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 www.apt.mw.tum.de
Motivation Theory of Diffusion Thermodynamic Factor Evaluation of Prediction with different Methods Summary 10.04.2015 Outline 2
Diffusion 10.04.2015 Motivation 3
Fick s Law: More commonly used Phenomenological approach 10.04.2015 Two Theories 4
Fick s Law: 10.04.2015 Two Theories 5
Fick s Law: More commonly used Phenomenological approach Maxwell-Stefan: Physically consistent theory More suitable for prediction 10.04.2015 Two Theories 6
Fick s Law & Maxwell-Stefan: 10.04.2015 Two Theories 7
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 10.04.2015 Two Theories 8
10.04.2015 Prediction of Fick coefficients via Maxwell-Stefan 9
Connection between Fick and Maxwell-Stefan: Prediction of Fick coefficients via Maxwell-Stefan 10.04.2015 9
10.04.2015 Thermodynamic Factor 10
? Prediction of Fick coefficients via Maxwell-Stefan 10.04.2015 11
- where to get from? Wilson NRTL UNIQUAC 10.04.2015 Thermodynamic Factor from exp. VLE-Data 12
- where to get from?? Group Contribution Methods UNIFAC ASOG 10.04.2015 Group Contribution Methods 13
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 10.04.2015 COSMO-RS 14
? 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 10.04.2015 Different ways to get the thermodynamic factor 15
10.04.2015 Evaluation of prediction 16
10.04.2015 Evaluation of prediction 16
10.04.2015 Evaluation of prediction 16
10.04.2015 Evaluation of prediction 16
10.04.2015 Evaluation of prediction 16
10.04.2015 chloroform - benzene 17
10.04.2015 carbon tetrachloride 1-butanol 18
10.04.2015 acetone - water 19
10.04.2015 1-propanol - water 20
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) 10.04.2015 Summary 21
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 www.apt.mw.tum.de