Computation of Distillat ion Apparatus for Hydrocarbon Mixtures E. W. THIELE AND K. L. GEDDES,Standard Oil Company (Indiana), Whiting, I n d -HE
A method of cornpulatiori i.s presented for the
d e v e l o p m e n t or
.
I
PRlNCIPLE O F
METHOD
for all components is assumed. The number of content of either of the conformance of a proposed colukn, so t h a t the d e r i e n of euuiw romnonenls may be pither f i d e or itrfinite. s t l t n e n t s in the vapor rking . . 1~ from a plate, provided the conment, so far as reflux ratio and p he method is &tended lo c&es ill which centration of that constituent number of plates are concerned, streams are druwn from the column, or the feed in l i q u i d on tile plate is has depended on e x p e r i e n c e Work been is admitted ut more than one point. k n o w n or vice v e r s a . Likewise a material balance makes duited in this laboratory for a number of years with a view t,o supplying the deficiency, and ponsible t.he computation of the concentration of either cont,he metlrod diicli has been developed is described in this stituent on a plate from its concentration in the vapors paper. It makes possible the solution of such problems rising from the plate below, provided that the liquid and vapor with a minimum of simplifying assumptions and witliout the quantities, and the concentration of the constituent in tlie expenditure of an unreasonable amount of labor. It has product, are known. Hence, when product compositions actually been used with success to attack a number of different have been assumed, it is possible to pass from plate to plate, column problems. computing liquid and vapor compositions successively. I n That the need for a method has been felt byothorsisshown the case of mixtures containing more than three components, by the recent appearance of a number of articles on the sub- tlie equations based on the material balance are still valid ject (2, 9, 4,8, 12). These methods, as well as tlie present but two difficulties arise. On tlie one hand, the concentraone, all agree in assuming that Raoult’s law or some modifioa- tion of B constituent in a vapor is not fixed m.heu its eoncentration of it is sufficiently valid for hydrocarbon mixtures, and tion in the corresponding liquid is known; the concentrations that the plate efficiency is the same for all constituents. The of all the other constituents of the liquid must also be k n o m . present method is believed, however, to have several ad- On the other hand, tlie composition of the products cannot be vantages over these various methods: (1) the computations arbitrarily chosen or assumed, because out of all the conare comparatively straightforward; (2) no further simplifying ceivable combinations of the constituents only a limited sssumptions are made; (3) it is worked out for mixtures in number can actually occur as products of a separation in a which individual constituents are not distinguishable; (4) single column. it is worked out for columns of any complexity. The method here proposed to overcome these difficulties is ~~
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INDUSTRIAL AND ESGINEERING CHEMISTRY
290
to fix in the first instance both the number of theoretical plates in the column, as well as the heat input, and to assume tentatively the temperature on each plate, since the composition of the products is the thing to be determined. This a t once makes possible a calculation of the concentration of each constituent in the vapor in equilibrium with a liquid when the concentration of that constituent in the liquid is known, or vice versa, provided that Raoult’s law can be assumed throughout. Since the composition of the products is not assumed but is to be found, it might appear that the material
1
4 (I. -2
15,700 GAL. 806 MOLES 53.44A.ll.
ro0,ooo La.
1-
(
I275
1079
13))1
PO3
0.2543
LJSS]
)
103
0.8470
Vol. 25, No. Y
of pure hydrocarbons of definite boiling point, (2) as composed of an infinite number of constituents, or (3) as composed of certain definite components in the lower range of boiling points, and of an infinite number in the upper range. The first assumption will be used for the most part; the necessary alterations by which the others may be used will be explained.
EXAMPLE OF COLUMN COMPUTATION METHOD The method will be illustrated by application to a simple reboiling column operated a t atmospheric pressure, without steam. The column is shown diagrammatically in Figure 1; it consists of two perfect plates above and one below the feed, with a reboiling still, and reflux returned a t the boiling point. The composition of the feed, a treated pressure distillate, is shown in Figure 2, the continuous line representing the actual true boiling point analysis, and the steps the assumed equivalent hydrocarbons. The steps are drawn so as to leave approximately equal areas on each side of the actual line. The assumption of nineteen constituents is considered sufficient in this case. The feed enters the column as a liquid a t 100” F. The feed of quantity as given in Figure 1 is assumed to go to overhead and bottoms of the indicated gravities in the proportions shown. The heat input to the reboiler is 28,579,000 B. t. u. per 15,700 gallons (100,000 pounds) of feed. The problem is to determine the composition of the two products under these conditions. I n column 1 of Figure 1 are given the plate temperatures assumed; column 2 gives the assumed gravities of the liquids on the plates above the feed, and the liquid gravities of the vapors below the feed.
LO10 GAL. 196, M O L E S 28,579.000
8.T.U.
31
A.P.I.
