TWILIGHT VIEW OF THE BAYTOWN REFINERYOF THE HUMBLE OIL AND REFINIKGCOMPANY
A Function of the Time-Temperature Integral
Octane-Number Improvement in Naphtha Reforming S. D. TURNER
E. J. LE ROI
Humble Oil and Refining Company, Baytown, Texas
Standard Oil Development Company, Elizabeth, h-.J.
HE reforming, by means of a cracking process, of naphthas in the gasoline boiling range. to effect an improvement in detonation characteristics, is nom an important step in petroleum refining. While the process was developed almost entirely by purely experimental methods, considerable has nom been learned concerning factors influencing it, and it is possible t o lay down a basis for the fundamental design of the necessary equipment. A correlation of plant cracking data has been effected that
Q
T
A correlation of plant cracking data is effected that satisfactorily gives the octane number obtainable in reforming naphtha in terms of the original octane of the charge and the amount of cracking to whic.h it is subjected. The amount of cracking is expressed in terms of equivalent seconds at 900' F. which are derivable from, or convertible to, an actual time-temperature curve on the assumption that the cracking rate doubles with a rise in temperature of 25' F. By mathematical treatment the octane improvement of naphtha can be predicted. For purposes of still design, the method may be worked backwards.
satisfactorily gives the octane number obtainable in reforming naphtha in terms of the original octane number of the charge and the amount of cracking to which it is subjected. The amount of cracking is expressed in terms of equivalent seconds a t 900" F. which are derivable from, or convertible to, an actual time-temperature curve on the assumption that the cracking rate doubles with a rise in temperature of 25" F.: that is, ' T - 900 Bpoo =
J2
25
where 0 and T are, respectively, the coordinates of the timetemperature curve. The correlation is given kiy the single curve shown in Figure 1. The application of the curve is illustrated by the following example: If it is desired to improve the octane number of a naphtha from 60 to 70 by reforming, the equivalent seconds of cracking a t 900' F. are found from the differences of the abscissas corresponding t o these octane number ordinates-i. e., (560 - 200) = 360 seconds required. The points shown on Figure 1 indicate an average deviation of about one octane number from the values predicted by the curve. Although all of the points except one were obtained on the same type of equipment, the data represent runs of both virgin and cracked naphthas, with initial octane numbers varying between 33.5 and 56.3, and arith variations in heater outlet temperature between 975" and 1025" F., heater outlet pressure between 250 and 800 pounds per square inch, charge rates between 3033 and 5480 barrels per day, and equivalent time a t 900" F. between 6 and 965 seconds. The data are not sufficient to show the primary influences of any variables except equivalent time 1347
INDUSTRIAL AND ENGINEERING CHEMISTRY
1348
TABLE I. Run S o . Type stock Charge rate, bbl./day Coil outlet pressure, lb./sq. in. Coil outlet temp., F. Octane No. ( C F R - M M ) : Coil outlet Charge Improvement 8 , equivalent-charge octane T o . Equivalent seconds a t 900' F. 9. equivalent-product octane S o . Charge characteristics: Gravity, A. P. I. Initial B . P.. O F. 10% a t 50% a t 90% a t Final B. P., F. Molecular weight Abs. critical temp., O F. abs. Abs. critical pressure, lb./sq. in P
Calcd. time-temp curves: 0 = 10 R = 20 0 = 40 0 = 60
1 Virgin 4491 800 1000 70.4 35.2 34.t 0 499 499
2 Virgin 4680 800 980 63.4 36 2 27.2 0 235 2335
3 1-irgin 4700 800 1000 67.7 34 0 33.7 0 480 480
4 Virgin 3033 250 1020
SCXMARY O F 5 Virgin 4200 250 1020
69 8 34.6 352 0 426 426
50.3 50.7 5 1 2 50.1 51.4 242 230 246 240 210 280 270 284 274 276 316 312 320 312 3213 375 370 368 380 370 412 414 434 412 416 135 135 13.5 135 136 1110 1110 1110 1110 1110 410 410 410 410 410 0.81 0.60 0.60 0.60 0 81 997 992 954 862
97.5 965 936
818
99i 991 940 850
1011 947 790
....
Correlatioii of Data The time-temperature curve for each stock, expressed ab equivalent seconds a t 900" F. (Agao),was plotted against the octane number of each cracked product. Extrapolating ~ ~ this curve downward gave a good approximation of 6 ' corresponding to the octane numbers of the charge stocks. Adding to these the corresponding values of A h gare valuesof OWO corresponding to the octane numbers of the cracked products. T h e b e s t smooth curve through these points is shown in Figure 1 . Slight adjustments were made o n p o i n t s where the initial octane number value of €$,a was a p p r e c i a b l y altered by the new curve. Constructed in this way, the o c t a n e n u nib e r s shown by the curve are those p r e d i c t e d from the cracking d a t a , w h i l e the Bwo -FOUIVALFNT SECONDS AT 90O'F (-257 points show the FIGURE1. CORRELiTIOV O F P L i i v T o c t a n e numbers CR4CKIKG D i T i
56.1 33.5 22.6 0 147 147
....
