2. The Modeling Equations

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 volume

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.
AArea for heat exchange
CAConcentration of A in reactor
CAfConcentration of A in feed stream
cpHeat capacity (energy/mass*temperature)
FVolumetric flowrate (volume/time)
k0Pre-exponential factor (time-1)
RIdeal gas constant (energy/mol*temperature)
rRate of reaction per unit volume (mol/volume*time)
tTime
TReactor temperature
TfFeed temperature
TjJacket temperature
TrefReference temperature
UOverall heat transfer coefficient (energy/(time*area*temperature))
VReactor volume
DEActivation energy (energy/mol)
(-DH)Heat of reaction (energy/mol)
rDensity (mass/volume)



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

and



2.3 Balance on Component A

The balance on component A is

(1)

where r is the rate of reaction per unit volume.

2.4 Energy Balance

The energy balance is

(2)

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)

(1a)

(2a)

where we have assumed that the volume is constant. The reaction rate per unit volume (Arrhenius expression) is

\b(3)

where we have assumed that the reaction is first-order.