Reflux ratio minimum infinite plates

Unequal Molal Flow, 63 Ponchon-Savarit Method, 63 Example 8-21 Ponchon Unequal Molal Overflow, 65 Multicomponent Distillation, 68 Minimum Reflux Ratio — Infinite Plates, 68 Example 8-22 Multicomponent Distillation by Yaw s Method, 70 Algebraic Plate-to-Plate Method,... 

Fig. 2.3.2-9 Balance lines and staircase construction, a) Minimum reflux ratio, infinite plate number, b) Finite reflux ratio, resp. finite plate number, c) Total reflux, minimum plate number.

This graphical representation is easier to use for nonideal systems than the calculation method. This is another limiting condition for column operation, i.e., below this ratio the specified separation cannot be made even with infinite plates. This minimum reflux ratio can be determined graphically from Figure 8-23, as the line with smallest slope from xp intersecting the equilibrium line at the same point as the q line for mixture following Raoul t s Law. 

Using Figure 8-33 the separation from Xq, initial kettle volatile material to X3 as the distillate of more volatile overhead requires three theoretical plates/stages at total reflux. Using finite reflux R4, and four theoretical plates the same separation can be achieved with infinite theoretical plates and the minimum reflux ratio, Rmin- The values of reflux ratio, R, can be determined from the graph with the operating line equation as,... 

As the specified value of the reflux ratio (Ll/D) is decreased, the intersection of the two operating lines moves closer to the equilibrium curve and the minimum number of plates required to effect the specified separation (xB = 0.05, XD = 0.96) increases. On the other hand, as L /D is decreased, the condenser and reboiler duties decrease. The minimum reflux ratio is the smallest one which can be used to effect the specified separation. This reflux ratio requires infinitely many plates in each section as demonstrated in Fig. 1-10. It should be noted that for this case, the plates at and adjacent to the feed plate have the same composition. (In the case of multicomponent systems, these limiting conditions do not necessarily occur at and adjacent to the feed plate as discussed in Chap. 11). From the standpoint of construction costs, this reflux ratio is unacceptable because infinitely many plates are required, which demands a column of infinite height. 

Figure 1-10 At the minimum reflux ratio (LXJD infinitely many plates are required to effect the specified separation (XD, xB).

MINIMUM REFLUX. At any reflux less than total, the number of plates needed for a given separation is larger than at total reflux and increases continuously as the reflux ratio is decreased. As the ratio becomes smaller, the number of plates becomes very large, and at a definite minimum, called the minimum reflux ratio, the number of plates becomes infinite. All actual columns producing a finite amount of desired top and bottom products must operate at a reflux ratio between the minimum, at which the number of plates is infinity, and infinity, at which the number of plates is a minimum. If is the operating reflux ratio and (Lg/B) the minimum reflux ratio,... 

With a normal equilibrium curve it is seen from Fig. 18.19 that at minimum reflux ratio the intersection of the q line and the equilibrium curve gives the concentrations of liquid and vapor at the feed plate (and at an infinite number of plates on either side of that plate). So an invariant zone forms at the bottom of the rectifying section and a second one at the top of the stripping sec tion. The two zones differ only in that the liquid-vapor ratio is LjV in one and LjV in the other. 

MINIMUM REFLUX RATIO. The minimum reflux ratio for a multicomponent distillation has the same significance as for binary distillation at this reflux ratio, the desired separation is just barely possible, but an infinite number of plates is required. The minimum reflux ratio is a guide in choosing a reasonable reflux ratio for an operating column and in estimating the number of plates needed for a given separation at certain values of the reflux ratio. 

V Flow rate of vapor, in general or in rectifying section, mol/h F i , at minimum reflux ratio [Eq. 19.30)] V +j, from plate + 1 for an infinite number of plates V, in stripping section X Mole fraction of component in liquid phase in bottoms x, in... 

This figure, 1.65, is the minimum reflux ratio, at which an infinite number of plates would be required for separation. Since in this case points x, x and y lie on the operating line the minimum reflux ratio may also be expressed as [103]... 

Optimum Reflux Ratio. The choice of the proper reflux ratio is a matter of economic balance. At the minimum reflux ratio, fixed charges are infinite, because an infinite number of plates is required. At total reflux, both the operating and the fixed charges are infinite. This is due to the fact that an infinite amount of reflux and a column of infinite cross section would be required for the production of a finite amount of product. The tower cost therefore passes through a minimum as the reflux ratio is decreased above the minimum. The costs of the still and condenser both increase as the reflux ratio is increased. The heat and cooling requirements constitute the main operating costs, and the sum of these increases almost proportionally as the... 

