Fractionation in Multiple-Draw
Petroleum Columns
W.L. NELSON AND C. H.ROLAND University of Tulsa, Tulsa, Okla.
F
RACTIONATING towers are the very heart of petroCabe-Thiele (7) graphical method ( 3 ) . None of these methleum refinery processing, and thousands of them are ods have been applied to heavy-oil mixtures whose composiemployed in the industry. A few of these towers are tion cannot be given in terms of pure hydrocarbons. Most of used to separate only two products, but most of them are the methods utilize the simplifying assumption that the molal utilized for the separation of several products by withdrawing latent heat is a constant. liquids from trays intermediate between the top and the botA short and approximate method of determining the number tomof the column. I n many of plates required-in heavy-oil cases six different products may columns was used by Huntingbe withdrawn from a single ton (6). This method is based f r a c t i o n a t i n g column. Alon the M c C a b e - T h i e l e (7) though the principles of fracgraphical method for twoEquations are derived by which tionation as applied to twocomponent systems. The feed the fractionation that occurs in a component systems have been stock is arbitrarily separated multiple-component fractionating treated exhaustively, scarcely into two parts by selecting a tower can be studied. In a modiany methods of designing fraccut temperature, and the two tionating columns for complex fractions lying closest on each fied form these equations can also side of the cut point are conmixtures or for multiple-draw be used to study multiple-product systems have been developed. sidered as key c o m p o n e n t s fractionating systems. The theowhose separation or distribuThe purpose of this paper is retical formulations were checked to present one method of studytion into the two main prodagainst commercial plant operaucts may be studied by a Mcing the theory underlying the C a b e - T h i e l e diagram. Aldesign of such columns. tion and were found to duplicate Many designers have dethough the method neglects plant results with reasonable acthe fact that the reflux in a scribed and used methods of curacy. The plate efficiency in the heavy-oil column is not a confractionator design which concommercial column was about 80 stant quantity and hence does sist essentially of computing per cent. not yield a linear operating line the equilibrium composition on a McCabe-Thiele diagram, from plate to plate by a trialThe A. S. T. M. type of distillation it appears to be a reasonably and-error method of assuming is not suitable for measuring the accurate method of estimating and checking the temperature degree of fractionation. True-boilthe number of plates required. on each successive plate. Such ing distillation curves must be emThe method indicates little methods are laborious and have ployed. The distillation curves about the degree of fractionanot proved to be of great praction or the shape of the distical value. S t i l l a n o t h e r must be extremely exact, particutillation curves of the prodgroup of authors (9, S, Q), larly at the ends, because errors ucts that are produced. under the leadership of G. G. are greatly magnified by the equaA logical manner of approach Brown, utilize a modification tions. The equations are closely is to handle each hydrocarbon of the absorption and striprelated to and behave in general as in the mixture as an individual ping factor method of designing product and trace the behavior natural gasoline a b so r b e r s exponential types. of the several hydrocarbons which was developed b y The importance of plate temperaon each plate until finally they Kremser (6). These methods tures has been overstressed in the are found in one or both of the have been applied mainly to past. The degree of fractionation major products. If the feed the design of natural gasoline attained by the use of a given stock cannot be analyzed for stabilizers and are all long the hydrocarbons contained m e t h o d s b e c a u s e trial-andnumber of plates is not changed in it, nearly the same results error solutions are necessary. to a practical extent by the use of may be attained by dealing with V a r i o u s modifications have erroneous but reasonably accurate a series of mixtures of narrow been tried, such as to use a plate temperatures. However, the boiling range, whose vaporsingle component as the basis computed distillation curves are disphase properties may be evaluof the design; to assume and ated by considering the narrow check by trial-and-error methplaced upward or downward by the cuts as pure hydrocarbons. ods for a representative or use of different plate temperatures, Part of each of these narrow average temperature for each but not greatly, if reasonably accuts finds its way into the two part of the column ( 2 ) ; or to curate plate temperatures are used. major products by the series of use a combination of these two equilibrium contacts that are modifications with the Mc-
730
.
JULY, 1938
IKDUSTRIAL AND ENGINEERING CHEMISTRY -. .
K€R
.
.
u
/yS/DL-DUAW PRODUCT
J
BOTTOM PRODUC~
FIGURE1. REFLUX RELATIONIN COMPLEX-MIXTCRE COLUMPI'
established on the plates, and the total accumulation of fractions may then be assembled as a distillation curve for comparison with suitably fractionated commercial products. Most commercial petroleum products are a mixture of hydrocarbons, and hence they are compared by means of distillation curves. The analysis of products by distillation is so well established as a means of judging the degree of separation that no method of studying fractionation will be entirely successful unless it is able to define the products in terms of their complete boiling range.
