Batch Systems with Heat Effects Example  top 
Balance on a system volume that is wellmixed:
Adiabatic batch reactor with no work:
The following reaction occurs in a batch reactor:
1) 

2) 

3) 

4) 

5) 

6) 

7) 
Parameter Values 
Adiabatic Reaction


or use one of the integration formulas, e.g.: , to find the reaction time, t. Even better, use Polymath. 
Cooling:
Control of Chemical Reactors  top 
Unsteady State CSTR: 
For a batch reactor, F_{AO} = 0 
For the reaction in a CSTR: 

Linearized Stability Theory  top 
Energy Balance (Applied to a CSTR)  
1. 

2. 

3. 

4. 

CSTR Mole Balance 

5. 

6. 

Manipulating the Energy and Mole Balances 

Let andsignify steady state values. Then at steady state: 

7. 

Adding equations (6) and (7): 

8. 

Linearizingby expanding it in a Taylor Series: 

To obtain: 

9. 

10. 
Let 
11. 

12. 

13. 

Using these substitutions, we can arrive at the following equations that describe the behavior of temperature and concentration, when the steady state conditions are perturbed in a CSTR: 

14. 

15. 

16. 

17. 

18. 

19. 

20. 

21. 

22. 
Predicting the Behavior of a CSTR using LST  top 
At time t = 0, y_{1} = y_{10}, where:
Making use of Equation 20
we notice that for the case of b^{2} = 4c:
if b < 0 , then the amplitude (i.e., T  T_{S}) will increase
if b > 0 , then the amplitude (i.e., T  T_{S}) will decrease
and that:
if b^{2} > 4c , thenis real (i.e., nonoscillatory behavior)
if b^{2} < 4c , thenis imaginary (i.e., oscillatory behavior)


Reference: 
^{*} All chapter references are for the 4th Edition of the text Elements of Chemical Reaction Engineering .