chbe2120spring2011hw3

chbe2120spring2011hw3 - ChBE 2120 Homework 3 Due: Friday,...

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ChBE 2120 Homework 3 Due: Friday, February 4 at 8:05 AM Part 1 : Adapted from Felder and Rousseau, problem 4.37: Ethylene oxide is produced by the catalytic oxidation of ethylene: 2C 2 H 4 + O 2 Æ 2C 2 H 4 O An undesired competing reaction is the combustion of ethylene: C 2 H 4 + 3O 2 Æ 2CO 2 + 2H 2 O The feed to the reactor ( not the fresh feed to the process) contains 3 moles of ethylene per mole of oxygen. The single-pass conversion of ethylene is 20%, and for every 100 moles of ethylene consumed in the reactor, 90 moles of ethylene oxide emerges in the reactor products. A multiple-unit process is used to separate the products: ethylene and oxygen are recycled to the reactor, ethylene oxide is sold as a product, and carbon dioxide and water are discarded. We will assume a basis of 100 mol/h total feed to the reactor. Using the fact that the reactor feed is 3 parts ethylene per mole of oxygen, we immediately know that the feed to the reactor on a 100 mol/h basis would be 75 mol/h of ethylene and 25 mol/h of oxygen. The following diagram reflects this process. separator (1) Write species balances on the mixing point, atomic species balances on the reactor, and two more equations in order to yield a system of seven equations and seven unknowns. (2) Cast this system of equations into matrix format Ax = b , where x is a vector containing the 7 unknowns: n 1 : molar flow of ethylene from the reactor n 2 : molar flow of molecular oxygen from the reactor n 3 : molar flow of ethylene oxide from the reactor n 4 : molar flow of carbon dioxide from the reactor n 5 : molar flow of water from the reactor n C2H4 : molar flow of process feed of ethylene n O2 : molar flow of process feed of oxygen
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(3) Solve for the vector of unknowns, x , in MATLAB using your Gaussian elimination code that includes pivoting, from the previous homework assignment (or use the code supplied along with this homework). This means that the order of the equations you use should not impact the results that you get. Make sure to submit with your homework the file you are using for this Gaussian elimination function, naming it as
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chbe2120spring2011hw3 - ChBE 2120 Homework 3 Due: Friday,...

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