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Phase Plane Analysis Application: CSTR with Heat Exchange

Phase Plane Analysis Application: CSTR with Heat Exchange. What will happen?!. http://www.pdcmachines.com/graphics/benfit_sr_3.jpg. Phase Plane Analysis. Phase Plane Analysis can be used to find stable states in a system

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Phase Plane Analysis Application: CSTR with Heat Exchange

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  1. Phase Plane Analysis Application: CSTR with Heat Exchange What will happen?! http://www.pdcmachines.com/graphics/benfit_sr_3.jpg

  2. Phase Plane Analysis • Phase Plane Analysis can be used to find stable states in a system • Phase Planes can be used to see the effects of changing system parameters http://controls.engin.umich.edu/wiki/index.php/Image:Spirals.JPG

  3. Example: CSTR with Heat Exchange Example from Wiki page: ODE & Excel CSTR Model w/heat exchange http://controls.engin.umich.edu/wiki/index.php/CSTRHeatExchangeModel • CSTR at steady state • Exothermic reaction • Heat exchange (cooling jacket)

  4. CSTR with Heat Exchange V=3000 L

  5. Differential Equations Mass Balance: Energy Balance:

  6. Enter Equations in PPlane Applet

  7. T0 = 400 K Equilibrium Point T=368.38 K C=6.3063 mol/L Stable!

  8. T0 = 300 K Equilibrium Point T=295.45 K C=9 mol/L Stable!

  9. T0 = 800 K Nodal Sink: Undesirable T0

  10. Phase Plane Analysis Application • Use PPlane to create phase planes • Phase Planes can be used to determine stability and the number of stable states • Phase plane analysis is useful for choosing operating parameters

  11. Phase plane analysis rocks! http://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Chemical_reactor_CSTR_AISI_316.JPG/800px-Chemical_reactor_CSTR_AISI_316.JPG

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