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# MEng Chemical Engineering / Course details

Year of entry: 2021

## Course unit details:Chemical Engineering Optimisation

Unit code CHEN20051 10 Level 2 Semester 1 Department of Chemical Engineering & Analytical Science No

### Overview

Chapter 1: Introduction to Chemical Engineering Optimisation

• Scope and hierarchy of engineering optimisation
• Types of mathematical models in chemical engineering
• Types of optimisation (programming) problems

Chapter 2: Construction of Mathematical Models

• Formulation of general optimisation problems
• Process models and constraints

Chapter 3: Fundamentals of Optimisation Theory

• Degrees of freedom
• Unimodality vs. Multimodality
• Review of matrix algebra

Chapter 4: Convexity and Optimality

• Convex functions and regions
• Necessary & sufficient conditions for convexity
• Necessary & sufficient conditions for an optimal solution

Chapter 5: Nonlinear Programming

• Lagrange function for constrained optimisation
• Necessary & sufficient conditions for constrained optimisation problems

Chapter 6: Nonlinear Programming Algorithms

• General algorithms to solve an unconstrained optimisation problem
• General algorithms to solve a constrained optimisation problem

Chapter 7: Linear Programming and Mixed-integer Programming

• Introduction to linear programming
• Graphical solution for two variable problems
• Introduction to mixed-integer programming

### Aims

The unit aims to:

This course introduces the main concepts of engineering optimisation theories (e.g. convexity, optimality) and general optimisation algorithms that are predominantly used in the chemical and biochemical industry. Its main aim is to equip the students with the essential mathematical skills for analysing, optimising, and designing (bio)chemical processes.

The course also provides a range of case studies during the class and coursework sessions to enable students to practise optimisation techniques and apply them to real chemical engineering problems. The students will learn about fundamental optimisation theories, how to formulate optimisation problems (both linear and nonlinear), select appropriate mathematical algorithms, implement curve fitting and data analysis, and calculate a high-quality numerical solution.

### Learning outcomes

Students will be able to:

1. Demonstrate fundamental knowledge of optimisation theory.
2. Build mathematical models for engineering optimisation problems.
3. Choose appropriate optimisation algorithms to calculate a high-quality optimal solution.
4. Extend knowledge to the concept of complexity and optimality.
5. Apply classic methods to solve unconstrained and constrained optimisation problems.
6. Describe the general procedure to solve linear programming, nonlinear programming, and mixed-integer programming problems.

### Teaching and learning methods

• Lectures
• Tutorials
• Coursework sessions
• Drop-in sessions

### Assessment methods

Continuous assessment 30%
Exam style assessment 70%

1. T. Edgar, D. Himmelblau, and L. Lasdon. Optimization of Chemical Processes (2nd edition). McGrawHill.
2. R. Smith. Chemical Process Design and Integration, Wiley.
3. S. Boyd & L. Vandenberghe. Convex Optimization, Cambridge University Press.

### Study hours

Scheduled activity hours
Lectures 16
Seminars 8
Tutorials 8
Independent study hours
Independent study 68

### Teaching staff

Staff member Role
Dongda Zhang Unit coordinator