1. ISOTHERMAL REACTOR DESIGN
PTT 255 REACTION ENGINEERING
ISOTHERMAL REACTOR DESIGN
Dr Noor Hasyierah Mohd Salleh
Department of Chemical Engineering Technology

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.

3. OUTLINE Algorithm for Isothermal Reactors
Design Structure for Isothermal Reactors
- Batch Reactor
- CSTR
- Tubular Reactor/PFR
Pressure Drop in Reactors
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4. Algorithm for Isothermal Reactors
To design an isothermal reactors, the following sequence is
highly recommended.
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)

5. Steps/Procedure to Design Isothermal Reactor
Apply mole balance and design equations of reactors – (chap 1 & 2)
Find rate law – (chap 3)
Use stoichiometry to express as a function of X – (chap 3)
Combine and evaluate to find Volume of CSTR and PFR or reaction time for batch reactor. – (chap 4)
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6. 1. The general mole equation
START
Algorithm for Isothermal Reactor
END
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
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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
6. Combine steps 4 and 5 to obtain –rA=f(X)

7. Design Structure for Isothermal Reactors
Batch Reactor
Analysis on laboratory scale batch reaction are sometimes needed in the scale up of laboratory experiments to pilot plant operation or to full scale production.
Data from batch reactor can be used as a references to determined the reaction time, t needed to achieve a conversion, x for specific reaction or sometimes to find the reaction rate constant, k and also to determine the volume, V of reactors.

8. Batch Reactor – Liquid Phase Operation
Case : Calculation of time taken, (t) to achieve a given conversion (X)
Elementary irreversible 1st order reaction
A  B
Step 1: Write the mole balance in term of x
Step 2: Write the rate law
Step 3: Derive concentration term from stoichiometry

9. Step 4: Combine equation from step 1,2,3
Step 5: Evaluate by integration
The reaction time or tR

10. Summary : Estimation of reaction time of batch reactor for first and second order
Mole Balance
Rate Law
First order
Second order
Stoichiometry
Combine
Evaluate (integrate)

11. Batch Reactor- Example
A  B
Calculate the reaction time of the above process to reach 90% conversion in a constant-volume batch reactor scales, if k = 10-4 s-1.
For first order

12. Design Structure for CSTR
CSTR can be used for liquid and gas phase reaction but are typically used for liquid-phase reaction
Thus CSTR Design covered in this part consists of :
-1st order liquid phase Irreversible reaction
-2nd order liquid phase Irreversible reaction

13. Damköhler number
Damkohler number (Da) 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
Damkohler number (Da) gives a quick estimation of the degree of conversion in CSTR

14. Damköhler number For 1st order irreversible reaction;
For 2nd order irreversible reaction;
Rule of thumb to estimate degree of conversion :
If Da  0.1,  X < 0.1
If Da  10,  X > 0.9

15. CSTR – Liquid Phase Operation
A  B
Step 1: Write the mole balance in term of x
In term of space time, τ = V/ v0
Elementary irreversible 1st order reaction

16. tk is often referred to as Damköhler number
Step 2: Write the rate law
Step 3: Derive concentration term from stoichiometry
*Liquid phase: constant volume : v = v0
Step 4: Combine equation from step 1,2,3
Rearrange :
tk is often referred to as Damköhler number
(for 1st order)

17. Step 5: Evaluate – Several parameters can be evaluate based on derived equations . For examples:
Space time (τ)
Conversion (X)
Exit concentration (CA)

18. CSTR – Liquid Phase Operation
2A  B
Step 1: Write the mole balance in term of x
In term of space time, τ = V/ v0
Elementary irreversible 2nd order reaction

19. tkCA0 is often referred to as Damköhler number
Step 2: Write the rate law
Step 3: Derive concentration term from stoichiometry
*Liquid phase: constant volume : v = v0
Step 4: Combine equation from step 1,2,3
tkCA0 is often referred to as Damköhler number
(for 2nd order)

20. Step 5 : Evaluate Space time (τ): Conversion (X): Da number
*negative sign must be chosen because X cannot be greater than 1

21. CSTR Design (Gas phase)
Example:
2A  B
Step 1: Write the mole balance in term of x
Step 2: Write the rate law
Elementary irreversible 2nd order reaction

22. Isothermal & no pressure drop
Step 3: Write concentration in terms of conversion
(from stoichiometry)
Step 4 : Combine all the equations
For gas phase
v v0
Isothermal & no pressure drop

23. Exercise 1 Example: The elementary liquid phase reaction 2A  B
is carried out isothermally in a CSTR. Pure A enters at a volumetric flow rate of 25 dm3/s and at a concentration of 0.2 mol/dm3. What CSTR volume is necessary to achieve a 90% conversion when k = 10 dm3/(mol*s)?
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24. Design Structure for PFR
Gas and liquid phase reactions generally carried out in tubular reactors.
Assume no dispersion and no radial gradients in either temperature, velocity, or concentration and in the absence of pressure drop or heat exchange.
Thus PFR Design considers on:
-1st order liquid phase Irreversible reaction
-1st order gas phase Irreversible reaction
-2nd order liquid phase Irreversible reaction
-2nd order gas phase Irreversible reaction

25. Elementary irreversible 2nd order reaction
PFR Design
Example:
2A  B
Step 1: Write the mole balance in term of x
Step 2: Write the rate law
Elementary irreversible 2nd order reaction

26. Isothermal & no pressure drop
Step 3: Write concentration in terms of conversion
(from stoichiometry)
Step 4 : Combine all the equations
Rearrange
For liquid phase
v = v0
For gas phase
v v0
Isothermal & no pressure drop
For liquid phase
v = v0

27. Step 4 :continue
For gas phase
v v0

28. Pressure Drop in Reactors
In liquid-phase reactions, the concentration of reactants is insignificantly affected by even relatively large changes in total pressure.
Thus, the effect of pressure drop on the rate of reaction can totally be ignored in liquid-phase reactor sizing.
However in a gas-phase reactions, the concentration of the reacting species is proportional to the total pressure.
This fact is especially true in micro reactors packed with solid catalyst (PBR) whereas the channels are so small that pressure drop can limit the throughput and conversion for gas-phase reactions.
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29. PBR Design Presence of Pressure Drop
Example: 2A  B + C A gas phase reaction is being carried out in a PBR with pressure drop existence.
Elementary irreversible 2nd order reaction
Step 1: Write the mole balance in term of x
Step 2: Write the rate law
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30. Step 3: Write concentration in terms of conversion
(from stoichiometry)
Step 4 : Combine all the equations
Before evaluation (step 5),we now need to relate the pressure drop to the catalyst weight (W) in order to determine the conversion (X) as a function of W
Isothermal
T = T0
Pressure drop exist
P P0
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31. Ergun equation for single reaction
The majority of gas phase reaction are catalyzed by passing the reactant through a packed bed of catalyst particles
Ergun equation for single reaction
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32. For isothermal operation, we have two sets of equation with two unknowns, X & P
Special case: if ε=0, an analytical solution to Eq.2 is obtained as follows
(Eq.1)
(Eq.2)
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Used only when ε=0
(Eq.3)

33. Step 5 : Evaluate by integration
Combine Eq. 1 and Eq.3
Step 5 : Evaluate by integration
Rearrange to obtain conversion (X) and catalyst weight (W).
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34. For gas phase reactions, as the pressure drop increases, the concentration decreases, resulting in a decreased rate of reaction, hence a lower conversion when compared to a reactor without a pressure drop
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35. Thank You
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