Feed lines calculating line slope

Equation 11.66 is not of much practical use in distillation, as the slopes of the operating and equilibrium lines will vary throughout the column. It can be used by dividing the column into sections and calculating the slopes over each section. For most practical purposes, providing the plate efficiency does not vary too much, a simple average of the plate efficiency calculated at the column top, bottom and feed points will be sufficiently accurate. 

The way in which such a diagram may be used is shown in Fig. 5.20 for three stages. The point A, 14,04), represents the state of the partially reacted feed which is to be blended sith cold unreacted feed. To find this blended feed we join A to the origin and take the intersection with Fs,B yU4 is the ratio OB/OA. To find the product tsiCs) we take a line of unit slope through B to F3 = F2, and the intersection C is the required point. Continuing in this way, D lies on OC and F2 and 1x3 = OD/OC DE is of unit slope and E lies on F2 F lies on OE and Fi and fxz = OF/OE finally, the product state is G on Fi. From the values of ix the values of X may be calculated. 

If the reflux ratio, or L,/D, and the distillate rate, D, are specified, the rectifying section operating line slope, L,/y, can be calculated. The feed composition and thermal conditions are also known, which allows the -line to be plotted and and V, to be calculated from Equations 5.16 and 5.17. Thus, the slopes of the two operating lines are known as well as the locus of their intersection points. 

This equation relates the liquid and vapor profiles above and below the heater/ cooler tray to the heat duty qj. Referring to Figure 5.7, if the slope of the operating line below the side cooler stage is known or can be calculated, the line is constructed directly. If the number of stages between the side cooler and the upper feed is known, the slope of the operating line must be varied to match the number of stages. 

The complete definition of column performance when the number of stages and feed location are fixed requires two specifications (Section 5.2.2). In studying the effect of reflux ratio on separation, other parameters, including product rates, are assumed constant. In Y-X graphical representation, a fixed product rate is implied by fixing the 7-line slope. This slope depends on the feed thermal conditions at feed tray temperature and pressure (Section 5.2.2). The column pressure is fixed, but its temperature depends on the product rates. Therefore, in order to maintain a fixed product rate, the (/-line slope must be held constant. The actual product rates corresponding to a given (/-line slope are calculated by material balance once the product compositions have been determined. 

Calculate the feed line slope for the following cases. 

This agrees with Figure 4-10. Despite considerable subcooling, this feed line is also steep. Note that feed rate was not needed to calculate q or the slope for any of these calculations. 

F. Generalize. Note that the y = x line is not always useful. Don t memorize locations of points. Learn to derive what is needed. The total condenser does not change conpositions and is not counted as an equilibrium stage. The total condenser appears in Figure 4-16 as the single point y = x = Xq. Think about why this is true. In general, all inputs to the column can change flow rates and hence slopes inside the column. The purpose of the feed line is to help determine this effect. The reflux stream and open steam are also inputs to the column. If they are not saturated streams the flow rates are calculated differendy this is discussed later. 

Develop feed line equations. Calculate q values, slopes, and y = x intersections. 

Next calculate the feed-line slope — (1 — ///) and plot the straight line through (Xf, Yp). 

Calculate the q-line slope, to compensatefor the feed not entering at its bubble point (40 C versus 94° C). The thermal condition of the feed is taken into account by the slope of a Hne, where... 

Similaily, the entice equilibiium curve is calculated and is plotted in Figure 10. The feed is at the boiFng point so the q line is drawn vertically with an infinite slope. 

Thermal Condition of the Feed The slope of the operating line changes whenever a feed stream or a sidestream is passea. To calculate this change, it is convenient to introduce a quantity q which is defined by the following equations for a feed stream F ... 

The slope of the operating line is F7S, just as in Eqs. (15-11) and (15-12), but only stages 2 through / — 1 will fall directly on the operating line. And one knows that X will be on the equihbrium line in equilibrium with by definition (see Fig. 15-12). One can calculate a pseudo feed concentration Ay that will fall on the operating line [Eq. 05-11)] at = Y, [Eq. (15-19)]. 

If 17% benzene is unacceptable in the bottom product, reflux and reboil can be raised to achieve the required esparation in 10 stages. The slope of the rectifying section component balance line is increased, and that of the stripping section component balance line is lowered, ThiB is a trial-and-error calculation, which ende when 10 theoretical stages are accommodated betwean the componant balance line and the equilibrium curve, the top and bottom products are at their desired specifications, and the feed enters between stages 4 and 5. The slopes of the component balance lines will determine the new required reflux and boilup rate. The final result is shown in Fig. 2.10c. From this diagram,... 

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