17) MATLAB solution to Calculate Concentration, Pressure Drop, and Reaction Rate in PBR

In this video, I show you how to calculate and plot the concentration, pressure drop and reaction rate in a packed bed reactor (PBR) with MATLAB. This is example problem 4-6 in Elements of Chemical Reaction Engineering, Fogler, 4th ed. The entire solution is in the book along with details of how to solve the equations in Polymath.

First part of video is the problem setup.
(16:00) Second part of video is the MATLAB scripts used to solve the problem.
(30:00) Third part of video is how to edit MATLAB plots to make them look good.

Problem Statement: Ethylene and oxygen are fed in stoichiometric proportions to a packed-bed reactor operated isothermally at 260 C. Ethylene is fed at a rate of 0.30 lb mol/s at a pressure of 10 atm. It is proposed to use 10 banks of 1 1/2 in-diameter schedule 40 tubes packed with catalyst with 100 tubes per bank. Consequently, the molar flow rate to each tube is to be 3x10^(-4) lb mol/s. The properties of the reacting fluid are to be considered identical to those of air at this temperature and pressure. The density of the 1/4-in catalyst particles is 120 lbm/ft^3 and the bed void fraction is 0.45. The rate law is:

-r_A' = k*P_A^(1/3)*P_B^(2/3) (lb mol) / (lbm cat*h)

with:

k = 0.0141 (lb mol) / (atm*lbm cat*h) at 260 C

This problem requires solving a system of two ODEs. The differential equations that we solve are the design equation for a PBR and the equation for the pressure drop.