731
a t the feed plate, to the lower temperatures a t which they issue from the column. The rest of the reflux (referred to as excess reflux) may be the result of three sources. It may be produced a t the base of the lowest column by extra heat added a t this point, which results in an excess vaporization and which is finally removed by adding reflux a t the top of the column; it may be produced a t the feed plate by the use of a completely vaporized or superheated feed (this heat must also be removed by top reflux) ; or in the upper columns it may be reflux which is necessary in order to provide heatbalance reflux for the lower columns. Thus in Figure 1 about two-thirds of the excess reflux in the top column is used in the two lower intermediate columns as heat-balance reflux. In the mathematical formulations or derivations which follow it is necessary to decide the rate at which the heatbalance reflux disappears from plate to plate. Although reflux diminishes most rapidly on the upper plates of a column, or, stated in another way, the plate temperatures differ most a t the top, for mathematical purposes it is assumed that the reflux decreases by the same amount on each plate. A study of the final equations indicates that this assumption or simplification is justified and that the error so introduced is of negligible magnitude, provided the computations are confined, as in this study, to the relatively short columns existing between adjacent tower products.
Top Column The top column or section of a multiple-draw tower differs from the intermediate columns that are situated below because the reflux has the same composition as the overhead product. For ease in following the mathematical derivation that follows, Figure 2 shows features of such a column. The top reflux may have the same composition as the overhead product, which is the most common commercial case and the one shown in Figure 2, or it may have any composition be-
Reflux Relation in Complex-Mixture Columns A mathematical derivation of the separation which occurs in a complex-mixture column requires a new conception of the reflux relations. In mixtures of wide boiling range the amount of reflux or overflow in the column decreases as it proceeds down the column whereas in the current computation methods for handling two-component systems the molal reflux is assumed to be a constant quantity over whole sections of plates. In petroleum columns such an assumption cannot be made because the molal latent heats of the widely differing hydrocarbons found in even a well-fractionated petroleum product are not equal and also because a wide difference in temperature exists between the top and bottom of most petroleum columns. For ease in developing a mechanism of fractionation, the reflux that is put into the top of the column may be considered as consisting of two kinds of reflux, depending upon its purpose and behavior in the column. Part of the reflux proceeds through the uppermost section (referred to as the top column) of a multiple-draw column without diminishing in quantity, as indicated in Figure 1,and acts as reflux for the intermediate columns situated below the first side-draw plate, whereas the rest of the reflux disappears in the top column because of the difference in temperature a t the top of the column and a t the first side-draw plate. That part of the reflux which disappears is here defined as heat-balance reflux because it can be computed by making a heat balance of the section of column under consideration. This reflux is sufficient in quantity only to cool the products which enter the column
FIGURE 2.
FEATURES OF A T O P
COLUMN
tween this composition and the composition of the liquid in equilibrium with the overhead product. Inasmuch as the former condition is .most common, the reflux composition in the following derivations was assumed to be the same as the composition of the overhead product, or XR
=
?J1
Reflux and Vapor Compositions The compositions of the vapor and liquid on each plate may be described in terms of the top reflux, excess reflux, and plate number, as follows:
INDUSTRIAL AND ENGINEERING CHEMISTRY
732
actual internal (or hot) reflux = R
+ CR = (1 + c)R = eR R a
decrease in heat-balance reflux per plate = moles reflux from nth plate = 0, = eR - ; R n
VOL. 30, NO. 7
For a one-plate tower the value of a is 1:
--ii1
= ~ ( e
SECONDPLATE.From Equation 7, eR reflux ratio = b = D
b [I + b - - ea (2 ya
b
- 1) + - (eKn e--
=
2b
b(e -
:)I
-
i)
eR1
~
l + b - z
The amount of vapor that arises from each plate may be de, scribed in terms of the same symbols:
Vn= D
(12)
Substituting the value of ga from Equation 9, ys =
R + eR ---(n
- 1)
Equilibrium Relation on Any Plate
Simplifying,
By a material balance, Vn+l ~
"
+ On-1xn-1
=Vnyn
n + l
+ On xn
y_s= (5)
1 (a:
Y1
X
+ea -2)
Eliminating liquid compositions by introducing equilibrium constants and the values of vapor and reflux from Equations 2 and 4,
D a - (ea R
-
2)
(ea
)
- l ) ( e a - 2)
K1Kz ( a :
+ ea -1
Or for a two-plate tower,
E = D~ 111
[;+
un+1 =
l
x
f e - 1 2D B (e
-
1)
(2e
)
l f b - z n ea
TOPPLATE.By a material balance (Figure 3), vlyl
+ ?(e
-
a> k12
= Vzyl
+ bDyl
-
l)(e
K 9 ( 2 D~ + 2 e - l
K1K2(2;
- 1)
+ 2e -1)
Vapor from Any Plate in Terms of Top Vapor The general equations for the composition of the vapor entering any plate of a tower in terms of the composition of the overhead product have been derived in a similar manner. For the first or top plate,
For the second plate, FIGURE 3. MATERIAL BALANCE FOR TOP PLATE
D a - (ea - 2)
R
1 a
( a x + ea
-2
Substituting values of VI and V2, and simplifying,
112
or
-
[l
+ b + ( e - :) 4
-b] For the third plate,
l + b - ; Y4
=
D
(aE
1
+ ea - 3)
D a - (ea R
- 3)
D
a = (ea
- 3)(ea - 2)
For the fourth plate,
y5 =-
(a,:
a -D (ea -:4) R
[a’+
1
+ ea - 4 )
(
K~ a E + e a - 3 D
D
ag(ea - 4)(ea KsKl(a:+
D
a -fj (ea
ea
- 3)
-3)(ag+
ea - 2
>+
- 4)(ea - 3)(ea - 2)
L”
>( R” + ea - 2 > (a -R” + ea - 1 > +
D K ~ K ~ Kea ~- 3( ~ a-~
+
(ea - 4)(ea - 3) (ea K1K2KaK4 (aR+.ea D -3
- 2)(ea -
1)
(191
Additional equations can easily be written by analogy. Although a general form can be written, it is so complicated that the safe procedure is to work directly from the equations listed here.
