## Mathematical Models

To describe the azeotropic distillation process, especially for the azeotropic distillation column, it is necessary to set up the reliable mathematical models. Once mathematical model is determined, it is possible to extend to the synthesis of distillation column sequence. Formerly, graphical method was popular for the analysis of azeotropic distillation column. Recently, the equilibrium (EQ) stage and non-equilibrium (NEQ) stage models, similar as those in extractive and catalytic distillation, have received more attention.

### 3.1. Graphical method

The principal concern in the graphical method is how to construct the maps of residual curve, distillation line and their boundaries so that the feasible composition space can be examined. After these are finished, the actual operating line with a certain reflux ratio between minimum and total reflux is plotted in the composition space. Consequently, the feasibility of a given separation process can be evaluated and the possible multiple steady-state may be found.

### 3.1.1. Residual curves

Residual-curve maps have been widely used to characterize azeotropic mixture, establish feasible splits by distillation at total reflux and for the synthesis and design of column sequences that separate azeotropic mixture. Schreinemakers [29, 39, 40] defined a residual curve as the locus of the liquid composition during a simple distillation process. Residue curves are conceived for «-component systems, but can be plotted only for ternary or, with more powerful graphical tools and some imagination, quaternary systems.

Since the residual curve is the locus of the liquid composition remaining from a differential vaporization process, we write by a stepwise procedure for a simple distillation still with only one theoretical stage:

where L0 is the amount of liquid in still at start of vaporization increment; L is the amount of liquid in still at end of vaporization increment; yi is mean equilibrium vapor composition over increment. A schematic representation of a simple distillation is diagrammed in Fig. 6.

Condenser

Still

Condenser

Still

Fig. 6. Schematic representation of a simple distillation still.

In a difference time dt, we have

dLI L

and for any two components i and j,

Introduce a dimensionless time dt = dL! L, Eq. (19) becomes dx.