FIGURE1. COLUMN WITH REBOILER balance equations could not be used. It turns out, however, that they can still be used to find the ratios of the concentrations of the constituents in the overhead and the bottoms, and this, combined with the known concentration in the feed, is sufficient to fix values of the concentration of each constituent in each liquid and vapor up and down the column. The sum of the concentrations thus found for the constituents of the various vapors and liquids will not, however, be equal to unity unless the original tentative assumptions as to the plate temperatures have been correct. The deviations from unity which are found when the calculation has been completed make possible a more correct assumption of temperatures for another trial, and so on. I n making heat balances to determine liquid and vapor quantities, the gravities of the various liquids and vapors have to be assumed, but accuracy in these assumptions is relatively unimportant. The composition of the feed is given by a true boiling point analysis. Theoretically, a perfect fractionation should be obtained, but for practical purposes a good column fractionation is sufficient. I n this investigation, the least efficient equipment which has been used with satisfaction comprises a 94-cm. vacuum-jacketed column (16 mm. internal diameter), packed with 5.5-mm. glass beads, a t a reflux ratio of 10 to 1, when a charge of about one liter is used. It is obvious that the labor of obtaining an exceedingly close fractionation of a proposed feed to a column would be unwarranted in view of the normal variation of composition of feed to a practical column in the refinery. For the light ends of gasoline a Podbielniak analysis is suitable. The resulting curve of percentage off against true boiling point may be treated either (I) as equivalent to a mixture of a moderate number
0
10
20 30 4 0 5 0 60 70 80 90 WEIGHT PERCENT DISTILLED
0
FIGURE2. TRUEBOILING ANALYSIS OF TREATED PRESSURE DISTILLATE These quantities, from which all the other quantities may be derived, are encircled or underlined to distinguish them from the others. (Sssumption of gravities and temperatures are sufficient to permit the molal quantities within the column to be calculated from heat balances, since the total heat of a stock may be expressed in terms of the temperature and gravity, and the molecular volume may be expressed as a function of the gravity.) Study will show that these quantities may be differentiated into two classes, which will be termed “primary assumptions” and “trial values.’’ The primary assumptions, shown underlined in the figure, are connected with variables, such as number of plates above and below the feed, heat input (or reflux ratio), and split of the feed in quantity between overhead and bottoms, which may
&larch, 1933
INDUSTRIAL AKD ENGINEERISG
CHEMISTRY
291
be given any desired arbitrary values (within limits). The trial values, shown encircled, are connected with variables, such as temperatures and gravities, which acquire fixed although as yet unknown values as soon as the primary assumptions are settled. Thus, any column problem reduces itself to the fixing of the primary assumptions and then adjustment by trial and error of the trial values until the correct values of the latter have been determined, the final result being to establish the product composition and the true values of the quantities for which trial values are required, for the given values of the primary assumptions. Relationships between molecular weights, boiling pointy, gravities, vapor pressures, total heatq, etc., are taken largely from published sources (1,i,6,7',13). The results of the heat balances are given in Figure 1: within the column are shon n the calculated liquid and vapor molal flows from plate to platc The drawing up of heat balances to determine the molal quantities within the column is made easier by considering the liquid and vapor streams within the column in the folloning JTay, which is most conveniently explained by referenre to Figure 3. I n that part of the column above the feed plate, the vapor rising from a plate is conceived of a5 consisting of two parts, one equal in quantity and composition (but not in temperature) to the net overhead product, the other equal in quantity and composition to the liquid overflow from the next plate above. This latter is a quantity which, so far as the heat balance is concerned, may be considered a. rising from a plate as vapor to the next plate above where it is condensed and returned as liquid reflux, "circulating," so to speak, between the two plates. Below the feed plate, in a similar manner, the liquid overflow from a plate is conceived of as consisting of two parts, one of the quantity and composition of the bottoms, the other of quantity and composition of the vapors rising t o the plate from the plate below (here the reboiler). An example of the heat balance for determining the molal quantities between plates 2 and 3 is as follows: Taking that part of the column below a plane drawn between plates 2 and 3 (all total heats are per gallon with 0" F. as base temperature), we h R ve : Heat entering: Feed (53.4" A. P. I. and 100' F.) 15,700 X 303 Reboiling heat Heat leaving: Bottoms (37" A. P. I. and 435" F.) 5010 X 1676 Product (62.5" A. P. I. and 355' F.) 10.690 X 1913
=
4,755,000 B. t. u. 28,579,000 33,334,000 =
8,395,000 =
20.460.000 I
,
28,855,000 Heat leaving section due to vaporization of overflow from plate 3: A. P.I. and Each gallon vaDor . (42.5" . 355' F.) Each gallon liquid (42.5' A. P. I. and 322" F.) Net heat leaving per gallon of reflux Gallons of overflow = 4,479,000 ____ R11 4920-2-8. 33 Moles of overflow = 193
