INDUSTRIAL A N D ENGINEERING CHEMISTRY
10
GRASSELLIMEDAL-Presented by the American Section of the Society of Chemical Industry to Bradley Stoughton, of Lehigh University, for his paper on “Light Structural Alloys.” ACHESONMEDAL-Awarded by the American Electrochemical Society to Edward G. Acheson, of the Acheson Graphite Co., for outstanding accomplishments in the electrochemical field, particularly the invention of carborundum and artificial graphite. JOHN SCOTTMEDALof the City of Philadelphia to C. P. Dubbs, originator of the Dubbs cracking process, for the discovery and development of a process for economically producing gasoline on a large scale. GOLDMEDALof the Society of Apothecaries of London to John J. Abel, of the Johns Hopkins University. HANBURY MEDALof the Pharmaceutical Society of Great Britain to Henry H. Rusby, of Columbia University, for
Vol. 22, No. 1
investigations in the field of botanical drugs in the river delta regions of the Amazon and in Colombia. COLWYN MEDALof the Institution of the Rubber Industry of Great Britain to G. Stafford Whitby, of McGill University, for services bearing on the improvement or development of rubber manufacture or production. GOLDMEDALOF HONORof the University of Hamburg to Francis G. Benedict, of the Carnegie Institution of Washington. COPLEY MEDALof the Royal Society to Max Planck, of the University of Berlin, for originating the quantum theory. DAVYMEDALof the Royal Society to G. N. Lewis, of the Cniversity of California, for his contributions t o classical thermodynamics and the theory of chemical valence. ELLIOTT CRESSONGOLDMEDALof the Franklin Institute to Sir James C. Irvine, of the University of St. Andrews, Scotland.
Distillate Yields in Cracking’ Stephen A. Kiss S T A N D A R D OIL
DEVELOPMENT C O M P A N Y , 26
B R O A D W A Y , K E W YoRK,
N. Y.
The law of the monomolecular reaction velocity has Note-Equation 1 and the enN PRESENTING some suing formula for x may be found in been applied to the calculation of distillate yields in formulas t h a t h a v e any textbook on physical chemistry. cracking. Several formulas have been developed coverp r o v e d satisfactory for The derivation has been repeated ing three types of cases: cracking without by-products the calculation of d i s t i l l a t e here on account of its close connec(Formulas 2 and 3), cracking with by-products (Formution with the following deductions. yields in the most important las 5, 8, and 9) ; and cracking with by-products and sectypes of cracking operations, If we agree to measure the ondary decomposition (Formulas 6 and 7). it is noteworthy that but a time in minutes and substiSome formulas (9 to 12) have been established giving single theoretical assumption tute 100 for xoJthen the perthe cracking rate as function of the temperature. in coniunction w i t h s o m e centage of cracked product well-known empirical facts is a t the end of t minutes is sufficient for the treatment of the problem. This assumption obtained by the formula is that cracking consists primarily in the decomposition of x = 100 (1 - e+t) (2) heavy hydrocarbon molecules into lighter ones by the law of The percentage y of uncracked product is equal to x, - 2, the monomolecular reaction velocity. or
I
Note-It is common experience in cracking that, not only lighter products than the original, but also heavier ones are invariably formed. The heavier products, however, are due to secondary reactions, such as polymerization of highly unsaturated light products, etc. The problem of calculating their yield will not be taken up in this paper.
The number of molecules, therefore, which undergo decomposition during a short period of time, dt, will be proportional to dt. Furthermore, if there are twice as many heavy molecules present, the number decomposed will be doubled. Therefore, if z designates the number of light molecules a t a given time, zo the original number of heavy molecules, and one heavy molecule decomposes into n lighter ones, then dz = k (BZ,
- Z ) dt
where k is a constant. Since nro and z are proportional to.the weights (or volumes) x. and x, respectively, the above equation may also be written d x = k (x,,
- X) dt
(1)
When x o - x = 1 and dt = 1, then dx = k. Therefore, k means the amount by weight (or volume) of cracked product formed in unit time from unit weight (or volume) of uncracked material. We shall call the constant k the cracking rate. The above equation gives on integration log ( x ,
and since t
=
- X)
x = xo (1 1 Received
= kt
+c
0, x = 0, it follows that C = log xo and October 25, 1929.
