Diels-Alder Reaction Experimental Design

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Model Formulation

Differential equation system:

$\begin{array}{rcl} \dot{n_{1}} (t) & = & - k \cdot \frac{n_{1} (t) \cdot n_{2} (t)}{m_{t o t}}, \\ \dot{n_{2}} (t) & = & - k \cdot \frac{n_{1} (t) \cdot n_{2} (t)}{m_{t o t}}, \\ \dot{n_{2}} (t) & = & k \cdot \frac{n_{1} (t) \cdot n_{2} (t)}{m_{t o t}} \end{array}$

Reaction velocity constant:

$k = k_{1} \cdot e x p (- \frac{E_{1}}{R} \cdot (\frac{1}{T} - \frac{1}{T_{r e f}})) + k_{c a t} \cdot c_{c a t} \cdot e x p (- λ \cdot t) \cdot e x p (- \frac{E_{c a t}}{R} \cdot (\frac{1}{T} - \frac{1}{T_{r e f}}))$

Total mass:

$m_{t o t} = n_{1} \cdot M_{1} + n_{2} \cdot M_{2} + n_{3} \cdot M_{3} + n_{4} \cdot M_{4}$

Temperature in Kelvin:

$T = ϑ + 273$

State variables
Name	Symbol	Initial value ( $t_{0}$ )
Molar number 1	$n_{1} (t)$	$n_{1} (t_{0}) = n_{a 1}$
Molar number 2	$n_{2} (t)$	$n_{2} (t_{0}) = n_{a 2}$
Molar number 3	$n_{3} (t)$	$n_{3} (t_{0}) = n_{a 3}$

Parameters
Name	Symbol	Value
Steric factor	$k_{1}$	X
Steric factor	$k_{k a t}$	X
Activation energie	$E_{1}$	X
Activation energie	$E_{k a t}$	X
Catalyst deactivation coefficient	$λ$	X

Control variables
Name	Symbol	Interval
Initial molar number 1	$n_{a 1}$	[0.4,9.0]
Initial molar number 2	$n_{a 2}$	[0.4,9.0]
Initial molar number 3	$n_{a 3}$	[0.4,9.0]
Concentration of the catalyst	$c_{k a t}$	[0.0,6.0]
Initial molar number 1	$ϑ (t)$	[20.0,100.0]

Parameters