ABSTRACT
Chemical processes are quite naturally modeled by systems of coupled differential and algebraic equations, where the differential equations arise from the dynamic balances of mass, energy, and momentum, while the algebraic equations typically include thermodynamic relations, empirical correlations, and quasi-steady-state relations. Often, the algebraic equations are nonsingular and can be readily eliminated from the Differential algebraic equation (DAE) models to obtain standard ordinary differential equation (ODE) models. However, such models exhibit stiffness/time-scale multiplicity, which leads to well-known problems in numerical simulation; these models are not particularly well-suited for controller design either. On the other hand, when these fast phenomena are approximated with appropriate quasi-steady-state (QSS) conditions, the resulting “equilibrium-based” models are given by high-index DAEs, which describe the essential slow dynamics of the process and are better suited for simulation and controller design purposes. In some processes the fast dynamics correspond to specific physical phenomena like fast mass transfer/reactions and the QSS conditions are intuitively apparent.