- e-kt)
y = 100 e-kt
(3)
For infinite time of cracking (t = 00) these formulas give y = 0 and 2 = 100, which means total cracking. Thus far we have assumed that only one kind of product, x,was formed during the cracking. However, it is a practical experience that a whole series of them are formed. When cracking a heavy stock-e. g., gas oil-there will be produced kerosene, gasoline, and gas. On further cracking, the kerosene decomposes similarly to the gas oil and yields gasoline, but the gas no longer yields gasoline, with the result that the yield of the latter does not reach 100 per cent on total cracking as required by Formula 2. With this in view the problem may then be treated as follows: When a stock y yields, in addition to a product x, another product, XI,which does not decompose into x on further cracking, then a t a certain time, t, the amount of the stocky will be 100 - (x 2‘). Reasoning as in the deduction of Equation 1, we find that
+
d x = k [lo0
and
- (X + x i ) ] d t
dxi = ki [lo0
-
(X
+ xi)]dt
where k and kl are, respectively, the cracking rates relative to the products x and xl. Adding these two equations we get dx
+ dxi = d ( x +
XI) =
(k
+ hi) [lo0 - + x i ) ] d t (X
which shows that the sum of the products 2 and x1follows the law of monomolecular reaction expressed in Equation 1. Hence by Formula 2,
IND CSTRIAL AND ENGINEERING CHEMISTRY
January, 1930 x
+ x I = 100 (1 - e (k + kd
L)
Substituting this value in the expression of dz, we obtain dx = 100 ke -(k
+ Wf dt
(4)
which integrates immediately into
11
line by Formula 2. (It was noticed in the deduction of Equation 4 that the sum z z1 follows the law of monomolecular reaction.) The calculated and experimentally obtained yalues are given in Table I.
+
Cent by Weight of Products from Cracking of Paraffin Wax ---RESIDUE---GAS AND GASOLINE-DURATION OF Calcd. Calcd. t Found krca = 0.02173 Found 0.01076 CRACKIISG, Minutes Per cent Per cenl Per cent Per cent 93.7 2.54 3.18 3 93.6 16.72 17 69.1 69.1 16,72 32 48.8 49.9 30.38 29.11 41.35 47 38.2 36.0 39.67 53.01 62 25.3 25.9 48.68 122 10.2 7.1 70.13 73.07 242 6.7 0 5 74,82 92.59 Table I-Per
--
,
...
Since a t the time t = 0, z = 0, it follows that C and
100 k k + h
= -
This formula co\*ers the gasoline yield in an important practical case, the so-called liquid phase cracking in which the highly heated stock is discharged into a soaking drum. The gas and gasoline leave the soaking drum practically as soon as formed, while the heavy stock remains behind and continues to undergo cracking for some time ( 2 hours or so). The yield increases with the cracking time and approaches asymptotically the maximum value. xm
100 k k + ki
=
for t = (complete cracking). Formula 5 does not cover the gasoline yield obtained by cracking in a bomb. I n this case the gasoline remains in the bomb and decomposes in its turn, so that its yield first increases with time, reaches a maximum, and then gradually decreases. During the infinitesimal time dt the decomposition of the gasoline will be equal to k2xdt and the expression dx = (100 k e - ( k + k i ) t - kz x ) dt gives the infinitesimal increase of the gasoline yield instead of Formula 4. This is a linear differential equation of the first order with t as the independent variable, the solution of which
It is seen that the discrepancy between the calculated and experimentally obtained values becomes serious in the 242 minutes' cracking owing to the formation of heavy polymerization products and coke from certain highly unsaturated cracked products in the gasoline range. However, instead of going into further detail on this point, let us consider matters of a different nature. By definition k,,, of Table I means the weight of gas plus gasoline and kerosene formed in unit time from unit weight of wax and k,+, the weight of gas plus gasoline. Assuming that the linkage of a straight-chain saturated hydrocarbon, such as a wax molecule, can be broken with equal facility a t any part of the chain, there will be equal probability for the formation of hydrocarbons with one, two, three, four, etc., carbon atoms. Therefore, in the decomposition products the weight of the hydrocarbons with a given number of carbon atoms will be proportional to their molecular weight. To the gas and gasoline fractions belong methane, ethane, etc., up to dodecane, the sum of their molecular weights being 1116. To the gas and gasoline and kerosene fractions belong methane, etc., up to heptadecane, with the sum of molecular weights equal to 2176. Therefore, the ratio k,,,/kp+p should be equal to 2176/1116 = 1.95.
