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

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|Molar number 1
 
|Molar number 1
 
|<math>n_1(t)</math>
 
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|<math>n_1(t_0) = </math>
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|<math>n_1(t_0) = n_{a1} </math>
 
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|Molar number 2
 
|Molar number 2
 
|<math>n_2(t)</math>
 
|<math>n_2(t)</math>
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|<math>n_2(t_0) = </math>
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|<math>n_2(t_0) = n_{a2} </math>
 
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|Molar number 3
 
|Molar number 3
 
|<math>n_3(t)</math>
 
|<math>n_3(t)</math>
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|<math>n_3(t_0) = </math>
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|<math>n_3(t_0) = n_{a3} </math>
 
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{| class="wikitable"
 
{| class="wikitable"
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|+Parameter(s)
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|+Control variables
 
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|Name
 
|Name
 
|Symbol
 
|Symbol
 
|Value
 
|Value
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|Unit
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|Interval
 
|-
 
|-
−
|Parameter
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|Initial molar number 1
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|<math>p</math>
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|<math>n_{a1}</math>
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|23
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|[0.4,9.0]
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|[-]
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|-
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|Initial molar number 2
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|<math>n_{a2}</math>
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|[0.4,9.0]
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|-
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|Initial molar number 3
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|<math>n_{a3}</math>
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|[0.4,9.0]
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|-
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|Concentration of the catalyst
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|<math>c_{kat}</math>
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|[0.0,6.0]
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|-
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|Initial molar number 1
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|<math>\vartheta(t)</math>
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|[20.0,100.0]
 
|}
 
|}
  

Revision as of 12:05, 4 December 2015

This page can now be filled with content.


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) = n_{a1}
Molar number 2 n_2(t) n_2(t_0) = n_{a2}
Molar number 3 n_3(t) n_3(t_0) = n_{a3}
Parameters
Name Symbol Value
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


Control variables
Name Symbol Value Interval
Initial molar number 1 n_{a1} [0.4,9.0]
Initial molar number 2 n_{a2} [0.4,9.0]
Initial molar number 3 n_{a3} [0.4,9.0]
Concentration of the catalyst c_{kat} [0.0,6.0]
Initial molar number 1 \vartheta(t) [20.0,100.0]

Parameters

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