Difference between revisions of "Diels-Alder Reaction Experimental Design"

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Revision as of 11:59, 4 December 2015

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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_{tot}}, \\ & & \\ \dot{n_2}(t) &=& -k \cdot \frac{n_1(t) \ \cdot \ n_2(t)}{m_{tot}}, \\ & & \\ \dot{n_2}(t) &=& \ \ k \cdot \frac{n_1(t) \ \cdot \ n_2(t)}{m_{tot}} \end{array}

Reaction velocity constant:

k = k_1 \ \cdot \ exp(- \frac{E_1}{R} \ \cdot \ (\frac{1}{T} \ - \ \frac{1}{T_{ref}}) ) \ + \ k_{cat} \ \cdot \ c_{cat} \ \cdot \ exp(-\lambda \ \cdot \ t) \ \cdot \ exp( - \frac{E_{cat}}{R} \ \cdot \ (\ \frac{1}{T} \ - \ \frac{1}{T_{ref}}) )

Total mass:

m_{tot} = n_1 \ \cdot \ M_1 \ + \ n_2 \ \cdot \ M_2 \ + \ n_3 \ \cdot \ M_3 \ + \ n_4 \ \cdot \ M_4

Temperature in Kelvin:

T = \vartheta + 273


State variables
Name Symbol Initial value (t_0)
Molar number 1 n_1(t) n_1(t_0) =
Molar number 2 n_2(t) n_2(t_0) =
Molar number 3 n_3(t) n_3(t_0) =
Parameters
Name Symbol Initial value (t_0)
Steric factor k_1 X
Steric factor k_{kat} X
Activation energie E_1 X
Activation energie E_{kat} X
Catalyst deactivation coefficient \lambda X


Parameter(s)
Name Symbol Value Unit
Parameter p 23 [-]

Parameters

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