Defined minimum reflux ratio

Porter and Momoh have suggested an approximate but simple method of calculating the total vapor rate for a sequence of simple columns. Start by rewriting Eq. (5.3) with the reflux ratio R defined as a proportion relative to the minimum reflux ratio iimin (typically R/ min = 1-D- Defining Rp to be the ratio Eq. (5.3) becomes... 

This also defines the minimum reflux ratio, r, according to... 

The relative volatilities are defined by Eq. (13-33), R m is the minimum reflux ratio, and q describes the thermal condition of the feed (1 for a saturated liquid feed and 0 for a saturated vapor feed). The Zfj values are available from the given feed composition. The 0 is the common root for the top section equations and the bottom section... 

The relative volatilities 0 are defined by Eq. (13-33), is the minimum-reflux ratio L +i/D) ia, and q describes the thermal condition of the feed (e.g., 1.0 for a bubble-point feed and 0.0 for a saturated-vapor feed). The values are available from the given feed composition. The 0 is the common root for the top-section equations and the bottom-section equations developed by Underwood for a column at minimum reflux with separate zones of constant composition in each section. The common root value must fall between ahk and aik, where hk and Ik stand for heavy key and light key respectively. The key components are the ones that the designer wants to separate. In the butane-pentane splitter problem used in Example 1, the light key is n-C4 and the heavy key is i-Cs. 

Eq. (1) is rewTitten for multicomponent mixtures by defining the effective light-key composition in the feed in a manner analogous to the effective product composition of Hengstebeck [7], The a in Eq. (1) is replaced by oci fdav The minimum reflux ratio is given by ... 

The values of and (L/D) - have been previously defined as the minimum number of equilibrium stages (Fenske equation) and minimum reflux ratio (Underwood equation). 

If an infinite or nearly infinite number of equilibrium stages is involved, a zone of constant composition must exist in the fractionating column. In this instance, there is no measurable change in the composition of liquid or vapor from stage to stage. Under these conditions, the reflux ratio can be defined as the minimum reflux ratio, R j, with... 

The concept of minimum reflux also applies to multi-component mixtures. It is defined as the reflux ratio below which a specified separation is infeasible, irrespective of the number of trays. At minimum reflux ratio, an infinite number of trays would be required to achieve the specified separation. With infinite trays there must exist in the column at least one section where the vapor and liquid compositions do not change from tray to tray. 

Minimum reflux is defined as the external reflux ratio, Rd, where the desired separation could be obtained with an infinite number of stages. Obviously, this is not a real condition, but the concept is useful because actual reflux ratios are often defined in terms of minimum reflux ratios. 

For Class 2 separations, (12-23) to (12-26) still apply. However, (12-26) cannot be used directly to compute the internal minimum reflux ratio because values of x,> are not simply related to feed composition for Class 2 separations. Underwood devised an ingenious algebraic procedure to overcome this difficulty. For the rectifying section, he defined a quantity <1> by... 

Minimum reflux ratio. The minimum reflux ratio can be defined as the reflux ratio that will require an infinite number of trays for the given separation desired of Xj, and x,y. This corresponds to the minimum vapor flow in the tower, and hence the minimum reboiler and condenser sizes. This case is shown in Fig. 11.4-11. If R is decreased, the slope of the enriching operating line R/(R + 1) is decreased, and the intersection of this line and the stripping line with the q line moves farther from the 45° line and closer to the... 

Mayur et al. (1970) formulated a two level dynamic optimisation problem to obtain optimal amount and composition of the off-cut recycle for the quasi-steady state operation which would minimise the overall distillation time for the whole cycle. For a particular choice of the amount of off-cut and its composition (Rl, xRI) (Figure 8.1) they obtained a solution for the two distillation tasks which minimises the distillation time of the individual tasks by selecting an optimal reflux policy. The optimum reflux ratio policy is described by a function rft) during Task 1 when a mixed charge (BC, xBC) is separated into a distillate (Dl, x DI) and a residue (Bl, xBi), followed by a function r2(t) during Task 2, when the residue is separated into an off-cut (Rl, xR2) and a bottom product (B2, x B2)- Both r2(t)and r2(t) are chosen to minimise the time for the respective task. However, these conditions are not sufficient to completely define the operation, because Rl and xRI can take many feasible values. Therefore the authors used a sequential simplex method to obtain the optimal values of Rl and xR which minimise the overall distillation time. The authors showed for one example that the inclusion of a recycled off-cut reduced the batch time by 5% compared to the minimum time for a distillation without recycled off-cut. 

A similar set of arguments gives us the same results as above when the solvent rate exceeds the distillate rate, i.e., when the A point is to the lower right in Fig. 65. Again, the lower curve defines a maximum reflux ratio, and the upper a minimum. 

A process is defined similar to Example 17.2, with the same components, initial charge and composition, the same constant distillate rate and required composition, and the same column pressure. In this case the reflux ratio is maintained at twice the minimum value. The column has six actual trays plus the reboiler, the equivalent of seven actual trays. The overall tray efficiency is 65%, and the relative volatility of butane to pentane is assumed constant at 2.315. 

The basic assumption of the Fenske-Underwood relation is that the ratio of the equilibrium constants or the relative volatility, as defined by Eq. (6.19), in a binary mixture or the two key components present in a multicomponent mixture remain constant over the temperatures encountered in the distillation column. If this can be assumed without the introduction of excessive error, the minimum number of plates at total reflux can be determined from... 

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