.... .. .
.... ....
...,
.. .
....
.... 952 926 856
1005 918 750
on the octane-number improvement effected : for example, points representing low-prewure rims fall both above and below the curve. The derivation of the relation and its utility depend on purely empirical work; but if i t is assumed that, on reforming, the charge changes to 76 octane-numher naphtha by a firstorder reaction with a constant of K = -0.0027, where time is expressed in equivalent seconds a t 900" F., all the experimental data can be predicted. The data (Table I) were all taken from runs on niodified tube-and-tank units, except run X' which was made on a converted tube still previously used for topping crude. The data represent coil cracking only; in the rum where coil and soaker were being used, the octaiie numbers reported are on heater outlet samples.
DATA
6 Virgin 6000 800 975
63.4 34 0 29.4 0 348 348
....
....
S'OL. 27, S O . 11
8 Virgin 5480 800 1012 65.1 46.0 19.1 3 361 364
10 Virgin 5175 800 982
9 Virgin 4950 800 1015 70 7 55 9 14.8 110 645 755
59 7 44 0 15.7 9 225 227
11 12 13 S Cracked Cracked Cracked Virgin 4758 4720 4530 1800 800 800 800 50 1000 1015 1025 995 69.1 50 0 19.1 30 403 438
73.0 50 0 23.0 30 735 765
74.1 50.0 24.1 30 965 995
57.8 56.3 1.5 120 6 126
50.2 45 2 50 2 45.2 45.0 45.4 60.7 256 276 94 226 230 21'2 257 258 266 254 312 312 316 153 302 294 340 341 340 254 296 361 364 366 376 374 370 369 403 454 490 415 415 402 398 135 135 136 145 146 145 112 1110 1110 1150 1150 1150 1130 1110 410 410 410 400 400 400 440 0.60 0 60 0.60 0.62 0.62 0 62 0.96 992 962 925 820
1006 998 965 825
974 962 910 810
992 986 935 855
1013 1009 952
860
1028 1016 970 875
.... ....
actually obtained. Throughout, a purely arbitrary origin has been used on the 8 scale, and values, other than differences, on this scale are meaningless. Similar correlations were made assuming that the temperature intervals in which the reaction rate doubled were i = 18" F. and i = 35" F., but a greater scattering of points was obtained in each case than when 25' F. was used. The use of 18" F. as the interval tends to move the points reprerenting higher heater-outlet runs to the right with respect to points representing lower heater-outlet runs. The use of an interval of 3.5' F. has the opposite effect.
Theoretical Considerations Many investigators have established that the exponential increase in reaction rate observed in most chemical reactions fits a t least the initial 30 decomposition in cracking reactions. The re$ forming of naphtha is 9: certainly a c o m p l e x k change involving con9 ' 10 secutive reactions, but if the initial decomposi8' tion were the control$ 5 ling reaction, equations 2+ set up considering i t alone might predict the 21 ultimate r e s u l t s obi tained. Since the data showed that these ulti- 1 mate results, expressed B ~ - € O U / V A L € N TJECONDS AT 9 0 O F - 4 = Z S 0 as octane number imFIGURE2. D A T ~ OP FIGURE1 provement, seemed t o PLOTTED h s ( H - N ) LS. 0 be a unique function of the timeexponential temperature integral, as theory would demand the initial decomposition to be, the following analysis was suggested: Suppose all naphtha consisted of two species of nioleculeq of high and low octane numbers, H and L, respectively, and that a naphtha of octane number ,V contained the fraction X of the molecules of octane number L:
s
tJ
AT
=
XL
+ (1 - X ) H , and X
=
H -N H~
Now assuming the reforming reaction to be L -+ H and to follow the first-order equation, d l n X = -Kd9
INDUSTRIPIL ,4XD ENGINEERING CHEMISTRY
SOVEbIBER, 1933
With the temperature and pressure established z's. tube position S,it was posiible to \et up an equation of time between tube 9 and the heater outlet, as follow:
giving, upon integration,
--
kXPax /C'Ta,
0.y
where 8 ib the equivalent time of cracking, corrected to some datum temperature. This equation demands that a plot of [log(H-N) YS. 81 be linear. By trial it was found that the data of Figure 1, if plotted in this manner with H = 76, mere linear, as is shown in Figure 2 . The slope of this line with common logarithms is -0.0012 or -0,0027 with natural logarithms; thus,
or -V = 76 - ('76
- .TO)e - 0 . 0 0 Z 7 1 . 8 9 ~ ~
Thebe last equations may be used to solve the example cited earlier-substituting N = 70 and A-o = 60, obtaining 180w = 362, checking the result previously obtained from Figure 1. The interpretation of this result is that, if it is assumed that the naphtha charged is changed t o 76 octane number by a first-order reaction rrith a constant K = -0.0027, when time i. expressed in equivalent qeconds a t 900" F., all of the experimental data can he predicted. The most serious objection to this result i j that it sets 76 Xaphthab 37 the maximum value obtainable by reforming. -ornewhat higher than this have actually been produced, but *ufficient data from these runs were unfortunately not available for thi. analysis. If a more reasonable value-for example, 80 or 90 octane number-is assumed for H, the maximum value obtainable, the curve of Figure 1 shows only -light curvature when plotted as in Figure 2. Therefore, it may be more satisfactory to say t h a t if it is aswmed that the reforming process consiits of the charge chaiiging to 80 or 90 octane-number naphtha, the data show that the process can nearly be represented by a first-order reaction, than to yay, as above, that if the charge is assumed to change to 76 octane-number naphtha, the data can be exactly predicted by a first-order equation. S o attempt is made to explain these deviations of the data from theory, since the theory was based on such untenable assumptions in the first place. It is thought to be remarkable that the theory fits the data ab closely as it does.
