Short‐Cut Distillation Columns: A Mathematical Approach

Abstract

AbstractThe distillation column is the basic apparatus for separation processes in chemical engineering. Mathematical models of this tool are nonlinear systems of (algebraic) equations in the steady‐state case and differential‐algebraic equations in the dynamic case. The number of equations for a single distillation columnn is N(2nc + 7), where N denotes the number of stages (trays) and nc is the number of components. In practical applications, the number of trays is within 10 × N × 100, and the number of components is less than 50. As a consequence, rigorous (tray‐by‐tray) models of distillation columns with thousands of equations are not uncommon. A realistic plant may include several distillation columns. Consequently, plant models may become very large and difficult to solve numerically. This has lead to several attempts to reduce the number of equations without sacrificing too much accuracy. The name “short‐cut distillation column” is common for a model of this type. The paper gives a mathematical approach in contrast to previous, engineering oriented attempts. For the sake of brevity it is restriced to the stationary case.