Net Heat of Combustion of Petroleum Hvdrocarbons J
R. S. FEIN, H, I. WILSON, AND JACK SHERMAN Beacon Laboratories, The Texas Co., Beacon, N . Y .
T
HE net heating value of a fuel is an important property in relation to its utilization; i t is also a difficult property to measure accurately. The gross heating value must first be determined in a bomb calorimeter by an extremely exacting and time-consuming technique. Water formed in the calorimeter is condensed and consequently the heat required to t r a n s form i t into the vapor state (the terminal condition in practical combustion processes) must be subtracted from the gross heat t o obtain the net heat of combustion. Calculation of the heat equivalent of this condensed water is based upon a determination of the fuel’s hydrogen content, which involves another exacting and time-consuming laboratory technique. The usefulness of the net heating value, in combination with the difficulty of its determination, gives considerable incentive to the development of methods for estimating net heating value from simpler properties-preferably from the properties that are usually measured as inspection tests on a fuel. Relationships for estimating the net heating value from physical tests have been developed previously. I n the present work, studies of this kind are extended with data from varying sources covering the range of gasolines, jet engine fuels, and Diesel fuels, and with data of individual hydrocarbons. A comparison of equations is made, with emphasis on aviation fuels.
ASTM distillation and specific or API gravity are the only data required to compute the characterization factor. As is generally known, K varies from about 10.0 for highly aromatic stocks through 11.3 or 11.4 for highly naphthenic stoclts to about 12.0 for highly paraffinic stocks. The characterization factor and API gravity have been used ( 4 ) with moderate success as variables from which gross heating value could be computed. The characterization factor has also been used to compute the hydrogen content of petroleum liquids (4). Therefore, it appeared logical to investigate the possibility of deriving a relationship between net heating value and these factors which depend only on gravity and distillation, Another approach t o the calculation of heating values of hydrocarbons is that given in the papers of Linden and Othmer ($), in which the gross heating value is based on the carbon-hydrogen ratio. The work described in this paper was initiated to develop relationships of net heating value of petroleum hydrocarbons with anilinegravity constant and with characterization factor and APT. gravity and to compare their relative merits. Preliminary investigations of the dependence of net heating value on aniline-gravity constant and on characterization factor and API gravity may be found in (Id). Emphasis was placed on aviation fuels because heating value is an important consideration in their utilization.
RELATIONS BETWEEN HYDROCARBON PROPERTIES AND PHYSICAL TESTS
About 20 years ago i t was suggested that the heat of combus tion of petroleum liquids could be related to the density of the liquid (1, 3 ) . It was noted, however, that the dependence of the heat of combustion on density was different for straight-run than for cracked stocks (3). Yotwithstanding this limitation, the relationship of net heating value to density has served a useful purpose for many years. Recently, a considerably more precise relation of net heating value to aniline-gravity constant has been proposed by Rothberg and Jessup (6, IS). The equation is -AH,
=
17944.9
+ 0.1043B
STOCKS INVEST1 GATED
The data on 158 petroleum fractions and 117 individual hydrocarbons used for this work are from varied sources and cover wide ranges of properties, as shown in Table I. I n this table the nature of the materials, number of samples, and origin of the data are also listed.
R. S. Jessup, in reviewing(Il+),brought to the authors’ attention the fact that some of the heating values are based on weighings in vacuum and others in air. However, correction for the buoyancy effect of the air has not been made in the work reported in this paper because the error introduced by this factor is small compared to the precision of prediction of the resulting equations.
(1)
which was identified as “Equation 7” in the original work. I n this equation - A H ? is the net heat of combustion in British thermal units per pound, calculated from the aniline-gravity constant, B , which is the product of the aniline point in O F. and the API gravity. The aniline-gravity constant is an index of a fuel’s physical properties and molecular structure. Another quantitative index that has been developed for indicating the properties of petroleum liquids is the characterization factor (16), which is widely used in the petroleum industry for this purpose, even though i t does have some limitations. The characterization factor, K , is defined as: ( T m)’h K = -
The pertinent basic data available on the materials under consideration and the derived variables which were used to characterize these materials for the heat of combustion studies are on file with the American Documentation Institute. TEST PROCEDURES USED TO OBTAIN BASIC DATA
s
in which T, is the mean average boiling point expressed in O
R(’ F.
