# 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

## 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 | ||

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 |

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 | ||

Steric factor | ||

Activation energie | ||

Activation energie | ||

Catalyst deactivation coefficient |

with

Name | Symbol | Interval | Initial value Exp 1 | Initial value Exp 2 | Initial value Exp 3 | Initial value Exp 4 |

Initial molar number 1 | [0,10.0] | 1.0 | 1.0 | 1.0 | 1.0 | |

Initial molar number 2 | [0,10.0] | 1.0 | 1.0 | 1.0 | 1.0 | |

Initial molar number 4 | [0.4,9.0] | 2.0 | 2.0 | 2.0 | 2.0 | |

Concentration of the catalyst | [0,10.0] | 0.0 | 1.0 | 2.0 | 3.0 |

Name | Symbol | Time interval | Value interval | Initial value Exp 1 | Initial value Exp 2 | Initial value Exp 3 | Initial value Exp 4 |

Initial molar number 1 | [20.0,100.0] | 20.0 | 60.0 | 40.0 | 20.0 | ||

Initial molar number 1 | [20.0,100.0] | 20.0 | 60.0 | 40.0 | 20.0 | ||

Initial molar number 1 | [20.0,100.0] | 20.0 | 60.0 | 40.0 | 20.0 |

**Measurement grid**

## Source Code

- The VPLAN code using VPLAN can be found in: Diels-Alder Reaction Experimental Design (VPLAN)

## 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