Minimum Reflux Ratio. The case of the minimum reflux ratio corresponds to conditions that require an infinite number of plates to obtain the desired separation. As in the case of the y x diagram, this necessitates a region in which succeeding plates differ only differentially in composition, f.s., a pinched-in region. 

Actually there is no sharp line of demarcation between these five sections, but this division serves as a useful picture for considering the case of the minimum reflux ratio. The feed to the fractionating column would be introduced on some plate in intermediate section 3, and the true criterion for the minimum reflux ratio should be based on matching the ratio of the concentrations of the key components above and below the feed plate under conditions such that a pinched-in section occurs both above and below the feed plate. For mixtures of normal volatility, a pinched-in region in only one section does not necessarily mean that an infinite number of plates would be required to perform the desired separation at the reflux ratio under consideration, since by relocating the feed plate, such as to shift the ratio of the concentrations of the key components at this plate, the section that was not limited could be made to do more separation and thereby relieve the load on the pinched-in section. In other words, for mixtures of normal volatilities the condition of the minimum reflux ratio is not determined by either the fractionation above or below the feed plate alone, but is determined such that the separation is limited both above and below the feed. The conditions in the intermediate feed section lead to... 

The minimum reflux ratio (for specified product purities and feed conditicHis) occurs when an infinite number of trays are required to make the separation. Figure 2.27 shows the normal minimum reflux ratio situation. It occurs when the operating lines just intersect on the VLE curve. An infinite number of trays are required to step past the feed plate because erf" the piiwli condition (the converging operating and VLE lines). The actual reflux ratio used must be higher than the minimum. 

If this process is carried out in a distillation column, the minimum energy required may be determined from the heat Qk supplied in the reboiler/gmol of feed at Tg if we may assume that the total heat supplied at the reboiler is equal to that withdrawn in the condenser (i.e. Qc) at Tc-Further, this minimum will occur at the minimum reflux ratio, which means that there will be an infinite number of plates. Following Humphrey and Keller (1997), we aissume the fallowing complete separation of feed into two pure products constant relative volatility i2 constant molar overflow feed at bubble point minimum reflux ratio single reboiler and condenser liquid feed at bubble point. Consider now the distillation column shown in Figure 10.1.5(a). The overall and component material balance equations are ... 

For the normal type of equilibrium curve, which is concave downward throughout its length, the point of contact, at minimum reflux, of the operating and equilibrium lines is at the intersection of the feed line with the equilibrium curve, as shown by lines ad and db in Fig, 18.19. A further decrease in reflux brings the intersection of the operating lines outside of the equilibrium curve, as shown by lines age and cb. Then even an infinite number of plates cannot pass point g, and the reflux ratio for this condition is less than the minimum. 

MINIMUM NUMBER OF PLATES. The Fenske equation (18.41) applies to any two components, i and j, in a conventional plant at infinite reflux ratio. In this case, the equation has the form... 

The plate equivalent is the minimum number of plates required at infinite reflux ratio to attain the same enrichment (xB- -Xg) as in a countercurrent distillation with a finite reflux ratio. All distillation conditions except the reflux ratio remain the same. Thus, in the McCabe-Thiele diagram the separating stages are drawn between the diagonal and the equilibrium curve v = oo). 

Operating and optimum reflux ratio. For the case of total reflux, the number of plates is a minimum, but the tower diameter is infinite. This corresponds to an infinite cost of tower and steam and cooling water. This is one limit in the tower operation. Also, for minimum reflux, the number of trays is infinite, which again gives an infinite cost. These are the two limits in operation of the tower. 

Looking back to Packie s work, it is known that for a given separation requirement expressed as (5-95) Gap, a given material balance expressed in terms of ASTM 50 volume percent temperature difference and a given number of trays in the separation section, there is a vdue, called F, which is the product of the number of actual trays and the volumetric reflux ratio in the section. Thus, a minimum allowable reflux falling from draw trays can be calculated. This is not minimum reflux in the sense that infinite plates are required for the separation. It is minimum allowable operating reflux for the specified number of trays and the required separation. 

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