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

Aspects to be Considered During theSynthesis of Separation Processes

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 %)

Prof. Dr. Joel Hildebrand (1978)

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)

Experimental and Predicted Vapor-Liquid EquilibriaUsing UNIFAC

Experimental and predicted (Mod. UNIFAC (Do) Resultsfor Different Alkane - Ketone - Systems

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

UNIFAC consortium members (January 2009)

Eastman Chemical Company

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

Experimental and Predicted Properties of Alkane-Ketone Systems VTPR (——) Mod. UNIFAC (Do) (- - - -)

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

Happy Birthday Dominique