Reflux ratio, minimum total

Here the feed rate is maximised while the reflux ratio is optimised. The bottom product composition imposes an additional constraint to the problem. The results are summarised in Table 11.8 which gives the maximum feed rate, minimum batch time, optimum reflux ratio, and total number of batches for each mixture and total yearly profit. 

Alternatively, results from a computer simulation can be plotted to determine the optimum feed stage. Simulation runs ere performed at several different feed points, keeping the material balance, reflux ratio, and total number of stages constant. Ksy component concentrations in the product streams are plotted against the feed stage number (Fig. 3.7). The minimum is at the optimum feed stage. 

Lj = Liquid flowrate down stripping section of distillation tow er, lb mols/hr Light key component in volatile mixture Internal reflux ratio Actual external reflux ratio Minimum external reflux ratio Molecular weight of compound Total mols steam required Number of sidestreams above feed, n Number of theoretical trays in distiUation tower (not including reboiler) at operating finite reflux. For partial condenser system N includes condenser or number theoretical trays or transfer units for a packed tower (VOC calculations) Nb = Number of trays from tray, m, to bottom tray, but not including still or reboiler Nmin = Minimum number of theoretical trays in distillation tower (not including reboiler) at total or infinite reflux. For partial condenser system,... 

The separation power base in the classic McCabe-Thiele graphical model of a binary distillation column is established by the reflux ratio, R/D, which is the ratio of the reflux flow rate divided by the distillate flow rate. For example, with a distillation column that is fed 1,000 kg/h of feed that produces 85 kg/h of distillate with 425 kg/h of reflux, the reflux ratio is 425/85 = 5. A minimum reflux ratio is required to achieve the desired separation with an infinite number of theoretical stages. The maximum reflux ratio, called total reflux, with zero distillate flow rate can be used in design calculations to determine the minimum number of theoretical stages required to achieve a desired separation. 

EXAMPLE 11.4-2. Minimum Reflux Ratio and Total Reflux in Rectification... 

Figure 11.4-13. Graphical solution for minimum reflux ratio and total reflux for Example 1.4-2.

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... 

Optimum Reflux Ratio The general effecl of the operating reflux ratio on fixed costs, operating costs, and the sum of these is shown in Fig. 13-39. In ordinary situations, the minimum on the total-cost cui ve wih geueraUy occur at an operating reflux ratio of from 1.1 to 1.5 times the minimum R = Lv + i/D value, with the lower value corresponding to a value of the relative volatility close to 1. 

However, the total number of equilibrium stages N, N/N,n, or the external-reflux ratio can be substituted for one of these three specifications. It should be noted that the feed location is automatically specified as the optimum one this is assumed in the Underwood equations. The assumption of saturated reflux is also inherent in the Fenske and Underwood equations. An important limitation on the Underwood equations is the assumption of constant molar overflow. As discussed by Henley and Seader (op. cit.), this assumption can lead to a prediction of the minimum reflux that is considerably lower than the actual value. No such assumption is inherent in the Fenske equation. An exact calculational technique for minimum reflux is given by Tavana and Hansen [Jnd. E/ig. Chem. Process Des. Dev., 18, 154 (1979)]. A computer program for the FUG method is given by Chang [Hydrocarbon Process., 60(8), 79 (1980)]. The method is best applied to mixtures that form ideal or nearly ideal solutions. 

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,... 

Because a column cannot operate at total reflux and produce net product from the column, a reflux ratio of about 1.1 to 1.5 times the mmmMm reflux will usually give practical results. Be aware that as the reflux ratio comes down approaching the minimum, the number of theoretical and then corresponding actual trays must increase. 

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,... 

Example 8-25 Scheibel-Montross Minimum Reflux, 80 Minimum Number of Trays Total Reflux — Constant Volatility, 80 Chou and Yaws Method, 81 Example 8-26 Distillation with Two Sidestream Feeds, 82 Theoretical Trays at Operating Reflux, 83 Example 8-27 Operating Reflux Ratio, 84 Estimating Multicomponent Recoveries,... 

The program starts up the column at total reflux (R very high). After steady state is reached on all plates, vary the reflux ratio interactively and attempt to carry out the distillation in minimum time, while attempting to... 

The two most frequently used empirical methods for estimating the stage requirements for multicomponent distillations are the correlations published by Gilliland (1940) and by Erbar and Maddox (1961). These relate the number of ideal stages required for a given separation, at a given reflux ratio, to the number at total reflux (minimum possible) and the minimum reflux ratio (infinite number of stages). 

Example 11.2 Using the Underwood Equations, determine the best distillation sequence, in terms of overall vapor load, to separate the mixture of alkanes in Table 11.2 into relatively pure products. The recoveries are to be assumed to be 100%. Assume the ratio of actual to minimum reflux ratio to be 1.1 and all columns are fed with a saturated liquid. Neglect pressure drop across each column. Relative volatilities can be calculated from the Peng-Robinson Equation of State with interaction parameters assumed to be zero (see Chapter 4). Determine the rank order of the distillation sequences on the basis of total vapor load for ... 

The errors associated with the Underwood Equations were discussed in Chapter 9, which tend to underpredict the minimum reflux ratio. This introduces uncertainty in the way that the calculations were carried out in Examples 11.2 and 11.3. The differences in the total vapor load between different sequences are small and these differences are smaller than the errors associated with the prediction of minimum reflux ratio and minimum vapor load using the Underwood Equations. However, as long as the errors are consistently low for all of the distillation calculations, the vapor load from the Underwood Equations can still be used to screen between options. Nevertheless, the predictions should be used with caution and options not ruled out because of some small difference in the total vapor load. 

Equality constraints. The Eduljee correlation involves two parameters Rm, the minimum reflux ratio, and Nm, the equivalent number of stages to accomplish the separation at total reflux. His operating equations relate N, a, XF, XD, and XB (see Table El2.4A for notation) all of which have known values except XB as listed in Table E12.4A. Once R is specified, you can find XB by sequential solution of the three following equations. 

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