Applied Numerical Methods in Chemical Engineering
Using Python
Zulfan Adi Putra, PDEng, PEng
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Outline
q Resources and Introduction to Python
q Python Basics: Conditionals, Functions, Loops, Arrays, Generate Plots, Solve Equations
q Linear Algebra
q Ordinary Differential Equations
q Partial Differential Equations
q Data Regression and Curve Fitting
q Machine Learning
q Optimization
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Python Resources
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Installation through Anaconda
• https://www.anaconda.com/products/individual
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Python Important Libraries
• Numpy (www.numpy.org) – array operation library
• Scipy (www.scipy.org) – scientific algorithm library that uses numpy
• Matplotlib (www.matplotlib.org) – provides the pyplot and pylab
plotting libraries
• Pandas (http://pandas.pydata.org/) – easy to use data structures and
data analysis tools
• Scikit-learn (https://scikit-learn.org/) – machine learning in python
• Xgboost (https://xgboost.readthedocs.io/en/latest/index.html) –
eXtreme Gradient Boosting algorithm, winning algorithm for Kagel
data science competitions in recent years
• Sympy (www.sympy.org) – symbolic mathematics library (optional)
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1st Aid
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Youtube Intro for Beginners in Python
• https://www.youtube.com/watch?v=rfscVS0vtbw&t=4669s
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Other Helps
1
2
3
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Python Basics
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Spyder
Working
directory
Working folder
address
Tab file
Created variables.
Run (F5), then check your
variables here
Console
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All files
available in
the working
folder
Python Programming Basics
• https://apmonitor.com/che263/index.php/Main/PythonBasics
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Some Basics
(not to memorize, but you’ll see them when you make any error)
• Case-sensitive
• Indentation-sensitive
• Numbering starts from 0
• Code and run line by line for easier debugging. Use “print()” to check
• Use comment “#” often
•…
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Some Basics: Data plotting using numpy and matplotlib
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Another Example
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Some Basics: simple calculation
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Some Basics: For loop
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Some Basics: While loop
• “while” loop
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Some Basics: Range()
• “range()” function
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Some Basics: Define function
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Some Basics: Function + IF-Else
sqrt() is a built-in
function within “math”
package
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Some Basics: Function + If-Else + While
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Linear Algebra
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https://docs.scipy.org/doc/scipy/reference/tutorial/linalg.html
Linear Algebra
x + 3y + 5z = 10
2x + 5y + z = 8
2x + 3y + 8z = 3
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1
2

 2
3
5
3
5   x  10 
1   y    8 
8   z   3 
 x  1
 y   2
  
 z   2
3
5
3
5
1 
8 
1
10 
8 
 
 3 
Linear Algebra with Gekko
3x + 2y = 1
x + 2y = 0
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Solving Ordinary Differential
Equations (ODE) with Python
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Runge Kutta method
• https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods
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Pressure Profile In A Vessel
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Zombie Population
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https://scipycookbook.readthedocs.io/items/Zombie
_Apocalypse_ODEINT.html
Zombie Population: Vary initial conditions
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Results
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SEIR model = ODE + Curve Fitting for Parameter Optimization
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Define necessary parameters
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Define more parameters
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Define functions
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Data fitting with data to obtain model parameters
Results:
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Using obtained model parameters to predict the trend
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Extending the prediction
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Further predictions
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Solving Partial Differential
Equations (PDE) with Python
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Partial Differential Equation
North
West
East
South
coeff = 2*(h2k2+1)
h2k2 = (h/k)2
h and k are steps in the integration
Centered Finite Different Approximation
 coeff  ci , j  ci 1, j  ci 1, j  h 2k 2ci , j 1  ci , j 1   0
 coeff  node  East  West  h 2k 2North  South   0
 ci , j 
c 
 i 1, j 
1 1 h 2k 2 h 2k 2 ci 1, j   0
c 
 i , j 1 
ci , j 1 
Linear Algebra:
Ax = b
 coeff
Node = j*(M+1) + i, with M = 15, N = 15
node = 255
node = 240
i=0
j=N
i=M
j=N
i=0
j=0
i=M
j=0
node = 16
node = 1
node = 2
node = 3
node = 15
The Code
node definition for:
ci,j --> current node
ci+1, j --> east node
ci-1, j --> west node
ci,j+1 --> north node
ci,j-1 --> south node
C = 0 or matrix b = 0 in all
sides, except at i = 0 (west)
 coeff  ci , j  ci 1, j  ci 1, j  h 2k 2ci , j 1  ci , j 1   0
0
 coeff  node  East  West  h 2k 2 North  South   0
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Linear Regression with Python
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Linear Regression with Polyfit and Linregress
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Regressions with Gekko
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Machine Learning with Python
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Black Box Machine Learning
Independent
variables, e.g.
P, T, F
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ML
Dependent
variables, e.g.
Machine Learning using NN (DME case)
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Print and plot results
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Machine Learning Using XGBoost (DME case)
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Optimization with Python
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Optimization and Root Finding
General Formulation for Optimization:
min
f x, y, z 
subject
to :
hi  x , y , z   0
g j x, y, z   0
x R
y   0 ,1 
z  I
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Optimization and Root Finding
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https://docs.scipy.org/doc/scipy/reference/tutorial/optimize.html
Optimization with Gekko https://gekko.readthedocs.io/en/latest/quick_start.html
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Linear Programming with linprog
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https://realpython.com/linear-programming-python/
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Linear Programming
“linprog” package ONLY receives general optimization formulation
Later, change x1 bound to below:
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Project Scheduling with MIP
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Dummy example
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Model
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Coding the model in Python (1)
Data input
Variables declaration
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Coding the model in Python (2)
General model
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Coding the model in Python (3)
Users’ manual constraint
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Coding the model in Python (4)
solving and printing results
write the model for checking
IMPORTANT!
This code can NOT be
included prior to the solve
code above
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MIP result
the model built is
saved here
the model
built
results printed
here
Project Scheduling Result
Case 1: No MAX total cost constraint
Case 2: MAX total cost until time 2 (3 period) is 15
Case 2a: MAX total cost until time 2 (3 period) is 15 AND forcing Project 1 to start earlier
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Non Linear Optimization (unconstrained)
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Non Linear Optimization (Constrained)
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Run and print the result
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Stochastic Optimization (1)
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Stochastic Optimization (2)
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available solvers are:
1. shgo,
2. dual_annealing,
3. differential_evolution,
4. basinhopping
Monte Carlo Simulation
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Monte Carlo Simulation with Machine Learning model
(checking inherent randomness in machine learning)
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Monte Carlo simulation loop
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