 1997
6b Aliphatic Hydrocarbons C7- C18 (2nd Ed. with minor changes) 1997 6c Aliphatic Hydrocarbons Supplement 1 1983 6d+e Alipatic Hydrocarbons C4- C30 1999 7 Aromatic Hydrocarbons (2nd Ed. with minor changes) 1997 7a/7b Supplement 1 2000
8 Halogen, Nitrogen, Sulfur and other Compounds 1984
8a Halogen, Nitrogen, Sulfur and other Compounds, Supplement 1 2001
2006/6/21 NTUST 27
Phase Equilibrium Data from Experimentsn VLE Apparatus:
u Static type
u Semi-flow type
Vapor sample
Liquid sample
P
Vapor sample
Liquid sample
P
2006/6/21 NTUST 28
Phase Equilibrium Data from Experiments
u Flow type
n VLLE Apparatus:u Static type
Vapor sample
Liquid sample
P
Vapor sampleLiquid I sample
P
Liquid II sample
2006/6/21 NTUST 29
Static VLE Apparatus
2006/6/21 NTUST 30
Vapor Pressures of Dimethyl Adipate (賴政海，2003)
0.0018 0.002 0.0022 0.0024 0.0026 0.0028 0.0031/T (K-1)
0.1
1
10
100
1000
P (k
Pa)
Expt. Calc. (Antoine eq.)
ln P (kPa) = 16.7683 – 6166.2/T (K)
2006/6/21 NTUST 31
VLE of Isopropyl Acetate (1) + 2-Propanol (2)(Hong et al., Ind. Eng. Chem. Res., 2003)
0.0 0.2 0.4 0.6 0.8 1.0x1 , y1
30
35
40
45
50
120
160
200
240
60
80
100
120
P (k
Pa)
333.15 Kexpt. (liquid phase)expt. (vapor phase)calc. (UNIQUAC)
353.15 Kexpt. (liquid phase)expt. (vapor phase)calc. (UNIQUAC)
373.15 Kexpt. (liquid phase)expt. (vapor phase)calc. (UNIQUAC)
2006/6/21 NTUST 32
Azeotropic Point of Isopropyl Acetate (1) + Isopropanol (2) at 333.15 K(Hong et al., Ind. Eng. Chem. Res., 2003)
-0.1
0.0
0.1
x 1-y1
0.3 0.3 0.4 0.5 0.6 0.7x1
45.0
45.5
46.0
46.5
P (k
Pa)
0.98
1.00
1.02∆
P y / ∆
P x
2006/6/21 NTUST 33
VLE of 1-Octanol + 1,2-Dimethoxybenzene + 2-Methoxyphenol at 433.15 K (Hwang et al., Ind. Eng. Chem. Res., 2001)
1-octanol
1,2-dimethoxybenzene 2-methoxyphenol0.0 0.2 0.4 0.6 0.8 1.0
0.25
0.50
0.75
1.0
0
0
0.25
0.5
1.0
0.75
liquid
vaporternary azeotrope
2006/6/21 NTUST 34
LLE Phase Behavior
2006/6/21 NTUST 35
LLE Apparatus
T Top sample
Bottom sample
L1
L2
To circulating thermostatic bath
From circulating thermostatic bath
Stir bar
2006/6/21 NTUST 36
LLE of Water + Ethanol + Ethyl Acetate with Glycerol, KAc, or CaCl2 at 313.15 K(Lee et al., Fluid Phase Equilibria, 2005)
ethyl acetate0.0 0.2 0.4 0.6 0.8 1.0
ethanol
0.0
0.2
0.4
0.6
0.8
1.0
water
0.0
0.2
0.4
0.6
0.8
1.0
ternary with glycerol (20 wt%)with KAc (20 wt%)with CaCl2 (20 wt%)
2006/6/21 NTUST 37
LLE of Water + n-Butanol + n-Butyl Acetate with Glycerol, KAc, or CaCl2 at 313.15 K (葉至恩，2003)
n-butyl acetate
0.0 0.2 0.4 0.6 0.8 1.0
n-butanol
0.0
0.2
0.4
0.6
0.8
1.0
water
0.0
0.2
0.4
0.6
0.8
1.0
ternarywith glycerol (20 wt%)with KAc (20 wt%)with CaCl2 (20 wt%)
2006/6/21 NTUST 38
Static VLLE Apparatus
9
31
3P
45
T
6
8
C7
2
to vac.8
B
10
A
2006/6/21 NTUST 39