Courtesy, Globe Oil and Refining Company
TOPOF CRUDE OIL FRACTIONATOR USED FOR SEPARATING SEVERAL PRODUCTS
Change i n Vapor Composition i n Entire Tower For a four-plate tower,
Summarizing equations similar to Equations 11 and 15 can also be written. These equations show the change in composition between the feed vapor and the overhead product. For a one-plate tower,
E= 1‘
D 4 -R (e
1
-
1)
>+
i f e - 1
D
4~ (4e -”
K 3 K 4 ( 4L) 2
-
3)(e - 1 )
+ 4e - 3
>+
For a two-plate tower, 2 -D ( e - 1 ) R
1
4
D
a (4e - 3)(4e - 2)(e - 1 )
-_
>+
>+ (4e - 3)(4e - 2 ) ( 4 e - l ) ( e - 1 ) KlKzK,K4(4;f
For a three-plate tower,
*=-~1
; + e - l
D
3--, (3e
[;+
3 - (e - I) R
(f:
K, 3 - + 3 e - 2
- 2)(e -
-3
:
>(4-+
4e
-2
>(4-+
4e
-
1
1
(212
Relation of Liquid-Volume Percentage to Mole Percentage
D
1
4e
>+
All of the relations developed so far are based on mole percentage. This is an awkward basis for petroleum studies because oils are always analyzed by distillation and the results reported as liquid-volume percentage. Difficulty is also encountered in computing the mole percentage because the molecular weights of the petroleum components must be estimated and in many cases assumed. For these reasons the following constant or relation was derived so that liquid-volume percentage can be used directly without computing the mole percentage
1)
733
.
INDUSTRIAL AND ENGINEERING CHEMISTRY
'734
VOL. 30, NO. 7
8.33dl Yn+1
8.33diY1
(23)
The physical properties of the particular fraction being studied (i. e., dl and ml) do not appear in Equation 23, and hence constant J does not affect the relative distribution of components as indicated by the distillation curve. Thus as a final step the derived distillation curve may be determined by bringing the sum of the components to a basis of 100 per cent, and constant J need not be evaluated.
Relation of Top Product t o First Side-Draw Liquid In designing or studying a multiple-draw system, the top tower down to the first drawplate is designed first, and then the sections between drawplates are designed one by one, working downward toward the feed plate. Thus, the relation between the top-plate vapor composition and the bottom or side-draw liquid composition is a more common case than the relation between the two vapor compositions which is the relation derived in the preceding equations. The relation between the top vapor and the first side-draw liquid which follows was derived from the fundamental equations already given but in a special form for this important case. For a two-plate tower (one equilibrium plate and drawing the side-draw product from the second plate),
For a three-plate tower (withdrawing the side-draw product from the third plate), X - a=
2J
-I
).[D(Z;+
2e
).[~(3:+
3e - 1
For a four-plate tower, X - 4=
3J
Degree of Fractionation Commercial petroleum products are usually tested for degree of volatility by means of A. s. T. M. distillation curves, and these distillations or curves are the common method of comparing the degree of separation or fractionation that has been attained. However, all attempts to check the formulations here described by means of the A. s.T. M. type of distillation curve were unsuccessful. It was necessary to resort to true-boiling-point curves or a high degree of fractionation in order to establish a check on commercial practice. The A. S.T. M . distillation is misleading because the front end of the distillation curve is too high and thus indicates smaller percentages of the low-boiling-point components than are actually present. Moreover, a similar condition exists among the high-boiling components; that is, the A. S. T. M. distillation indicates smaller percentages of the highboiling components than are actually present. These inadequacies are particularly troublesome in the analysis of fractionating towers by the above equations because they serve to move the computed curve up or down as much as 60" F. as well as to give an erroneous distribution of components in the derived distillation curve of the product. This discrepancy appeared in the plant study to be discussed here; in fact, when using A. S.T. M. distillation curves, the computed compositions of the products always indicated better fractionation on one end of the distillation curve than was obtained in the actual tower even though only one equilibrium contact was assumed. Thus, it is necessary to use the cumbersome true-boilingpoint type of distillation analysis of the products. This is unfortunate because refiners and most technical men are not sufficiently familiar with such distillation curves to judge what constitutes a well-fractionated product. For these reasons the main usefulness of the formulations is not in the design of a particular tower installation but in the disclosure of the fundamental theory that underlies the fractionation of complex mixtures and the performance of multipledraw fractionating systems. Several of these have already become apparent, such as (a) a large amount of excess reflux or vaporization does little good in improving the degree of fractionation, ( b ) the use of a large number of fractionating plates does not improve the fractionation greatly, and (c) fractionation of intermediate or side-draw products can be greatly improved by the use of a low-boiling narrow-boiling-range reflux material at the top of the tower rather than the entire overhead product.