+ 460)
and S is the specific gravity at 60” F. The method for computing T, from ASTM distillation data is given by Maxwell (IO).
610
Gross Heating Value. Gross heating values for samples 101 to 116, 160 to 161, 314 to 318, 360 t o 368, 201 to 207, 210 to 211, and 401 t o 498 were obtained using equipment and basic procedures meeting the ASTM D 240-39 test requirements; some of the data were obtained using an adiabatic bomb. A special technique involving sealed glass sample capsules was used to prevent loss of low-boiling front ends from volatile products (8). I n the case of samples 120 to 150 and 319 to 350, techniques generally comparable to the above were apparently used. The testing histories of samples 301 to 313, 401 to 498, and
INDUSTRIAL AND ENGINEERING CHEMISTRY
March 1953
61 1
TABLE I. DATASOURCES
Type of Material Aviation gasoline
*
JP- 1) (kerosene-type jet fuel) JP-3 (wide-boiling range type let fuel)
Miscellaneous petroleum fractions Individual hydrocarbons (1
b.
Literature Code Reference No. of for Data Designations Samples 8ource 15 101-115
120-150
31
160-161 20 1-207
2 7
2 10-2 11
2
301-313
13
314-318
5
319-350
32
360-368
9
401-498
74
1100 and over
117
(Ranges of properties and comments) Mean Average AniHyNet Heat AnilineGra- Boiling line drogen of ComGravity CharacConstant, terization Point“, Point, Weigh; buation O F . F. % B.t.u./Lb. B Factor, K Comments Max. 16.5 19,150 11,923 12.53 ,72.7 200 164 Net heat of combustion 65.9 183 129 is average of a t least Min. 14.7 18,870 12.08 8,501 two independent determinations. Std. deviation from universe mean not more than 39 B.t.u./lb. 15.5 9,952 12.23 Max. 68.4 205 147 18,963 Min. 59.3 103 18,558 14.0 7,280 11.77 178 10,555 12.50 Max. Testing history not com70.9 207 151 19,060 15.3 12.34 Min. pletely known 69.9 191 19,025 18,721 Same as 101 through 115 144 l4:4 6,782 11.57 Max. 47.1 402 12.7 11.24 18,435 above 115 4,255 Min. 37.0 377 131 14.0 48.2 391 11.79 Same as 160 through 161 18,560 6,314 Max. 11.62 18,550 13.8 Min. 42.0 340 15.3 12.26 164 10,644 Used only average of 19,019 Max. 64.9 367 data in which two 13.0 11.31 91 4,549 18,319 Min. 39.0 229 lndependent values checked within 200 B.t.u./lb. 14.3 Max. 55.2 300 123 18,739 4.727 11.69 Same as 101 through 115 45.2 233 13.4 above Min. 97 18,461 4,384 11.34 6 4 . 0 164 19,014 10,496 15.3 These data not used in Max. ... 38.8 developing equations Min. 81 18,230 3,698 12.4 presented herein, t o avoid duplication with 301 through 313 Max. 59.2 270 187 15.4 18,930 11,070 12.00 Same as 160 through 161 Min. 48.8 2 19 108 13.7 18 480 5,270 11.47 Max. 70.9 598 190 14.4 19 ‘090b 11,699 12.90 Same as 160 through 161 20.2 Min. 165 41 12.8 17’640b 1,273 10.43 103.9 19:340 13.28 Max. 579 198 16.8 16,130 17,125 9.7 49 6.3 966 9.72 Min. 68
zy+I
-
91.23 W E ,
in which
Q. is the gross heating value in B.t.u. per pound and
WE,is the weight per cent hydrogen N
...
