Short-cut distillation columns based on orthogonal polynomials of a discrete variable
نویسنده
چکیده
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. The 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 (however 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 to achieve a considerable reduction in the number of equations. The name short-cut 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 of a discrete variable, the tray number. It is a remarkable advantage of this technique that even very coarse models satisfy all global balances exactly.
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