Since for t
=
0, z = 0, the constant C is equal to 100 k
c =k
+ ki - kz
and the final formula becomes
Application
Let us now apply Formulas 2, 3, and 6 to the experimental study of Waterman and Perquin ( 2 ) . These authors subjected Rangoon paraffin wax to cracking in an autoclave a t 450" C. and measured the percentage of gas, gasoline (to 220" C.), kerosene (220' to 300" C.), and residue (above 300" C.) formed in a predetermined time of cracking. There was no carbon formation except in cracking for 122 minutes (0.3 per cent) and 242 minutes (4 per cent). The temperature of 450" C. was attained in about 24 minutes, so that during the last 2 minutes of this time cracking already took place. For this reason 2 minutes will be uniformly added to the time during which the autoclave was held a t the temperature of 450" C. Since coke and other heavy polymerization products were formed in considerable amount only when the cracking was continued for 242 minutes, we should expect that the residue could be calculated by Formula 3 and the sum of gas and gasoThe formulas of this theoretical part have all been presented either as
such of in a slightly different form,in a report entitled "Yields in Cracking," and submitted t o the former Development Department of the Standard Oil Company (N. J.) on November 28, 1925.
The experimental value is in fact close to 1.95. 1
Since e = 100.4343 = lo"", Formula 6 may be written in the form x = c loo (1o-Cz' - 10-(c + GI) 1 ) (7) c1 - c2
+
after substituting Formula 7 is somewhat preferable to 6 when the computation is done by the aid of logarithmic tables instead of a slide rule. The gasoline yield of Waterman and Perquin's experiments may be calculated with the following values of the constants
Table 11-Per
Cent by Weight of Gasoline i n Paraffin Wax DURATION OF CRACKING, 1 FOUND CALCD. Per cent Per cenf Minutes
Both the found and calculated values show that the gasoline yield passes through a maximum. The cracking time for this maximum may be obtained according to a known prin-
12
INDUSTRIAL AND ENGINEERING CHEMISTRY
ciple of analysis by putting the first derivative &/dt equal to 0-that is, (see Equation 6) by solving (k kl)e-(k + ki) t - k2 e - h t = 0
+
According to this formula, the maximum gasoline yield in Waterman and Perquin's bomb experiments would have been obtained by cracking for 131 minutes. It should be remarked that the finding of the constants in Formula 6 or 7 to fit a given series of experiments involves considerable labor, since it must be done mostly by trial. By definition the sum k kl in the calculation of gasoline yield is equal to k ,+ , (Table I), which is easily obtained. This artifice greatly simplifies the work of finding the constants. Let us now consider the so-called liquid-phase cracking as it is carried out in large-scale operation. The mixed feed is heated to cracking temperature in a coil, then discharged to anynsulated soaking drum in which the stock stays long enough to crack. The cracked stock is then fractionated in the bubble tower into gas, distillate, cycle stock, and tar. The cycle stock, which has a composition similar to gas oil, is mixed in a certain proportion with fresh feed-i. e., the original stock to be cracked. The mixed feed thus obtained is charged to the cracking coil. Let us call recycle ratio r the inverse of the proportion of the fresh feed in the mixed feed, that is
+
r =
mixed feed. fresh feed '
2 16
20
5 6 etc. 3 4 7 8 12.8 10.24 8.19 6.65 5.24 4.19 etc.