....
... ...
These were reduced to liquid fuel with latent heats of vaporiaation from ( 4 ) .
over 1100 are not completely available, although it is presumed that in general they are equivalent to the above. Hydrogen Content. Hydrogen determinations (by approved combustion techniques) were made on samples 101 to 161, 201 to 207, 210 t o 211, 314 t o 368, and presumably 301 t o 313. The complete data on samples 401 to 498 are not available, but i t is believed that, for calculating net heating value from gross heating value, the hydrogen contents on many of these samples were established through use of density relationships. Hydrogen contents for samples 1100 and over were calculated from molecular composition. i Net Heating Value. The net heating value was computed from the gross heating value and the hydrogen content according t o the equation
Qo
....
...
Actual boiling point of individual hydrocarbons. Some data in ( f l ) presented as heat of combustion of gaseous fuel.
-AHmeas. =
...
This equation corrects for the water vapor condensed in the bomb calorimeter and for the fact that the net heating value is defined a t constant pressure, whereas the bomb calorimeter measurement is a t constant volume. The samples coded 101 to 115, 201 to 207, and 314 to 318 were submitted to the testing laboratory in coded duplicate with instructions that check runs be made on each sample. All bomb calorimeter tests were run by one skilled operator and all hydrogen determinations by another skilled operator. As many samples were submitted a t one time, the interval between running the coded duplicates of each material was varied. From the range between single determinations on the duplicate samples, the standard deviation of a single determination from the universe mean was estimated as 60 B.t.u. per pound. From the range between check runs, the standard deviation of a single determination from the sample mean wm estimated as 31 B.t.u. per pound. (Because the skill of the test operator is known to be a very important factor in determining the accuracy of heating
value determinations, the exact numbers reported here are probably valid only for these data. However, the principles illustrated may be generalized.) By analysis of variance: Total variance = within-sample variance between-sample variance or (60)* = (31)a SB~
+
+
Hence, the standard deviation, SB, of a sample mean from the universe mean is 53 B.t.u. per pound. This sample-mean to sample-mean variation is the result of operator bias and sampling errors. An operator subconsciously treats check runs in a more uniform manner than coded duplicate runs (“coded” means that the operator is not aware that the samples are duplicates) and, consequently, tends to have a smaller range between check runs than between duplicates. The importance of the large deviation of the sample mean from the universe mean becomes apparent when deviation from the universe mean (presumably the “true” value of the quantity in question) of the mean of two check runs on one sample is compared with the deviation from the universe mean of the mean of single runs on coded duplicate samples. Standard deviation of mean of two check runs from universe (31)2 ‘ 1 2 mean = [(53)2 T ] = 56 B.t.u. per pound,
+
Standard deviation of mean of single runs on coded duplicate samples from universe mean =
[(y]”’
= 42B.t.u.perpound.
It is thus evident that, if only two runs are. to be made, a better estimate of the universe mean can be obtained from single runs on coded duplicate samples than from check runs on a single sample. The mean of a t least two check determinations on each of two coded samples was used for the heating value of samples 101 t o 116, 201 to 207, and 314 to 318. Hence, the standard deviation of the mean from the universe mean is no larger than = 39 B.t.u. per pound J Distillation. Distillation d a h on samples 101 t o 116, 201 t o 207, and 314 t o 318 were run by the ASTM D 216-40 procedure,
L
‘
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
612
Vol. 45, No. 3
TABLE11. CALCULATED NET HEATING VALCESAND HYDROUEN CONTENTS Part A Aniline-Gravitjp Constant Relation BnilineNet gravity heating constant, value,
-ARB
B 0
1 000
2:ooo 3 000 4 ,'OOO 5,000
6,000 7,000 8,000 9,000 10,000 11,000 12 000 13 :OOO 14,000
17,146 17,601 17,946 18,202 18,393 18,536 18,647 18,739 18,819 18,896 18,973 19,049 19,123 19,189 19,238
Part B , . char&cteriaation Pactor a n d Gravity Relatioa,
.~ ~
Characterization factor, K 9.5
0 16,650
10 16,766
20 17,007
....
