IXDUSTRIAL A S D ESGINEERISG CHEMISTRY
September, 1928
For the third tank the relations are particularly simple. In fact. by (2) and a repeated application of (3) and (3') one finds without trouble p n 3 = ffpn2 Spn-1 3 s2p7Z-Z 3 . . . Sn-'P13 (20) nhere p13 = a 3 p . Substituting p,, from (19) and writing pn3= a3p{1 e,s e,s2 . . . en-lsn-l ) it nil1 be readily seen that e,,-l = 1 e, + e , . . . en-a ci Thiq, together with (17') and (20). which gives pL7 = a 3 p il 35), i. e., el = 3, leads at once to e .. , = 3n 1 - (3s)" Thus pna = a3P 1 - 3s (21)
+
+
+
+
+
+
+
for the four-tank system, ap(1 - 2s) P1
+
+
+
+
+
901
=
PB
1 - 3s =
&(l
+ s2' p* = 1
- ;;p+
-
- 3s
s)
+ s2
s2)P4 = aPl
and for the five-tank system, P1 = ap(1 - 3s s2) P, =
+
(1 - s ) ( l - 3s)'
a2p(1 - 2s) (1 - s ) ( l - 3s)
+
Application
~
~
and for n
=
05,
the limit concentration
For the fourth tank a single application of (3) and (3') gives PPn-I,, = apn3 sPn-1,r Pn4 = aPna so that, all pn3being already known, pn4 is directly reduced to its predecessor in the same tank. A repelition of this process leads a t once t o pn, = 4Pn, spn-1 3 . . . sn-?p23) P-lPlr and since = a 4 p , nhile any p13 is given by (21)) n e have, after simde reductions. p n, = 2 % - 3 (3" - 1 p , (22) 1 - 3 s ( l - s 2 ! which holds for any n. Whence, for n = 03, the limiting concentration ff4P P4 = (IVK)
+
+
+
+ +
(1
+
- s)(l - 3s)
Finally, for the fifth tank, by (3'), pn5 = also, for:n:= a, P K =
Qpn4,
and thus (VK)
&C
To sum up, the limiting values of the concentrations are: For the three-tank system, p1 = aP(l-),p - ff2P p 3 = -a 3P 1-2s
*--
1 - 2s'
1 -- 2s
To illustrate these formulas by a practical example, consider a mass of material containing 37A pounds of adhering caustic soda solution of 40 per cent strength. Let this mass he leached by the countercurrent process in a series of tanks. each wash consisting of 700 pounds of liquid from the next tank. It is required to find the limit concentration of wash liquid in the last tank. The constants are 375 io0 -, s = 0.22iO p = 40 per cent, CY = 1075' - p = 1075 Thus, if three tanks only are used, the required concentration of the liquor to be discarded is ff3p - 3.1 per cent. 1 - 2s
+ s2 = 1.60
With the four-tank system it will be 1 - 3s per cent, and with five tanks
ff
5P
(1 - s ) ( l
- 3s)
= 0.84
per cent. The addition of a fourth tank results, therefore, in the recovery of 2.1 per cent, that is, of 7,875 pounds more caustic soda, and the addition of a fifth tank saves a further 3.0 pounds. With the same data, the concentration of the strong Rash liquid leaving the first tank amounts, in these three cases, by (I3), (I4), (I5),to 19.8, 20.8, and 21.0 per cent, respectively.
