Multiple Feeds, Side Draws

The versatility of the H-X method is also demonstrated in the analysis of the performance of multiple-feed and multiple-product columns. The basic approach is unchanged relate the passing vapor and liquid streams at the point of interest in the column by performing an energy balance, then implement the relationship graphically on the H-X diagram. 

The situation may arise, for instance, where it is necessary to study the effect 

Consider any tray j above which the only heat or material transfer across the column boundary occurs at the condenser, the distillate, and the side draw. An energy balance around the top part of the column down to and including tray j is written as 

Analyzing the effect of a feed above a given tray is analogous to the case with a side draw. The energy balance that includes the upper part of the column through any tray j below the feed takes the form 

The point D is the usual pivot that corresponds to the distillate and the condenser. The point F has the coordinates of the feed composition and enthalpy, (.Xp,h. The combined effect is represented by a new pivot point F, which corresponds to the difference D -Fhp. To locate F, a straight line is drawn from F to D and extended past D to F so that, by the lever rule, 

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Columns with Multiple Feeds, Side Draws, and Side Heaters/Coolers... 

FIGURE 5,7 Column with multiple feeds, side draws, and side heaters/coolers. 

Complex distillation may be defined as a multistage vapor-liquid separation process that includes one or more of the following features multiple feeds, side draws, pumparounds, and side heaters or coolers. 

Equations 17.18 through 17.28 may be solved using different strategies, including simultaneous or iterative methods. Distefano (1968) describes a computational procedure that solves the equations one at a time. Boston et al. (1981) describe a more flexible and efficient method that can handle a variety of specifications and column configurations, including multiple feeds, side draws, and side heaters. The method uses advanced numerical procedures to handle nonlinearity and stability problems. The object here is not to describe the details of the methods, which may be found in the references. The Distefano method is outlined here to illustrate briefly some of the potential numerical computational problems. 

Note that and D have the same composition, and, therefore, the operating line is vertical. Multiple Feeds, Side Draws... 

The lower part of the column is covered by stepping off stages in a fashion similar to that in the upper part of the column, and the final conni of theoretical stages is then determined. The Ponchon-Savarit method may be used for many situations more complex lhan the simple one just described mixed vapor-liquid distillate product, side draw streams, multiple feeds, and so on. Standard unit operations textbooks should be consulted for more dentils on this methnd. As mentioned, it suffers from a need for enthalpy-concentration data, but even a crude approximation based on linear variation of enthalpy with concentration can be better than the McCabe-Thiele approach if there is a very large difference in the latent heats of vaporization of the iwo components being distillnd. 

Similarly, one may consider the material balance across the side-draw stage too. Since the side-draw product stream is not terminated by a reboiler or a condenser, there is no exact value that the net flow in either CS3 or CS5 is required to be. Thus, just like the CSs across the feed stage, there are multiple flow directions that may exist across the side-draw stage. These are depicted in Figure 7.11a d. 

At this input-output level the following assumptions are considered ( ) steady-state modeling (n) multiple feeds (nfeed ), side draw-off streams (notr Z+), heat streams (n, Z+), reactions rirx Z+) and components (uc Z+) and Hi) single bottom and distillate streams. Component and energy balances are performed over the structure. The component molar balances MC) include the distillate, bottom, feed and draw-off streams and the production (or consumption) of species due to chemical reaction. 

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