For simplicity we assume that the cooling jacket temperature can
be directly manipulated, so that an energy balance around the
jacket is not required. We also make the following assumptions
ïPerfect mixing (product stream values are the same as the
bulk reactor fluid)
ïConstant parameter values
The constant volume and parameter value assumptions can easily
be relaxed by the reader, forfurther study.
2.1 Parameters and Variables
The parameters and variables that will appear in the modeling
equations are listed below for convenience.
|A||Area for heat exchange|
|CA||Concentration of A in reactor|
|CAf||Concentration of A in feed stream|
|cp||Heat capacity (energy/mass*temperature)|
|F||Volumetric flowrate (volume/time)|
|k0||Pre-exponential factor (time-1)|
|R||Ideal gas constant (energy/mol*temperature)|
|r||Rate of reaction per unit volume (mol/volume*time)|
|U||Overall heat transfer coefficient (energy/(time*area*temperature))|
|DE||Activation energy (energy/mol)|
|(-DH)||Heat of reaction (energy/mol)|
2.2 Overall material balance
The rate of accumulation of material in the reactor is equal to
the rate of material in by flow - the
material out by flow.
Assuming a constant amount of material in the reactor (= 0), we find that
If we also assume that the density remains constant, then
2.3 Balance on Component A
The balance on component A is
where r is the rate of reaction per unit volume.
2.4 Energy Balance
The energy balance is
where Tref represents an arbitrary reference temperature for enthalpy.
2.5 State Variable form of Dynamic Equations
We can write (1) and (2) in the following state variable form
(since dV/dt = 0)
where we have assumed that the volume is constant. The reaction
rate per unit volume (Arrhenius expression) is
where we have assumed that the reaction is first-order.