For a five-plate tower,
x6=
4J
Plant Results )4[D(4;+4e
- 1 >a
For a six-plate tower,
+
The theoretical formulations given above were checked against actual plant operation by the Kanotex Oil and Refining Company a t Arkansas City, Kans. Complete data and samples were taken during a 10-hour test run which was conducted during the regular commercial operation of the No. 1 crude oil fractionating tower of this company. The tower is used for separating light gasoline and blending naphtha from crude oil by distillation with a small or moderate amount of steam. The general flow diagram of the tower system, including quantities and operating conditions, is shown in Figure 4. The composition of the crude oil and the analysis of the gas product are shown in Table I, and the
JULY, 1938
INDUSTRIAL AND ENGINEERING CHEMISTRY
735
A. S. T. M. distillations of the toyer products in Table 11. The reflux and the gasoline product are- taken from the same line and hence have the same composition. The percentage yields of the products were as follows:
0
Yield, % Gas and loss 0.3 Choline 14.0 Na htha 4.0 Rezuced crude oil 81.7 Taken a t plant before pouring into sample can.
Gravity,
O
A. P. I.
...
68.4a 54.1 33.6
Other miscellaneous data not shown in Figure 4 are as follows : Charge rate, barrels/day Gas separator temp O F. Naphtha temp. intd'stripper, F. Naphtha temp. out of stripdper, F. Crude oil temp. a t pump, F. Crude oil temp. in line t o tower F. Process steam to stripper, lb./h;. Process steam t o reboiler, lb./hr. Process steam pressure, lb./sq. in. Steam t o heat reboiler, lb./hr. Steam to heat reboiler, O F. Tower pressure, top, lb./sq. in. gage Tower pressure, bottom, lb./sq. in. gage Water to condenser O F. Water from condeder O F. Water for cooling, gal.jhr. Diameter of tower, ft. Vapor velocity superficial, ft./sec. Vapor velocity'through caps, ft./sec. Reflux ratio, moles reflux/mole product
7700.0 177.5 247.0 238.5 67.0 382.0 87.0 691.0 27.4 3930.0 537.0 18.2 20.2 73.0 112.0 4150.0 6.0 0.6 3.3 0.63
The tower trays are of customary design except that the slot area of the caps is less than in most towers. However, the tower was operated a t a relatively low capacity and hence the actual linear slot velocity was far lower than in most towers. The trays are spaced 16.5 inches apart and are each equipped with fifty-seven 6-inch hexagonal caps. The essential plate areas are given as percentages of the total or free cross-sectional area of the tower: Slot area Vapor uptake area Downspout area
TABLEI. ---
4.5 3.75 0.506
DISTILLATION OF CRUDE OIL AND GASANALYSIS
DistillationQ-------Gash Analysis (Fractional)Percentage Temp., ;Mole, distd. a F. Component per cent First drop 80 Methane 3.95 1 80 Ethane 5.23 2 101 Propane 32.39 5 141 Isobutane 5.23 10 188 Butane 30.54 20 262 Isopentane 3.08 30 338 Pentane 12.73 40 413 Hexanes and heavier 6.85b 50 487 60 561 5 Hempel column, 39.3O A. P. I. gravity, 0.5 per cent sediment and water. b Gas sample cooled t o 60° F and the gasoline condensed during the cooling (19.6 ml. per 1000 ml. of gas) was considered as part of the gasoline product.
,404'E
13,500
CFH
FIGURE 4. FLOW DIAGRAM OF TOWER SYSTEM
True-boiling-point distillations were employed in all of these studies. The particular equipment used was described by Yelson (8) and was first introduced by Peters and Baker (9). I n operating the equipment, the maximum amount of reflux that is possible without flooding the column is used and a t times this amounts to almost total reflux. The number of equilibrium plates in the column probably does not exceed 3. True-boiling-point analyses of the tower products studied are shown in Table 111. The results of the gasoline-naphtha study are shown in Figure 6. Although the literature indicates that the plate efficiency in well-designed fractionating columns ranges from 70 to 120 per cent, the efficiency was not assumed in these computations but was arrived at by seeing what composition of gasoline would have resulted in the column if the six actual plates had behaved as two theoretically perfect plates, three
TABLE11. DISTILLATIONS (A. S. T. M.) The A. S. T. M. distillation curves of the products and plate liquids are given in Figure 5 . Little material is vaporized in the dehydrator which has a vapor outlet into the fractionating tower on plate 21. The quantity of reflux was checked in three different waysby an orifice meter, by pump strokes, and finally by a heat balance. The oquations derived here were checked by three separate computations. The composition of the gasoline was calculated from the composition of the unstripped naphtha product, that of the liquid on tray 28 from the analysis of the gasoline, and that of the liquid on tray 18 from the composition of the vapor present a t tray 24.
