Example: Mass Balances and Linear Algebra
Contents
4.6. Example: Mass Balances and Linear Algebra#
4.6.1. Learning Objectives#
After studying this notebook, completing the activities, and asking questions in class, you should be able to:
Solve a system of linear equations by creating a model and implementing it in matrix form in python.
Calculate results and interpret the meaning of the results.
# Import libraries
import numpy as np
import scipy.linalg as la
4.6.2. Atomic Species (Mass) Balance#
Reference: Example 4.7-1 in Elementary Principles of Chemical Process Engineering, Third Edition, Felder and Rousseau (2005)
Methane is burned with air in a continuous steady-state combustion reactor to yield a mixture of carbon monoxide, carbon dioxide, and water. The reactions taking place are:
CH\(_4\) + \(\frac{3}{2}\) O\(_2\) \(\rightarrow\) CO + 2 H\(_2\)O
CH\(_4\) + 2 O\(_2\) \(\rightarrow\) CO\(_2\) + 2 H\(_2\)O
The feed to the reactor contains 7.80 mole% CH\(_4\), 19.4% O\(_2\), and 72.8% N\(_2\). The percentage conversion of methane is 90.0%, and the gas leaving the reactor contains 8 mol CO\(_2\)/mol CO. What is the molar composition of the product stream?
Do the following using this handout:
Draw a picture
Propose a mathematical model using atomic species balances
Perform degree of freedom analysis
Convert your model to a linear system
Solve with Python
Print your answer to the screen with a reasonable number of significant digits
# Add your solution here