Inflammability of Automobile Exhaust Gas'sz G. W. Jones PITTSBURGH
EXPERIMENT STATION,
u. s. BUREAUOF
Composition of Exhaust Gas UTOMOBILE exhaust gas consists mainly of carbon dioxide, oxygen, carbon monoxide, hydrogen, methane, nitrogen, and water vapor. Gasoline vapor and unsaturated hydrocarbons exist to an appreciable extent only under abnormal operating conditions-for example, through faulty ignition or too rich carburetor adjustment. For normal conditions a t ordinary temperatures it may be assumed that the combustibles in exhaust gas are hydrogen, carbon monoxide, methane, and the inert gases, nitrogen and carbon dioxide. From 75 to 98 per cent of the exhaust gas consists of nitrogen and carbon dioxide, or 3.5 volumes or more of inerts for each volume of combustible. The combustibles carbon monoxide, hydrogen, and methane depend largely upon the carburetor adjustment or the air-fuel ratio of the mixture exploded in the engine. From
A
1 Presented b y G. D c'. Jones a n d G. St J. Perrott before t h e Division of Gas a n d Fuel Chemistry a t t h e 75th Meeting of t h e American Chemical Society, St. Louis, Mo., April 16 t o 19, 1928. 2 Published b y permission of t h e Director, U. S. Bureau of Mines. ( S o t subject t o copyright )
MINES, PWfSBURGH, P A .
another problem on the ventilation of vehicular tunnels3 a large amount of information was obtained on the composition of automobile exhaust gas with reference to carburetor adjustment. Table I gives typical analyses of exhaust gases collected during road tests in that investigation. The mixtures were chosen to cover a wide range of air-fuel rat'ios. As would be expected, the proportions of combustibles decreased with increasing air-fuel ratios. The proportions of inerts (air-free analysis) varied from 76.9 to 98.5. The small percentages of oxygen shown in the analyses are typical for samples of exhaust gas collected on road tests. Application of Law of Mixtu,res t o Inflammability of Gases One of the laws used by chemists and engineers for determining certain properties of complex gases is the so-called 8 Appendix ICo. 3, Tunnel Gas Investigations, Amount a n d Composition of Automobile Exhaust Gases, b y Fieldner, Straub, and Jones. Report of
New York S t a t e Bridge a n d Tunnel Commission, 1921, p. 91; Fieldner, Straub, and Jones, J. IND. EXG.CHEM.,13, 51 (1921); J . SOC.Automotive E n g , , 8 , 295 (1921); Bur. Mines, Repls. Inwesligalions 2226 (March, 1921); Fieldner and Jones, J . F r a n k l i n Insl., 194, 613 (1922); Fieldner and Jones, Bur. Mines, Repts. Investigations 2487 (1923).
Vol. 20, No. 9
ISDUSTRIAL A N D ENGINEERING CHEMISTRY
902 Table I-Composition SAM-
BIR-FUEL
Co~~~~~~ESSI BUSTION
1 2 3 4 5
6 7 8 9 10 11 12
9.0 9.6 10.1 10.6 11.0 11.5 12.0 12.6 13.1 13.5 13.9 14 d
and Inflammability of Automobile Exhaust Gas with Varying Air-Fuel Ratio Dry Basis
%
50 53 55 57 62 67 71 75 78 81 87 95
I
l
CO,
%
5.7 5.9 6.7 7.5 8.2 8.9 9.4 10.4 10.7 11.5 12.9 13.4
~
~~
COMPOSITION OF EXHAUSTGAS 0 2
%
1.1 1.0 1.0 1.2 0.8 0.7 0.6 0.4 0.9 0.6 0.3 1.1
CO
%
13.0 12.8 11.2 9.8 8.9 8.0 7.0 5.9 4.6 3.8 1.9 1.2
CH4
Hz
1
Nz
%1.7 %7.0 %71.5 I 6.5 5.8 4.8 4.4 3.9 3.2 2.4
1.4 1.4 1.4 1.1 0.8 0.7 0.7 0.8 0.6 0.4 0.1
1.6
1.3 0.8 0.2
law of mixtures. An example of this is the calculation of the density of a complex gas from the composition of the mixture and the density of the individual constituents. Likewise, the heating value of a gas mixture may be accurately determined from a knowledge of the composition of the mixture a n d the heating value of the individual constituents. A special rase of this law is expressed as follows: When two o r more substances which possess the same values of any one property are mixed, the mixture possesses the same value of $his property. Applying this rule to the inflammability of 5 6
8 9
72.4 73.9 75.3 76.6 77.7 79.1 80.2 81.4 82.2 83.7 84.0
~