Sample No. Gravity, 'A. P. I . Distn., OF.: Initial b. p. 5% 10%
%% 40
c7,
gli
95 End point Recovery, % Residue, % 0
--Gas 3a 67.4
oline36 67.5
107 132 155 171 185 195 204 2 14 225 239 259 277 293 97.8 1.2
114 148 160 176 188 199 208 218 229 243 264 285 298 97.6 1 4
--Naphtha-4a 4b 54.2 54.0 231 252 267 278 285 292 301 309 316 325 337 350 363 97.8 1.1
233 261 267 279 289 297 303 310 316 324 333 341 351 98.4 0.6
OF
TOWERPRODUCTSO
Unstripped Naphtha 5 55
Tray 28 23 58.2
Tray 18 18 52.5
Tray 8 13 49.5
185 236 250 267 279 289 299 308 3 17 326 33s 350 37 1 98.4 0.6
167 219 228 241 249 256 264 27 1 280 289 303 314 326 98.0 0.9
181 249 267 288 305 320 329 337 344 351 359 366 376 98.4 0.6
187 252 276 308 329 348 361 373 383 395 415 445 479 98 3 0.6
Additional analyses of tray liquids are given in Figure 5.
736
INDUSTRIAL AND ENGINEERING CHEMISTRY
VOL. 30, NO. 7
TABLE 111. TRUE-BOILING-POINT ANALYSESOF TOWER PRODUCTS Temperature F. 105 115 125 135 145 155 165 175 185 195 205 215 225 235 245 255 265 275 285 295 305 315 325 335 345
a
FIGURE 5. A. S. T. M. DISTILLATIONS
theoretical plates, or five theoretical plates. The computed compositions of the gasoline for each of these cases are given in Figure 6 as well as the actual composition of the gasoline. From the computed compositions of the gasoline it appears that the six actual plates produced a gasoline similar to the gasoline that would be produced from five theoretical plates, and thus the actual plates must have operated a t an over-all
Gasoline, tray 30 4.5 6.2 8.5 11.7 15.3 19.4 23.6 29.0 34.9 41.7 48.9 57.1 64.5 71.2 77.4 83.3 88.2 92.2 95.3 97.7 99.0 99.65 99.85a 99.94a 99.98Q
Cumulative Percentage Distd. Unstripped naphtha, Liquid, tray 25 tray 28 0.8 1.4 0.9 2.0 1.1 2.3 1.4 2.9 1.8 3.2 2.3 3.9 3.0 4.3 4.0 5.0 5.1 7.1 6.3 10.6 8.4 15.5 11.0 21.0 14.0 26.4 17.7 32.0 22.0 38.1 26.4 45.2 32.0 53.3 37.8 62.2 44.5 71.0 52.0 79.1 60.0 86.3 69.3 92.0 80.5 95.9 88.6 98.7 93.1 99.7
Liquid, tray 18 1.0 1.2 1.6 1.9 2.3 3.0 3.6 4.4 5.3 7.0 8.4 10.2 11.8 13.8 15.9 18.2 20.3 23.1 26.2 29.9 34.0 38.9 44.0 51.0 60.0
Estimated.
plate efficiency of 83 per cent or a little lower. The agreement between the actual gasoline and the gasoline that would be produced by the action of five theoretical plates is not perfect but is sufficiently good to identify the behavior or effectiveness of the six actual plates. The true-boiling-point analysis of the unstripped naphtha from which the gasoline compositions were computed is also given. A study of the composition of the liquid on tray 28 is summapized in Figure 7. The liquid composition (tray 28) was computed from the gasoline product which is the overhead product issuing from tray 30. The circles represent the composition on tray 28 if the three actual plates are assumed to behave as two theoretically perfect plates; the triangles indicate the liquid composition on tray 28 if the three actual plates are assumed to provide only one equilibrium contact. The tray from which the sample is withdrawn is not quite equal to a perfect plate in its effectiveness, and hence the actual number of effective plates is something less than 3. Consideration of this fact and the agreement of the circle points with the actual distillation curve of the tray-28 liquid indicates that the efficiency of these plates is something more than 67 per cent and probably again of the magnitude of 80 per cent. The study of tray 18 (Figure 8) is not as satisfactory a check of the fundamental equations as the foregoing because several involved computations were necessary. The composition on tray 18 was calculated by using tray 24 as a reference point. However, the vapor composition from tray 24 is unknown, and hence this composition, as given in Figure 8, had to be computed by compounding the reflux vapor and the overhead product which both contribute to the vapor from the twenty-fourth tray. The circles were then computed by the foregoing equations, but it was necessary to correct them for the fact that the reflux flowing into tray 24 does not have the same composition as the vapor leaving the tray. The seven actual plates behaved as about five and a half theoretical plates, judging from the circles representing the product that would be produced by the action of five theoretical plates. Thus, the efficiency is again of the magnitude of 80 per cent.
