Numerical Methods for Chemical Engineering: Differential-Algebraic Equations

Chemical engineering systems often involve a complex mix of dynamic changes and physical constraints, which are mathematically represented as differential-algebraic equations (DAEs). Understanding how to formulate and solve these equations is essential for accurate process simulation, safety modeling, and system design. This course provides a clear, step-by-step path to mastering these numerical techniques without requiring advanced mathematical prerequisites. By completing this written course, you will transform your approach to process engineering by learning how to translate physical systems into robust numerical models. You will gain the confidence to select the right solver, identify index problems, and ensure numerical stability in your simulations. What you'll learn: - Understand the fundamental concepts of differential-algebraic equations and how they differ from standard ordinary differential equations. - Formulate consistent initial conditions for complex chemical process models. - Analyze the index of a DAE system to determine its solvability and numerical behavior. - Apply modern numerical methods, including backward differentiation formulas, to solve algebraic constraints. - Implement modern Python-based libraries and solvers to simulate transient chemical engineering systems. - Evaluate numerical stability and error bounds to ensure the reliability of your simulation results. This course begins with foundational definitions and key terminology of numerical analysis before guiding you through the step-by-step formulation of chemical engineering models, such as reactors and distillation columns. You will progress through practical, text-based walkthroughs that demonstrate how to set up, solve, and troubleshoot DAE systems using industry-standard numerical strategies. This course is designed for undergraduate students, entry-level chemical engineers, and process simulation beginners who want to build a strong foundation in numerical methods. No prior experience with advanced differential-algebraic equations is required. Start reading today to master the numerical methods that power modern chemical process simulation.