Simple Distillation Boundaries

23) approximates the operating lines at total reflux and, because i and h are dimensionless variables and Eq. (7.19) is identical in form, the residue curves approximate the operating lines of a distillation tower operating at total reflux. 

Furthermore, assuming operation in vapor-liquid equilibrium, the mole fractions on tray n, x , and lie at the ends of the equilibrium tie lines. 

Note that distillation lines are generated by computer as easily as residue curves and,l -cause they do not involve any approximations to the operating line at total reflux, are preferred for the analyses to be performed in the remainder of this section. However, simulation programs compute and plot only residue curves. It can be shown that distillation lines have the same properties as residue curves at fixed points, and hence, both families of curves are sketched similarly. Their differences are pronounced in regions that exhibit extensive curvature. 

To find the roots, they construct the following homotopy to replace Eqs. (7.25) and (7.26), based on gradually moving fixtm an ideal AT-value based on Raoult s law to the more rigorous expression ofEq. (7.26)  

Initially, the homotopy parameter, t, is set to 0 and all values of Xj are set to 0 except for one, which is set to 1.0. Then t is gradually and systematically increased until a value of 1.0 is obtained. With each increase, the temperature and mole fractions are computed. If the resulting composition at f = 1.0 is not a pure component, it is an azeotrope. By starting from each pure component, all azeotropes are computed. The method of Fidkowski, Malone, and Doherty is included in many of the process simulation programs. Eckert and Kubicek (1997) extended the method of Fidkowski, Malone, and Doherty to the estimation of heterogeneous multi-component azeotropes. 

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Distillation boundaries for continuous distillation are approximated by simple distillation boundaries. This is a very good approximation for mixtures with nearly linear simple distillation boundaries. Although curved simple distillation boundaries can be crossed to some degree (16,25—30,32,33), the resulting distillation sequences are not normally economical. Mixtures such as nitric acid—water—sulfuric acid, that have extremely curved boundaries, are exceptions. Therefore, a good working assumption is that simple distillation boundaries should not be crossed by continuous distillation. In other words, for a separation to be feasible by distillation it is sufficient that the distillate and bottoms compositions He in the same distillation region. 

Since residue curves do not cross simple batch distillation boundaries, the distillate and bottoms compositions must be in the same distillation region with the mass balance line intersecting a residue curve in two places. Mass balance lines for mixing and for other separations not involving vapor-liquid equilibria, such as extraction and decantation, are of course not limited by distillation boundaries. 

Vinyl acetate-ethyl acetate Propane-propylene Ethanol-isopropanol Hydrochloric acid-water Nitric acid-water Close-boiling Close-boihng Close-boihng Maximum-boiling azeotrope Maximum-boiling azeotrope Phenol, aromatics Acrylonitrile Methyl benzoate Sulfuric acid, calcium chloride for salt process Sulfuric acid, magnesium nitrate for salt process Alternative to simple distillation Alternative to simple distillation, adsorption Alternative to simple distillation Sulfuric acid process rehes heavily on boundary curvature Sulfuric acid process rehes heavily on boundary curvature... 

E.xample problems are included to highlight the need to estimate the entire set of products that can be reached for a given feed when using a particular type of separation unit. We show that readily computed distillation curves and pinch point cur es allow us to identify the entire reachable region for simple and e.xtractive distillation for ternary mixtures. This analysis proves that finite reflux often permits increased separation we can compute exactly how far we can cross so-called distillation boundaries. For extractive distillation, we illustrate how to find minimum. solvent rates, minimum reflux ratios, and, interestingly, ma.xinnim reflux ratios. 

From the above examples, it may be concluded that simple thermodynamic information, as boiling points of pure components and azeotropes, is sufficient to sketch the main features of a RCM, as the direction of trajectories and distillation boundaries. However, drawing correctly the curvature of boundaries needs accurate knowledge of phase equilibrium. 

The geometric properties of a RCM allow its simple sketch. Figure 9.5 shows the construction for the mixture methyl-isopropyl-ketone (MIPK), methyl-ethyl-ketone (MEK) and water. Firstly, the position of the binary azeotropes and of the ternary azeotrope is located. Then the boiling points for pure components and azeotropes are noted (Fig. 9.5a). The behaviour of characteristic points (node or saddle) is determined by taking into account the direction of temperatures. Finally, straight distillation boundaries are drawn by connecting saddles with the corresponding nodes (Fig. 9.5b). 

Feasible separation alternatives identified at total reflux remain valid for finite reflux. However, if the distillation boundary at infinite reflux has a strong curvature, it can be crossed at finite reflux (Wahnschafft and Westerberg, 1992). This means that the top and bottom products may belong to different residue curves in different distillation regions. Thus, it seems that we might speak about an effective distillation border that is a function of reflux. There is no simple way to predict it, but its extent can be framed by simulation. This topic will be illustrated in the next example. 

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