the universal group contribution equation of state vtpr
TRANSCRIPT
The Universal Group Contribution Equation of
State VTPR – Present Status and Potential for Process Development
Jürgen GmehlingIndustrial Chemistry
University of Oldenburg, Germany
Paris, September 3-4, 2009
60th birthday of Dominique Richon
Basic Structure of a Chemical Plant
preparation reaction separation
feed:A + B
products: C + D
purgerecycle of A and B
by-products: E + FA + B C + D
Phase
Phase
β
α
z , z , ....1 2
z , z , ....1 2
β β
α α
Pressure
Temperature
Theoretical Stage1.cdr
Typical vapor-liquid equilibrium problem:
Typical Question Asked bythe Chemical Engineer: Ki as f(T, P, xi)
Additionally required:
Densities, enthalpies including heats of vaporization, heat capacities, etc. for the pure
compounds as f(T,P) and the mixtures as f(T,P, composition)
Different Approaches for the Calculation of VLE
1∞ ∂ ϕ = − −
∂ ∫
j
i
iv T,v,n
P RT Pvln dv ln
RT n v RT
L V
i i i ix yϕ = ϕs
i i i ix P yPγ ≈
α β α βµ = µ =
=
i i i i
L V
i i
Gibbs : Lewis : f f
f f
required:
•equation of state for both phases, e.g. cubic equations of state
•reliable mixing rules
required:
•reliable gE-model, e.g. Wilson, NRTL, ..
•vapor pressure as f(T)
∂= =
∂ , ,
lnγ
j
EE
i i
i T P n
GRT g
n
Overview on the Requirement and the Available VLE Data for
Binary Systems (August 2009)
Assuming that 1000 (500) compounds are of technical interest VLE data for appr. 500 000 (125 000) binary systems are required
VLE data for 11 000 binary systems: 2.20 % (8.80 %)
Number of VLE Data Sets stored in the Dortmund Data Bank:
DDBDDB58 900 isothermal / isobaric binary VLE data sets for non-electrolyte systems(but 245 data sets for ethanol-water, 150 data sets foracetic acid-water, 190 data sets for methanol-water, ..
Situation 1973: 17600 isothermal / isobaric data sets
VLE data for 3 803 binary systems: 0.76 % (3.04 %)
Group Contribution Method
-CH2 -CH2
-OH
-OH
-CH3
-CH3
-CH3-CH3
-CH2
-CH2
-CH2 -CH2-CH2 -CH2
-OH
-CH2
Ethanol:
n-Hexane:
Lupe_gl_e.cdr
( )γ γ γ
γ ν
= +
= Γ − Γ∑ ( ) ( )
ln ln ln
ln ln ln
C R
i i i
R i i
i k k ki
06.02.03
Great advantage: Number of possible structural groups << number of different components
Required group interaction parameters are fitted to experimental VLE data
Distillation Symposium Brighton 1969
ASOG (solution of groups concept)
(based on the Wilson and Flory-Huggins equation)
1975 the UNIFAC method was
published by Aa. Fredenslund et al.
(based on the UNIQUAC equation,
also published 1975)
Absolute Deviation Between Experimental and Predicted VLE Data (Data base: 2200 Consistent Data Sets, 1993)
08 00 025 GC-gE
P [kPa]∆
0.55
0.87
1.68
∆ T [K]
0.42
0.68
1.06
∆ y [%]
0.58
0.88
1.41
UNIQUAC Mod. UNIFAC (Do) UNIFAC
Equations of State: van der Waals (1873)
attrep PPP +=
bv
RTPrep
−=
2v
aPatt −=
• a - intermolecular attraction
• b - closest packing volume
023 =−+
+−
P
abv
P
av
P
RTbv
05.02.03
Molar volume v [dm3 / mol]
Pre
ssure
P [bar]
nobel
price
winner
for
physic
s
1910
Otto Redlich, John M. Prausnitz, Giorgio Soave, ...
