\!>vi1
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
1932
451
puli der were neelglled into a glass-stoppered Erlenmeyer flask.
vent,; 17 was made in cyclohexane. Not eiiougli copper dissolves in a n-heptane solution of sec-amyl mercaptan to color it.
the solution was filtered, and the solvent and any excess mercaptan were evaporated off a t room temperature under a vacuum of about 3 mm., the distillate being condensed with Dry-Ice.
ACKNOWLEDGMENT This paper contains results obtained in an investigation on a study of the Reactions of a number of Selected Organic Sulfur Compounds, listed as Project 28 of the American Petroleum Institute Research. Financial assistance in this work has been received from a research fund of the American Petroleum Institute, donated by John D. Rockefeller. This fund is being administered by the Institute with the cooperation of the Central Petroleum Committee of the Kational Research Council. These results were communicated to thp ilmericsn Petroleum Institute in December 1929.
To this were added 200 cc. oi a solution of a secondary mercaptan in benzene, of such strength that it contained 0.2 per cent sulfur. The flask was shaken in a mechanical shaking machine from 2 to 4 days. After the shaking was completed,
In this way, samples of 0.2 to 0.25 gram were obtained as red gummy masses which redissolved readily in benzene. The analyses of these are given in Table VI. Attempts to remove the solvent by heat caused the material to break u p into what apparently was copper sulfide and a high-boiling sulfur compound. In order to determine the valence state of the copper in the soluble compounds, the benzene solution of one of them wab shaken with 1:l hydrochloric acid to break up the compound and get the copper into the water layer. This was treated with caustic soda to precipitate the copper hydroxide. A yellow precipitate was obtained which darkened little on boiling. This indicates that the copper changes valence in its reaction with the secondary mercaptan and is present in the cuprous condition. Samples 1,5 and 16 s e r e made using ra-heptane as sol-
LITERlTURE
CITED
IND. EKG.CHEM.,23, 381 (1931). (2) Morgan and Sedbury, J . Chem. Soc., 127, 1917 (1925). (3) Wood, Sheely, and Trusty, ISD. ENG.CHEM.,17, 798 (1925). (1) Duncan, Ott, and Reid,
RECEIVED .lugust 15, 1931. Presented before t h e Division of Petroleum Chemistry a t t h e 81st Meeting of t h e American Chemical Society, Indianapolis, Ind., March 30 t o April 3, 1931. R . H. Slagle is a n American Petroleum Institute Research Fellow.
Kinetics of a Type of Heterogeneous Reactions 11.
The Mechanism of the Combustion of Lump Fuel
S. P. RLHKE AND T. E. W. SCHUII~NN, West ITirginiaUniversity, Morgantown, W. Va. ITC'E; the plll~llcatloll01 H Tlie physical inecliaiiisiii oi I n u precious paper ( 1 ) the mathematical previous paper ( 1 ), the rethe c o m b u s t i o n of solid fuel decelopnient i i f a theory of the kinetics of exosults of a new experimental has p r e v i o u s 1y b e e n postuthermic cheni ical reactions occurring between study hy Smith and Chidmuridlated by the writers ( 1 ) . The a solid and a fluid, in which fhe products of yen (4) on t h e Inecliani-in s u r f a c e temperature and the reaction are entirely fluid, was presented. The of combustion of solid fuel ha. specific reaction v e l o c i t y (kb) a p p e a r e d . Since the tlieciry will be conqidereti here, as decase qf the mechanism of combustion of p u l as proposed and dereloped h! fined by Smith and Gudmundverized solid .fuel (individual particles less than the w r i t e r s is of g e n e r a l apsen, i. e., milligrams loss per 1 mm. i n diameter) was developed in detail in plication, it is of interest to desquare m i l l i m e t e r of surface order to permit of a direct and quantitative termine whether it is in agrerper second. T h e s y m b o l s comparison with the existing reliable data a m i l ment with the findings of thi. employed in the mathematical more recent evperimental able in fhe liferature ( 2 ) . p r e s e n t a t i o n carry the signifistiidy. cance adopted in the previous I n fhe present paper the aufhors extend the T h e e x p e r i n i e n t a l proce(1). Referring to Equapaper theory to the combustion of l u m p f u e l , limited, dure employed by Smith and tion 20 of the earlier paper, howecer, to the case where a single piece of solid Gudmundsen (4) was to suse x p r e s s i n g the rate of diffuf u e l is under consideration. T h e results of the pend a small sphere of electrode sion of oxygen to a uniformly carbon, approximately 5 mm. theory are compared with recent work by S m i t h b u r n i n g s u r f a c e , it is found in d i a m e t e r , in a stream of that and Gudmundsen. In general, it is found that a i r . T h e s y s t e m ivas c o n the predictions of the theory are again in agreetained in a furnace a t a conment with the experimental results. stant temperature sufficiently high to maintain conibustion of Ti2 - Tz' ' / 2 the carbon. The loss in weight of the carbon sphere wa5 ,vhere (19) followed, and the surface temperature of the sphere during combustion as measured by a n optical pyrometer was reT1 = corded. The velocity and moisture content of the air and .l4 = mass of oxygen consumed by carbon sphere per second. stream were varied in these experiments. From the results obtained, the specific reaction rates of the carbon under various (Equations previously derived are numbered as in the preconditions of temperature, air velocity, size of particles, etc., vious paper. S e w equations required in this discussion are \I ere calculated. designated by letters.)
