1. Steady-state Nonisothermal reactor Design Part I
CSTRs with Heat Exchange.
PFRs with Heat Exchange.

2. Non Isothermal Process
Most reactions are not carried out isothermally
Focus is then on heat effects in chemical reactors
Basic design equation such as rate laws, stoichiometric relationships used for isothermal reactor design are valid for non-isothermal reactors
The major difference is method of evaluating the temperature effect
e.g. length of PFR, or heat is removed from a CSTR

3. Non Isothermal Process
So what additional information is needed to design non-isothermal reactors ?
Example: For the following reaction
A → B
Calculate the reactor volume necessary for 70% conversion
Note: The reaction is exothermic, reactor is operated adiabatically. So temperature increases with conversion down the length of reactor

4. Non Isothermal Process
Solution:
Mole Balance (design equation)
Rate Law (Arrhenius equation)
k = f(T)

5. Non Isothermal Process
Stoichiometry (liquid phase), v = vo
Combining
and cancelling the entering concentration CA0=0

6. Non Isothermal Process
The final equation
We require a relationship which relates X and T, T and V to solve the above equation
The energy balance will provide the relationship

7. Non Isothermal Process
Energy Balance
we need appropriate energy balance to relate temperature and conversion or reaction rate
For adiabatic reaction we have
So we have all equations needed to solve the conversion and temperature profile

8. The Energy Balances
We know that for a closed system, the energy balance is
For open (continuous) flow system where mass crosses the system boundaries

9. The Energy Balances
The energy balance of the case of only one species entering and leaving becomes

10. The Energy Balances
The unsteady-state energy balance for an open well-mixed system that has n species, entering and leaving the system at their respective molar flow rates Fi (moles of i per time) and their respective energy Ei (joules per mole of i)

11. The Energy Balances Evaluating work term
W is separated into flow work (W) or other work (Ws)
Ws is shaft work and produce such stirrer in CSTR or turbine in PFR
Flow work is the work necessary to get the mass into and out of the system
J/s

12. The Energy Balances
Combining the energy balance term derived earlier and work term we get
We know that
In chemical reactor these energies are often negligible as compared to enthalpy, heat transfer and work term
J/mol

13. The Energy Balances
Enthalpy in case of into and out of the system can be expressed as the sum of the net internal energy carried into (or out of) the system by mass flow plus the flow work
Combining we get
We can also write

14. The Energy Balances
Adiabatic (Q=0) CSTR, PFR, Batch or PBR. The relationship between conversion, XEB and temperature for Ws = 0, constant CPi and ∆CP = 0
For an exothermic reaction