Estimation of Vapour Pressures of Organic Liquids using Group Contributions and Group Interactions B. Moller*, J. Rarey**, D. Ramjugernath* * University of Kwazulu-Natal, Durban 4041, South Africa ** Technische Chemie (F5), Universität Oldenburg, 26111 Oldenburg ICCT Warsaw 2008 1
Overview Motivation Project Timeline Properties of the Vapor Pressure Curve Performance of Different Equations Model Description Software Tools Results Future Work Acknowledgement ICCT Warsaw 2008 2
P (kpa) What are Important Properties? Usually need to know information about the vapour-liquid boundary, useful for example in: Distillation applications Environmental applications 1 E+05 1 E+03 T m T c 1 E+01 1 E-01 T t T b Water 1 E-03 1 E-05 100 200 300 400 500 600 700 T (K) ICCT Warsaw 2008 3
Project Timeline Rarey 2000 2002 2004 2006 2008 T b W. Cordes, J. Rarey, A New Method for the Estimation of the Normal Boiling Point of Non-Electrolyte Organic Compounds, Fluid Phase Equilibria, 201/2, 397-421 (2002). ICCT Warsaw 2008 4
Project Timeline Rarey 2000 2002 2004 2006 2008 T b New T b Y. Nannoolal, J. Rarey, D. Ramjugernath, W. Cordes, Estimation of Pure Component Properties, Part 1: Estimation of the Normal Boiling Point of Non-Electrolyte Organic Compounds via Group Contributions and Group Interactions, Fluid Phase Equilibria, 226, 45-63, 2005. ICCT Warsaw 2008 5
Project Timeline Rarey 2000 2002 2004 2006 2008 T b New T b T c, P c, V c Nannoolal, Y., Rarey, J., Ramjugernath, D., Estimation of Pure Component Properties Part 2: Estimation of Critical Data by Group Contribution., Fluid Phase Equilib., 252 (2007) 1. ICCT Warsaw 2008 6
Project Timeline Rarey 2000 2002 2004 2006 2008 T b New T b T c, P c, V c P s (T) Nannoolal, Y., Rarey, J., Ramjugernath, D., Estimation of Pure Component Properties Part 3: Estimation of the Vapour Pressure of Non-Electrolyte Organic Compounds via Group Contributions and Group Interactions., Fluid Phase Equilib. accepted for publication. ICCT Warsaw 2008 7
Project Timeline Rarey Nannoolal 2000 2002 2004 2006 2008 T b New T b T c, P c, V c P s (T) μ(t) Nannoolal, Y., Rarey, J., Ramjugernath, D., Estimation of Pure Component Properties Part 4: Estimation of the Liquid Viscosity of Non-Electrolyte Organic Compounds via Group Contributions and Group Interactions., Fluid Phase Equilib. in preparation. ICCT Warsaw 2008 8
Project Timeline Rarey Nannoolal Moller 2000 2002 2004 2006 2008 T b New T b T c, P c, V c P s (T) μ(t) New P s (T) Moller, B., Rarey, J., Ramjugernath, D., Estimation of the Vapour Pressure of Non-Electrolyte Organic Compounds via Group Contributions and Group Interactions., J. Mol. Liq. accepted for publication. ICCT Warsaw 2008 9
Methods for Predicting Physical Properties Group contribution methods Fairly simple Good accuracy Need groups to make predictions Quantum chemistry (COSMO-RS, COSMO-SAC ) Great potential but not at the required level of accuracy Statistical thermodynamics (molecular simulations ) Can get good results when fitted to some reference data points ICCT Warsaw 2008 10
