Total reflux ratio

For a given product purity of x D = 0.70, Mujtaba and Macchietto (1997) solved the maximum profit problem for a number of cost parameters using the method described above. The results are presented in Table 9.3. For each case, Table 9.3 also shows the optimal batch time, amount of product, reflux ratio, total reboiler duty and maximum conversion (calculated using the polynomial equations). 

Type of condenser Reflux ratio Total Total... 

Two limits of reflux ratio total reflux and minimum reflux... 

A8.2.1 A sufficient quantity of the sample is distilled in a low efficiency column under atmospheric pressure at zero reflux ratio (total takeoff) to 130 C, the water decanted, and dry components recombined. 

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... 

Beyond certain limits increase of the reflux ratio does not appreciably increase the separating power or efficiency of the column. As a rough guide, if the column has an efficiency of n plates at total reflux, the reflux ratio should be between 2>t/3 and 3n/2. 

Fig. 13. Fixed, operating, and total costs of a typical distillation, as a function of reflux ratio.

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. 

Example 8 Calculation of Rate-Based Distillation The separation of 655 lb mol/h of a bubble-point mixture of 16 mol % toluene, 9.5 mol % methanol, 53.3 mol % styrene, and 21.2 mol % ethylbenzene is to be earned out in a 9.84-ft diameter sieve-tray column having 40 sieve trays with 2-inch high weirs and on 24-inch tray spacing. The column is equipped with a total condenser and a partial reboiler. The feed wiU enter the column on the 21st tray from the top, where the column pressure will be 93 kPa, The bottom-tray pressure is 101 kPa and the top-tray pressure is 86 kPa. The distillate rate wiU be set at 167 lb mol/h in an attempt to obtain a sharp separation between toluene-methanol, which will tend to accumulate in the distillate, and styrene and ethylbenzene. A reflux ratio of 4.8 wiU be used. Plug flow of vapor and complete mixing of liquid wiU be assumed on each tray. K values will be computed from the UNIFAC activity-coefficient method and the Chan-Fair correlation will be used to estimate mass-transfer coefficients. Predict, with a rate-based model, the separation that will be achieved and back-calciilate from the computed tray compositions, the component vapor-phase Miirphree-tray efficiencies. 

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,... 

Derivatives or rates of change of tray and condenser-reflux drum hquid holdup with respecl to time are sufficiently small compared with total flow rates that these derivatives can be approximated by incremental changes over the previous time step. Derivatives of liquid enthalpy with respect to time eveiywhere can oe approximated in the same way. The derivative of the liquid holdup in the reboiler can likewise be approximated in the same way except when reflux ratios are low. 

Colburn relationship found that the optimum number of trays varies from 2 to 3 times the number at total reflux. Gilliland [Ind. Eng. Chem, . 32, 1220 (1940)] from the establishment of an empirical relationship between reflux ratio and theoretical trays based on a study of existing columns indicated that... 

N = Total equilibrium stages in the column including reboiler and partial condenser R = Actual reflux ratio... 

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. 

As the reflux ratio is decreased from infinity for the total reflux condition, more theoretical steps or trays are required to complete a given separation, until the limiting condition of Figure 8-23 is reached where the operating line touches the equilibrium line and the number of steps to go from the rectifying to stripping sections becomes infinite. 

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,... 

UK. = Light key component in volatile mixture L/V = Internal reflux ratio L/D = Actual external reflux ratio (L/D) ,in = Minimum external reflux ratio M = Molecular weight of compound Mg = Total mols steam required m = Number of sidestreams above feed, n N = Number of theoretical trays in distillation 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 Nrain = Minimum number of theoretical trays in distillation tower (not including reboiler) at total or infinite reflux. For partial condenser system,... 

Distillation calculations result in a reflux ratio L/D = 0.8, with 4 theoretical trays for rectification and 4 theoretical trays for stripping, or a total of 8 trays. The design heat balance (neglecting heat losses) is as follows ... 

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). 

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