Numerical Methods for Differential Algebraic Equations in Chemical Engineering

Chemical engineering systems often involve complex physical processes, such as mass transfer, chemical reactions, and thermodynamic equilibria, which are modeled using combined differential and algebraic equations (DAEs). Understanding how to set up and solve these mathematical models is essential for designing and optimizing chemical reactors, separation columns, and process piping networks. This text-based course guides you through the fundamental theory and practical numerical methods needed to resolve these coupled systems. By working through this course, you will transition from a basic understanding of calculus and algebra to confidently setting up, analyzing, and solving structured DAE systems. You will learn how to identify index problems, apply robust numerical solvers, and interpret your simulation results to make informed engineering decisions. What you'll learn: - Understand the fundamental differences between ordinary differential equations (ODEs) and differential algebraic equations (DAEs) in chemical processes. - Classify DAE systems by their index and apply index reduction techniques to make them solvable. - Implement numerical integration methods, such as backward differentiation formulas (BDF) and implicit Runge-Kutta methods, to solve stiff systems. - Model multi-component flash distillation and chemical reaction kinetics using structured mathematical formulations. - Apply modern numerical software workflows and scripting practices to automate process simulation and ensure convergence. The course begins with foundational definitions of DAEs, index classification, and core mathematical concepts. You will then progress step-by-step through numerical solvers, error control, and realistic chemical engineering case studies that you can work through on your own. This course is designed for undergraduate students, graduate researchers, and practicing chemical engineers who have a basic background in calculus and linear algebra but are new to numerical DAE modeling. No advanced programming experience is required. Start reading today to master the mathematical modeling of complex chemical systems.