Short-cut distillation columns based on orthogonal polynomials of a discrete variable

Increasing competition in the process industries enforces theapplication of mathematical simulation techniques both in thedesign phase and in the operating phase of a plant. A basicapparatus for separation processes is the distillation column.Its rigorous (tray by tray) mathematical modelling results ina system of simultaneous nonlinear equations (algebraic in thesteady-state case, differential-algebraic in the dynamic case).For high (and realistic) numbers of trays and components, thesesystems may become rather large (thousands of equations). Inaddition, realistic plant models often include several distillationcolumns. As a consequence, the numerical solution of these modelsmay become difficult and time-consuming. This has led to attemptsto model the distillation columns less rigorously with the aimof achieving a considerable reduction in the number of equations.The name shortcut distillation columns is common for modelsof this type. The present paper uses a discrete weighted residualmethod for the development of short-cut models. It suggestsa Galerkin method based on orthogonal polynomials in a discretevariable: the tray number. It is a remarkable advantage of thistechnique that even very coarse models satisfy all global balancesexactly.