1. http://www.pdcmachines.com/graphics/benfit_sr_3.jpg What will happen?!

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/CSTRHeatExcha ngeModel 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. T 0 = 400 K Equilibrium Point T=368.38 K C=6.3063 mol/L Stable!

8. T 0 = 300 K Equilibrium Point T=295.45 K C=9 mol/L Stable!

9. T 0 = 800 K Nodal Sink: Undesirable T 0

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