Chapter 2: Conversion and Reactor Sizing

Topics

1. Conversion
2. Design Equations
3. Reactor Sizing
4. Numerical Evaluation of Integrals
5. Reactors in Series
6. Space Time
7. Useful Links

Conversion	top

Consider the general equation

The basis of calculation is always the limiting reactant. We will choose A as our basis of calculation and divide through by the stoichiometric coefficient to put everything on the basis of "per mole of A".

The conversion X of species A in a reaction is equal to the number of moles of A reacted per mole of A fed.

Batch	Flow

What is the maximum value of conversion?

    For irreversible reactions, the maximum value of conversion, X, is that for complete conversion, i.e. X=1.0.

    For reversible reactions, the maximum value of conversion, X, is the equilibrium conversion, i.e. X=X_e.

Batch	Flow
Moles A remaining = NA = Moles A initially - Moles A reacted	Rate of Moles of A leaving FA = Rate of Moles of A fed - Rate of Moles of A reacted
NA= NA0 - moles A initially * (moles A reacted)/(moles A fed)	FA= FA0 - Rate of moles A fed * (moles A reacted)/(moles A fed)

Design Equations	top

The design equations presented in Chapter 1 can also be written in terms of conversion. The following design equations are for single reactions only. Design equations for multiple reactions will be discussed later.

Reactor Mole Balances in Terms of Conversion (Click on Reactor to see picture)

Reactor	Differential	Algebraic	Integral
Batch
CSTR
PFR
PBR

Reactor Sizing	top

By sizing a chemical reactor we mean we're either detering the reactor volume to achieve a given conversion or determine the conversion that can be achieved in a given reactor type and size. Here we will assume that we will be given -r_A= f(X) and F_A0. In chapter 3 we show how to find -r_A= f(X).

Given -r_A as a function of conversion,-r_A=f(X), one can size any type of reactor. We do this by constructing a Levenspiel plot. Here we plot either or as a function of X. For vs. X, the volume of a CSTR and the volume of a PFR can be represented as the shaded areas in the Levenspiel Plots shown below:

Numerical Evaluation of Integrals	top

The integral to calculate the PFR volume can be evaluated using a method such as Simpson's One-Third Rule:

NOTE: The intervals ( ) shown in the sketch are not drawn to scale. They should be equal.

Simpson's One-Third Rule (above) is one of the more common numerical methods. It uses three data points. Other numerical methods (see Appendix A) for evaluating integrals are:

1. Trapezoidal Rule (uses two data points)
2. Simpson's Three-Eighth's Rule (uses four data points)
3. Five-Point Quadrature Formula

Reactors in Series	top

Given -r_A as a function of conversion, one can also design any sequence of reactors by defining the total conversion up to a point "i":

Only valid if there are no side streams

Consider a PFR between two CSTRs

Space Time	top

The Space time, tau, is obtained by dividing the reactor volume by the volumetric flow rate entering the reactor:

Space time is the time necessary to process one volume of reactor fluid at the entrance conditions. This is the time it takes for the amount of fluid that takes up the entire volume of the reactor to either completely enter or completely exit the reactor.

Sample Industrial Space Times

	Reaction	Reactor	Temperature	Pressure atm	Space Time
(1)	C2H6 → C2H4 + H2	PFR	860°C	2	1 s
(2)	CH3CH2OH + HCH3COOH → CH3CH2COOCH3 + H2O	CSTR	100°C	1	2 h
(3)	Catalytic cracking	PBR	490°C	20	1 s < τ < 400 s
(4)	C6H5CH2CH3 → C6H5CH = CH2 + H2	PBR	600°C	1	0.2 s
(5)	CO + H2O → CO2 + H2	PBR	300°C	26	4.5 s
(6)	C6H6 + HNO3 → C6H5NO2 + H2O	CSTR	50°C	1	20 min

Useful Links	top

 

^* All chapter references are for the 1st Edition of the text Essentials of Chemical Reaction Engineering.

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