Report

1 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 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, 10-11.01.2008 3 Thermodynamic modelling - challenges Vapour – liquid equilibria (VLE) Chemical equilibria (liquid phase) Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008 4 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 5 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 6 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 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, 10-11.01.2008 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, 10-11.01.2008 9 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 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, 10-11.01.2008 11 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 12 Model selection and development General model requirements: 1. 2. 3. 4. 5. 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 13 Model selection and development Numerous models found in literature. Most are GE based. GE 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 Non-rigorous models • • • • • 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. • 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 (-) Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008 14 Model selection and development Electrolyte-NRTL model: • Ya and Yc kept constant in differentiation to yield activity coefficients • 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 15 Model selection and development The Clegg-Pitzer model • 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) 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 16 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 17 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 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 CO2 and carbonate neglected! Fewer parameters than e.g. eNRTL Applied to mixed solvents Symmetrical Introduced by Li & Mather • Kundu, M., Bandyopadhay, S., J. Chem. Eng. Data, 2006 (++) – – Based on the Li-Mather model Free CO2 and carbamate neglected Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008 19 Speciation plot, 30 wt% MEA Erik Troøien Hessen, Research Review Meeting, 10-11.01.2008 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, 10-11.01.2008