The University of Texas at Austin
College of Engineering

Plug Flow Reactor Problem

THE DESIGN EQUATION FOR A PFR

is written for each component and the set of ODE's is solved subject to the initial condition.  The rate of production of each component is

which reduces to the following for a single reaction:

THE PROBLEM STATEMENT

The thermal cracking of propane

 

is first order in the concentration of C3H8.   The reaction will be conducted in an isothermal PFR at 800°C and at a constant pressure of 1 atm.  At 800°C the rate constant is 4.1 sec-1.  The feed contains a steam diluent (3 moles of steam fed per mole of propane fed.)
    Since this problem involves a single reaction, the set of ODE's can be reduced to one ODE.  For a gas phase problem we express component concentration using an equation of state for the total concentration and multiply it by the mole fractions.   The mole fractions are related to the molar flows and all molar flows can be expressed in terms of one component.  For this specific example we find:

where p designates propane and for which the mole fraction of propane

is dependent on the initial conditions and the amount of steam diluent.  To determine the reactor volume needed to produce 300 million pounds of ethylene per year that operates at a propane conversion of 95%, integrate the following.  (Np,f = 0.358 lb-moles/sec)  The answer is 1,730 ft3. 

You need to recognize that the single ODE was dependent on the initial stoichiometry and on the amount of diluent.  If these process parameters change, the ODE may change.   Modifying the ODE is straight forward and could be done in a cumbersome way to explore the effect of changing the process conditions.  A more efficient approach and a more appealing method is to solve the set of ODE's and follow the changes in the molar flowrates of all the components.  This enables you to find the volume for any conversion of propane and for any set of initial conditions.  Such an approach employs numerical techniques to solve the set of ODE's.

THE QUESTIONS

  1. Examine the reference case that was generated for the initial conditions listed above and notice how the molar flowrates of each component change along the length (increasing volume) of the reactor.   How many dependent variables are there and what are their initial values?  Why are the flowrates of methane and ethylene identical?

  2. Why does the molar flowrate remain constant yet the mole fraction changes?

  3. Run the program to increase and decrease the amount of steam diluent and examine the changes this makes to the molar flowrate of propane.   Provide a justification for the effect you observe.