INDUSTRIAL AND ENGINEERING CHEMISTRY
JULY, 1938
737
FIGURE6 . TRUE-BOILING-POINT ANALYSES OF UNSTRIPPED NAPHTHA AND GASOLINE, AND COMPUTED COMPOSITIONS OF GASOLINE
Example Calculation Consider a two-plate tower section producing a vapor or overhead product a t the top and a liquid side-draw product from the second plate. The tower section functions under the following conditions : Temperature at top tray Temperature at draw tray Actual hot or internal reflux at top Overhead product Heat-balance reflux: Mol. weight of overhead product Sp. heat of vapors between 263" and 246" F. Latent heat of vapors at 246' F. Heat-balance reflux
=
100
;!:
R =
_- 9.6 moles
eR =
10 000 = 100 moles 100
e
= = _ eR = _loo R 9.6
D - 150 R - 9.6
15.6
263' F.
= 10,000 pounds =
15,000 pounds
=
100
=
0.47
= 125
15,000 (263 - 246) 0.47 125
150 moles
= D = -151000
= 246" F. =
10.4
=
960 pounds
FIGURE7. TRUE-BOILING-POINT ANALYSES OF GASOLINE LIQUIDON TRAY28, AND COMPUTED COMPOSITIONS OF THISLIQUID ANALYSISOF THE LIQUID FIGURE8. TRUE-BOILING-POINT ON TRAY 18, AND ESTIMATED VAPOR COMPOSITION FOR TRAY24
AND THE
If the two actual plates are assumed to have an efficiency of 100 per cent or to behave as two theoretically perfect plates, Equation 24 will apply:
INDUSTRIAL AND ENGINEERING CHEMISTRY
738
VOL. 30, NO. 7
TABLEIV. CALCULATION OF EXAMPLE la
Temp. Range of Fraction, F. 100-110 110-120 120-140 140-160 160-200 200-240 240-260 2 60-280 280-290 290-300 300-330
4d 5 Yi, Liquid Kifor Kz for B. P. of Vol. Percent- Each Each Fraction, age of each Fraction a t Fractlon a t a F. Fraotion 246' F. 263O F. 2b Av.
6
3c
105 115 130 150 180 220 250 270 285 295 315 Total
0.9 3.0 10.0 13.0 20.0 23.0 16.0 10.0 3.0 1.0 0.1
-
4.50 3.92 3.25 2.54 1.65 0.89 0.58 0.43 0.34 0.29 0.20
KiKz
5.50 4.85 4.00 3.15 2.10 1.16 0.75 0.57 0.45 0.39 0.29
24,80 19.00 13.00 8.00 3.46 1.03 0.43 0.25 0.15 0.11 0.06
100.0
Arbitrar fractions covering the entire boiling ranges of both products. b The aritgmetic average is adequate if short boiling-range fractions are used. The temuerature ranges of the fractions in Bhis example are a little too large. c Obtained from a true-boiling-point analysis of the overhead product. If d Equilibrium constants for each fraction a t the top-plate temperature.
X P - = Yi
J
9.6(15.6
+ 10.4 - 1)Kz [150 -k
9.6(10.4 - 1) K1
1
This eauation is aDplied to each of the narrow-boiling fractions (or pure compokints) in the mixture being studied, and the sum of the X z terms constitutes the side product. Thus, factors Y1, K1, and Kz can be determined for each of the fractions found in the two products. Equilibrium constants K 1 and K z can be computed from the vapor pressures of each of the components a t the plate temperatures by dividing the vapor pressure by the total pressure. Term J need not be computed, as explained previously, and may be assigned a value of 1 for simplicity in computations. The composition of one of the two products must be known; thus in this illustration it is assumed that the composition of the o v e r h e a d p r o d u c t (or Y1 terms) is known* and the X 2 terms are computed as a function of the Y 1 terms:
xz=
(F
+'A) 0 376 y,
KiKz
The values of Y l may be adopted by considering the overhead product as a series of narrow-boiling-range fractions, the size of which will depend to some extent on the distribution of components in the overhead product. The adoption of these terms and other operations involved in using the equation are indicated in Table IV.
7e
86
0 625 K2
E KiK2
0.114 0.129 0.156 0.198 0.298 0.540 0.835 1.096 1.390 1.603 2.155
0.015 0,020 0.029 0.047 0.109 0.365 0.875 1.505 2.505 3.420 6.280
9f
xz,
(Cols. 7
(3)
+
0.12 0.45 1.85 3.18 8.14 20,80 27.40 26.01 11.70 5.02 0.84
100 llh Liquid Vol. Side Product Percentage of Compn. as 8 ) Each Fraction Cumulative i n Side Product Per Cent 0.11 0.43 1.75 3.01 7.70 19.73 25.95 24.65 11.12 4.75 0.80
-
-
106.51
100.00
0.1 0.5 2.3 5.3 13.0 32.7 58.7 83.3 94.4 99.2 100.0
steam is present, the equilibrium constants can be computed by dividing the vapor, pressure by the partial pressure of the total oil vapors. e First and second terms, respectively, in the special equation. f Relative amount of each component in the side product. 0 Column 9 on a percentage basis. h Cumulative percentages (true-boiling-point distillation curve) of fractions or materials in side-draw product.