AIR-FREEANALYSIS
LIMITS OF INPLAMMABILITY
COz
%
6.0 6.2 7.0 7.9 8.5 9.2 9.6 10.6 11.2 11.8 13.1 14.1
Nz
CO
CHI
%
%1.8 %7.5 %70.9 l
13.8 13.4 11.8 10.3 9.3 8.3 7.2 6.0 4.8 3.9 1.9 1.2
1.5 1.5 1.5 1.1 0.8 0.7 0.7 0.8 0.6
0.4 0.1
Hz
Lower
%
32.0 35.0 40.0 46.0 53.0 61.5
72.1 73.6 75.2 76.5 77.7 79.2 80.3 81.5 82.4 83.8 84.4
6.8 6.1 5.1 4.6 4.0 3.3 2.4 1.7 1.3 0.8 0.2
Upper
% 67.0 66.5 68.0 67.5 69.0 69.5
Non-inflammable
mation put it in a more useful form for calculating the limits of any mixture of combustible gases which obey it, as follows: 100
L = p1
P
Pa
TI + Z + K
in which PI, P2, Paare the percentages of each combustible gas present in the original mixture (free from air and inert gases), so PI P2 Pa . .. = 100 and N I ,N z , N B .. ., are the limits in air for each combustible gas separately. An example of the use of the law will make its application clear. To calculate the lower limit of a combustible mixture containing hydrogen, carbon monoxide, and methane:
+
+
s
10
/I II
: .: E
I3
I
I,
6
LOWER
CONSTITUENTS Methane Carbon monoxide Hydrogen
I5
$6
:
7
8
Per cent 65 20 15
INFLAMMABLE LIMIT Per cenf
5.0 13.0
4.0
Substituting, we have
L =
65
100 20
15
=
5.47 per cent
5+13+4 Figure 1 -Limits of Inflammability of Hydrogen Methane and Carbon Monoxide Containing Varying Proportions of Nitrogen and Carbon Dioxide
gases, if a given combustible gas and air mixture which is just inflammable (lower-limit mixture) is mixed with another combustible gas and air mixture which is just inflammable (lower-limit mixture), the resultant mixture will be just inflammable. I n this way the law of mixtures has been found to apply to the phenomenon of inflammability of gases. Calculation of Lower Limit
LeChatelier4 amplified and developed the law of mixtures to apply to the inflammability of gases and stated that the lower limit might be calculated by means of the following formula: $ + - 122 = I Nz where W1 and N z are the limits for the individual gases, and nl and n2 are the percentages of each gas in any lower-limit mixture of the two combustible gases in air. The formula, generalized to apply to a mixture of any number of inflammable gases, has been shown by Coward and others5 to hold for both lower- and upper-limit mixtures of hydrogen, methane, and carbon monoxide, and for coal gas. These investigators rearranged the original statement of the law as given by LeChatelier, and by a slight algebraic transfor4 5
Ann. mines, 19, 388 (1891). Coward, Carpenter, and Payman, J
27 (1919).
Chem. SOC. (London), 115,
The law as stated confines its application to combustible gases containing no inert gases, with the further provision that these gases be mixed with normal air. Inflammability of Exhaust Gas Containing Inert Gases
From another investigation on the inflammability of complex gases, data were obtained whereby LeChatelier's law may be applied to combustible gas mixtures containing large proportions of inert gases. I n order to calculate the inflammability of exhaust gas it is necessary to know the inflammable limits of hydrogen, carbon monoxide, and methane when mixed with varying proportions of the inert gases nitrogen and carbon dioxide. These values have been obtained and are shown graphically in Fi.gure 1. The tests were conducted in an apparatus, previously described,6 consisting of a 2-inch tube, 6 feet long, in which the flames propagated upward. Inflammable limits obtained under these conditions are somewhat wider than those for horizontal or downward propagation. Figure 1 shows that hydrogen requires by far the greatest amount of inert gas (nitrogen or carbon dioxide) to render it non-inflammable; next in order is methane; carbon monoxide comes last. Calculation of Inflammable Limits
Instead of considering the combustibles alone, the inerts are combined with the different combustibles before applying 8
Jones and Perrott, IND. END.CHEX.,19,985(1927).
