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Thermodynamic models
for CO2-alkanolamine-water systems
Erik T. Hessen and Hallvard F. Svendsen
Norwegian University of Science and Technology (NTNU)
Department of Chemical Engineering
Trondheim, NORWAY
Erik Troøien Hessen, Research Review Meeting - Austin, 10-11.01.2008
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Outline
• Problem description and challenges
• Electrolyte theory
– Debye-Hückel
– Frameworks for electrolyte thermodynamics
• Model selection and development
– Recapitulation
– eNRTL
– Clegg-Pitzer model
Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008
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Thermodynamic modelling - challenges
Vapour – liquid equilibria (VLE)
Chemical equilibria (liquid phase)
Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008
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Thermodynamic modelling - challenges
Many species – complex reactions
System changes character as CO2 is absorbed
into the liquid phase
Molecular components  Electrolyte components
Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008
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Thermodynamic modelling - challenges
General model structure (short range and long range terms):
Helmholtz energy formulation (EOS) :
A = ASR + ALR
e.g.
A = Aclassical eos + ADH/MSA + (ABorn)
Excess Gibbs energy formulation
GE = GE,SR + GE,LR
e.g.
GE = GE,NRTL + GE,DH/MSA + (GE,Born)
Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008
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Thermodynamic modelling - challenges
A = ASR + ALR
GE = GE,SR + GE,LR
Short range interactions
Long range interactions
Typically: Debye-Hückel, MSA, (Born term)
Typically: NRTL, UNIQUAC, UNIFAC, Pitzer
Electrolyte theory: Theoretical basis not fully explored
Many components many interaction parameters
Problems with mixed solvents (varying ε)
Difficult parameter estimation
Different frameworks: McMillan-Mayer, Lewis-Randall
Model equations are empirical
Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008
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Electrolyte theory
• Electrolytes dissociate into ions
 Long range coloumbic forces  non-idealities
 Important at high loadings
• Field not entirely explored
•Ion pairing, association, dielectricum effects, mixed solvents
Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008
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Electrolyte theory – Debye-Hückel
• Debye, P., Hückel, E., Zur Theorie der Elektrolyte,1923
• Presented a model for the ”additional electrostatic energy” (Zusatzenergie)
Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008
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Electrolyte theory – Debye-Hückel
Assumptions made (partly by Debye and Hückel):
E
Ael (T , V , n ) = G (T , P , n ) Þ R T ln( g )
Correct assumption?
In reality:
Legendre transformation
Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008
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Electrolyte theory – Debye-Hückel
The correct Debye-Hückel activity coefficient may then be found as:
Which corresponds to a McMillan-Mayer – Lewis-Randall framework
conversion.
Thus the different frameworks of electrolyte theory should not be understood
as something being on the side of ordinary thermodynamics.
Literature: Breil, Mollerup (2006)
Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008
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Electrolyte theory – shortcomings
Mixed solvents:
   T , V , n s 
• Dielectricum assumption is probably an oversimplification
• Inconsistencies arise when differentiating ε (mixed solvents)
• Inconsistent use of the model equations (e.g. A vs. GE)
Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008
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Model selection and development
General model requirements:
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3.
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6.
Thermodynamic consistency
Accurate predictions for variable loadings and process conditions
Must be able to deal with mixed solvents and molecular solutes
Reasonable computational effort
Reasonable number of parameters to be estimated
Versatility (applied to different systems, and properties)
Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008
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Model selection and development
Numerous models found in literature. Most are GE based.
GE models (γ-φ)
Rigorous models:
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eNRTL, Pitzer, UNIFAC, UNIQUAC, etc.
More complex (-)
Often more parameters (-)
Better predictability (+)
Parameter databases (+)
Much experience and know-how (+)
Especially eNRTL is much used
Non-rigorous models
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Kent-Eisenberg, Desmukh-Mather
Narrow validity ranges (-)
Simple structure (+)
Few parameters (+)
Limited usefulness (-)
 Not speciation, γH2O, γamine
EOS based models
Few models found – weak basis.
Most work is done in this field.
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Fürst - Renon (Cubic EOS + MSA)
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CPA models (cubic + association)
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Versatile models (+)
Complex models (-)
Mixing rules (-)
Less experience and know-how (-)
Many parameters to be estimated (-)
Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008
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Model selection and development
Electrolyte-NRTL model:
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Ya and Yc kept constant in differentiation to yield activity coefficients
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Inconsistency error:
G
E

 n RT
i
G
E
ni
 RT ln  i
ln  i
i
•
With this approximation the eNRTL model will not fulfill the Gibbs-Duhem
equation for multi-cation/anion systems
Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008
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Model selection and development
The Clegg-Pitzer model
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Clegg, S. L. , Pitzer, K. S., J.Phys. Chem., 92, 1992
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Based on a Margules expansion term (SR) and a Debye-Hückel based term (LR)
gE = gE, short range + gE,long range
Two models – symmetrical and unsymmetrical electrolytes
Mole fraction based
Complex mathematical structure
Few sources in literature
Not applied to mixed solvents
Unsymmetrical model
(short range term)
Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008
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Model selection and development
The Clegg-Pitzer model
Full activity coefficient sheet
For the unsymmetrical model
Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008
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Model selection and development
The Clegg-Pitzer model
Symmetrical matrix
Zeros on diagonal
Asymmetrical matrix
Aji = -Aij
Zeros on diagonal
Revised structure
Possible to differentiate
Implemented in automatic
differentiation package.
Collaboration with
associate professor
Tore Haug-Warberg
Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008
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Clegg-Pitzer based models
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Li, Y., Mather, A. E., Ind. Eng. Chem. Res., 1994 (++)
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Simplified model with easier mathematical structure.
Theoretical basis not treated well (single solvent  mixed solvent)
Based on CP for symmetrical electrolytes.
Free CO2 and carbonate neglected!
Fewer parameters than e.g. eNRTL
Applied to mixed solvents
Symmetrical
Introduced by Li & Mather
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Kundu, M., Bandyopadhay, S., J. Chem. Eng. Data, 2006 (++)
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Based on the Li-Mather model
Free CO2 and carbamate neglected
Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008
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Speciation plot, 30 wt% MEA
Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008
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Conclusion
•Many existing models found in literature
• Hard to conclude upon which model to use
• Difficult parameter estimations
• eNRTL and Clegg-Pitzer models are explored
•Theoretical basis is weak in some fields (especially for mixed solvents)
• Ongoing investigations, especially related to Debye-Hückel terms
Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008