Light key

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. 

Phase separation in this way is most effective if the light key component is significantly above its critical temperature. If a component is above its critical temperature, it does not truly condense. Some, however, dissolves in the liquid phase. This means that it is bound to have an extremely high K value. 

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.). 

With respect to selecting measurements, emphasis should include measurements within the equipment such as tower internal temperatures and compositions, internal reac tor conditions, and intermediate exchanger temperatures in multipass exchangers. Trace component compositions provide particular insight into distillation-column performance. Those components that fall between the heavy and light keys and distribute in the products can usually be described by a variety of models and parameter estimates They provide little insight into the column performance. 

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. 

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... 

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... 

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. 

In general, light ends towers are named after the light key. Thus, a depropanizer will take overhead the propane and lighter in the feed, and will have butane and heavier as the bottoms product. 

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)... 

Yn + 1 = average light key mol fraction of vapor entering plate n... 

Diffusivity of the liquid light key component is calculated by the dilute solution equation of Wilke-Chang [243]. 

LK = liquid light key mix = binary mixture n = plate number t = total... 

Bto = mols total batch charge to still V = total mols per hour vapor overhead XiD = mol fraction light key component in overhead product... 

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. 

Light key the designation of the key component with the highest 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 ... 

Also calculate co for all components lighter than light key. 

Determine approximate pinch zone liquid composition for light key component... 

Note that the calculations are only made for the heavy key, h light key, 1 and all components lighter than it, L. If there are split keys, the calculation is to include all components lighter than the heavy key. Stripping pinch compositions ... 

Because the second term of the denominator is usually negligible when the light key in the bottoms is very small less them 0.1 mol fraction, this term is often omitted. 

Note that these calculations are made for the light key, 1 heavy key, h and all components heavier them the heavy key, H. For split key systems, the calculations are made for all components heavier them the light key. 

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