09.01.00
( )bvvT
a
bv
RTP
/ +−
−=
21
( )( )a TRT
Pv b v v b
= −− +
a(T) = a(Tc) α(T)
Otto Redlich, J. M. Prausnitz, ... Giorgio Soave
Introduction of Improved Mixing Rules (GE-Mixing Rules)
E
E
i ii
i
P , g model : Wilson,NRTL,..
x a (T)a(T) g
b b -0.6931
= ∞ −
= +∑
Acetone (1) - Water (2)
at 60°C
05.02.03
classical mixing rule
gE mixing rule
E*
i i i i
gx ln ln x ln
RT= Σ γ = ϕ − Σ ϕ
Jean Vidal
PSRK (Predictive SRK Equation of State)
E
i ii
i
x a (T)a(T) g
b b -0.6931= +∑
05.02.03
PSRK (Predictive SRK)*
Pref = 1 atm
gE-model: original UNIFACGroup interaction parameters:
UNIFAC matrix + parameters for 30 gases, such as CO2, CH4, H2, H2S, ..
fitted to VLE of normal and low boiling substances, gas solubilities
*Holderbaum, Gmehling (1991)
(((( ))))ln
( )
.
E
iii ii i
i i
bg RT xbx a Ta T
b b
++++
= += += += +−−−−
∑∑∑∑∑∑∑∑
0 64663
Huron, Vidal (1979)
P = ∞∞∞∞
gE-model: Wilson, NRTL, ...
Experimental and Predicted Results Using PSRK
with already Available UNIFAC Parameters (VLE Data)
09 00 006 GC-EOS
10.02.03
Ethanol (1) + Water (2) Acetone (1) + Water (2)
150°C
200 °C
250°C
300°C
325°C
log
P /
ba
r
x ,y1 1
150°C
200°C
250°C
log
P /
ba
r
x ,y1 1
100°C
Experimental and Predicted VLE Data for Different
CO2 + n-Alkane Systems Using PSRK
09 00 008 GC-EOS
10.02.03
CO (1) + Propane (2)2
CO (1) + Hexane (2)2 CO (1) + Decane (2)2
328 K 294 K
311 K
278 K
393 K
313 K
311 K
378 K
444 K
511 K
411 K
344 K378 K
311 K
353 K
CO (1) + Butane (2)2
Group Contribution Equations of State - from PSRK to VTPR**
VLE, GLE, hE, SLE, γ∞VLE, GLEdata base
temp.-dependent
VTPR parameters
a) original UNIFAC
b) temp.-dependent PSRK parameters
gE information
b = Σ xi bi
mixing rule for
the parameter b
mixing rule for
the parameter a
TwuMathias-Copemanα-function
volume translated
Peng-Robinson
Soave-Redlich-Kwongequation of state
VTPRPSRKmodule
,
A
0.53087
E R
iii
i i
aa gx
b b
A
= +
= −
∑1
ln
0.64663
E
iii i
i ii i
aa g bx x
bRT b RT A RT b
A
= + +
= −
∑ ∑
* J. Chen, K. Fischer, J. Gmehling (2002) ** J. Ahlers, J. Gmehling (2001, 2002,2003, 2004)
( )3/4 3/4 3/4
ij ii jj
i j iji j
b = b +b /2
b= x x b∑∑
VTPR equation of state and calculated density datafor methanol using various cubic equations of state
( )( ) ( )* RT a(T)
VTPR : Pv c b v c v c b b v c b
= −+ − + + + + + −
( ) ( )
( )
( )
c
exp calc r
cc
c
a T a T
T function von Twu
translation parameter c :
c v v at T .
generalized :
RTc . . z .
