http://www.pdcmachines.com/graphics/benfit_sr_3.jpg

What will happen?!

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

Example: CSTR with Heat Exchange

Example from Wiki page:ODE & Excel CSTR Model w/heat exchangehttp://controls.engin.umich.edu/wiki/index.php/CSTRHeatExchangeModel

• CSTR at steady state• Exothermic reaction• Heat exchange (cooling jacket)

CSTR with Heat Exchange

V=3000 L

Differential Equations

Mass Balance:

Energy Balance:

Enter Equations in PPlane Applet

T0 = 400 K

Equilibrium PointT=368.38 KC=6.3063 mol/L

Stable!

T0 = 300 K

Equilibrium PointT=295.45 KC=9 mol/L

Stable!

T0 = 800 K

Nodal Sink:Undesirable T0

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

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!