Significance of Plate Temperatures One of the confusing factors in applying the equations to design is the selection of plate temperatures. These mag be assumed with fair accuracy by referring to plant experimental data or may be estimated by various methods which appear in the literature (8). However, in connection with the equations given here, temperature seems to have little effect on the degree of fractionation. If the wrong plate temperatures are used, the derived distillation curve of the product is slightly shifted up or down, but the degree of fractionation (or distribution of components) is scarcely different regardless of the plate temperatures that are used, provided they are reasonably correct. As an indication of the influence of plate temperature, the compositions of several gasolines (Figure 9) were computed from the composition of the naphtha product by using several sets of plate temperatures. The different sets of plate temperatures are as follows:
0
PETROLEUMFRACTIONATING TOWER FOR THE SIMULTANEOUB
SEPARATION OF SEVERAL SIDEA S WELLAS DRAWPRODUCTS AN OVERHEAD VAPOR PRODUCT AND A LIQUIDBOTTOM PRODUCT
Courtesy, Arthur G. M c K e e & CO.
INDUSTRIAL AND ENGINEERING CHEMISTRY
JULY, 1938 Plate
Case I
Case I1
F. 246 272 326
F. 246 257 326
a
TOP
Second Side-draw
Case I11
Case I V
Case V
246
F. 200 246
F. 272 326 350
'F. 290
326
281
The correct plate temperatures were used in case I. I n cases I1 and 111the temperature on the second of the three plates was changed, respectively, to 15" low and 18" high, and the final curves were displaced from the correct value by only about 4" F. All three temperatures in case IV were about 45" low, but the derived curve was only 18" low. Likewise, the temperatures in case V were about 25" high, and the curve derived by using these temperatures was only 15" high. However, all of these curves, regardless of plate temperature, had almost the same curvature. This behavior is illustrated in Figure 10. The five curves are compared in Figure 10 by superimposing all of them on the curve for case I. Only the last 40 per cent is shown so that the exaggerated scale will disclose any discrepancy. For the tower conditions here studied, the use of erroneous plate temperatures does not affect the degree of fractionation to an important degree. The fact that approximate plate temperatures can be used greatly simplifies the computations and points the way to a practical use of the equations derived here. Refiners are interested primarily in the degree of fractionation rather than the position of the distillation curve with respect to temperature. Thus, if the product has too high a boiling range, the inadequacy can be corrected in the plant by a slight adjustment of the amount of material being withdrawn from the column.
739
BO
Sensitivity of Equations I n the final analysis the equations yield factors by which the quantity of a given component in one of the products can be converted to the quantity of the component in the other product by simple multiplication. These factors are very small for the low-boiling components and very large for the high-boiling components. For this reason an inaccuracy in the ends of the distillation curve is tremendously important. Thus, an error of only 1 per cent in the percentages of the highboiling components may result in an error of over 10 per cent in the derived curve. This extreme accuracy is not justified in plant laboratory tests, and hence the method given here is not suitable for routine plant control. The real usefulness of these equations is in the study of the fundamental principles that underlie multiple-component and multiple-draw fractionating systems. One point became forcefully evident in the study. Theoretically the distillation curves of any two products must overlap throughout the entire temperature range of both products. The same is true in applying the equations derived above or the results will be unintelligible. However, since laboratory distillation technic is not sufficiently accurate to disclose these long "tails" of high- and low-boiling material in the products, it is necessary to estimate the extreme ends of the curves. As an example, the end point of the gasoline shown in Figure 7 was 315" F. a t a total distilled of 99.65 per cent. The remaining part of the curve, or 0.35 per cent, was extended upward to a 100 per cent point of 370" F. (although theoretically i t goes even higher) in order to obtain the entire curve of the material on tray 28. These small amounts above 99.65 per cent may appear negligible, but the factors by which they are multiplied in order to obtain the percentage of these same components in the tray-28 liquid are extremely large, amounting to more than 1000 in some instances; hence they become extremely important and entirely necessary if the high end of the tray-28 distillation curve is to be completed, Should the 0.35 per cent of material boiling above 315" F. be neglected, then the tray-28 liquid will also end a t 315" F., which is obviously fa!se.
PERCENT D/Sr/LL€D
FIGURE 9. COMPOSITIONS OF GASOLINES FROM COMPOSITION OF NAPHTHA PRODUCT FIGURE 10. COMPARISON OF UPPERPORTION OF CURVES OF FIGURE 9, SUPERIMPOSED ON CURVE FOR CASEI
Equilibrium Data In the foregoing computations the equilibrium data were taken from a paper by Beale (I). These data apply particularly to narrow-boiling-range petroleum fractions, but in subsequent computations, vapor pressure data of the normal paraffin hydrocarbons were used and little difference could be found in the final results. The independence of the equations
INDUSTRIAL AND ENGINEERING CHEMISTRY
740
from inaccuracies in the equilibrium data is not surprising because all equilibrium data, even though inaccurate, are always a smooth function of temperature and would thus result in a small translation of the derived curve in temperature range but not affect the degree of fractionation to a great extent.