P
α
α
=
−
= − =
= ⋅ −
0 7
0 252 1 5448 0 4024
*Peneloux et al. (1982)
Experimental and calculated vapor pressures for selected solvents
using the Peng-Robinson equation of state and the Twu-αααα-function
■▲●■� experimental data taken from the Dortmund Data Bank
Experimental and calculated liquid densities using the Peng-
Robinson equation of state in the temperature range Tr = 0.5 – 0.8
■▲●●�� experimental data taken from the Dortmund Data Bank
Experimental and calculated liquid densities using the volume translated
Peng-Robinson equation of state in the temperature range Tr = 0.5 – 0.8
■▲●●�� experimental data taken from the Dortmund Data Bank
n-Decane
Water
Benzene
n-Butane
PSRK
VTPR
∆h
[kJ/m
ol ]
v
T [-] r
1-Butanol
p-Xylene
Acetone
Ammonia
PSRK
VTPR
∆h
[kJ/m
ol ]
v
T [-] r
Ethylene
Carbon Dioxide
Methane
Enthalpy of Vaporization
Prediction of Vapor-Liquid Equilibria of Alkane-Alkane Systems VTPR ( ) and PSRK (- - -)
no interaction parameters required
393 K
343 K
423 K
373 K
313 K
P[ M
Pa
]
propane (1)
n-butane (2)
x ,y1 1
328 K
313 K
293 K
2-methylpentane (1)
n-octane (2)
P[ b
ar]
x ,y1 1
Experimental and Predicted Vapor-Liquid Equilibria of Asymmetric Alkane-Alkane-Mixtures VTPR (——) PSRK (- - - -)
AlkAlk2e.cdr
573 K
423 K
348 K
373 K338 K313 K273 K
ethane (1)
octacosane (2)
ethane (1)
dodecane (2)
x ,y1 1x ,y1 1
P[M
Pa
]
P[ M
Pa
]
no interaction parameters required
Objective Function F and Data Base Used
for Fitting Group Interaction Parameters for VTPR
often the only information for strong
non-ideal systems
LLE
supporting data at low temperatureSLE of eutectic systems
in the dilute range
for asymmetric systems
activity coefficients at infinite dilution γ∞
in the dilute range gas solubilities (GLE)
f(T)
supporting data at high temperature
hE , (cPE)
f(x)VLE of normal and low boiling substances,
azeotropic data (AZD)
delivers the following information
about the real behavior:
mixture data type
γγ∞
∞
= ∆ + ∆ + ∆ + ∆ + ∆
+ ∆ + ∆ + ∆
∑ ∑ ∑ ∑ ∑∑ ∑ ∑
E EP
E E
VLE AZD P GLEh c
SLE LLE
F w VLE w AZD w h w c w GLE
w w SLE w LLE
( )1
E
i iln h
/ T R
γ∂=
∂
DDB
29700 (VLE)
7700 (ELE)
29200 (HPV)
VLE**
(total: 66600 data sets)
* detailed information is available via internet (www.ddbst.de) ** including unpublished VLE data from chemical companies, e.g. from the former German Democratic Republic
18800 data sets for non-electrolytes
20200 data sets
LLE
51300 data points
azeotr. data
3600 data sets
AAE
38300 data sets
vE
3100 data sets
cPE
19400 data sets
hE
30400 data sets for non-electrolytes
27700 data sets for electrolytes
(E)SLE
55200 data points for pure solvents
cPη ρ
PiS
183000 data sets
(E)GLE
1500 data sets for electrolytes
1410 data sets for solvent mixtures
1960 data sets
CRI
Pure Component Properties
9150 data points
KOWKI
Polymers new16950 data sets
Experimental facilities used for the systematic measurement of γ∞, excess enthalpies, vapor-liquid equilibria, …
T
F 45.3HE
Electronic Flowmeter
On Mode Set
HeZero
DMFC
H2 O2
GC
Helium
40.28 °C
1023 mbar
FID/WLD
Computer
Gasversorgung
Mess-zelle
Sättiger-zelle
Durchflussmesser6-Wege-
VentilT
HPLC-Pumpen
KontrollheizungMischstrecke
Kalibrierwiderstand
T = konst.
