Extended UNIQUAC model and its application to geothermal systems

Extended UNIQUAC model and its application to geothermal systems

ETH, 5th of December 2008

Kaj Thomsen

DTU Chemical Engineering

Technical University of Denmark

E-mail: [email protected]

DTU Chemiccal Engineering, Technical University of Denmark

The Technical University of Denmark

• Founded in 1829 by the Danish physicist Hans Christian Ørsted

• Moved to Lyngby in the sixties - 10 km north of Copenhagen

• Leading centre of engineering education and research in Denmark, the largest technical university in Northern Europe

• 7000 students

• 700 Ph.d. students

• 1500 researchers

• 18 departments


Models for electrolytes

• Activity coefficient models

– Long range interactions: Debye-Hückel electrostatic term

– Short range interactions:

• Pitzer virial expansion in molality

• Electrolyte NRTL

• OLI Aqueous model and OLI MSE model

• UNIQUAC

– Gas phase fugacity

• PR or SRK equation of state

• Equation of state for electrolytes

– Long range interactions: MSA

– Short range interactions: PR, SRK, SAFT

3

DTU Chemiccal Engineering, Technical University of Denmark 4

Extended UNIQUAC

• Excess gibbs energy function

– Debye-Hückel term

– UNIQUAC term

• Activity coefficients and thermal properties are derived by standard methods known from classical thermodynamics

• Standard UNIQUAC parameters

– Volume parameter for each species

– Surface area parameter for each species

– Interaction energy parameter for each pair of species

• Temperature dependence of interaction energy parameters

• Number of parameters:

– eUNIQUAC ~OLI MSE < ElecNRTL << Pitzer


Databank

• Over 120,000 experimental data on electronic form

– Activity/osmotic coefficient

– Enthalpy of mixing

– Heat capacity

– Degree of dissociation

– Gas solubility

– Density

– Salt solubility (Solid-liquid equilibrium)

– Liquid-liquid equilibrium

– Vapor-liquid equilibrium

5


Parameter estimation

• No binary solution of one ion in water

• No absolute data for single ions

• The hydrogen ion is used as anchor

– Parameters for the hydrogen ion are given fixed values

• UNIQUAC volume and surface area parameters considered adjustable

• Critical review of data

• Binary and ternary data of all types used

• Non-linear least squares optimization

• By using thermal properties in the parameter estimation a better temperature dependency of activity coefficients is achieved

05.12.2008 Extended UNIQUAC model and its application to geothermal systems

6


Parameters

•H+, Na+, K+, NH4+, Ca2+, Mg2+, Mn2+, Fe2+, Co2+,

Ni2+, Cu2+, Zn2+, Ba2+, Sr2+

•F-, Cl-, Br-, NO3-, SO4

2-, HSO4-, OH-, CO3

2-, HCO3-

, S2O82-, SO3

2-, HSO3-, HPO4

-, H2PO4-

•H2O, CO2, NH3, SO2, H2SO4, H2S, HNO3, H3PO4, C12H22O11, CH3OH, C2H5OH, n-C3H7OH, i-C3H7OH, n-C4H9OH, i-C4H9OH, s-C4H9OH, t-C4H9OH, Monoethylene glycol, MDEA, MEA

7

DTU Chemiccal Engineering, Technical University of Denmark 05.12.2008 Extended UNIQUAC model and its application to geothermal systems

8

Relative permittivity of aqueous solutions

0

10

20

30

40

50

60

70

80

90

0 10 20 30 40 50 60 70 80 90 100

Mass % solute

Re

lati

ve

pe

rm

itti

vit

y

.

NaCl, Hasted et al, 1948Ethanol, Åkerlöf, 1932

Relative permittivity


Extended UNIQUAC versus ”Mixed solvent” approach

• In the ”Mixed solvent” approach, the standard state chemical potentials are functions of solvent composition


9

* *

* *

, refer to chemical potential and activity

coefficient in the unsymmetric, mole fraction scale

Extended UNIQUAC approach:

ln ln

"Mixed solvent" approach:

i i

i i i i

ideal excess

M

i i

RT x RT

ln lnixed solvent Mixed solvent

i i

ideal excess

RT x RT


Solubility of NaCl in aqueous ethanol


10

0%

5%

10%

15%

20%

25%

30%

0% 20% 40% 60% 80% 100%

Wt%

NaC

l

Wt% ethanol, Saltfree

T = 15 °C

ExperimentalElecNRTL

ElecNRTL optimized

OLI MSE

Extended UNIQUAC


Standard state properties

• The numerical values of standard state chemical potentials are needed for equilibrium calculations

• Such values for most solutes in the aqueous standard state and many salts have been published by NIST

• Those not found were fitted to experimental data

• Temperature dependency calculated with classical thermodynamic method

– Constant value for the heat capacity of solids

– Three parameter expression for the heat capacity of ions

• The pressure dependency will be discussed later

• Standard state properties independent of composition!