Purpose of this Work A large number of good group contribution methods already developed Objective of this work was to rework the vapour pressure method Nannoolal based his vapour pressure method on the Antoine equation, the first step was therefore to review this decision ICCT Warsaw 2008 11
Hvap (kj/mol) The Slope of the Vapor Pressure Curve 40 1.00 30 20 0.80 0.60 Zvap Hvap/Zvap (kj/mol) S dlnp 1 1 R d T H Z vap vap 10 0.40 0 0.45 0.65 0.85 1.05 T r 37 0.20 35 33 Component: Benzene 31 29 0.45 0.55 0.65 0.75 0.85 0.95 ICCT Warsaw 2008 12 T r
Approximate Modeling of the Slope Hvap/Zvap (kj/mol) 35 33 31 a) 10 kpa T b 1000 kpa 3000 kpa b) Benzene H Z vap vap 29 0.45 0.55 0.65 0.75 0.85 0.95 T r T r T T c a) Linear with respect to: 1/T b) Constant ICCT Warsaw 2008 13
The Antoine Equation B logp s A T C 36 Hvap/Zvap (kj/mol) 35 34 33 32 31 30 T b Benzene Deviation: 3.6% 29 0.45 0.55 0.65 0.75 0.85 0.95 T r ICCT Warsaw 2008 14
The Cox Equation s P Tb log A' 1 atm P T log A' log A E(1 T )( F T ) c r r 36 Hvap/Zvap (kj/mol) 35 34 33 32 31 Benzene T r T T c 30 T b 29 0.45 0.55 0.65 0.75 0.85 0.95 T r ICCT Warsaw 2008 15
Kinetic Theory of Vaporization Hvap/Zvap (kj/mol) 35 33 31 29 B lnp A C T DT ET T 2 0 ln A s s T b T b Benzene 0.45 0.55 0.65 0.75 0.85 0.95 T r R E ln ( 0.5)ln ln ( ) ln Vw R E B 0 s 1 C 1.5 s D R E 0 R 2( s3)( s1) E E R E o s 2 - Characteristic energy - Number of loosely coupled harmonic oscillators Applicable to pressures lower than 200 kpa 0 Abrams, D. S., Massaldi, H. A., Prausnitz J. M., Vapor Pressures of Liquids as a Function of Temperature. Two-Parameter Equation Based on Kinetic Theory of Fluids., Ind. Eng. Chem. Fundam. 13(3) (1974) 259. Moelwyn-Hughes, E. A., The Chemical Statics and Kinetics of Solutions, Academic Press, London (1971). ICCT Warsaw 2008 16
Model Derivation The A parameter in the Antoine equation is substituted by using the normal boiling point as a reference point: B B lnp lnp atm T C Tb C In order to further reduce the number of model parameters it is assumed that C is a function of the normal boiling point: ln P T Tb B' Patm T C( Tb ) For aliphatic alcohols and carboxylic acids the new form is: P T T b T ln B' D'ln Patm T C( Tb ) Tb ICCT Warsaw 2008 17
Model Equations P T T b T ln B' D'ln Patm T C( Tb ) Tb (55 GI s) n n 1 B' A db GIi 2 1.485 i1 j1 (158 Groups) j Tb CT ( b ) 2.65 135 Aliphatic alcohols & carboxylic acids m 1 D' D vide n a i 1 (5 Groups) i db v db n v db db i i a j j k i j k Group interactions (H-bonding groups) Frequency Existence Size n a v - number of atoms except H - frequency of a group ICCT Warsaw 2008 18
Group Contributions - db i as Function of the Number of Heavy Atoms dbi 0.8 0.6 0.4 0.2 alkyne-groups dbi 6 5.5 5 aliphatic alcohol groups 0 4.5-0.2 4-0.4 1 3 5 7 9 11 13 number of atoms 3.5 2 7 12 17 22 number of atoms 5 4.5 dbi 4 3.5 3 2.5 2 1.5 aliphatic carboxylic acid groups Short and longer chain alcohols and carboxylic acids require separate groups 1 4 9 14 19 number of atoms ICCT Warsaw 2008 19