Peltierkühler
P Druck-regulator
N2
excess enthalpies activity coefficients at infinite dilution
Vakuumthermostatisierter Drucksensor
Vakuum
Thermostat- rührerZellenrührer
Thermostatisolierung
Schrittmotorgetriebene DosierventileSchrittmotorgetriebene
Dosierpumpe
Vorratsvolumen
Vorratsgefäß T
P
Thermostatisierung
T
P
T
P
Vakuum
vapor-liquid equilibria
high pressure VLE critical data ROLSI
Number of hE-Data Sets Stored in the DDB as a Function of Temperature
0
2000
4000
6000
8000
10000
12000
260 300 340 380 420
Temperature [K]
Nu
mb
er
of
data
sets
Total:
~19600 data sets
(Juli 2008)
mainly measurements
(~900 data sets)
from our
research group
0
20
40
60
80
100
0 0,5 1P
[b
ar]
x1, y1N2O (1) – Methyl acetate (2)
0.5
CO2 (1)– Methyl acetate (2) ♦, ♦ Ohgaki et al. (1977)
0
20
40
60
80
100
0 0,5 1
P [
ba
r]
x1, y1
T = 322.9 K
T = 298.15 K
0.5
Experimental VLE data measured with the static apparatus equipped with ROLSI`s for the online analysis of the liquid and vapor phase
T = 343.25 K
T = 323.15 K
Main Group
Selection
Component
Selection
Retrieval of
Mixture Data
( ), , ,...EVLE h γ ∞
Data Evaluation
and Reduction
Parameter-
Regression
Examination
Software PackageParameter Regression
Consistency Tests Plausibility Tests ...
Graphical Representation
new VTPR Parameters
Pure Component Data Bank
Structural Information for
27 000 Components
Mixture Data Banks
VLE 58 000 Data Sets GLE 18 800 Data Sets
HE 19 400 Data Sets SLE 28 700 Data Sets
ACT 54 000 Data Points AZD 51 000 Data Sets
... ...
Pure Component
Properties Parameters α(T) Critical Data, ω, ci
Heat of Fusion,...
Confidential
Data from
Chemical
Industry
Fitting of Parameters for the Group Contribution Equation of State VTPR
New
Experimental
Data
Status: August 2009
Experimental and predicted VLE data for different CO2 – n-alkane systems using VTPR (____) and PSRK (- - - -)
0
20
40
60
80
0 0,5 1
P [
ba
r]
x1
328 K
311 K 294 K
278 K
0
20
40
60
80
100
120
140
0 0,5 1
P [
ba
r]
x1
393 K
353 K
313 K
0
20
40
60
80
0 0,7
P [
ba
r]
x1
423 K
373 K
348 K
CO2(1)–C3(2)
CO2(1)–C6(2)
CO2 (1) – C20 (2)
0
20
40
60
80
0 0,7
P [
ba
r]
x1
373 K
348 K
323 K CO2 (1) – C28 (2)
x1x10.70.5
VLE, azeotropic and critical data for the system CO2 (1) – ethane (2)
30
40
50
60
70
80
0 0,5 1
P [
ba
r]
x1
0
20
40
0 0,5 1
P [
ba
r]
x10 0.5 1
♦ experimental VLE ▲ azeotropic data— VTPR — critical line
283 K
298 K
293 K
288 K
0.5x1
270 K
260 K
250 K
230 K
0 0.5 1x1
Fields of Application of Group Contribution Methods for Process Development
prediction of phase equilibria and excess properties (VLE,
SLE, GLE, SCF,.., hE, ..)
group contribution EOS VTPR
(γi, ϕi, PVT, (X-Xid))
detection of separation problems, e.g. azeotropic points
construction of residue curves
selection of suitable solvents for separation processes, chemical processes, SCF, ..
design of separation columns (Nth,H) consideration of the real
behavior (Kγ, Kϕ) on the chemical conversion
prediction of flash points of flammable
liquid mixtures
prediction of the fate of chemicals
(bioaccumulation)
prediction of thermo-dynamic properties
(h, ∆hv, s, ∆hR(P), ..)
diffusional mass transfer
(∆ai, ∆fi, ∆µi instead of ∆ci)
Experimental and predicted azeotropic data for the quaternary system CO2 (1) – Ethane (2) – H2S (3) – Propane (4) at 266.5 K
* Mean value of the experimental azeotropic data stored in the Dortmund Data Bank
predicted ( VTPR) experimental*
systemtype of
azeotrope
T [K] P [bar] y1,az type of
azeotrope
T [K] P [bar] y1,az
1-2 homPmax 266.5 33.36 0.6888 homPmax 266.6 33.27 0.67
1-3 none none
1-4 none none
2-3 homPmax 266.5 20.49 0.9034 homPmax 266.7 20.68 0.896
2-4 none none
3-4 homPmax 266.5 9.03 0.8248 homPmax 266.5 n.a. 0.83
1-2-3 none n.a.