Calculation Methods From the A. S.T. &I.distillation and gravity, the molecular weight and critical temperature and pressure of each charge stock were estimated. From these values, the gas-law correction factor, p,1 was determined for a temperature and pressure intermediate between the heater inlet and outlet. S o attempt was made to allow for the variation of p with change< in temperature, pressure, or molecular weight as the charge passed through the heater. The temperature-tube number curves were obtained experimentally. Using the Fanning equation withf = 0.005, and the value of p obtained as above, a pre-ure-tube number equation was then set u p in the form where
X
Px
= = =
Ph.o. C = Tay. =
K 1
=
number of tubes from heater outlet nhs. pressure a t tube X , lb./sq. in. shs. pressure at heater outlet, lb./sq. in. charge rate, bbl./day arithmetic av.oof ahs. temp. at heater outlet and tube X, F. a constant containing f i : f, the gas constant, the tube cross section, and conversion factors
Lewis, W .K . , and Luke,
1349
C.D., IND.ENQ.CHEM.,26,725-7 ,11933).
(3)
where Pa,. and Ta>,.are mean absolute pressures and temperatures between the heater outlet and the tube in question and k contains the tube dimensions, the gas constant p , and conversion factors. With 0 thus calculated, the temperaturetime curve and the curve of time us. 2are readily plotted. The area under this latter curve, from the heater outlet back to a point where the remaining area is negligible (about 800" to 850" F.), is the required equivalent time at 900" F., or 8900. Equations 2 and 3 for P X and Ox are different for each stock charged but are identical for all runs at the same preqsure on a single stock. The setting u p of Equations 2 and 3 is illustrated for the following example : Tube length, ft. Frictional length, ft. Tube cross section, sq. ft. Charge (gravity at 51.5" A. P. I.), lh./gal. Charge molecular weight Charge p Density
Mass velocity
=
mol. mt. 380 x
=
135 X 520 X P 380 X 14.7 X 0.60
=
P
22 33 4 0.0412 6.436 135 0 60
520
1
- x - x T-
14.7
C X 1.75 X 6.436
p
L 1L. 0_P-
T =
o,0757
3600 X 0.0412
Fanning equation: =
AL
2 X 0.005 X (0.0757 C)z x T 32.2 x 12 x 2.75 x 2 1 . 0 7
AP - -- 2.57 AL
x
10-9c2T
P
TX= 33.4 x -PL AP
AX
=
=
171.6 X
85.8
x
10-9 C ~ T
P C2T
Cu. ft. vapor - 1.75 X C X 6.436 X T Second 3600 X 2 1 . 0 X P
- 0.00015 -__CT P
Volume per tube = 0.95 cu. ft. X X X P - 6340 X P e = 0.95 0.00015 CT - CT
(3)
For purposes of design, it is necessary to work backwards, from a desired i l O s 0 0 read from Figure 1, to an actual tinietemperature curve, and finally to a feed rate and furnace design. S o direct method of doing this is recommended. I n practice, the time-temperature curves must be estimated, resulting values of AOWOmust be calculated for various designs, heater outlet temperatures, and feed rates, and a conibination must be selected with proper consideration of metal temperatures, efficiency, and capacity that gives t'he amount of cracking desired. RECEIVED May 11, 1935. Presented before the Division of Petroleum Chemistry at the 89th Meeting of the American Chemical Society, New York, N. Y., April 22 to 26, 1935.
