1. ISOTHERMAL REACTOR DESIGN
ERT 316
ISOTHERMAL REACTOR DESIGN

2. OBJECTIVES Students should be able to:
Describe the algorithm that allows the reader to solve chemical reaction engineering problems through logic rather than memorization.
Size batch reactors, CSTRs, PFRs, and PBRs for isothermal operation given the rate law and feed conditions.
Account for the effects of pressure drop on conversion in packed bed tubular reactors.

3. Algorithm for Isothermal Reactor
START
END
Algorithm for Isothermal Reactor
1. The general mole equation
2. Design Equations:
Batch
CSTR
PFR
Evaluate the algebraic (CSTR) or integral (PFR) equations
3. Is –rA=f(X) given?
YES NO
4. Determine the rate law in terms of the concentration of the reacting species
5. Use Stoichiometry to express concentration as a function of conversion
Liquid phase or Gas phase
Constant Volume Batch
Constant P and T
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6. Combine steps 4 and 5 to obtain –rA=f(X)

4. 4.1 Design Algorithm for Isothermal Reactors
To design an isothermal reactors, the following sequence is
highly recommended.

5. 4.1 Design Algorithm for Isothermal Reactors
To carry out the evaluation, the following method can be used:
Graphically (Chapter 2 plot)
Numerical (Quadrature Formulas Chapter 2 and Appendix A4)
Analytical (Integral Tables)
Software (Polymath)

6. Algorithm for isothermal Reactor (PFR reactor volume
For 1st order gas-phase rxn
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7. Scale up of Batch Reactor to the design of CSTR
-pilot plant-costly
-instead-build microplant(laboratory bench scale)
-example: analyze data from a laboratory batch reactor-determine specific reaction rate, k-use it to design full-scale flow reactor

8. In order for you to use data from batch reactor-get data in terms of measured variable

9. Scale up of Batch Reactor to the design of CSTR
- Calculation of time taken to achieve a given conversion X
A  B
Step 1: Write the mole balance
Step 2: Write the rate law
Step 3: Derive concentration term from stoichiometry
Example for second order reaction

10. Scale up of Batch Reactor to the design of CSTR
- Calculation of time taken to achieve a given conversion X
A  B
Step 4: Combine equation from step 1,2,3
Step 5: Evaluate
This is the reaction time or tR

11. Algorithm to estimate reaction time
Mole Balance
Rate Law
First order
Second order
Stoichiometry
Combine
Evaluate (integrate)

12. Scale up of Batch Reactor to the design of CSTR
- Calculation of time taken to achieve a given conversion X
A  B
To reach 90% conversion in a constant-volume batch reactor scales:
if k = 10-4 s-1
For first order

13. 4.2 Design of CSTR Step 1: Write the mole balance of CSTR
Design equation for CSTR is
If volumetric flow rate does not change with the reaction, (i.e. v = v0), then
where t is the space time

14. tk is often referred to as Damköhler number (for 1st order)
4.2 Design of CSTR
Step 2: Write the rate law
For 1st order irreversible reaction,
Step 3: Derive concentration in terms of conversion (from stoichiometry)
Step 4: Combine eq from step 1,2, 3
Rearranging;
tk is often referred to as Damköhler number (for 1st order)

15. 4.2 Design of CSTR Step 2: Write the rate law
For 1st order irreversible reaction,
Step 3: Derive concentration in terms of conversion (from stoichiometry)
Step 4: Combine eq from step 1,2, 3
Rearranging;

16. Damköhler number
Is the ratio of the rate of reaction of A to the rate of convective transport of A at the entrance to the reactor.
rate of reaction at entrance
entering flow rate of A
For first order irreversible reaction;
For second order irreversible reaction;

17. How to estimate degree of conversion for a CSTR?
By using Damkohler number,
Rule of thumb
If Da  0.1, X < 0.1
If Da  10, X > 0.9
If first degree order, Da = k
If second degree order, Da =kCA0

18. 4.2 Design of CSTR (for first order)
For CSTRs in series, conversion as a function of the number of tanks in series:
For CSTRs in parallel, conversion is:
Just like a single CSTR

19. Example: Producing 200 Million Pounds per Year in a CSTR
It is desired to produce 200 million pounds per year of ethylene glycol (EG). The reactor is to be operated isothermally. A 1lb mol/ft3 solution of ethylene oxide (EO) in water is fed to the reactor shown in figure together with an equal volumetric solution of water containing 0.9 wt% of the catalyst H2SO4. The specific reaction rate constant is min-1 .
If 80% conversion is to be achieved, determine the necessary CSTR volume.
If 800-gal reactors were arranged in parallel, what is the corresponding conversion?
If 800-gal reactors were arranged in series, what is the corresponding conversion?

20. Example: Producing 200 Million Pounds per Year in a CSTR
v0VV

21. Example: Producing 200 Million Pounds per Year in a CSTR
Extract the given information:
FC = 2 x 108 lbm/yr x 1 yr/365 days x 1day/24 h x 1hr/60 min x 1lbmol/62lbm
= lbmol/min
From reaction stoichiometry,
FC = FA0X

22. Example: Producing 200 Million Pounds per Year in a CSTR
STEP 1: Design equation of CSTR
STEP 2: Rate Law
STEP 3: Stoichiometry (Liquid phase, v = v0 )
STEP 4: Combining;

23. Example: Producing 200 Million Pounds per Year in a CSTR
v0VV
Example: Producing 200 Million Pounds per Year in a CSTR
STEP 5: Evaluate
The entering volumetric flowrate of stream A, with CA01 = lb mol/ft3 before mixing is;
From the problem statement,
Thus, the total entering volumetric flow rate of liquid is
Substituting all the values to calculate volume of reactor;

24. Example: Producing 200 Million Pounds per Year in a CSTR
b) CSTR in parallel.
Rearranging the equation of volume in part a)

25. Example: Producing 200 Million Pounds per Year in a CSTR
b) CSTR in parallel.

26. Example: Producing 200 Million Pounds per Year in a CSTR
b) CSTR in series

27. 4.3 PFR
Assume no dispersion and no radial gradients in either temperature, velocity, or concentration and in the absence of pressure drop or heat exchange.
STEP 1: Write the mole balance of PFR:
STEP 2: Write the rate law
Eg: For second order,

28. 4.3 PFR STEP 3: Write concentration in terms of conversion
(from stoichiometry)
For liquid phase
For gas phase

29. 4.3 Tubular Reactor STEP 4: Combine all the equations Rearranging,
For liquid phase
For gas phase

30. Design a PFR: summary
In case of 2nd order rxn, liquid phase, isothermal
No pressure drop
mole balance
rate laws
Stoichiometry
combination
No heat exchange or
Damköhler number for 2nd-order reaction

31. Design a PFR: summary In case of 2nd order rxn, gas phase, isothermal
No pressure drop
mole balance
rate laws
Stoichiometry
combination
No heat exchange