Thermal Condition of the Feed

Thermal Condition of the Feed The slope of the operating line changes whenever a feed stream or a sidestream is passea. To calculate this change, it is convenient to introduce a quantity q which is defined by the following equations for a feed stream F ... 

The primes denote the streams below the stage to which the feed is introduced. The is a measure of the thermal condition of the feed and represents the moles of saturated hquid formed in the feed stage... 

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. ... 

Underwood minimum reflux constant XjF = Mol fraction of component i in the feed XjD = Mol fraction of component i in the distillate q = Thermal condition of the feed Bubble point liquid q =1.0 Dew point vapor q =0 General feed q = (Ls - Lr)/F... 

The thermal condition of the feed is designated as q, and is approximately the amount of heat required to vaporize one mole of feed at the feed tray conditions, divided by the latent heat of vaporization of the feed. One point on the q line is on the 45° line at Xp. 

Reading Figure 8-17 for (L/D)niin assuming a liquid feed at the boiling point, (L/D)niin = 1-2- This demonstrates the value of taking the thermal condition of the feed into account. 

The q vtilue is the same as previously described for the thermal condition of the feed. 

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. 

The flow rates above and below the feed stage are related by the liquid-vapor proportions of the feed stream, or more generally by the thermal condition of the feed, q, which is the ratio of the heat ... 

Figure 13.7. Features of McCabe-Thiele diagrams for constant molal overflow, (a) Operating line equations and construction and minimum reflux construction, (b) Orientations of -lines, with slope = ql q — 1), for various thermal conditions of the feed, (c) Minimum trays, total reflux, (d) Operating trays and reflux, (e) Minimum reflux determined by point of contact nearest xD.

The Gilliland correlation appears to be conservative for feeds with low values of q (the thermal condition of the feed), and can be in error when there is a large difference in tray requirements above and below the feed. The principal value of the correlation appears to be for preliminary exploration of design variables which can be refined by computer calculations. Although it is often used for final design, that should be done with caution. Other possibly superior but more difficult to use correlations have been proposed and are described in standard textbooks for example, Hines and Maddox (1985). 

Underwood s method (36). This method solves an equation which relates feed composition, thermal condition of the feed, and relative volatility at the average temperature of the column for a factor 6 which lies numerically between the relative volatilities of the keys. This factor is substituted in a second equation which relates minimum reflux to relative volatility and distillate composition. The method assumes constant relative volatility at the mean column temperature and constant molar overflow (Sec. 2.2.2). This method gives reasonable engineering accuracy for systems approaching ideality (28). The Underwood method has traditionally been the most popular for minimum reflux determination, When no distributed key components are present, the method is... 

It takes on the following values for various thermal conditions of the feed ... 

The relative volatilities are defined by Eq. (13-33), R m is the minimum reflux ratio, and q describes the thermal condition of the feed (1 for a saturated liquid feed and 0 for a saturated vapor feed). The Zfj values are available from the given feed composition. The 0 is the common root for the top section equations and the bottom section... 

The manner in which rectifying and stripping-section calculations are meshed at the feed stage depends upon the thermal condition of the feed. Eig-ure 13-45 shows three possible ways in which fresh feed can affect the L and V rates between the feed stage and stage M -H 2. The superscript bar denotes the stream rate when the stream enters a stage, while the lack of a bar denotes the rate when the stream leaves a stage. 

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