10.0
16,974
17,140
17,330
10.5
....
17,513
17,654
11.0
....
....
11.5
....
.,..
12.0
....
12.5
....
.... .... ....
Aniline point, TA, F.
....
13.0 Part C.
30
....
60
70
80
....
....
....
17,545
....
....
....
. . .
....
17,820
18,009
....
....
....
17,978
18,094
18,234
18,408
18,587
.... ....
18,368
18,458
18,583
18,711
.... ....
....
18,682
18,757
18,836
18,950
19,088
....
....
....
....
18,932
18,961
19,025
19,113
....
....
....
....
,..
19,086
19,100
19,138
19,202
...
.
,
90
.... ....
....
,..-
, . . ,
....
....
....
Hydropen Content Relation. Weight % Hydrogen f o r Combinations of T A and G
20 10.46 10.88 11.23 11.51 11.72 .
Combinations of K a n d G
....
A P I Gravity, G 40 50 60 40 11.69 60 12.24 12: 69 80 12.71 13.23 13:61 100 ... 13.12 13.71 14.15 120 ... 13.47 14.12 14.62 140 ... 13.75 14.46 15.03 160 ... ... 13.96 14.73 15,37 180 .., ... ... 14.10 14.94 15.64 200 ... 14.17 15.08 15.84 Extrapolations should not be made beyond limits for which calculated values are tabulated. 10 9.62 9.98 10.26
- ABK for
A P I Gravity, G 40 50
I
30 11.15 11.63 12.04 12.39 12.67 12.88 13.03
...
...
which is more reproducible for volatile materials than the ASTM
D 86-46 procedure, which was presumably used for all other materials (except individual hydrocarbons); the data are used on an evaporated basis (distillation plus loss). Gravity. API gravity values were obtained according to the ASTM D 287-39 procedure or converted from specific gravity data. Aniline Point. ilniline points for samples 101 t o 116, 160 t o 161,314 to 318, 319 to 350, 360 to 362, 201 to 207,210 to 211, and 400 to 498 were obtained by the ASThl D 611-47T procedure. The data on 120 to 150 and 301 to 313 were probably obtained by the same procedure and it is presumed that the data on 1100 and over were also obtained in a like manner. For samples having aniline points in the region above 100" F., vaporization losses incurred from products containing significant quantities of light ends can result in aniline points of questionable significance.
- AHK =
8505.4
70
80
... ...
...
14144 14.98 15.45 15,85 16.18 16.45
15.72 16.18 16.58 16.92
, . .
...
i5:k
90
100
... ... ... ...
... ... ...
15:84 16.37 16 84
...
+ 846.81K + 114.92G f 0.12186G2
... ... 16:41
...
.
I
.