(q)
-
INDUSTRIAL AND ENGINEERING CHEMISTRY
452
k. =
Vol. 24, No. 4
0.00127 GE (E - F )
0
From this equation is derived the important result that the specific reaction rate is independent of the size of the particle, provided the ambient and surface temperatures are the same, since E, F , and G are functions depending upon the temperatures only. I n general, however, the surface temperature of the particle will be unknown. To find the reaction velocity in terms of known variables, it is therefore necessary to have a further equation. For this purpose the dependence of film thickness upon the velocity of the forced draught is used. Rice (3) gives the formula:
m
>
sd" 5 R *d
d E
*0
d d
'I
B = 2.0
rna
ys)1'2
II
where D
3
fi
I
I
p
u
Area, sq. mm.
FIGURE 1
VARIATION IN SPECIFIC REACTION RATEWITH SIZE OF PARTICLE
T2 = 1000" C ) -(Ambient _ _ _ temperature, Experimental curves, Smith and Gudmundsen, Figure 7 (4, Theoretical curves (1) Air velocity = no = 1 09 f t /sec. (2) Air velocity = no = 3 50 f t /sec.
diameter of particle, cm. viscosity of fluid a t temperature d/TX poises = density of fluid, grams per cc. = velocity of fluid, cm. per second = =
If the values of the different factors are substituted in the above equation, the result is
-
(3) Air velocity = LO = 6 75 ft /sec (4) Air velocity = wo 10 25 it /sec
VO
=
A -r1
(i)
B2 T10.8ii
Adopting the definition of k, as given above and giving C1 its value for dry air, Ta
Ca = 0.00030~-
where
A
=
0.0154 ~20.12~
(k)
(1)
T2
and remembering that 12 grams of carbon are consumed for every 32 grams of oxygen, it is found that
The rate of reaction can now be calculated directly from this equation for given ambient and surface temperatures, if the value of the film thickness, B , is known. To determine the value of B , use is made of the fact that the heat developed by chemical reaction ( H ) must be equal to the heat conducted away (HI) plus the heat radiated away (Hz). From Equations 20, 22, 23, and 24
Velocity of Air, ft./sec.
FIGURE 2.
\rARIATION OF
REACTION RATE
WITH
AIR VELOCITY
---- Experimental curves, Smith and Gudmundsen, Figure 14 (4)
When this value of H is put equal to H I Equations 8 and 21, the result is
E
T 1 h
+m
B
=
Tl(T1
+ B) F
B
+
+ H B ,as given by GT1*
Theoretical curves (1) Area of sphere = 10 sq. mm. (2) Area of sphere = 30 sq. mm. (3) Area of sphere = 50 sq. mm.
From Equations g and h it follows that (c)
where Substitute this value in Equation i, and the result is
G = 1.38
-
From (c),
Substitute this value for B in Equation a, and it follows that
I n this equation k,, E , and A are functions of TI and T1 only, and hence the value of T I can be determined in terms of T z and ro. However, it is easier to assume values for T1and T Band then to determine the corresponding values of v0. The values of k,, E , and A , as calculated from Equations h, d, and k are given in Table I. Calculations were carried out to fiiid the relation between z'o and T1for different values of the radius; Table I1 gives the value of v0 for different values of T1,T ~ and , TB.
Ipril, 1932
Tg
O
INDUSTRIAL AND ENGISEERING
TABLEI. VALUESOF k,, E, AND -4 K.: T I 1400' K. 1500' K. 1600' K. 1700' K. 1800' K. 2000' K . ks 0.00338 0.00581 0.00918 0.10325 0.01872 0.0334 E
A
0.545 3.70
0,589 3.92
0.627 4.13
0.665 4.39
0.707 4.58
0.790 5.02
k.
0,00182
0,00420 0.578
0.00732 0.615 4.09
0,01132 0.654 4.34
0.01635 0.692 4.54
0.0305 0.771 4.97
0,00273 0.600 4.03
0.00630 0.632 4.26
0,01085 0.668 4.46
0.0238 0.742 4.88
1300 { E
A
ks
1500
{E A
.....
. . . . . 3.90 ..... .,.. . . . . . . . . . . .., ., , . , .
( I n cm. per second a t 24' C.) TI, 0 K
TABLE111. VALUESOF TI
7.-
0.07 0.1 0.15 0.2 0.3
1400
1500
.. ..
... ...
2.6;
T?
...
I'r
... ...
...
...
6.05 23 2
0.07 0.1 0.15 0.2 0.3
1600 1700 = 1200° K . 14.5 36.0 83.3 = 1300'
... ...
