Collection-Of-Numerical-Methods-In-ChE

This repository contains a collection of representative problems in chemical engineering solved using numerical methods with Python.
The problems are based on the document:
"A COLLECTION OF REPRESENTATIVE PROBLEMS IN CHEMICAL ENGINEERING FOR SOLUTION BY NUMERICAL METHODS"
This project aims to provide a practical learning resource for applying computational techniques to chemical engineering challenges.

List of Problems

How to Use This Repository

The repository is organized as follows:

• Main_Document/: Contains the original PDF file of the complete problem set.
• Problem_X/ (e.g., Problem_1/): Each problem is stored in a separate folder containing:
  • solution.py: The Python code solving the problem.
  • Problem_X.pdf: The specific problem statement extracted from the main document.

Steps to Explore:

1. Browse through the Main_Document/ folder to view the full problem set.
2. Navigate to the corresponding Problem_X/ folder to access:
   • Python solution (solution.py).
   • The problem statement (Problem_X.pdf).
3. Run the Python scripts locally to explore the solutions.

Installation

1. Clone the repository:

   git clone https://github.com/sajjad-zeinali/Collection-Of-Numerical-Methods-In-ChE.git
   
   

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Problem 1: Molar Volume and Compressibility Factor

Calculate the molar volume and compressibility factor of ammonia at different pressures and temperatures using the van der Waals equation.

Results:

• (a) At P = 56 atm and T = 450 K:

  • Molar volume (V) = 0.5749 L/mol
  • Compressibility factor (Z) = 0.8718

• (b) At different reduced pressures (Pr):

  • Pr = 1 → V = 0.2335 L/mol, Z = 0.7038
  • Pr = 2 → V = 0.0773 L/mol, Z = 0.4658
  • Pr = 4 → V = 0.0607 L/mol, Z = 0.7313
  • Pr = 10 → V = 0.0509 L/mol, Z = 1.5334
  • Pr = 20 → V = 0.0462 L/mol, Z = 2.7835

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Problem 2: Steady State Material Balances on a Separation Train

Solve the system of linear equations to determine the molar flow rates and compositions in a distillation separation train.

Results:

• (a) Molar flow rates of streams:

  • D1 = 24.5152 mol/min
  • D2 = 19.1136 mol/min
  • B1 = 5.7248 mol/min
  • B2 = 20.3601 mol/min

• (b) Molar flow rates of streams:

  • D = 30.2401 mol/min
  • B = 39.4737 mol/min

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Problem 3: Vapor Pressure Data Representation by Polynomials and Equations

Use various regression methods to model vapor pressure data for benzene versus temperature using polynomials, the Clausius-Clapeyron equation, and the Antoine equation.

Results:

• (a) Polynomial fit (degree 3):

  • R² = 0.9996

• (b) Linear fit (Clausius-Clapeyron equation):

  • R² = 0.9915

• (c) Model fit (Antoine equation):

  • R² = 0.9997

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Problem 4: Reaction Equilibrium for Multiple Gas Phase Reactions

Solve the system of nonlinear algebraic equations for a gas-phase batch reactor at equilibrium, considering multiple reactions with known equilibrium constants.

Results:

• Concentrations at equilibrium:

  • CA = 0.421 mol/L
  • CB = 0.243 mol/L
  • CC = 0.154 mol/L
  • CD = 0.705 mol/L
  • CX = 0.178 mol/L
  • CY = 0.552 mol/L
  • CZ = 0.374 mol/L

• Equilibrium constants:

  • KC1 = 1.06
  • KC2 = 2.63
  • KC3 = 5.00

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Problem 5: Terminal Velocity of Falling Particles

Calculate the terminal velocity of coal particles falling in water under the influence of gravity and centrifugal acceleration.

Results:

• Terminal velocity for gravity 9.81 m/s²:

  • vt = 0.015787 m/s

• Terminal velocity for gravity 294.20 m/s² (centrifugal separator):

  • vt = 0.206023 m/s

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Problem 6: Heat Exchange in a Series of Tanks

This problem involves solving simultaneous first-order ordinary differential equations for a series of three tanks used to preheat an oil solution. The tanks are heated by steam, and the goal is to determine the steady-state temperatures and the time required for the third tank to reach 99% of its steady-state value during startup.

Results:

• Steady-state temperature for T3:

  • T3 = 51.29 °C

• Time for T3 to reach 99% of steady-state value:

  • 6.26 minutes

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Problem 7: Diffusion with Chemical Reaction in a One Dimensional Slab

This problem involves numerically solving a second-order ordinary differential equation for the diffusion and simultaneous first-order irreversible chemical reaction in a one-dimensional slab. The solution utilizes an ODE solver with a shooting technique and compares the numerical results with the analytical solution for concentration profiles.

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Problem 8: Binary Batch Distillation

This problem involves calculating the amount of liquid remaining in a still during the batch distillation of a benzene (component 1) and toluene (component 2) mixture. Initially, there are 100 moles of liquid in the still, consisting of 60% benzene and 40% toluene by mole fraction. The goal is to determine the remaining liquid when the toluene concentration reaches 80% at a pressure of 1.2 atm.

Results:

• Initial temperature:

  • 95.59 °C

• Final temperature:

  • 108.57 °C

• Remaining liquid at x2 = 0.8:

  • 14.06 moles

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Problem 9: Reversible, Exothermic, Gas Phase Reaction in a Catalytic Reactor

This problem involves the design of a packed bed reactor for a first-order reversible gas-phase reaction with a pressure drop along the reactor length. The reaction occurs in the presence of a heat exchanger, and the system follows plug flow assumptions. The goal is to analyze conversion, pressure, temperature, and concentration profiles along the reactor.

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Problem 10: Dynamics of a Heated Tank with PI Temperature Control

This problem simulates the dynamics of a heated tank with a PI temperature controller. The system consists of a well-stirred tank, a heater, and a temperature controller. The objective is to maintain the tank's temperature at a set point despite disturbances in the inlet temperature.

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✨ Feel free to contribute, explore, or suggest improvements to make this repository even better! ✨

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