© 1999 by Institute of Mathematics and its Applications
Short-cut distillation columns based on orthogonal polynomials of a discrete variable
Institut für Wirtschaftsinformatik Universität Regensburg D-93040 Regensburg, Germany
Increasing competition in the process industries enforces the application of mathematical simulation techniques both in the design phase and in the operating phase of a plant. A basic apparatus for separation processes is the distillation column. Its rigorous (tray by tray) mathematical modelling results in a system of simultaneous nonlinear equations (algebraic in the steady-state case, differential-algebraic in the dynamic case). For high (and realistic) numbers of trays and components, these systems may become rather large (thousands of equations). In addition, realistic plant models often include several distillation columns. As a consequence, the numerical solution of these models may become difficult and time-consuming. This has led to attempts to model the distillation columns less rigorously with the aim of achieving a considerable reduction in the number of equations. The name shortcut distillation columns is common for models of this type. The present paper uses a discrete weighted residual method for the development of short-cut models. It suggests a Galerkin method based on orthogonal polynomials in a discrete variable: the tray number. It is a remarkable advantage of this technique that even very coarse models satisfy all global balances exactly.
Keywords: Mathematical models; distillation columns; discrete weighted residual method; discrete Galerkin method; Hahn polynomials