11


Equilibrium calculations

• Speciation equilibrium

• +

• Solid-liquid equilibrium

• Vapor-liquid equilibrium

• Liquid-liquid equilibrium


Speciation equilibria

NH3(aq)+H2O NH4+(aq)+OH-(aq)

Equilibrium condition:

-3 2 4

- -3 24 4

3 2

* * * 0 * *

*

- -- ln

NH H O NH OH

NH H ONH OH NH OH

NH H O

a a

RT a a

DTU Chemiccal Engineering, Technical University of Denmark 16.10.2008 Thermodynamic modelling of phase equilibria and thermal properties of

the CO2 – NH3 – H2O system 14

Speciation at 40 °C in 12 molal NH3 measured by IR spectrometry (Lichtfers, 2000)

Same scale on the ordinate axis on the two figures (mol/kg water)


Solid-liquid equilibrium

• CaSO4·2H2O (s) Ca2+(aq)+ SO42-(aq) + 2H2O (l)

• At equilibrium, the chemical potential of the pure crystalline salt(hydrate) equals the sum of the chemical potentials of the salts components in solution

• It is required that other salts are not supersaturated.

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2 24 2 24·2 ( ) ( )( ) ( )

2CaSO H O s H O lCa aq SO aq


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 20 40 60 80 100

Temperature, °C

CO

2/N

H3 m

ol

rati

o

Extended UNIQUAC

Jänecke (1929)

Terres & Weiser (1921)Terres & Behrens (1928)

Guyer & Piechowicz (1944)

(NH4)2CO3•H2O

NH2COONH4

NH4HCO3

(NH4)2CO3•2NH4HCO3


Vapor-liquid equilibrium

• Equality of chemical potential in gas phase and in liquid phase (Gamma-phi method)

• Gas phase fugacities are calculated with the Soave-Redlich-Kwong equation of state

2 2

2 2 2 2 2 2

( ) ( )

0, * *

0

ˆln ln

CO g CO aq

ig

CO CO CO CO CO CO

PRT y RT x

P

17

DTU Chemiccal Engineering, Technical University of Denmark 16.10.2008 Thermodynamic modelling of phase equilibria and thermal properties of

the CO2 – NH3 – H2O system 18

Partial pressures at 20 °C

K. Thomsen and P. Rasmussen “Modeling of Vapor-liquid-solid equilibrium in gas-aqueous electrolyte systems”, Chemical Engineering Science 54(1999)1787-1802


Liquid-liquid equilibrium

• The activity products of salts rather than the activities of the individual ions ions are compared

I II

* * I * * II

* I * II

ln( ) ln( )

( ) ( )

i i

i i i i i i

i i i i

RT x RT x

x x

• Equilibrium between component i in phase I and phase II


20

100

90

80

70

60

50

40

30

20

10

0100

90

80

70

60

50

40

30

20

10

0

0.0

0

10.0

0

20.0

030.0

0

40.0

0

50.0

0

60.0

0

70.0

080.0

0

90.0

0100.0

0

0 10 20 30 40 50 60 70 80 90 100

Iino et al. (1971)Do & Park (1974)Extended UNIQUACSeries2Series3Series4Series7

iso-propanol

K2CO3

H2O

30 °C


Pressure dependency

• No pressure dependency in activity coefficient model

• High pressure applications

– Scale formation in oil production equipment and reservoirs

– Scale formation in equipment used for producing geothermal energy


Pressure dependency

• BaSO4 (s) Ba2+(aq) + SO42-(aq)

• Solubility product:

• Activity coefficients:

0

0

2

0 0ln ln ( ) ( )2

dis P disP P

VK K P P P P

RT RT

0

0

,* * 2

, , 0 0ln ln ( ) ( )2

ex exi P i

i P i P

VP P P P

RT RT


Equilibrium expression

• The resulting equation for equilibrium is:

• Alfa and beta have physical meanings.

• We treat them as adjustable parameters

0

0

2

0 0

,

ln ln ( ) ( )

ln ln

p P

p i i i P

i

K K P P P P

K x


BaSO4 solubility at 500 bar

1.00E-06

6.00E-06

1.10E-05

1.60E-05

2.10E-05

2.60E-05

3.10E-05

3.60E-05

4.10E-05

4.60E-05

0 50 100 150 200 250 300

T (oC)

BaS

O4 (

m)

Extended UNIQUAC model

Blount (1977)

Lyashchenko and Churagulov (1981) García A.V., Thomsen K., Stenby E.H.,

Geothermics 34(2005)61-97


SrSO4 solubility isotherms

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

1.0E-03

1.2E-03

1.4E-03

0 100 200 300 400 500 600 700

P (bar)

SrS

O4 (

m)


Howell et al. (1992)

25 °C

100 °C

200 °C


CaCO3 solubility at 30 bar CO2

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0 50 100 150 200

T (oC)

CaC

O3 (

m)


Segnit et al. (1962)

Miller (1952)

García A.V., Thomsen K., Stenby E.H., Geothermics 35(2006)239-284


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0

0.005

0.01

0.015

0.02

0.025

0 0.5 1 1.5 2 2.5 3 3.5 4

So

lub

ilit

y o

f S

rS

O4,

mo

lality

NaCl concentration, molality

NaCl-SrSO4, 300 bar, 250°C

Experimental

Extended UNIQUAC

OLI Scale-Chem

MultiScale

Experimental data

from Howell, Raju,

and Atkinson, 1992


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Multiscale had no solubility limit for BaCO3!

Experimental data

from Malinin,

Geokhimiia, 1963


Conclusion

• The Extended UNIQUAC model is a simple model for solutions with salts. It has only few parameters. Yet it can accurately reproduce data for electrolyte solutions in wide temperature and pressure ranges.

• The model is currently being used at DTU Chemical Engineering for modeling CO2 absorption/desorption with various solvents.

• The model can probably be improved by

– Adjusting the standard state properties of ions and salts

– Including new experimental data for parameter estimation

– Adding more components


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Extended UNIQUAC model and its application to geothermal systems