Difference between revisions of "Diels-Alder Reaction Experimental Design"
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Revision as of 16:34, 8 December 2015
The Diels-Alder Reaction is an organic chemical reaction. A conjugated diene and a substituted alkene react and form a substituted cyclohexene system. Stefan Körkel used this model in his PhD thesis to compute optimum experimental designs.
Model Formulation
The reactionkinetics can be modelled by the following differential equation system:
The reaction velocity constant consists of two parts. One part reflects the non-catalytic and the other the catalytic reaction. The velocity law follows the Arrhenius relation
Total mass:
Temperature in Kelvin:
The ODE system is summarized to:
Optimum Experimental Design Problem
The aim is to compute an optimal experimental design which minimizes the uncertainties of the parameters . So, we have to solve the following optimum experimental design problem:
Name | Symbol | Initial value () |
Molar number 1 | ||
Molar number 2 | ||
Molar number 3 | ||
Solvent |
Name | Symbol | Value |
Molar Mass | 0.1362 | |
Molar Mass | 0.09806 | |
Molar Mass | 0.23426 | |
Molar Mass | 0.236 | |
Universal gas constant | 8.314 | |
Reference temperature | 293 | |
St.dev of measurement error | 1 |
Name | Symbol | Value |
Steric factor | ||
Steric factor | ||
Activation energie | ||
Activation energie | ||
Catalyst deactivation coefficient |
with
Name | Symbol | Interval |
Initial molar number 1 | [0.4,9.0] | |
Initial molar number 2 | [0.4,9.0] | |
Initial molar number 4 | [0.4,9.0] | |
Concentration of the catalyst | [0.0,6.0] | |
Initial molar number 1 | [20.0,100.0] |
Measurement grid
Constraints
The control variables are constrained with respect to the mass of sample weights:
and to the mass of active ingredient content: <p>
References
R. T. Morrison and R.N. Boyd. Organic Chemistry. Allyn and Bacon, Inc., 4th edition, 1983S. Körkel. Numerische Methoden für Optimale Versuchsplanungsprobleme bei nichtlinearen DAE-Modellen.PhD thesis, Universität Heidelberg, Heidelber,2002