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Norwegian University of Science and Technology (NTNU)
Thermodynamic consistency in modeling
- f SLE and VLE
Norwegian University of Science and Technology (NTNU) 1 Outline - - PowerPoint PPT Presentation
Thermodynamic consistency in modeling of SLE and VLE in aqueous alkanolamine solutions Ardi Hartono and Hallvard F Svendsen PCCC2 Conference Bergen, September 17-20, 2013 Norwegian University of Science and Technology (NTNU) 1 Outline
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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
x1 (-) γi (-)
γMEA γH2O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 10
110
2x1,y1 (-) P (kPa)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x1 (-) HE (kJ/mol)
25°C (Touhara, et al., 1982) 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
x1 (-) Θ1 (°C)
Fosbøl, et al., 2011 Cheng, et al., 1992
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
x1 (-) γi (-)
γMEA γH2O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x1 (-) HE (kJ/mol)
25°C (Touhara, et al., 1982) 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
x1 (-) Θ1 (°C)
Fosbøl, et al., 2011 Cheng, et al., 1992 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 10
110
2x1,y1 (-) P (kPa)
5
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x1 (-) HE (kJ/mol)
25°C (Touhara, et al., 1982) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
x1 (-) γi (-)
γMEA γH2O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 10
110
2x1,y1 (-) P (kPa)
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
x1 (-) Θ1 (°C)
Fosbøl, et al., 2011 Cheng, et al., 1992
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
x1 (-) γi (-)
γMEA γH2O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 10
110
2x1,y1 (-) P (kPa)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x1 (-) HE (kJ/mol)
25°C (Touhara, et al., 1982) 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
x1 (-) Θ1 (°C)
Fosbøl, et al., 2011 Cheng, et al., 1992
6
, ,
( ) ln
E i i T P ni
nG RT n g é ù ¶ ê ú = ê ú ¶ ë û
2 ,
( )
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s i s s i s i i s i
T p T p T p T p RT f T p T p RT f f G R T RT a f
m m m m m m = = + = + D = × × = - ( , ) ( , ) ( , ) ( , ) ln ( , ) ( , ) ln
v i v v i v v i i i i i i i
T p T p T p T p RT f T p T p RT f f f x P P y
m m m m m m g = = + = + = × × = × × F
( ) exp 1
i i ì i i
V P P RT
f f ° ì ü ï ï
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D
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1 1 ln 1
T T f P i i R P f T T f f
H C x T C dT dT RT RT R T
g D D
D
T f P Tf T P f Tf s P P P
G H T S H H C dT C S S dT T C C C
D = D
D = D + D D D = D + D =
Prausnitz, et al., 1999, Molecular Thermodynamics of Fluid-Phase Equilibria Hojjati and Rohani, 2006, Measurement and prediction solubility of Paracetamol in Water-Isopopanol solution
7 1 1
T T P P T T f f
C C dT dT RT R T D D º
ln 1
f i i R f
H x T RT
g D =
R
T T T =
1 1 ln 1
T T f P i i R P f T T f f
H C x T C dT dT RT RT R T
g D D
D
ln ln
f i i R f
H x T RT
g D
P f
C S D @D
P Tf
C k D @
ln 1 1 ln
f P i i R R R f
H C x T T T RT RT
g D D
+
8
P
C a bT D = +
1 ln 1 1 ln 2 2
f f i i R R R R R f
H bT a x T T T T T RT R R
g D æ ö ÷ ç
+
ç ÷ è ø
( )
P
c C a bT T TQ D = + +
2
1 ln 1 1 ln ln ln 2
f f i i R R R f R f f
H bT T T T a x T T T T T c T RT R RT T T T
g
Q Q
ì ü ï ï D
ï
+
ý ï ï
ï î þ
1 1 ln 1
T T f P i i R P f T T f f
H C x T C dT dT RT RT R T
g D D
D
Ge and Wang (2009) and Hartono, et al. (2013) Fosbøl, et al. (2009 and 2011)
9
6009.4
f
J H mol
D =
50 100 150 200 250 300 350 400 450 500 550 10 20 30 40 50 60 70 80 90 100
Heat Capacity, Cp (J⋅mol-1⋅K-1) T (K)
∆Cp=Cpl-Cps ∆Cp= a + b.*T Cps Cpl
∆Cp
Tf=273.15K
37.97
P
J C K mol D = × 75.929 0.1405
P
J C T K mol D =
×
( )
4
2.45634 10 75.929 0.1405 200
P
J C T T K mol
D =
DIPPR-Design Institute for Physical Properties (2004)
10
2 2 2 2 Sol Sol Sol Sol i i 1 1 1 1 i Sol Sol
( ) ( ) ( ) ( ) ( ) ( )
Exp calc E Exp E calc F Exp F calc Exp calc n n n n Sol Sol Exp Exp E Exp F Exp i i i i Sol
P P H H OF P H g g g
= = = =
æ ö æ ö æ ö æ ö
÷ ÷ ÷ ç ç ç ç ÷ ÷ ÷ ÷ = + + + ç ç ç ç ÷ ÷ ÷ ÷ ç ç ç ç ÷ ÷ ÷ ÷ ç ç ç ç Q è ø è ø è ø è ø
model exp 1 exp
1
n i
AARD n
=
Â
= Â
Hertzberg, T and Mejdell, T., 1998, MODFIT for Matlab: Parameter Estimation in a General Nonlinear Multiresponse Model.