P (kpa) P (kpa) Model Improvements Alcohol and carboxylic acid representation Smaller and larger molecules Low pressure data Current work - - - Nannoolal 10000 5 000 100 1 0.01 4 000 3 000 2 000 1 000 0.0001 0.0014 0.0019 0.0024 0.0029 0.0034 1/T (K -1 ) 250 350 450 550 650 T (K) 1-Nonanol (data from the DDB) ICCT Warsaw 2008 20
Absolute Error (K) Model Parameters Error Relationship Error for the prediction of the boiling point increases with number of model parameters! 16 14 12 Gani, Constantinon Marrero, Pardillo EWOR 10 8 6 Stein, Brown Cordes, Rarey 50 100 150 200 250 300 350 Number of parameters EWOR = Ericksen, Wilding, Oscarson, Rowley ICCT Warsaw 2008 21
Simplification of Group Definitions Replace specific groups with more widely applicable groups: Example: double bonded carbon group: Previously (Nannoolal et al.) New method C C HC CH C H C C H 2 C CH CH H 2 C C H 2 C CH 2 CH 2 6 groups to describe all combinations Only 3 groups required to describe all combinations These simplifications may not be applicable to the estimation of other properties! ICCT Warsaw 2008 22
Introduction of New Structural Groups aromatic iso-cyanate hydrazine cyclic tertiary amines halo-silicon groups (F,Cl,Br,I) fused ring carbon (and other structural groups) silicon group expanded ICCT Warsaw 2008 23
Software Tools for Group Analysis ICCT Warsaw 2008 24
Vapour Pressure Data Dortmund Data Bank (DDB) VAP data for 6000+ compounds 180000+ VAP points Data needed to be validated Used VBA to streamline the process ICCT Warsaw 2008 25
Data Validation ICCT Warsaw 2008 26
Results for All Available Data Relative mean deviations (%) for the different vapour pressure ranges exp P P RMD(%) 100% exp P This work Nannoolal et al. (NC = 2332) (NC = 2207) Average (All Pressures) 5.0 113887 6.6 111757 HP (>500 kpa) 5.0 14678 5.7 14310 MP (10 kpa - 500 kpa) 2.3 68729 2.6 67518 LP (10 Pa - 10 kpa) 9.8 28232 13.1 27687 ELP (<10 Pa) 25.7 2211 55.2 2205 NC number of compounds ICCT Warsaw 2008 27
Detailed Results (Relative Mean Deviation (%)) Group NC ELP LP MP HP total All oxygen compounds 638 27.3 882 12.4 10919 2.9 22708 6.3 2175 6.5 36701 Carboxylic acids 35 23.9 116 12.2 1823 3.8 1106 13.8 10 9.6 3056 Aromatic carboxylic acids 1-1.6 111 2.7 22-1.8 133 Aliphatic carboxylic acids 34 23.9 116 12.8 1712 3.8 1084 13.8 10 9.9 2923 Alcohols 167 28.3 312 17.2 3761 4.1 7186 10.8 626 9.2 11886 Aromatic alcohols 55 39.9 26 25.1 678 3.1 1277 6.9 69 11.0 2050 Aliphatic alcohols 112 27.3 286 15.5 3083 4.3 5909 11.3 557 8.8 9836 Ethers 92 23.7 17 6.5 771 1.8 3743 3.4 738 2.8 5269 Esters 158 29.0 326 8.4 2445 2.2 5622 5.6 403 5.1 8809 Ketones 64 19.0 75 8.9 886 1.9 2637 4.4 271 4.0 3869 Aldehydes 30 6.1 4 12.1 393 2.4 736 5.1 19 5.7 1153 Carbonate diesters 3-1.8 30 0.8 289-0.9 319 Anhydrides 6-14.9 54 4.4 81-8.6 135 Epoxides 11-2.9 33 1.8 280 2.3 43 1.9 356 Carbonates 3 38.7 3 9.1 150 3.2 92 4.4 10 7.2 255 Ureas 5 14.8 3 10.5 59 2.2 40-7.4 102 NC number of compounds ELP extremely low pressure P < 10 Pa LP low pressure 10 Pa < P < 10 kpa MP medium pressure 10 kpa < P < 500 kpa HP high pressure P > 500 kpa total whole vapour pressure range ICCT Warsaw 2008 28