- 9.9510KG
(3)
Equation 2 is plotted in Figure 1 along with Rothberg and Jessup's equation and Equation 3 is plotted in Figure 2. Ket heating values calculated from these equations a t uniformly spaced intervals of the parameters are presented in Table 11. I n solving for the constants of Equation 3, i t was noted that. the solution was moderately unstable. This signifies that within the range of the available data i t is possible to have compensating changes in the constants and the resultant equations would
DERIVATION OF EQUATIONS
The parameters in empirical equations relating net heat of combustion to B , K , and G ( G is API gravity) were determined by the method of least squares. Computations were made on I.B.M. machines. Reduction of the sum of squares-Le., variance UP to regression-for each term was compared with the error variance for significance b y the F-test. Terms not significant a t the 95% level were omitted and the normal equations resolved. The original polynomial used for developing the anilinegravity constant relationship included the fifth-degree term. However, the fifth-degree term was not statifitically significant and, therefore, the resulting equation is
-
AHB = 17145.9
+ 0.51959B - 0.69113 X 10d4B2+ 0.47772 X 10-*B3
- 0.1235 X 10-'*B4
(2)
The original polynomial used for developing the characterization factor and gravity relationship included all srcond-degree terms, AHthe K2 term was insignificant, the resulting equation is as follows:
4000 8000 12,000 ANlLl NE -GRAVITY CONSTANT
I
Figure 1. Variation of Heat of Combustion with Aniline-Gravity Contest
INDUSTRIAL AND ENGINEERING CHEMISTRY
March 1953
fit the data almost as well as the one presented. Therefore, the inclusion of additional data may change the constants of the equation appreciably and, hence, change the appearance of the curves of Figure 2. However, the calculated values within the range of the present data would not be appreciably different. In addition to the heating value equations, an equation obtained for weight per cent hydrogen from a polynomial including all second-degree terms is
+
+
TVE~= 7.86 0.929 X 1O-'G 0.228 X lo-' TA TA' 0.322 X lo-' TAG(4) 0.739 X 1O-'G2 - 0.84 X
.w
+
I n this equation, TA denotes the aniline point in degrees Fahrenheit. Values of weight per cent hydrogen calculated from this equation are also given in Table I1 and a graph of the equation is shown in Figure 3. In using these relationships for stocks containing more than a few tenths per cent sulfur, water, or ash, the calculated heating values must be corrected as shown by Cragoe (1). COMPARISON O F HEATING VALUE EQUATIONS
Table I11 summarizes the deviations of the net heating values calculated from Equations 2 and 3 as well as from Equation 1, which was proposed by Rothberg and Jessup. All are tabulated according to data source and type of material. From the last row of Table 111,i t is seen that the over-all rootmean-square deviations for the Rothberg and Jessup equation, Equation 2, and Equation 3 are 136, 103, and 131 B.t.u. per pound, respectively, Although these values are somewhat higher than the standard deviation of a single measurement, they are nevertheless sufficiently precise for most engineering purposes. A statistical analysis of these root-mean-square deviations (standard errors of estimate) shows that the value of 103 given for Equation 2 is significantly lower than the corresponding deviations for the other two equations. The breakdown of deviations for various groups of data shows that the root-mean-square deviations of the predicted heats of combustion from the measured values vary considerably among the groups. It also shows that the algebraic-average differences between the calculated and observed values vary considerably. These significant groupto-group differences from the equa-
613
tions arise from various causes, among which the principal ones probably are: 1. Differences in chemical composition not accounted for by the aniline-gravity constant or API gravity and characterization factor variables. 2. Differences in both precisiqn and accuracy of the heats of combustion determined in the various laboratories.