11
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
x1 (-) γi (-)
γMEA γH2O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 10
110
2x1,y1 (-) P (kPa)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x1 (-) HE (kJ/mol)
25°C (Touhara, et al., 1982) 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
x1 (-) Θ1 (°C)
Fosbøl, et al., 2011 Cheng, et al., 1992 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
x1 (-) γi (-)
γMEA γH2O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 10
110
2x1,y1 (-) P (kPa)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x1 (-) HE (kJ/mol)
25°C (Touhara, et al., 1982) 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
x1 (-) Θ1 (°C)
Fosbøl, et al., 2011 Cheng, et al., 1992 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
x1 (-) γi (-)
γMEA γH2O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 10
110
2x1,y1 (-) P (kPa)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x1 (-) HE (kJ/mol)
25°C (Touhara, et al., 1982) 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
x1 (-) Θ1 (°C)
Fosbøl, et al., 2011 Cheng, et al., 1992
12
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
x1 (-) γi (-)
γMEA γH2O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 10
110
2x1,y1 (-) P (kPa)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x1 (-) HE (kJ/mol)
25°C (Touhara, et al., 1982) 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
x1 (-) Θ1 (°C)
Fosbøl, et al., 2011 Cheng, et al., 1992 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
x1 (-) γi (-)
γMEA γH2O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 10
110
2x1,y1 (-) P (kPa)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x1 (-) HE (kJ/mol)
25°C (Touhara, et al., 1982) 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
x1 (-) Θ1 (°C)
Fosbøl, et al., 2011 Cheng, et al., 1992
13
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
x1 (-) Θ1 (°C)
Fosbøl, et al., 2011 Cheng, et al., 1992
14
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6
x1 (-) γi (-)
γAMP γH2O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 80 90 100 110 120 130 140 150 160 170
x1,y1 (-) t (°C)
xAMP @ 66.7 kPa yAMP @ 66.7 kPa xAMP @ 80.0 kPa yAMP @ 80.0 kPa xAMP @ 101.3 kPa yAMP @ 101.3 kPa 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x1 (-) HE (kJ/mol)
35°C (Mathonat, et al., 1997) 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
x1 (-) Θ1 (°C)
Fosbøl, et al., 2011 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6
x1 (-) γi (-)
γAMP γH2O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 80 90 100 110 120 130 140 150 160 170
x1,y1 (-) t (°C)
xAMP @ 66.7 kPa yAMP @ 66.7 kPa xAMP @ 80.0 kPa yAMP @ 80.0 kPa xAMP @ 101.3 kPa yAMP @ 101.3 kPa 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x1 (-) HE (kJ/mol)
35°C (Mathonat, et al., 1997) 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
x1 (-) Θ1 (°C)
Fosbøl, et al., 2011 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6
x1 (-) γi (-)
γAMP γH2O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 80 90 100 110 120 130 140 150 160 170
x1,y1 (-) t (°C)
xAMP @ 66.7 kPa yAMP @ 66.7 kPa xAMP @ 80.0 kPa yAMP @ 80.0 kPa xAMP @ 101.3 kPa yAMP @ 101.3 kPa 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x1 (-) HE (kJ/mol)
35°C (Mathonat, et al., 1997) 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
x1 (-) Θ1 (°C)
Fosbøl, et al., 2011
15
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6
x1 (-) γi (-)
γAMP γH2O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 80 90 100 110 120 130 140 150 160 170
x1,y1 (-) t (°C)
xAMP @ 66.7 kPa yAMP @ 66.7 kPa xAMP @ 80.0 kPa yAMP @ 80.0 kPa xAMP @ 101.3 kPa yAMP @ 101.3 kPa 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x1 (-) HE (kJ/mol)
35°C (Mathonat, et al., 1997) 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
x1 (-) Θ1 (°C)
Fosbøl, et al., 2011 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6
x1 (-) γi (-)
γAMP γH2O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 80 90 100 110 120 130 140 150 160 170
x1,y1 (-) t (°C)
xAMP @ 66.7 kPa yAMP @ 66.7 kPa xAMP @ 80.0 kPa yAMP @ 80.0 kPa xAMP @ 101.3 kPa yAMP @ 101.3 kPa 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x1 (-) HE (kJ/mol)
35°C (Mathonat, et al., 1997) 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
x1 (-) Θ1 (°C)
Fosbøl, et al., 2011
16
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
x1 (-) Θ1 (°C)
Fosbøl, et al., 2011
17
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10
10 10
110
2γDEEA γH2O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10
110
2x1,y1 (-) P (kPa)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x1 (-) HE (kJ/mol)
25°C (Mathonat, et al., 1997) 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
x1 (-) Θ1 (°C)
Arshad, et al., 2013 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10
10 10
110
2γDEEA γH2O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10
110
2x1,y1 (-) P (kPa)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x1 (-) HE (kJ/mol)
25°C (Mathonat, et al., 1997) 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
x1 (-) Θ1 (°C)
Arshad, et al., 2013 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10
10 10
110
2γDEEA γH2O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10
110
2x1,y1 (-) P (kPa)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x1 (-) HE (kJ/mol)
25°C (Mathonat, et al., 1997) 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
x1 (-) Θ1 (°C)
Arshad, et al., 2013
18
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10
10 10
110
2γDEEA γH2O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10
110
2x1,y1 (-) P (kPa)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x1 (-) HE (kJ/mol)
25°C (Mathonat, et al., 1997) 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
x1 (-) Θ1 (°C)
Arshad, et al., 2013 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10
10 10
110
2γDEEA γH2O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10
110
2x1,y1 (-) P (kPa)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x1 (-) HE (kJ/mol)
25°C (Mathonat, et al., 1997) 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
x1 (-) Θ1 (°C)
Arshad, et al., 2013
19
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
x1 (-) Θ1 (°C)
Arshad, et al., 2013
20
21
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
x1 (-) Θ1 (°C)
Fosbøl, et al., 2011
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
x1 (-) Θ1 (°C)
Arshad, et al., 2013
22 Norwegian University of Science and Technology