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Appendix A- Van der Vusse CSTR Equations and Parameters

The state-space model employed in this study is taken from [Chen et al.(1995)Chen, Kremling, and Allgöwer].



\( \frac{dC_{A}}{dt}=\frac{\dot{V}}{V_{R}}(C_{AO}-C_{A})-k_{1}(\upsilon )C_{A}-k_{3}(\upsilon )C_{A}^{2} \)
\( \frac{dC_{B}}{dt}=-\frac{\dot{V}}{V_{R}}C_{B}+k_{1}(\upsilon )C_{A}-k_{2}(\upsilon )C_{B} \)
\( \frac{d\upsilon }{dt}=\frac{\dot{V}}{V_{R}}(\upsilon _{O}-\upsilon )+\frac{k_{w}A_{R}}{\rho C_{p}V_{R}}\left( \upsilon -\upsilon _{K}\right) \)
  \( -\frac{1}{\rho C_{p}}\left( k_{1}C_{A}\Delta H_{RAB}+k_{2}C_{B}\Delta H_{RBC}+k_{3}C_{A}^{2}\Delta H_{RAD}\right) \)
\( \frac{d\upsilon _{K}}{dt}=\frac{1}{m_{K}C_{PK}}\left( F_{K}C_{PK}(\nu _{ko}-\nu _{K})+k_{w}A_{R}\left( \upsilon -\upsilon _{K}\right) \right) \)
   \( k_{i}(\nu )=k_{io}e^{\left( \frac{E_{i}}{\upsilon +273.15}\right) } \)



The model parameters are detailed below.



\( k_{1}o=1.287\cdot 10^{12}h^{-1} \) E1=-9758.3K
\( k_{2}o=1.287\cdot 10^{12}h^{-1} \) E2=-9758.3K
\( k_{3}o=9.043\cdot 10^{9}\frac{1}{mol\, A\, h} \) E3=-8560K
\( \Delta H_{RAB}=4.2{{kJ}\over {mol\, A}} \) \( \rho =0.9342\cdot 10^{-4}{{kg}\over l} \)
\( \Delta H_{RBC}=-11{{kJ}\over {mol\, A}} \) \( C_{P}=3.01{{kJ}\over {kg\, K}} \)
\( \Delta H_{RAD}=-41.85{{kJ}\over {mol\, A}} \) \( C_{PK}=2.0{{kJ}\over {kg\, K}} \)
\( k_{w}=4032{{kJ}\over {h\, m^{2}\, K}} \) \( m_{k}=5.0\, kg \)
\( A_{R}=0.215\, m^{2} \) \( V_{R}=0.1\, m^{3} \)
\( F_{KC}=10.52{{kg}\over {h}} \)  




Edward Price Gatzke
1999-07-12