For the aviation fuels (code Nos. 101 to 368) it is seen from the root-mean-square deviations that the Rothberg and Jessup equation and Equation 2 are comparable in precision for predicting heats of combustion and are somewhat better than the equation based upon the characterization factor and API gravity. In addition, the values of 52 and 57 for the root-mean-square deviation of the aniline-gravity constant equations are comparable to the standard deviation of a single measurement of the heat of combustion; hence, i t may be concluded that for aviation fuels the heat of combustion may be satisfactorily predicted in terms of the aniline point and API gravity. However, Equation 2 may be of more general validity than the Rothberg and Jessup equation, as i t was derived from a large number of data and terms of higher order than the first were found to be significant. In order to cover as wide a range of values of gravity and aniline point as possible, data on individual hydrocarbons were included for computation of Equation 2. Table I11 shows that the values predicted from Equation 2 for heats of combustion of individual hydrocarbons (code Nos. > 1100) are not generally as close to the measured values as for aviation fuels but are better than the predicted values from the other equations. Although Equation 3, based on characterization factor and gravity, does not predict heating values of aviation fuels and individual hydrocarbons a8 well as Equation 2, it is seen that for the miscellaneous petroleum fractions (code Nos. 401 to 498), i t is apparently more precise than Equation 2. The probable reason for this is that the characterization factor more adequately represents the properties of the stocks with lower heating values-i.e., higher aromatic contents-which are included in this group than does the aniline-gravity constant. It is also seen that the precision of Equation 3 is about the same for avia-
17.0
16.0 -
5
1
1
1
1
1
1
1
15.0
zn
14.0
z!w
0
a 13.0
w
L1
% 212.0 w
3 11.0
[ / . * * , * . , I
0 102030405060708090 A P I GRAVITY
Figure 2. Variation of Heat of Combustion with Characterization Factor and Gravity
-
-
w 80
10.0 60
0 10 20 30 40 50 60 70 80 90 A P I GRAVITY
Figure 3. Variation of Hydrogen Content with Aniline Point and Gravity
Vol. 45, No. 3
INDUSTRIAL AND ENGINEERING CHEMISTRY
614
TABLE
111. of
SUMMARY OF
DEVIATIONS OBTAINED
BY USE OB
veidpment Correlations Root-Mean-Square Deviation
101-115
15
15
15
67
Eq. 2 55
70
$18
120-150
31
31
31
25
49
112
+ 1
160-161
2
1
2
14
45
43
- 14
Subtotal
48
47
48
43
51
98
4-6
201-207
7
7
7
63
32
76
- 56
210-211
2
1
2
43
118
70
+43
Subtotal
9
8
9
61
51
75
- 43
301-313
13
13
13
56
70
91
314-318
5
4
5
62
29
319-350
32
32
..
39
360-368
9
3
9
Subtotal, 301-318 and 360-368 Subtotal, 301-368 Subtotal, 101-368
27
20
27
59
52
...
84
75
54
74
60
Subtotrtl, 101-498
158
135
less 319-350 >1100
117
55
Over-all
275
190
less 319-350 401498
CORREIATIONS
Deviation Gravity Characterization
Average
. Code No
HEATING VALUE
-
14
+ 38 -
45
+ 19 + 13 +118
-37 3-98
-27 4-61 - 66
+39
- 8
+ 26 + 44
+51
34
- 55
$ 6
- 8
72
...
$4
104
111
103
+82
66
72
88
- 8
51
73
...
+ 1
52
57
93
$2
72
161
134
107
- 22
156
114
99
99
-11
117
178
112
163
273
136
103a
131a
- 19 - 13
+ 59 +I10
-43
, .
- 5
+ 46 + 54 + 27
+31
+ 4
+34
+ 17
+21
..
4-32
- 42
-42
0
0
Maximum Deviation . Aniline-Gc
Rothbere f171 - 59 - 40 68 - 14
+
+114 - 83 $100 - 6 45
4-171 - 59 - 11 - 89 43
4-114 - 83 f 59 - 15 +I18
+ +- 43 89
-
+llS
+-1136 00
15 +--1.69 57
+
25 +-- 127 3
-
27 - 94 101 - 62 +I70 lo 170 - 136 170 - 136 +171 - 136 f440 -342 +440 -342 4-696 -317
++ +
+698
-317
-I- 36
+- 123 66 $212 - 5 +
7
- 60 +212 123 -131 - 11 - 97 20 97 -131 102 - 78
-
+ +
+ + 15 - 63 *..
+ 124 $116
+is7
+l57 - 59 157 - 59 157 - 83 +338 -308 f338 -308 +238 -277 +338 -308
+iii - 140 +a52 - 145 f252 - 145
+ +
140 +-- 140 192
...