... ..,
4.54 15.7 6.i6 44.8 Tz = 1500'
1800
....
14.2 53.3 101 180.5
rl,
2000
14.8 55.9 139.3 237 433
129 282 547 830 1435
....
5.82 33.6 97 169 318
97.5 223 447 681 1220
A N D k, FOR AND
-113
VO
Feet/sec.
-
TZ
1'0,
_-____-
.IRE.% (sq. mm
50.2
28
12.55
6.15
rI (cm.b------------
0 2
0.3
SPECIFIC VALUESOF
0 :15
0.1
0.07
1650 1760 1842 1893
1750 1855 1940 2000
1855 1967 2032 2110
0.0087 0.0111 0.0130 0.0164 0.0163 0.0215 0.0204 0.0252 Tg = 1300" K.
0.0159 0,0224 0.0287 0.0334
0.0224 0.0308 0.0360 0,0429
1696 1800 1876 1930
1790 1895 1975 3040
1890 2000 2085
0.0088 0.0111 0.0132 0.0164 0.0171 0.0212 0.0205 0.0252 Tz = 1500" K.
0.0158 0.0227 0.0286 0.0336
T2 = 1200' K. Ti
Ii. 5.71 31.9 64.8 138
453
concentration of oxygen. Moreover, it was found experimentally that, although the absence of moisture increased the reaction rate, it decreased the surface temperature of the particles. This result definitely contradicts the present theory. The authors believe-as Smith and Gudmundsen have suggested-that the explanation of this phenomenon is involved in the production of carbon monoxide during combustion. I n a subsequent paper, a quantitative treatment of the theory, modified to include the effect of carbon monoxide formation, mill be presented.
TABLE11. VALUESOF vo 1
CHEMISTRY
1.09 3.50 6.75 10.25
1515 1618 1688 1750
1.09 8 50 6.75 10.25
0.0064 0.0098 0.0127 0.0154
1.09 3.50 6.76 10,25
1570 1666 1734 1785
1587 1695 1755 1825
k.
K.
TI
-1set of curveb was constructed from the data so computed, and from these curves the temperatures, T I ,were read off for given air flows, expressed in feet per second a t 24' C. The values of the corresponding k, are also given. The solid curves shown in Figures 1, 2, and 3 were drawn from the data computed in Table 111. The experimental curves (broken) were drawn from the data given by Smith and Gudmundsen (6). d direct comparison of the experimental and theoretical results is thus afforded. It is to be noted that the experimental points are for wet air. It is believed that the relative absence of carbon monoxide effects, when using moist air, causes the combustion mechanism to be more in accord with that postulated by the writers. When using dry air, Smith and Gudmundsen obtained an increased rate of reaction of approximately 10 per cent. This is scarcely in agreement with the theory which would predict an increase in reaction rate of approximately 3 per cent, owing to the increased
1
'0 Area of Particle, sq. am.
410
FIGURE
3.
SURF.4CE
51,
1" n
it
/
!o
TEMPERATURE OF P A R T I C I X S OF DIFFEREhT SIZES
(Ambient temperature, T2 = 1000° C.) Experimental curves, Smith and Gudmundsen, Figure 7 (4) Theoretical curves (1) Air velocity = 1.09 ft./sec. (3) Air velocjty = 6.75 ft./sec. (2 Air velocity = 3.5 ft./sec. (4) Air velocity = 10.25 ft./sec.
---_
1640 1740 1812 1865
....
ks 1.09 3.50 6.75 10.25
0.0063 0.0098 0.0129 0.0155
1.09 3.50 6.75 10.25
1705 1782 1840 1882
1760 1848 1910 1955
0.00665 0 IO0990 0.0130 0.0157
ks 0.00855 0.0137 0.0175 0.0206
0.0223 0.0306 0.0370
....
TI
1.09 3.50 6.76 10.25
1810 1900 1965 2015 0.0114 0.0168 0.0214 0.0250
1880 1981 2065
....
0.0156 0.0224 0.0288
1975 2078
....
....
0.0220 0.0298
....
....
....
DISCUSSION OF RESULTS I n the previous paper ( I ) , excellent agreement was shown between the results of this theory and the experimental results obtained for the combustion of pulverized fuel. It is evident from the curves presented that, although the agreement is not quite so good, the theory is unquestionably confirmed in general by the experimental results obtained for the combustion of small spheres of carbon. The greatest discrepancy between theory and experiment is found in the actual magnitude of the surface temperatures of the carbon particles. Even here, however, the increase in surface temperature as the particle becomes smaller is quite in agreement with theoretical predictions. The effect of velocity on the rate of reaction (Figure 2) and the rather surprising increase in the rate of reaction with diminution in size of particle (Figure 1) are both in excellent agreement with theoretical predictions. The theory, thus far presented, does not however account for the effect of moisture on the combustion process.
I
LITERATURE CITED (1) Burke and Bchumann. IND.ESG. CHEM..23. 406 119311. ~~~~. ~
~~~
~
~
~~~
~~
~