Quality Analysis Can use the error tables to give an approximate quality of prediction: Compound to be predicted Give quality analysis based on training set errors Select most specific group which the compound falls into (e.g. n-alcohols) ICCT Warsaw 2008 29
Number of Compounds RMD(%) Histogram for the Data in the Training Set 900 800 8% 7% 700 600 19% 31% 500 400 300 200 35% 100 0 0-2 2-5 5-10 10-15 15-20 20-40 40-60 >60 RMD (%) Typically compounds with large amounts of low vapour pressure data for example squalane (C30H62) ICCT Warsaw 2008 30
Results for a Test Set not Used in the Regression New Method Nannoolal et al. Compound Class NC RMD% NC RMD% Hydrocarbons 59 6.5 486 59 7.5 486 Halogen compounds 14 7.0 73 14 7.1 73 Oxygen compounds 46 7.1 1952 44 8.5 1938 Nitrogen compounds 19 7.3 172 18 8.9 169 Sulfur compounds 3 5.6 24 3 11.0 24 All compounds 157 7.1 2879 154 8.2 2859 Test set contains data with higher scatter or where the reliability could not be verified (only one author, ) ICCT Warsaw 2008 31
P (kpa) Specific Test Set Examples 100 O OH 10 4-Methyl-4-hydroxy-2-pentanone 1 0.1 0.0022 0.0024 0.0026 0.0028 0.003 0.0032 0.0034 1/T (K -1 ) ICCT Warsaw 2008 32
P (kpa) Specific Test Set Examples 100 OH 10 O alpha-hydroxy-isobutyric acid,methyl ester O 1 0.0024 0.0026 0.0028 0.003 0.0032 0.0034 1/T (K -1 ) Danov S.M., Obmelyukhina T.N., Chubarov G.A., Balashov A.L., Dolgopolov A.A., J.Appl.Chem.USSR, 63(3), 566-568, 1990 Matin N.B., Khitrin S.V., Spasskaya R.I., Trachenko V.I., Zilberman E.N., Soluyanova T.F., Zh.Prikl.Khim.(Leningrad), 53(9), 1999-2003, 1980 ICCT Warsaw 2008 33
P (kpa) Specific Test Set Examples 100 HO O F F 10 F Trifluoroacetic acid 1 0.0028 0.003 0.0032 0.0034 0.0036 0.0038 0.004 1/T (K -1 ) ICCT Warsaw 2008 34
Heat of Vaporization at 298.15 K C( Tb) Tb Hvap RZ vap B ' D' T 2 CT ( b) 1 T This Work Kolská et al.* Compound Class NC RMD(%) NC RMD(%) Hydrocarbons 197 2.9 236 2.0 Halogen Compounds 89 2.1 103 2.0 Oxygen Compounds 224 4.2 262 2.3 Nitrogen Compounds 101 2.9 104 2.4 Phosphorous Compounds 1 6.9 - - Sulphur Compounds 38 2.6 52 2.2 Metals 4 5.6 - - Other Compounds 1 7.4 - - Silicon Compounds 12 9.2 11 3.1 All Compounds 718 3.5 831 2.2 *Kolská Z., Růžička V., Gani R., Ind. Eng. Chem. Res., 44, 8436-8454, 2005 ICCT Warsaw 2008 35
Future Work Prediction of further properties Ground work has been done Overlap project so there is a transfer of knowledge Prediction of mixture properties ICCT Warsaw 2008 36
Acknowledgements Supervisor: Prof. J. Rarey Project Leaders: Prof. D. Ramjugernath Prof. J. Gmehling Software: DDBST GmbH ICCT Warsaw 2008 37