I LO CAT I NGn designing new columns or analyzing existing columns, the feed tray must he located, either explicitly by setting the total number of trays in each section, or implicitly by setting optimum feed location (11). Doing this presents a real problem and considerable uncertainty is involved. A misplaced feed can seriously impair separation efficiency. These facts are well known, hut apparently a quantitative analysis of the problem has not been attempted. In this article, the results of such an analysis for a typical depropanizer operation is given, and three new approaches to the problem are suggested.
I
Analysis of Depropmirer
Distillate and bottom rates for the depropanizer were chosen so that, given enough trays and reflux, the propane and isohutane would be completely separated (Table I). Computations were made on a Burroughs B-205 computer, programmed for the Thiele-Geddes calculation (27). This program uses the Braun equilibrium ratios (3, 72). Internal flow rates were established by enthalpy-halancing around each tray, using standard pure component enthalpies (2, 16, 19). Program. For computer calculation, the ThieleGeddes method has two advantages over the more common Lewis-Matheson technique (74). It uses integral numbers of theoretical trays, and thus eliminates the problem of how to handle fractional trays. Also, it cames all feed components entirely through the column. This avoids the problem of how to add the “ disappearing” components which are present in negligihle concentrations in either product stream. However the Thiele-Geddes method is practically impossible for hand computation, because it requires assumption of all temperatures in the column before making an iteration. With a computer, such calculations are entirely feasible. In the work described here, estimated temperature gradients or a constant temperature is used for the first iteration; for subsequent iterations, temperatures were corrected for each tray in proportion to the extent that sums of mole fractions deviated from Unity. 34
INDUSTRIAL AND ENGINEERING C H E M I S T R Y
R. 6. FLOYD H. C . H l P K l N
FEED I l r
TRAYS H m much does a misplaced feed tray cost?
I
IN
F R A C T IO N A T O R S The program continues to iterate until all compositions on all trays add up to unity within a specified tolerance. For all trays it was specified that ZX = ZY = 1.000 f. 0.001. When the worst tray meets this criterion, the sums of mole fractions for other trays are closer to unity. Results
x
I n the test depropanizer, product contamination approximated that found in most commercial units, and the pattern of key compositions was as expected. For separation of propane and isobutane an optimum feed location existed for each total number of trays (Table 11, and Figures 2 and 3). Interestingly, this location when expressed in a relative fashion remains essentially constant for the key components, regardless of the total number of trays. Also, for minimum contamination of products by disappearing components, relative feed location is independent of the total number of trays, but the relative feed location where the optimum occurs differs from that for the key components (Figures 4-7). Further, it is different for each component-the more volatile the component, the higher its optimum feed location. For pentane, however, the least volatile component in the feed, it was startling to find distillate contamination was highest when the feed was placed too low. Thus feed location is important. Separation efficiency can be seriously impaired by misplacing the feed only a few trays. This is true for misplacement either higher or lower than optimum. Criteria for locating Feed Troy
For binary systems, rigorous criteria have been developed (75). For example for saturated liquid feed, composition on the feed tray should be the same as that of the feed. For multicomponent systems, however, these two compositions usually differ, and no rigorous criteria have been developed. Optimum location is where separation is achieved with fewest trays (20). Several empirical criteria have been developed (70, 76, 78,ZO). Figure 8 shows optimum location in the depropanizer, placed by criteria of Maxwell (76) and Gilliland (70). Both methods are adequate.
Component
Feed, Moles/ Hr .
Ethane Propylene Propane Isobutane n-Butane Pentane
50 150 350 200 150 100
io00
Run Number
Total Trays
Rectiyying Trays
Strippin,< Trays/ Total Trays
5
29 29 29 29 29
14 10 6 19 23
0.52 0.66 0.79 0.35 0.21
21 22 6 7 8
29 29 21 21 21
28 1 27 14 10
0.035 0.965 0.19 0.33 0.52
9 10 11 12 13
21 21 25 25 25
7 18 13 10
0.67 0.81 0.28 0.48 0.60
14 15 16 17 18
25 25 17 17 17
8 5 16 11 7
0.68 0.80 0.06 0.35 0.59
la
2 3 4
4
19 17 3 0.82 1 20 17 0.94 Run I was done twzce. Dzferences in compositaon resulted from wide summation tolerances allowed. Other rum were made with the tighter
summation tolerances noted in the text.
VOL. 5 5
NO. 6 J U N E 1 9 6 3
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4
n
RESULTS O F COMPUTER STUDIES
OF
A TYPICAL DEPROPANIZER
For the uwlysis of n &pmpanim, D toto1 of 22 scparationr were made, w i n g f w feed hay locationrfor each of 77, 27, rmd 25 total thcorcticd t r a y ond rmmfeed tray lmationr f w 29 theorcticol trays. Dbtillation and bottom rate$ were chosen so that given enough hays and reflux, the propme and butmc would be sepporated completely. Feed composition and t h m a l condition, rCpux rotio, ond ratio of distillntc to bottomr werefxed
.
SI,? '03 v
J
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