Heavy key

If the light and heavy key components form an azeotrope, then something more sophisticated than simple distillation is required. The first option to consider when separating an azeotrope is exploiting change in azeotropic composition with pressure. If the composition of the azeotrope is sensitive to pressure and it is possible to operate the distillation over a range of pressures without any material decomposition occurring, then this property can be used to... 

Ideally, the K value for the light key component in the phase separation should be greater than 10, and at the same time, the K value for the heavy key should be less than 0.1. Having such circumstances leads to a good separation in a single stage. However, use of phase separators might still be effective in the flowsheet if the K values for the key components are not so extreme. Under such circumstances a more crude separation must be accepted. 

Assuming a sharp separation with only the light key and lighter-than-light key components in the overheads and only the heavy key... 

Because only light key and lighter components go to the distillate and heavy key and heavier components go to the bottoms, Eq. (5.7) can be written in terms of the molar flow rate of each component in the feed ... 

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) ... 

The relative volatiHties Ot) are defined by Eq. (13-33), is the mini-mum-reflux ratio (L v + i/D)min,. nd 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 Xi p 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 06/, and Ot/, 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 /1-C4 and the heavy key is i-C. ... 

The (x, i )), values in Eq. (13-37) are minimum-reflux values, i.e., the overhead concentration that would be produced by the column operating at the minimum reflux with an infinite number of stages. When the light key and the heavy key are adjacent in relative volatihty and the specified spht between them is sharp or the relative volatilities of the other components are not close to those of the two keys, only the two keys will distribute at minimum reflux and the Xi D),n values are easily determined. This is often the case and is the only one considered here. Other cases in which some or all of the nonkey components distribute between distillate and bottom products are discussed in detail by Henley and Seader (op. cit.). 

In normal applications of extractive distillation (i.e., pinched, closeboiling, or azeotropic systems), the relative volatilities between the light and heavy key components will be unity or close to unity. Assuming an ideal vapor phase and subcritical components, the relative volatility between the light and heavy keys of the desired separation can be written as the produc t of the ratios of the pure-component vapor pressures and activity-coefficient ratios whether the solvent is present or not ... 

For more than two components, calculation is not so easy. Bounds can, however, often be perceived. If in the feed there is only an insignificant amount of materials of volatility intermediate between the light and heavy keys, the following applies ... 

Minimum total reflux (lbs or mols/hr) corresponding to given total feed will be greater than if only the actual total mols of heavy and light key components were present. Reflux need will be less than if the actual total mols of feed were present, but composed only of light and heavy keys. The more closely non-keyed components are clustered to volatilities of the keys, the nearer are reflux needs to that calculated for the binary and total feed volume. 

The value of 0 will lie between the relative volatilities of the light and heavy key components, which must be adjacent. 

LK = subscript for light key Nn, = minimum theoretical stages at total reflux Xhk = mol fraction of heavy key component Xlk = mol fraction of the light key component otLK/HK = relative volatility of component vs the heavy key component... 

B = subscript for bottoms D = subscript for distillate HK = subseript for heavy key... 

To determine the reasonableness of the top and bottom compositions of a fractionation column, a Hengstebeck plot is fast and easy (Reference 4). First, select a heavy key component and determine the relative volatility (a) of all column components to the heavy key. The a can be otfeed or perhaps more accurately cc = (a,op oCboitom) - Plot In D/B versus In a and the component points should fall close to a straight line. If a fairly straight line does not result, the compositions are suspect. A nomenclature table is provided at the end of this chapter. 

Relative volatility of component i versus the heavy key component... 

An additional series of process tests and plots can be helpful. The Delta-P over each section should be monitored and the reflux increased/decreased at constant bottom temperature. The composition of the heavy key in the overhead should be monitored. Plots should then be made of both Delta-P and of composition vs. reflux. Additional information concerning these tests can be found in Norman Lieberman s book entitled Troubleshooting Process Operations. ... 

N,n = Minimum theoretical stages at total reflux Q = Heat transferred, Btu/hr U - Overall heat transfer coefficient, Btu/hrfP"F u = Vapor velocity, ft/sec U d = Velocity under downcomer, ft/sec VD(js = Downcomer design velocity, GPM/fL Vioad = Column vapor load factor W = Condensate rate, Ibs/hr Xhk = Mol fraction of heavy key component Xlk = Mol fraction of the light key component a, = Relative volatility of component i versus the heavy key component... 

Problem A structured packing vacuum tower had too much heavy key in a vapor side-draw between the feed and the column bottom. The side-draw heavy key concentration was several times the design value. 

Select a heavy key component and compute of all components to this key. 

The following is a simplified estimating procedure for recovery in multicompnent distillation. In the working expressions provided below, the parameters b, d, and f rpresent the bottoms, distillate, and feed, respectively. Subscripts i, HK, and LK represent the component i, the heavy-key component, and the light-key component, repsectively. Relative volatility is represented by symbol a. Calculations can be readily set up on an Excel Spreadsheet. 

Sm = total number of calculated theoretical trays at total reflux, from Equation 8-30 X]k = xlk = liquid mol fraction of light key Xhk = xhk = liquid mol fraction of heavy key Ik - hk = LK - HK= average relative volatility of column (top to bottom)... 

Heavy key the designation of the key component with the lowest volatility of the two key components. 

For adjacent key systems, all components lighter than the light key appear only in the overhead, and all components heavier than the heavy key appear only in the bottoms, and the keys each appear in the overhead and bottoms in accordance with specifications. 

Yaws [124] et al. provide an estimating technique for recovery of each component in the distillate and bottoms from multicomponent distillation using short-cut equations and involving the specification of the recovery of each component in the distillate, the recovery of the heavy key component in the bottoms, and the relative volatility of the light key component. The results compare very well with plate-to-plate calculations. Figure 8-46, for a wide range of recoveries of 0.05 to 99.93% in the distillate. 

The correlation constants required for Equations 8-127 and 8-128 are obtained by specifying a desired recovery of the light key component LK in the distillate and the recovery of the heavy key component HK in the bottoms. Then the constants are calculated as follows ... 

Assume a multicomponent distillation operation has a feed whose component concentration and component relative volatilities (at the average column conditions) are as shown in Table 8-3. The desired recovery of the light key component O in the distillate is to be 94.84%. The recovery of the heavy key component P in the bottoms is to be 95.39%. 

From Equation 8-131 expressing 9 and q evaluate 9 by trial and error, noting that 9 will have a value between the a of the heavy key and the a of the light key evaluated at or near pinch temperatures, or at a avg. Suggested tabulation, starting with an assumed 9 t alue, 9a ... 

---