aixi,F
FIG. 13-41 Comparison of rigorous calculations with Gilliland correlation. [Henley and Seader, Equilibrium-Stage Separation Operations in Chemical Engineering, Wiley, New York, 1981; data of Van Winkle and Todd, Chem. Eng., 78(21), 136 (Sept. 20, 1971); data of Gilliland,, Elements of Fractional Distillation, 4th ed., McGraw-Hill, New York, 1950; data of Brown and Martin, Trans. Am. Inst. Chem. Eng., 35, 679 (1939).]
FIG. 13-41 Comparison of rigorous calculations with Gilliland correlation. [Henley and Seader, Equilibrium-Stage Separation Operations in Chemical Engineering, Wiley, New York, 1981; data of Van Winkle and Todd, Chem. Eng., 78(21), 136 (Sept. 20, 1971); data of Gilliland,, Elements of Fractional Distillation, 4th ed., McGraw-Hill, New York, 1950; data of Brown and Martin, Trans. Am. Inst. Chem. Eng., 35, 679 (1939).]
or as
The relative volatilities a are defined by Eq. (13-33), Rm is the minimum-reflux ratio (Ln+i/D)min, and 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 xiF values are available from the given feed composition. The © 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 ahk and alk, 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 n-C4 and the heavy key is i-C5.
The a values in Eqs. (13-37) and (13-38) are effective values obtained from Eq. (13-35) or Eq. (13-36). Once these values are available, © can be calculated in a straightforward iteration from Eq. (13-38). Since the (a - ©) difference can be small, © should be determined to four decimal places to avoid numerical difficulties.
The (xt,o)m 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. en the light key and the heavy key are adjacent in relative volatility and the specified split 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 (xt D)m 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.).
The FUG method is convenient for new-column design with the following specifications:
1. R/Rm, the ratio of reflux to minimum reflux
2. Split on the reference component (usually chosen as the heavy key)
3. Split on one other component (usually the light key) However, the total number of equilibrium stages N, N/Nm, 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 [Ind. Eng. 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 1: Calculation of FUG Method A large butane-pentane splitter is to be shut down for repairs. Some of its feed will be diverted temporarily to an available smaller column, which has only 11 trays plus a partial reboiler. The feed enters on the middle tray. Past experience on similar feeds indicates that the 11 trays plus the reboiler are roughly equivalent to 10 equilibrium stages and that the column has a maximum top-vapor capacity of 1.75 times the feed rate on a mole basis. The column will operate at a condenser pressure of 827.4 kPa (120 psia). The feed will be at its bubble point (q = 1.0) at the feed-tray conditions and has the following composition on the basis of 0.0126 (kg-mol)/s [100 (lb-mol)/h]:
Component
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