a | Lecture Chemical process control - Chapter 2 Mathematical Modeling of Chemical Processes Chapter 2 Mathematical Model (Eykhoff, 1974) “a representation of the essential aspects of an existing system (or a system to be constructed) which represents knowledge of that system in a usable form” Everything should be made as simple as possible, but no simpler. General Modeling Principles • The model equations are at best an approximation to the real process. • Adage: “All models are wrong, but some are useful.” • Modeling inherently involves a compromise between model Chapter 2 accuracy and complexity on one hand, and the cost and effort required to develop the model, on the other hand. • Process modeling is both an art and a science. Creativity is required to make simplifying assumptions that result in an appropriate model. • Dynamic models of chemical processes consist of ordinary differential equations (ODE) and/or partial differential equations (PDE), plus related algebraic equations. Table . A Systematic Approach for Developing Dynamic Models 1. State the modeling objectives and the end use of the model. They determine the required levels of model detail and model accuracy. Chapter 2 2. Draw a schematic diagram of the process and label all process variables. 3. List all of the assumptions that are involved in developing the model. Try for parsimony; the model should be no more complicated than necessary to meet the modeling objectives. 4. Determine whether spatial variations of process variables are important. If so, a partial differential equation model will be required. 5. Write appropriate conservation equations (mass, component, energy, and so forth). Table . (continued) 6. Introduce equilibrium relations and other algebraic equations (from thermodynamics, transport phenomena, chemical kinetics, equipment geometry, etc.). 7.