4,479,000 =
2060 B. t. u.
=
=
1149 911
=
4920
=
212
Here 193 is the molecular volume corresponding to the assumed gravity of the liquid on plate 3, and 8.33 is the i\eight in pounds of one gallon of water a t 60" F. Hence the total moles of vapor rising to plate 3 will be 610 212 = 822. The details of the first trial computation are given in Table I; the nomenclature used in the subsequent discussion is as folloTvs:
+
I N D U S T R I A L A N D E:N G I N E E R I N G C H E M I S T R Y
292
n = subscripts for plates, numbered from bottom upward (reboiler = 0) v, = vapor risin from late n, moles 0, = liquid overlowing From plate n to plate (n - I), moles 2, = mole fraction of constituent in liquid on plate n Yn = mole fraction of constituent in vapors above plate n Yn' = mole fraction of constituent in va or above plate n t o which feed vapors have been adzed P, = vapor pressure of pure constituent a t temperature of plate n Pn = total pressure of all hydrocarbon vapors above plate n F = total feed, moles f = mole fraction of a constituent in total feed F, = total vapor in feed, moles Y = mole fraction of a constituent in feed vapors = total liquid in feed, moles mole fraction of a constituent in feed liquid total overhead product (C, D . . . for side streams, etc.), moles a = mole fraction of a constituent in overhead product (c, d . . . for side streams, etc.) B = total bottoms, moles b = mole fraction of a constituent in bottoms w = weight of a constituent or fraction v = volume of a constituent or fraction
iL
2:
Ff
+ Bb Ff
Bb =
F is determined by the time unit, and f is based upon the feed analysis (Fffor each constituent is given in column 13, Table I). Hence Bb, and Aa by difference from Ff,may be found (columns 12 and 14). By multiplying yo/b by Bb, By, is found (column 4). If the solution to the computation is correct, obviously the calculated Zyo = 1, and ZByo = B . In other words, the sum of the values of 1 9 6 ~ 0(column 4) should equal 196 for the correct solution. The same applies to 196b and 190y1, and similarly the summation of 6102, and 6 1 0 should ~~ be 610.
Considering any one component (for concreteness, the constituent whose normal boiling point is 207" F.), then by definition the mole fraction in the bottoms (or in the reboiler) is b. By Raoult's and Dalton's laws: gob = P ~ P ,
= Aa
Vol. 25, No. 3
FEED
(1)
A material balance over the part of the still below plate 1 gives
+
01x1 = VOVO Bb \
xl/b =
vo (y_ - 1) + I 01
P -' x1 or P
yl/b =
H EIA T
P P
f (xl/b)
(3)
so that yl/b may be found when xl/b is known. I n Table I, columns 3, 5, and 8 give the results of these computations; p is in all cases 760 mm. Starting a t the top of the column, and assuming the vapor above the top plate to be of the same composition (y3) as the overhead product, a:
(4) and by a material balance of the vapor and liquid passing through a plane just below plate 3: VZYZ= A a yda =
+ OSXS
Os ( x d a - 1)
vz
/
'7- /'
b
so that xl/b may be calculated from yo/b. The last form, Equation 2, is most convenient for slide rule computation. By a repetition of Equation 1 with changed subscripts: y1 =
/
'\
+1
(5)
so that y,/a may be found from x3/a. By an equation similar to (l), x,/a may obviously be found from y2/a; and by an equation similar to (5), yl/a may be found from a / a (columns 19, 18, 15, and 9 of Table I). Division of yl/b by yl/a gives a/b (column 10). I For the lightest constituents the plate temperature is above the critical. Experience indicates that the vapor pressure curves may be extrapolated for a considerable distance above the critical for in calculations involving Raoult's law.
FIGURE3. FLOWOF PRODUCTS AND REFLUX The deviations of the summations from the correct values show the errors in the assumptions as t o plate temperatures. The gravity assumptions may also be changed. Since a change in any one quantity affects all the others to some extent, corrections require much judgment, but one or two repetitions of the calculation will generally give a fairly correct solution to one familiar with the process. Even if the first trial is quite inaccurate, it will give a fairly good idea of the sharpness of fractionation obtainable with a given heat input and number of plates, and will often show that, in order to obtain the desired fractionation, it would be better to change the primary assumptions (assumed number of plates, heat, input, or proportion of overhead), rather than to attempt a more accurate solution for the product composition, on the basis of the original assumptions, by altering the trial values. If open steam is used in the column, it must be considered in the heat balances, and the value of p , which includes only the hydrocarbon vapors, will be different in different parts of the column, depending upon the moles of hydrocarbon vapors present. The last columns of Table I show how the gravity of the bottoms may be computed from the known molecular weights and molecular volumes (liquid volume of one mole a t 60" F.) of the constituents. Multiplication of column 12 by columns 22 and 24 gives columns 23 and 25, respectively; the summation of column 23 divided by the summation of column 25 nives the sDecific a a v i t v a t 60" F. The true boil& poini analysesof the products will usually have to be interpreted in terms Of practical tests* Dew points and bubble points are obtained very easily; flash points de-
-
I N D U S T R I A 1, A N D E N G I N E E R I N G C H E M I S T R Y
March, 1933
pend on vapor pressure, and viscosities can doubtless be worked out as a special case of blending oils, though not much has been done along these lines as yet. The A. S. T. M. distillation, however, is not determinable a t present from the true boiling point curve, and there is need for information along this line (see, however, Lewis and Robinson, 9). I n some studies made in this laboratory, gasoline has been defined by its dew point; that is, the cut between gasoline , and the next higher boiling product has been so made that
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-
040
,6020
030
Mi5
-
q$ _I
020
.0010
-
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