+
627 -441 $627 -441
Standard deviation.
tion fuels as for miscellaneous petroleum fractions. Moreover, this equation has the advantage that i t depends only upon characterization factor and API gravity, and i t can therefore be used for any fuel for which an ASTM distillation can be obtained. ESTIMATION O F HYDROGEN CONTENT OF FUELS
Equation 4,with a standard error of estimate of 0.34% hydrogen, may be used for calculation of the net heating value from measured values of the gross heating value. As 0.34% hydrogen is equivalent to 31 B.t.u. per pound on the net heating value, the use of this equation, rather than a measurement of hydrogen content, will decrease the precision of the estimate of net heating value from a single bomb calorimeter measurement by only approximately lO%-i.e., by approximately 7 B.t.u. per pound. CONCLUSIONS
The equation for predicting net heating value from the anilinegravity constant can be used for aviation fuels with a precision comparable to that of a single careful calorimeter measurement. The equations for predicting net heating value from anilinegravity constant or from Characterization factor and gravity can be used for all petroleum fractions (for which aniline points or ASTM distillations can be measured) with sufficient accuracy for most engineering purposes. The equation for predicting weight per cent hydrogen can be used to calculate net heating values from measured gross heating values with only a small decrease in precision from that of a single bomb calorimeter and hydrogen content measurement. ACKNOWLEDGMENT
The authors wish to express their appreciation to Harry Levin and R. H Krug for the many determinations of heating value which were made, to J. H. Matheny for IBM machine computations, and to E. &I. Barber for his many suggestions and his helpful guidance.
LITERATURE ClTED
Cragoe, C. S.,Natl. Bur. Standards, Misc. Pub. M97 (1929). (2) Doss, AM.P., “Physical Constants of the Principal Hydrocarbons,” New York, Texas Co., 1943. (3) Faragher, W. F., Morrell, J. C., and Essex, J. L., IND.E m . CHEM.,21,933 (1929). (4) Hougen, 0. A., and Watson, K. PI.,“Chemical Process Principles Charts,” New York, John Wiley & Sons, 1946. (5) Jessup, R. S., and Cragoe, C. S., Natl. Advisory Comm. Aeronaut., NACATN996 (1945). (6) Jessup, R. S.,and Rothberg, S . , “Final Report on the Relation between Net Heat of Combustion, Aniline Point, and Gravity of AN-F-58 Fuels,” Natl. Bur. Standards, July 18, 1949. (7) Lamneck, J. H., and Wise, P. H. Natl. Advisory Comm. Aeronaut., NACA TN2230 (1950). (8) Levin, H., and Schlagel, C., presented before Division of Potroleum Chemistry at the 105th Meeting, AM. CHERI.Soc., Detroit, Mioh., 1943. (9) Linden, H. R., and Othmer, D. F., Chem. Eng., 54, 115 (April 1947). (IO) Maxwell, J. B., “Data Book on Hydrocarbons,” pp. 1(F-10,New York, D. Van Nostryd Co., 1950. (11) Natl. Bur. Standards, Selected Values of Properties of EIydroCarbons,” A P I Project No. 44. (12) Roberts, D. E., and Jessup, R. S., J . Resehrch Natl. Bur. Stondurds, 46, 11 (1961). (13) Rothberg, S., and Jessup, R. S.,IND.ENG. CHEM., 43, 981 (1951). (14) Texas Co., Technical and Research Division Report, “Estirnation of Net Heat of Combustion of Petroleum Hydrocarbons,” Jan. 22, 1981. (15) Texas Co., unpublished data. (16) Watson, K. M., Nelson, E. F., and Murphy, G. B., TND. ENG. CHEM., 25, 880 (1933). (17) Wise, P. H., Serijan, K. T., and Goodman, I. A., Natl. Advisory Comm. Aeronaut., NACA TN2081 (1950). (18) Wright-Patterson Air Force Base, “Carbon Deposition Tests of JP-3 Type Fuels in a Small-Scale Burner,” MCREXP531-510 (Jan. 24, 1950). RECEIVED for review April 23,1952. ACCEPT,ED October 30,1952. For supplementary material-Table IV-order Document 3673 from the American Documentation Institute, 1719 N St., N.W., Washington 6,D. C., remitting $1.00 for microfilm (images 1 inch high on standard 35-mm. motion picture film) or 83.40for photocopies (6X 8inches) readable without optical aid. (1)
