Prediction of Binary Fick Diffusion Coefficients using COSMO-RS

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1 Prediction of Binary Fick Diffusion Coefficients using COSMO-RS Sebastian Rehfeldt, Tobias Sachsenhauser, Sandra Schreiber, Harald Klein Institute of Plant and Process Technology Technische Universität München

2 Motivation Theory of Diffusion Thermodynamic Factor Evaluation of Prediction with different Methods Summary Outline 2

3 Diffusion Motivation 3

4 Fick s Law: More commonly used Phenomenological approach Two Theories 4

5 Fick s Law: Two Theories 5

6 Fick s Law: More commonly used Phenomenological approach Maxwell-Stefan: Physically consistent theory More suitable for prediction Two Theories 6

7 Fick s Law & Maxwell-Stefan: Two Theories 7

8 Fick s Law: More commonly used Phenomenological approach Maxwell-Stefan: Physically consistent theory More suitable for prediction Connection between both: Simple transformation between both diffusion coefficients Two Theories 8

9 Prediction of Fick coefficients via Maxwell-Stefan 9

10 Connection between Fick and Maxwell-Stefan: Prediction of Fick coefficients via Maxwell-Stefan

11 Thermodynamic Factor 10

12 ? Prediction of Fick coefficients via Maxwell-Stefan

13 - where to get from? Wilson NRTL UNIQUAC Thermodynamic Factor from exp. VLE-Data 12

14 - where to get from?? Group Contribution Methods UNIFAC ASOG Group Contribution Methods 13

15 COSMO-RS - where to get from? Combination of quantum chemistry and statistical thermodynamics Definition of molecular geometry Quantum chemical COSMO calculation K OW Hij μi γi Γ Statistical thermodynamics of interacting surface segments COSMO-RS 14

16 ? Experimental VLE Data 4 random exp. data sets Recommended parameters if available Wilson, NRTL, UNIQUAC Group Contribution Methods UNIFAC ASOG COSMO-RS Direct calculation of thermodynamic factor Wilson, NRTL, UNIQUAC Evaluation: Which is the best method? Test with 28 different binary Fick diffusion data sets Different ways to get the thermodynamic factor 15

17 Evaluation of prediction 16

18 Evaluation of prediction 16

19 Evaluation of prediction 16

20 Evaluation of prediction 16

21 Evaluation of prediction 16

22 chloroform - benzene 17

23 carbon tetrachloride 1-butanol 18

24 acetone - water 19

25 propanol - water 20

26 Summary : Fick diffusion coefficients can be predicted with usage of Maxwell- Stefan and thermodynamic factor Prediction works best in nearly ideal systems, shows larger deviations in strongly non-ideal systems In most systems, the best result is predicted with thermodynamic factor from VLE-data, but Results from different VLE-data sets can vary strongly no check possible without exp. diffusion data Results with COSMO-RS are in the same range as UNIFAC, both are good alternatives; ASOG shows larger deviations In strongly non-ideal systems without demixing, Wilson yields the best results (from exp. VLE or COSMO-RS) Summary 21

27 Prediction of Binary Fick Diffusion Coefficients using COSMO-RS Sebastian Rehfeldt, Tobias Sachsenhauser, Sandra Schreiber, Harald Klein Institute of Plant and Process Technology Technische Universität München