Reflux ratio, minimum

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. 

The definition of minimum reflux is linked to a specification of separation between two components. In multi-component mixtures, the specified components are the light key and the heavy key components. Minimum reflux is meaningless if the column is specified in a manner that does not define a particular separation between two components, such as a specification of the number of trays and a product rate. Also, minimum reflux in this context is associated with singlefeed, two-product columns. For a given feed composition, the minimum reflux depends on the key components, their separation specification, and the feed thermal conditions. 

The equation in its final form is presented here. The reader is referred to the original article (Underwood, 1948) for detailed derivation. The minimum reflux ratio R is given by the equation 

The number of trays in an actual column is, of course, never infinite, and columns will never achieve the specified separation if operated at minimum reflux ratio. What the estimation of minimum reflux does provide is a limiting condition or a reference point. The operating reflux ratio is commonly expressed as a factor multiplied by the minimum reflux ratio. This factor must be greater than one in order to make the specified separation possible. The minimum reflux ratio is also used for correlating the required number of trays and reflux ratio as described in Section 12.3. 

Using Eqs. (2.11) and (2.16), Eq. (2.9) for the rectifying section component balance line can be expressed in terms of the reflux ratio 

As the reflux ratio decreases, so does the slope of the upper component balance line, The effect of reflux ratio on the component balance lines is illustrated in Fig, 2,11, using the benzene-toluene system in Exampla 2.1. 

Any practical separation requires that the component balance lines intersect below the equilibrium curve, as for a reflux ratio of 3.0 in Fig. 2,11c. The McCabe-Thiele construction corresponding to this ratio is shown in Fig. 2.9c, If insufficient reflux is provided, the component balance lines intersect above the equilibrium curve, as for a reflux ratio of 1,0 in Fig. 2.11c, The McCabe-Thiele construction (Fig. 2,116) for these conditions shows that even with an infinite number of stages, the separation cannot be achieved. 

At minimum reflux, the pinch occurs at the intersection of the component balance line and the g-line when the equilibrium curve has no inflection points (Fig. 2,11c), This would be expected because the component balance lines intersect on the q-line. When the equilibrium curve has a point of inflection (Fig. 2.12), the pinch between the equilibrium curve and the component balance line may occur at the point of tangency instead of the intersection of the g-line and the component balance line. This condition is termed tangent pinch. 

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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... 

Distillation capital costs. The classic optimization in distillation is to tradeoff capital cost of the column against energy cost for the distillation, as shown in Fig. 3.7. This wpuld be carried out with distillation columns operating on utilities and not integrated with the rest of the process. Typically, the optimal ratio of actual to minimum reflux ratio lies in the range 1.05 to 1.1. Practical considerations often prevent a ratio of less than 1.1 being used, as discussed in Chap. 3. 

McCabe-Thie/e Example. Assume a binary system E—H that has ideal vapor—Hquid equiHbria and a relative volatiHty of 2.0. The feed is 100 mol of = 0.6 the required distillate is x = 0.95, and the bottoms x = 0.05, with the compositions identified and the lighter component E. The feed is at the boiling point. To calculate the minimum reflux ratio, the minimum number of theoretical stages, the operating reflux ratio, and the number of theoretical stages, assume the operating reflux ratio is 1.5 times the minimum reflux ratio and there is no subcooling of the reflux stream, then ... 

Simple analytical methods are available for determining minimum stages and minimum reflux ratio. Although developed for binary mixtures, they can often be applied to multicomponent mixtures if the two key components are used. These are the components between which the specification separation must be made frequendy the heavy key is the component with a maximum allowable composition in the distillate and the light key is the component with a maximum allowable specification in the bottoms. On this basis, minimum stages may be calculated by means of the Fenske relationship (34) ... 

For minimum reflux ratio, the following equations (35) may be used ... 

In the example, the minimum reflux ratio and minimum number of theoretical plates decreased 14- to 33-fold, respectively, when the relative volatiHty increased from 1.1 to 4. Other distillation systems would have different specific reflux ratios and numbers of theoretical plates, but the trend would be the same. As the relative volatiHty approaches unity, distillation separations rapidly become more cosdy in terms of both capital and operating costs. The relative volatiHty can sometimes be improved through the use of an extraneous solvent that modifies the VLE. Binary azeotropic systems are impossible to separate into pure components in a single column, but the azeotrope can often be broken by an extraneous entrainer (see Distillation, A7EOTROPTC AND EXTRACTIVE). 

Minimum-reflux ratio Entrainment or occlusion ratio ... 

As a first step in the calculation, the minimum-reflux ratio should be determined. In Fig. 13-100, point D, representing the distillate, is on the diagonal since a total condenser is assumed and Xo = yo- Point F represents the initial condition in the still pot with coordinates ip, y. Minimum internal reflux is represented by the slope of the line DF,... 

The effect of utilities costs on optimum operation was noted by Kiguchi and Ridgway [Pet. Refiner,. 35(12), 179 (1956)], who indicated that in petroleum-distillation columns the optimum reflux ratio varies between 1.1 and 1.5 times the minimum reflux ratio. When refrigeration is involved, 1. IRmm < flopt < 1 is used in the condensers, 1.2Rrniii < fLpt < 1 -4Rrn... 

After finding 0, the minimum reflux ratio is determined from... 

Lr = Liquid molar rate in the reetifieation seetion F = Feed molar rate Rm = Minimum reflux ratio... 

The recommended method to use to determine the actual theoretical stages at an actual reflux ratio is the Erbar/Maddox relationship. In the graph, N is the theoretical stages and R is the actual reflux ratio L/D, where L/D is the molar ratio of reflux to distillate. N, is the minimum theoretical stages and R, is the minimum reflux ratio. 

The limiting condition occurs at minimum reflux ration, when an infinite number of trays will be required to effect separation. Most columns are designed to operate between 1.2 to 1.5 times the minimum reflux ratio because this is approximately the region of minimum operating costs (more reflux means higher reboiler duty). 

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. 

Underwood s algebraic evaluation [73] for minimum reflux ratio is acceptable for handling ideal or near ideal systems ... 

If the minimum reflux ratio is 2.0 and the minimum number of theoretical plates is 20, how many plates will be required if a reflux ratio 1.5 times the minimum is used ... 

Smin = minimum number of theoretical plates R = any reflux ratio Rmin = minimum reflux ratio... 

The following is a short approximation method for minimum reflux ratios for multicomponent mixtures [98] ... 

A. Calculate the minimum reflux ratio if the feed is liquid at its boiling point. 

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,... 

Assume xi values of bottoms compositions of light key for approximate equal increments from final bottoms to initial feed charge. Calculate L/V values corresponding to the assmned xi values by inserting the various xi values in the Fenske equation for minimum reflux ratio of l-(d). The xi values replace the x b of this relation as the various assumptions are calculated. The actual (L/D) are calculated as in l-(d) keeping the minimmn number of trays constant. Complete the table values. 

For systems with one sidestream drawoff, either above or below the feed, Tsuo et al. [102] propose a method for recognizing that the minimum reflux ratio is greater for a column with sidestream drawoff. At the sidestream the operating line has an inflection. For multifeed distillation systems, the minimum reflux is determined by factoring together the separate effect of each feed [103]. 

Example 8-23 Minimum Reflux Ratio Using Underwood Equation Calculate the Minimiun Reflux Ratio... 

Example 8-24 Using the Colburn Equation Calculate the Minimum Reflux Ratio... 

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