Number of Equilibrium Stages

Gilliland correlation is used to calculate number of equilibrium stages, N. Select a reflux ratio that isR = (1.1 - 1.5)] n,in 

The Gilliland correlation is good for preliminary estimates, but has some 

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N Number of equilibrium stages X Mole fraction in liquid ... 

Apphcation of a constant efficiency to each stage as in Fig. 13-40 will not give, in general, the same answer as obtained when the number of equilibrium stages (obtained by using the true-equilibrium cui ve) is divided by the same efficiency factor. 

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. 

Equations (13-40) and (13-41) are plotted in Fig. 13-43. Components having large values of or absorb or strip respectively to a large extent. Cooresponding values of and approach a value of 1 and are almost independent of the number of equilibrium stages. 

An estimate of the minimum absorbent flow rate for a specified amount of absorption from the entering gas of some key component K for a cascade with an infinite number of equilibrium stages is obtained from Eq. (13-40) as... 

One way of calculating the number of equilibrium stages (or number of theoretical plates, NTP) for a mass exchanger is the graphical McCabe-Thiele method. To illustrate this procedure, let us assume that over the operating range of compositions, the equilibrium relation governing the transfer of the pollutant from the... 

From Fenske s equation, the minimum number of equilibrium stages at total reflux is related to their bottoms (B) and distillate or overhead (D) compositions using the average relative volatility, see Equation 8-29. 

The combined Fenske-Underwood-Gillilland method developed by Frank [100] is shown in Figure 8-47. This relates product purity, actual reflux ratio, and relative volatility (average) for the column to the number of equilibrium stages required. Note that this does not consider tray efficiency, as discussed elsewhere. It is perhaps more convenient for designing new columns than reworking existing columns, and should be used only on at acent-key systems. 

Figure 4. Effect of number of equilibrium stages on heating value and H2 content of product gas Conditions 20 atm, 371 °C, and Hu.CO = 3 1...

In this type of apparatus, the two phases do not come to equilibrium, at any point in the contactor and the simulation approach is based, therefore, not on a number of equilibrium stages, but rather on a consideration of the relative rates of transport of material through the contactor by flow and the rate of interfacial mass transfer between the phases. For this, a consideration of mass transfer rate theory becomes necessary. 

Consider the accuracy of the equilibrium data required to calculate the number of equilibrium stages needed for the separation of a mixture of acetone and water by distillation (see Chapter 11, Example 11.2). Several investigators have published vapour-liquid equilibrium data for this system Othmer et al. (1952), York and Holmes (1942), Kojima et al. (1968), Reinders and De Minjer (1947). 

Determine the stage and reflux requirements the number of equilibrium stages. 

A column is to be designed to separate a mixture of ethylbenzene and styrene. The feed will contain 0.5 mol fraction styrene, and a styrene purity of 99.5 per cent is required, with a recovery of 85 per cent. Estimate the number of equilibrium stages required at a reflux ratio of 8. Maximum column bottom pressure 0.20 bar. 

Number of equilibrium stages above and below the feed point. 

However, before the above set of equations can be solved, many important decisions must be made about the distillation column. The thermal condition of the feed, the number of equilibrium stages, feed location, operating pressure, amount of reflux, and so on, all must be chosen. 

Equilibrium data and material-and heat-balances to determine the number of equilibrium stages (theoretical plates or transfer units) required for the desired separation. The required height of the column can be calculated if data are available for the specific rate of transfer of material between the two phases, expressed in terms of the plate-efficiency or the height of one transfer unit. 

In the TAYLOR method, the number of equilibrium stages are fixed by the user, as are the amounts of products, including side-streams. As options, the reflux ratio may be specified or found in the calculations. As output, the program gives the complete temperature, flow rate, and composition gradients. 

A short-cut design method for distillation is another subroutine. This method is based upon the minimum reflux of Underwood (17, 18, 19, 20), the minimum stages of Fenske (21) and Winn (22), and the reflux vs stages correlation of Erbar and Maddox (23) and Gray (24). In SHORT, which uses polynomial K and H values, the required number of equilibrium stages may be found for a specified multiple of minimum reflux, or alternatively, the reflux ratio may be found for a given multiple of minimum stages. 

Thus, the key result from the tray-by-tray calculation is that the column design must ensure complete alcohol consumption in the reactive zone, only lauric acid and water are allowed in the top vapor stream. The column behaves more as a reactive absorber than reactive distillation. A higher number of equilibrium stages... 

Too low a reflux ratio cannot produce the required product specification no matter how many trays are installed. Conversely, even infinite reflux will not be sufficient if an inadequate number of equilibrium stages has been provided. 

It is reasonable to allow a pressure drop of 3 mmHg per tray. Then the reboiler pressure will be 50 + 3(157) = 521 mmHg. At this pressure, the relative volatility (from Fig. 8.22) is 1.14, and the average relative volatility in the column is then (see step 1) (1.265 + 1.14)/2 = 1.2. From Fig. 8.5, the estimated number of equilibrium stages is 107, which confirms that the initially selected 110 trays was a reasonable assumption. 

Chemical equilibrium constant for dimerization Liquid-liquid distribution ratio Liquid flow rate Number of equilibrium stages Number of relationships Number of design variables Minimum number of equilibrium stages Number of phases Number of repetition variables Number of variables Rate of mass transfer Molar flux... 

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