Acknowledgment The authors wish to acknowledge the valuable assistance of Fred A. Deering of the Kanotex Refining Company in conducting plant-scale experimental work.
Nomenclature V 0 R
= moles vapor = moles overflow = moles internal (or hot) heat-balance reflux at top of tower
D
= moles overhead product
(7)
= composition of vapor, mole fraction Y = composition of vapor, liquid-volume percentage x = composition of liquid, mole fraction X = composition of liquid, liquid-volume percentage a = number of theoretical plates in tower n = plate number, counting from top c = excess vaporization or reflux as a fraction of R eR = total moles internal (or hot) reflux at top b = reflux ratio, total internal reflux divided by overhead product y
VOL. 30, NO. 7
equilibrium constant, or vapor pressure divided by total tower pressure J = a constant mp = mol. weight of overhead roduct q = mol. weight of vapor f e e l d, = density of overhead product df = density of vapor feed Subscripts: n, 1, 2, 3, etc. = plake numbers n - 1 = plate above nth plate n 1 = plate below nth plate
K
=
+
Literature Cited (1) Beale, E. L., J . Inst. Petroleum Tech., 23, 211 (May, 1937). (2) Brown and Souders, Refiner Natural Gasoline M f r . , 11, No. 6, 376 (June, 1932). (3) Brown, Souders, and Nyland, IND.ENG.CHEM.,24, 522 (1932).
(4) Brown, Souders, Nyland, and Hesler, Refiner Natural Gasoline Mfr., 14, No. 4, 187 (April, 1935); 14, No. 5, 227 (May, 1935). (5) Garton and Huntington, Ibid., 14, No. 2, 60 (Feb., 1935); Cannon and Huntington, Ibid., 14, No. 10, 490 (Oct., 1935). (6) Kremser, A., Natl. Petroleum News, 43 (May 21, 1930); Proc. Calif, Natural Gasoline Assoc., 5, No. 2 (1930). (7) McCabe and Thiele, IND.ENQ.CREM.,17, 605 (1925). (8) Nelson, “Petroleum Refinery Engineering,” Chap. XXI and p. 57, New York, McGraw-Hill Book Co., 1936. (9) Peters and Baker, IND.ENQ.CHEM.,18, 69 (1926). R ~ C E I V ENovember D 15, 1937.
THE SULFUR INDUSTRY History and Development DONALD B. MASON a b l e p a r t of t h e m a r k e t f o r HE great interest accorded Sicilian sulfur in the early days, sulfur in the United States Freeport Sulphur Company, New York, N. Y. b u t s u c h use p r o b a b l y debecause of its technically clined with the fall of the Roman unisue Drocess of production and Empire and it was not until some time after crusaders brought its high’ state of purity has perhaps obscured the fact, in the back the knowledge of such uses from the East that the sulfur public mind, that the sulfur industry is world-wide, not only in industry again flourished. The use of pyrotechnical powder respect to markets but also to production. began in Europe about the twelfth century, and the demand The sulfur industry is sometimes thought of as a recent defor sulfur started the steady rise which has made i t one of the velopment, coincident with the development of the chemical basic materials of all industry. industry. There has always been a sulfur industry, and the The earliest mention of sulfur mining in original documents production of this valuable element has kept pace with the is contained in grants of mining rights in northern Italy about increasing number of uses for it which have been developed. the year 1000. I n some of these old documents the right to Not only has the quantity produced been adequate but, exmine sulfur is specifically granted. Mining methods of that cept for a few short periods, this raw material has been availtime undoubtedly differed little from those carried out by the able a t remarkably low prices, considering the extreme difancients and consisted mainly in driving inclined shafts into ficulty of production. the lenses of sulfur-bearing rock which occur in bedded limeThe few exceptions have dramatically proved the rule, for stone. As most of the mines were carried deeper and deeper the one or two attempts made by European producers to into the deposit, water became a problem, and for many years establish unwarranted prices ended in costly failure. Presthe only pumps used consisted of pails or buckets carried up sure of competition by other producers and other nations has the incline on the shoulders of boys. The sulfur was removed been, in the sulfur industry as elsewhere, the prime factor in from the ore by piling the ore in large conical heaps which adjusting prices. were then ignited. The heat from the burning sulfur melted The very early literature of the race contains sufficient menthe sulfur in the rock, and the liquid sulfur was collected in tion of the use of sulfur to indicate that it has been in general trenches where it solidified (1). w e a t all times. Archeological investigation of the Etruscan mines in northern Italy shows that these workings have always provided the production for part of the world commerce in Early Chaotic Conditions this commodity. The use of sulfur for Greek fire in war and for pyrotechnical The mines both in Italy and Sicily were operated in very small units with little consideration for efficiency in either the displays in the Roman circus probably constituted a consider-
T
