1. Conversion and Reactor sizing
Chapter 2
Conversion and Reactor sizing

2. Overview
In the first chapter the general mole balance was derived for different reactors
In this chapter, these equations are used to size CSTR and PFR using “Conversion”
Value and overall conversion of CSTR and PFR arranged in series

3. 2.1 Definition of Conversion
Conversion is the number of moles of reactant A (limiting reactant) that has been reacted per mole of A fed to the system
For irreversible XA=1 complete conversion
For reversible Xmax=Xe equilibrium conversion

4. 2.2 Batch Reactor Design Equation
After time t, the number of moles of A remaining is
differential form
Batch reactor design equation used for reaction rate data analysis
Integral form
This equation gives the time required to achieve a specified conversion X
The longer the reactants are left in the reactor, the greater the conversion

5. 2.3 Design equation for flow reactor
Mole balance for reactant A around the reactor
In liquid phase CA0 is the solution molarity (moles/volume)
In gas phase

6. CSTR The mole balance for CSTR yields
This equation calculates the CSTR volume necessary to achieve a specified conversion X
Because of perfect mixing, the exit conc is identical to the conc inside the reactor and the reaction rate is evaluated at the exit conditions
FA0 FA

7. Levenspiel CSTR Plot
Volume =
Area of rectangle

8. 2.3.2 Tubular Flow Reactor (PFR)
No gradient change in T, CA & -Ra
The reactants are consumed as they enter and flow axially down the reactor
Differential form of design for PFR
Integral form
used to calculate volume required to achieve specified conversion X

9. Levenspiel PFR Plot
Volume=
area under the curve

10. 2.3.3 Packed Bed Reactor Packed bed reactors are analogous to PFR
Differential form of the design equation used to analyze the reactor pressure drop
Integral form used to determine the catalyst weight in the absence of pressure drop

11. Applications of the design equations
We can size the reactor from the reaction rate, as a function of conversion
For the first order
For irreversible reactions of greater than zero order
For reversible reactions

13. 2.5 Reactors in series
For reactors in series where no side stream either fed or withdrawn, the conversion at point i is defined as
The molar flow rate at point i is given by
FA0
FA1
FA2
FA3
i=1 X1
i=2 X2
i=3 X3

14. 2.5.1 CSTR in Series For 2 CSTR in series FA0 i=1 X1 FA1 -rA1 i=2 FA2

15. Levenspiel CSTR Plot
Volume
of CSTR2
Volume
of CSTR1
For the same overall conversion, the total volume for 2 CSTRs in series is less than that required for one CSTR

16. CSTR and PFR Comparison
PFR can be modeled with a large number of CSTRs in series. This concept can be used in
Catalyst decay in packed bed reactors
Transient heat effects in PFRs V5 1 2 3 4 5 V4 V1 V3 V2 1 2 3 4 5

17. Reactor Mole Balance Summary