1 Thermodynamic models for CO 2 -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,

2 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,

3 Thermodynamic modelling - challenges Vapour – liquid equilibria (VLE) Chemical equilibria (liquid phase) Erik Troøien Hessen, Research Review Meeting,

4 Thermodynamic modelling - challenges Many species – complex reactions System changes character as CO 2 is absorbed into the liquid phase Molecular components  Electrolyte components Erik Troøien Hessen, Research Review Meeting,

5 Thermodynamic modelling - challenges General model structure (short range and long range terms): Erik Troøien Hessen, Research Review Meeting, Helmholtz energy formulation (EOS) : A = A SR + A LR e.g. A = A classical eos + A DH/MSA + (A Born ) Excess Gibbs energy formulation G E = G E,SR + G E,LR e.g. G E = G E,NRTL + G E,DH/MSA + (G E,Born )

6 Thermodynamic modelling - challenges Erik Troøien Hessen, Research Review Meeting, A = A SR + A LR G E = G E,SR + G E,LR Typically: NRTL, UNIQUAC, UNIFAC, Pitzer Many components  many interaction parameters Difficult parameter estimation Model equations are empirical Typically: Debye-Hückel, MSA, (Born term) Electrolyte theory: Theoretical basis not fully explored Problems with mixed solvents (varying ε) Different frameworks: McMillan-Mayer, Lewis-Randall Short range interactions Long range interactions

7 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,

8 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,

9 Electrolyte theory – Debye-Hückel Assumptions made (partly by Debye and Hückel): Correct assumption? In reality: Legendre transformation Erik Troøien Hessen, Research Review Meeting,

10 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,

11 Electrolyte theory – shortcomings Mixed solvents: Erik Troøien Hessen, Research Review Meeting, Dielectricum assumption is probably an oversimplification Inconsistencies arise when differentiating ε (mixed solvents) Inconsistent use of the model equations (e.g. A vs. G E )

12 Model selection and development General model requirements: 1.Thermodynamic consistency 2.Accurate predictions for variable loadings and process conditions 3.Must be able to deal with mixed solvents and molecular solutes 4.Reasonable computational effort 5.Reasonable number of parameters to be estimated 6.Versatility (applied to different systems, and properties) Erik Troøien Hessen, Research Review Meeting,

13 Model selection and development EOS based models Few models found – weak basis. Fürst - Renon (Cubic EOS + MSA) CPA models (cubic + association) Versatile models (+) Complex models (-) Mixing rules (-) Less experience and know-how (-) Many parameters to be estimated (-) G E models (γ-φ) Rigorous models: eNRTL, Pitzer, UNIFAC, UNIQUAC, etc. More complex (-) Often more parameters (-) Better predictability (+) Parameter databases (+) Much experience and know-how (+) Especially eNRTL is much used Most work is done in this field. Numerous models found in literature. Most are G E based. Erik Troøien Hessen, Research Review Meeting, Non-rigorous models Kent-Eisenberg, Desmukh-Mather Narrow validity ranges (-) Simple structure (+) Few parameters (+) Limited usefulness (-)  Not speciation, γ H2O, γ amine

14 Model selection and development Electrolyte-NRTL model: Y a and Y c kept constant in differentiation to yield activity coefficients Inconsistency error: With this approximation the eNRTL model will not fulfill the Gibbs-Duhem equation for multi-cation/anion systems Erik Troøien Hessen, Research Review Meeting,

15 Clegg, S. L., Pitzer, K. S., J.Phys. Chem., 92, 1992 –Based on a Margules expansion term (SR) and a Debye-Hückel based term (LR) –g E = g E, short range + g E,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, Model selection and development The Clegg-Pitzer model

16 Full activity coefficient sheet For the unsymmetrical model Erik Troøien Hessen, Research Review Meeting, Model selection and development The Clegg-Pitzer model

17 Revised structure Possible to differentiate Implemented in automatic differentiation package. Collaboration with associate professor Tore Haug-Warberg Symmetrical matrix Zeros on diagonal Asymmetrical matrix A ji = -A ij Zeros on diagonal Model selection and development The Clegg-Pitzer model Erik Troøien Hessen, Research Review Meeting,

18 Clegg-Pitzer based models Li, Y., Mather, A. E., Ind. Eng. Chem. Res., 1994 (++) –Simplified model with easier mathematical structure. –Theoretical basis not treated well (single solvent  mixed solvent) –Based on CP for symmetrical electrolytes. –Free CO 2 and carbonate neglected! –Fewer parameters than e.g. eNRTL –Applied to mixed solvents Kundu, M., Bandyopadhay, S., J. Chem. Eng. Data, 2006 (++) –Based on the Li-Mather model –Free CO 2 and carbamate neglected Symmetrical Introduced by Li & Mather Erik Troøien Hessen, Research Review Meeting,

19 Speciation plot, 30 wt% MEA Erik Troøien Hessen, Research Review Meeting,

20 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,