Diels-Alder Reaction Experimental Design
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.
Contents
[hide]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:
Constraints
The control variables are constrained with respect to the mass of sample weights (initial mass):
and to the mass of active ingredient content (fraction of active substances):
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 | ![]() |
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Molar number 2 | ![]() |
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Molar number 3 | ![]() |
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Solvent | ![]() |
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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 |
Remember, in an optimum experimental design problem the parameters of the model are fixed. But, we minimize the parameter's uncertainties by optimizing over the control variables and functions.
Name | Symbol | Value |
Steric factor | ![]() |
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Steric factor | ![]() |
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Activation energie | ![]() |
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Activation energie | ![]() |
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Catalyst deactivation coefficient | ![]() |
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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] |
Name | Symbol | Time interval | Value interval | Initial value |
Initial molar number 1 | ![]() |
![]() |
[20.0,100.0] | 20.0 |
Initial molar number 1 | ![]() |
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[20.0,100.0] | 20.0 |
Initial molar number 1 | ![]() |
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[20.0,100.0] | 20.0 |
Measurement grid
References
R. T. Morrison and R.N. Boyd. Organic Chemistry. Allyn and Bacon, Inc., 4th edition, 1983 S. Körkel. Numerische Methoden für Optimale Versuchsplanungsprobleme bei nichtlinearen DAE-Modellen.PhD thesis, Universität Heidelberg, Heidelber,2002