Fig. 7-6. Optimum reflux ratio.
operating line to the other must therefore occur at some value of x between the values corresponding to c and e, and a change at any value within this range will give an operable design. In general, for a given reflux ratio, it is desired to carry out the rectification with as few plates as possible in order to reduce the plant costs; i.e., the minimum number of steps from a to d between the equilibrium curve and the operating line is desired. This minimum number of steps for the design conditions selected is obtained by taking the largest possible steps at all points between a and d. It is obvious that for values between e and b larger steps will be obtained between the equilibrium
Fig. 7-7. Diagram for limits of feed-plate be obtained for the operating con-
to fall directly on b, then the feed may be introduced either at b or on the plate below without changing conditions.
/Partial vs. Total Condenser, In the foregoing discussion the column was assumed to be operating with a total condenser, i.e., a condenser that completely liquefies the overhead vapor and returns a portion of the condensate as reflux, removing the remainder as product. However, partial condensers are quite frequently used in commercial operations, especially where complete liquefaction of the overhead would be difficult. In this case, only enough condensate for the reflux to the column may be produced, and the product is withdrawn as a vapor. In other cases, mixtures of vapor and liquid are withdrawn. For example, in gasoline stabilizers employed by the petroleum industry, where the overhead contains appreciable percentages of methane, ethane, and ethylene, together with C3 and C4 hydrocarbons, in order to condense the methane and C2 hydrocarbons, very low temperatures
x curve and operating line abc than would be obtained with operating line dbe. Likewise, for values between c and b larger steps will be obtained by using line dbe than by using abe. Therefore it is desirable to use operating line abc for values from a to b, and line dbe for values between d and 6; and by making the feed plate, i.e., the shift from one line to the other, straddle the value b, the minimum number of theoretical plates will composition.
ditions chosen. If a step happens would be required with resulting high refrigeration costs. However, sufficient of the C3 and C4 hydrocarbons can be liquefied at moderate temperatures and pressures to serve as reflux, and the remainder of the overhead containing a large portion of the Ci and C2 hydrocarbons can be removed as vapor and sent to the gas lines.
A partial condenser may operate in any of several ways:
1. The cooling may be so rapid and the contact between condensate and uncondensed vapor so poor that essentially no transfer of components back and forth is obtained, with the result that the condensate and uncondensed vapor are of the same composition. (This is possible if part of the vapor condenses completely and the balance does not condense at all.) In this case, the partial condenser is equivalent to the total condenser with the exception that the product is removed as vapor instead of as liquid.
2. The vapor product may be in sufficiently good contact with the returning reflux for the two to be in equilibrium with each other, in which case the partial condenser acts as a theoretical plate, and one less theoretical plate may be used above the feed plate in the column when this condition exists than when a total condenser is employed. Such a condition can be approximated by requiring an overhead vapor to bubble through a pool of reflux to the column.
3. The vapor is differentially condensed, and the equilibrium condensate continually removed, giving a differential partial condensation. Alternately, the vapor may be condensed on vertical tubes such that the condensate flows countercurrent to the rising vapor, and fractionation occurs between the vapor and condensate. Theoretically, such a condenser can give a separation equal to a number of theoretical plates; actually, such conditions are seldom employed, since to obtain efficient transfer of components from vapor to liquid, low rates of condensation per unit area are required, thus necessitating large and costly condensers, and, in general, it is found more satisfactory and cheaper to obtain additional rectification by adding more plates to the column and using a condenser to produce condensate rather than make it perform composite duties.
Actual partial condensers usually operate somewhere between Cases 1 and 2. For an absorption naphtha stabilizer, Gunness (Ref. 6) (see page 116) found good agreement with Case 2. In actual design calculation, the conservative assumption is to assume operation as in Case 1, and any fractionation that does occur will act as a factor of safety; with ordinary condenser design, with the most optimistic assumption, f-T-vJ-
not more than one theoretical plate should be taken for the partial condenser.
Open vs. Closed Steam. When rectifying mixtures in which the residue is water and in some cases where the mixture undergoing fractionation is immiscible with water, the steam for heating may be introduced directly into the still. Such a procedure may materially reduce the temperature and pressure of the steam necessary for the distillation by giving in effect a steam distillation.
Considering the distillation of an ethyl alcohol-water mixture, the lower operating line when a closed-steam heating is used was shown to have a slope of (0/V)m and to pass through the y = x line at x = xw. In Fig. 7-8, a column operating with S mols of live steam is shown. A material balance between the m and m + 1 plate gives s------
Fig. 7-8. Diagram of column using live steam.
and with the usual simplifying assumptions, S would equal Vm, making 0 = W. An alcohol balance gives
This is an operating line of slope 0m/Vm; but at x = y, x is equal to ^ xw instead of xw; and at x equal to xw, y becomes zero corresponding to the composition of the vapor (steam) to the bottom plate. For a given O/D and feed condition, 0m/Vm must be the same whether closed or open steam is used, so that the lower operating line must cross the y = x diagonal at the same x value in both cases, Xw for the live steam being lower than Xw for closed steam because of the dilution effect of the steam. In stepping off theoretical plates, the step must start at y = 0 and Xw; i.e., in Fig. 7-9, the bottom plate corresponds to the step abc. In such a case, the introduction of live steam can eliminate the still, but it dilutes the bottoms and requires more plates in the lower section of the column. Since the steps in the case of live steam start lower, it always requires at least a portion of a step to come up to the intersection of the operating line and the y = x
diagonal, and more plates are required with live steam than with closed steam. In Fig. 7-9, about 1% more plates would be necessary. One plate is needed to replace the still, and the additional "fraction of a plate" is required to offset the dilution.
As an example of using open steam to obtain a steam distillation, consider the steam stripping of an oil containing 2.54 mol per cent propane at 20 p.s.i. The temperature will be maintained constant at 280°F. by internal heating. The molecular weight of oil may be taken as 300, and 4 mols of steam will be used per 100 mols of oil stripped. It is desired to estimate the number of theoretical plates necessary to reduce the propane content of the oil to 0.05 mol per cent. The oil may be assumed nonvolatile, and the vapor-
2,6SmoJs C3Hq 4 mote Steam
4 mots Steam fOO mo/s Oil
0.05 mots CjH3
Fig. 7-10. Figure for illustration.
liquid relation of the propane in the oil may be expressed as y = 33.4$.
It is obvious that the mois of vapor will increase up the tower, since the steam does not condense under the conditions given, and the propane vaporizes into it as it passes up the tower. This will cause O/V to vary through the tower, and points on the operating line must
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