VLLE of Water (1) + PGMEA (2) (Hsieh et al., Ind. Eng. Chem. Res., 2006)
UNIQUAC
0.10 0.15 0.20y1
320
330
340
350
360
T (K
)
0.000 0.030 0.060x1
II
0.4 0.6 0.8 1.0x1
I
expt. calc. ( NRTL-HOC )calc. ( UNIQUAC-HOC )
b12 (K) = 2.6262 + 0.1007 T (K)
b21 (K) = -573.2592 +0.3682 T (K)
2006/6/21 NTUST 40
Saturated Pressures at VLLE for Water (1) + PGMEA (2)(Hsieh et al., Ind. Eng. Chem. Res., 2006)
0.0027 0.0028 0.0029 0.003 0.00311 / T (K-1)
10
100
P (k
Pa )
expt.calc. ( NRTL-HOC )calc. ( UNIQUAC-HOC )
2006/6/21 NTUST 41
VLLE of Water + PGME + PGMEA at 343.15 K(Hsieh et al., Ind. Eng. Chem. Res., 2006)
0.00 0.25 0.50 0.75 1.000.00
0.25
0.50
0.75
1.000.00
0.25
0.50
0.75
1.00
PGM
E
liquid phase vapor phase expt. tie-lines NRTL-HOC correlation (liquid) NRTL-HOC correlation (vapor) NRTL-HOC prediction (liquid) NRTL-HOC prediction (vapor)
PGM
EA
Water
2006/6/21 NTUST 42
VLLE of Water + Butyl Propionate + n-Butanol at 363.15 K (Lee et al., Fluid Phase Equilibria, 2004)
n-butanol0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
water
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
butyl propionate
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
organic phaseaqueous phasevapor phaseNRTL prediction
2006/6/21 NTUST 43
Prediction LLE Properties from UNIFACLLE of Water + Isopropyl Acetate + 2-Propanol(洪桂彬，2003)
isopropyl acetate
0.0 0.2 0.4 0.6 0.8 1.0
2-propanol
0.0
0.2
0.4
0.6
0.8
1.0
water
0.0
0.2
0.4
0.6
0.8
1.0
expt. UNIFAC-LLEUNIFAC-LyngbyUNIFAC-Dortmund
2006/6/21 NTUST 44
Prediction VLE Properties from UNIFACVLE of Isopropyl Acetate(1) + 2-Propanol (2) (洪桂彬，2003)
0.0 0.2 0.4 0.6 0.8 1.0x1 or y1
0
50
100
150
200
250
P (k
Pa)
expt.UNIFAC-LLEUNIFAC-OriginalUNIFAC-DortmundUNIFAC-Lyngby
333.15 K
353.15 K
373.15 K
2006/6/21 NTUST 45
Key Points to Parameter Determinationn Vapor pressures
u Pure compounds
n Phase compositions and equilibrium pressures
u Binary, ternary
n Existence of azeotropic points
u Binary, ternary, quaternary
n Location of azeotropic points
u Binary, ternary, quaternary
n Existence of phase splitting
u Ternary, quaternary
n Compositions of two-liquid phases (binodal curves)
u Ternary, quaternary
2006/6/21 NTUST 46
Concluding Remarksn For completely miscible systems
u φ-φ method« Equations of State with proper mixing rules
u γ-φ method« φ: Two-term virial equation« γ: Wilson, NRTL or UNIQUAC model
n For partially miscible systemsu γ-φ method
« φ: Two-term virial equation« γ: NRTL or UNIQUAC model
n Vapor pressure data (or Antoine constants) are essentially needed for each constituent.
n For type-1 LLE systems, ternary LLE data are important to determine model parameters.
n For type-2 LLE systems, binary LLE data are crucial to determine model parameters.