1-2-4 none n.a.
1-3-4 none n.a.
2-3-4 none n.a.
1-2-3-4 none n.a.
Experimental and predicted azeotropic data and residual curve map for the ternary system CO2(1)–ethane (2)–H2S(3) at 266.5 K using VTPR
Ethane (20.32 bar)
CO2 (29.11 bar) H2S (8.4 bar)
33.36 bar
20.49 bar
border line
residual curve
— CO2 (1) - Ethane (2) — + 80 mol-% Propane
— CO2 (1) - Ethane (2) — + 80 mol-% Butane
0
0,5
1
0 0,5 1
y1
s
x1s
0
0,5
1
0 0,5 1
y1
sx1
s
Predicted VLE behavior of the system CO2(1)-ethane(2)-propane(3) at 266.5 K using VTPR
Experimental and predicted (VTPR ) solubilities of varioussolid compounds (aromatics) in supercritical CO2 (1)
2.5 % Methanol
Phenanthrene
P [bar]
T = 323.15 Klo
g y
2
P [bar]
0. 100. 200. 300. 400.-8.
-7.
-6.
-5.
-4.
-3.
-2.
-1.
0.
log
y2
NaphthalenePhenanthreneAnthracene
T= 328.15 K
T= 323.15 K
-7.
-6.
-5.
-4.
-3.
-2.
0. 100. 200. 300. 400.
41
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0 500 1000 1500 2000
Pressure / atm
KP
- - - - VTPR . . . . . PSRK _ . _ . SRK ______ ideal
Experimental and Calculated Equilibrium Constants KP
for the Ammonia Synthesis as f(P) at 450°C
K/atm = KP Kϕ
Pressure dependence of the reaction enthalpy(example: ammonia synthesis)
- - - VTPR
_____ reference equation of state
__ __ __ Ullmann (ammonia)
450 °C
-62
-55
0 200 400 600 800
pressure [atm]
∆∆ ∆∆h
R [kJ/m
ol]
T = constant
enthalpy
P
ideal gas
III I
II
( )PhR∆
eductsproducts
( ) ( )
( ), ,
, ,o o
R R
id
i i T Pi
h T P h T P
h hν
∆ = ∆
+ −∑
- 52.88 kJ/mol
Great progress has been achieved in the field group contribution methods:
UNIFAC →→→→ modified UNIFAC →→→→ PSRK →→→→ VTPR
1975 1987 1991 2002
The Dortmund Data Bank with the available experimental data and systematic measurements were important for these developments.
Disadvantage: VTPR parameter matrix still small
•Extension of the parameter matrix is planned within an AiF project
• but there also exist different ideas to use the already existing modified UNIFAC parameters for VTPR
Conclusion
I would like to thank Prof. Dr. Ulfert Onken, Dr. Hermann Stage Prof. Dr. Aage FredenslundProf. Dr. Jiding LiProf. Dr. Jian ChenProf. Dr. Weidong YanProf. Dr. John M. PrausnitzDr. Antje Jakob
all PhD students, in particular:
Jürgen Rarey, Jochen Menke, Wolfgang Arlt, Ulrich Weidlich, Bärbel Kolbe, Hans-Martin Polka, Thomas Holderbaum, Martin Schiller, Kai Fischer, Jens Ahlers
the long standing technical co-workers Rainer Bölts, Bernd Werner
a large number of foreign guests
and the different institutions:
Deutsche Forschungsgemeinschaft (DFG), the Ministry of Research (BMFT), AiF, DDBST team, members of the UNIFAC consortium
Acknowledgement