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, ie
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: Moles A remaining = N_{A} = Moles A initially  Moles A reacted
N_{A}= N_{A0}  moles A initially x (moles A reacted)/(moles A fed)
N_{A} = N_{A0}  N_{A0}X 
Flow: Rate of Moles of A leaving F_{A} = Rate of Moles of A fed  Rate of Moles of A reacted =
F_{A} = F_{A0}  F_{A0}X 
Design Equations (p. 3441)  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  Differential  Algebraic  Integral  

Batch  
CSTR  
PFR  
PBR 
Reactor Sizing (p. 4156)  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 eitheroras a function of X. Forvs. 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 (Appendix A.4)  top 
The integral to calculate the PFR volume can be evaluated using a method such as Simpson's OneThird Rule (pg 1014):

NOTE: The intervals ( ) shown in the sketch are not drawn to scale. They should be equal. 
Simpson's OneThird Rule is one of the more common numerical methods. It uses three data points. Other numerical methods (see Appendix A, pp 10091015) for evaluating integrals are:
Reactors in Series  top 
Given r_{A} as a function of conversion, one can also design any sequence of reactors:
Only valid if there are no side streams 
Consider a PFR between two CSTRs
Space Time (p. 57)  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.
Reaction 
Reactor  Temperature  Pressure atm  Space Time  
(1)  C_{2}H_{6} → C_{2}H_{4} + H_{2} 
PFR  860°C  2  1 s 
(2)  CH_{3}CH_{2}OH + HCH_{3}COOH → CH_{3}CH_{2}COOCH_{3} + H_{2}O 
CSTR  100°C  1  2 h 
(3)  Catalytic cracking  PBR  490°C  20  1 s < τ < 400 s 
(4)  C_{6}H_{5}CH_{2}CH_{3} → C_{6}H_{5}CH = CH_{2} + H_{2}  PBR  600°C  1  0.2 s 
(5)  CO + H_{2}O → CO_{2} + H_{2}  PBR  300°C  26  4.5 s 
(6)  C_{6}H_{6} + HNO_{3} → C_{6}H_{5}NO_{2} + H_{2}O  CSTR  50°C  1  20 min 
Useful Links  top 
^{*} All chapter references are for the 4th Edition of the text Elements of Chemical Reaction Engineering.