+ (2 X 16) + ( 3 X 12.8) + (4 X 10.24) + 100 (5 X 8.19) + (6 X 6.55) + (5 X 5.24) + . . = 100
Similar computations show that the relation p = r is generally true.8 Therefore, in applying formula 5 which covers this case: (k kt) t = ( k k l ) tl p = np = nr where tl is the time in minutes for which the stock is held under cracking conditions during one pass and n = ( k kl)tl is a characteristic constant for the unit as long as the temperature and pressure of the operation remain the same. The distillate yield on the fresh feed is consequently governed by the relation
+
+
+
x = xm (1
- e-nr)
(8)
where x m is the maximum distillate yield obtainable on total cracking (T = a). Since mixed feed equals T times fresh feed, the distillate yield on the mixed feed or, as it is usually called, conversion per pass, xp,will be
-
Cracking Rate vs. Temperature
The cracking rate, like the rate of most chemical reactions, increases with the temperature. Arrhenius (1) gave the following rule for the variation of reaction rates with the temperature: log -d = -
k
Qa
RP where k is the constant of the reaction velocity, T i s absolute temperature in degrees Kelvin, &a is heat of activation in gramcalories, and R is the gas constant 1.986 gram-calories. This equation integrates into dT
log k =
Q. - 1.986 T
or, multiplying through with loglo e log,, k = a
= 0.4343
- 4.571 AT
where a = 0.4343, al is a constant. It follows from this euuation that \
This is true because 80 per cent of the mixed feed is cycle stock, the components of which have made varying numbers of prior passes. Therefore, the average number of passes of the unit of cracked material is
P =
After computing the constants E m and n from two runs with different values of r, the yield and conversion per pass can be calculated for any recycle ratio.
~
When, for example, the mixed feed charged to the cracking coil is composed of 40 per cent fresh feed and 60 per cent cycle stock, the recycle ratio is T = 100/40 = 2.5. It is impracticable to calculate the exact time for which the hydrocarbons of the original fresh feed stay under cracking conditions, but it is apparent that under the same temperature and pressure conditions in the soaking drum the original hydrocarbons are passed through the cracking system a greater number of times when the recycle ratio is large than when this ratio is small. When, for example, a recycle ratio T = 5 is used, the percentages of the cracked material that went through a various number of passes are the following: Number of passes 1 Per cent 20
Vol. 22, No. 1
The writer owes the relation p r to E. B. Peck, of the Standard Oil Development Co.. who Erst used it in one of his reports.
J
where TI and K T designate ~ the reaction rates a t two different temperatures T1 and TZ. The heat of activation is obtained from the ratio of two reaction rates by Formula 11. Waterman and Perquin found that the cracking rate of Rangoon p a r a 5 wax increased in the ratio 1 : 1.9 when the temperature was raised from 450' C.(723' K.) to 460' C. (733' KJ. Then Qa.10
loglo 1.9 = 0.301 = 4.571.723.733
Q. = 67,530 gram-calories Substituting this value for Q. in Equation 10, it follows for the cracking constant of Rangoon paraffin wax that loglo k = a
- --14770 T
so that k may be calculated for any temperature after its value has been determined at some one temperature. It should be realized that there are several types of cracking constants (k,,,, k,+,, k , kl, kz, etc.) :depending on the products to which they relate, but probably no great error will be made by applying the same formula (12) to all of them. Acknowledgment
The writer wishes to acknowledge here the unpublished work of P. L. Young, of the Standard Oil Development Company, who calculated the coke yield in the soaking drum on the basis of the first order reaction velocity as early as April, 1925. Literature Cited (1) Arrhenius, Z . physik. Chcm., 4,226 (1889). (2) Waterman and Perquin, J . Inst. Petroleum Tech.. 11,36 (1925).
Imperial Chemical Industries is conducting a propaganda and advertising campaign in New Zealand in an effort to find a market for its ammonium sulfate there. The product costs $58.40 per long ton landed ex ship Wellington. In 1928 imports of ammonium sulfate into New Zealand amounted to 2121 long tons, of which 592 tons came from the United Kingdom, 1052 from Australia, 32 from Germany, and 445 from the United States.