INDUSTRIAL AND EXGIXEERIXG CHEMISTRY
September, 1928
LeChatelier’s law. For example, take an automobile exhaust gas of the following composition (dry basis) : CONSTITUEXT Per cent Carbon dioxide 6 30 Carbon monoxide 1 2 . 0 5 Methane 2.40 Hydrogen 6 25 h’itrogen 73 00
gas from explosives, gases after mine explosions, and blastfurnace gases have been tested.’ Two typical exhaust gases were prepared, their limits of inflammability were determined and then calculated as just explained. The following results were obtained: &fIXTURE S O .
The nitrogen and carbon dioxide may be combined in various ways with the different combustibles. However, the calculated values agree fairly closely irrespective of how the combinations are made; it is only necessary to proportion the inerts so that each combination has inflammable limits as given in Figure 1. I n this example the combinations will be made as follows:
+ 3630% 15% Nz = COz = +4-366 S5% Nz =
(1) 12 05% CO 2 40% CHI
(2)
(3)
6 25% Hz
Per cent 4 s 20 8 70 43 10
100 00
If added together, these three mixtures give the original exhaust gas whose limits of inflammability are desired.
k8
h
3
Composition (dry basis) : Carbon dioxide Carbon monoxide Methane Hydrogen h-itrogen Lower limit: Calculated Determined Upper limit: Calculated Determined
$.
%a
?
L
P
s Y
s:
9 T
e 5
s
w
:
B
s2
3
8
AIR-FUEL RATIO. POUNDS OF AIR PER POUND OF GAS01 INE
of Automobile Exhaust Gases
The, volumes of inerts per volume of combustible for these three mixtures are as follows: LIMITSOF INFLAMMARATIOO F PREVIOUS IXERT TO BILITY FROM FIGURE 1 Lower Cpper CALCN. COMBUSTIBLE Per cent 48.20 3.0 54.0 73.0 8.70 2.6 21.0 29.5 43.10 5.9 29.5 76.0 TOTAL
FROM
(1) (2) (3)
Substituting these values in LeChatelier’s law: _ -33’500 = - 100 36.0 per cent 8.7 43.1 928 48.2 E O + 21.0 + 2 7 5 100 ‘63,30° = 65.7 per cent Upper limit = 8.7 43.1 2486 48.2 73.0 + 29.5 + -6.0
Lowerlimit
=
Per Cent 6 30
12 2 6 73
05 40 25
00
1 MIXTURE N O 2 P P Icent 7.75 7 60 1.35 4.10 79.20
36.5 36.5
58.0 55.5
66.0 65.0
68.0 67.0
If these tests are considered as a fair average of the accuracy of calculating the inflammable limits of automobile exhaust gas, the calculated values may vary from the actual limits over a range varying from 0 to 2.5 per cent. The limits of inflammability of the different samples have been calculated by using the exhaust-gas analyses given in Table I. The area of inflammability and also the range of oxygen percentage? over which the mixture? are inflammable are shown graphically in Figure 2.
5
5
Figure 2-Inflammability
903
Effect of Air-Fuel Ratio on Inflammability
Automobile exhaust gas a t ordinary temperatures is inflammable only when the air-fuel ratio is below about 11.75 pounds of air per pound of gasoline. The limits continue to widen as the air-fuel ratio is reduced, so that when the ratio becomes 9.0 the limits of inflammability extend from about 31.0 lower limit to 66.5 upper limit. Also, it is noted that exhaust gas propagates flame when very low in oxygen, the content ranging from 7.0 to 14.4per cent; this is due to the large proportions of hydrogen and carbon monoxide. It has previously been shown6 that either of these combustibles will propagate flames when the content is low. The above results are obtained when the average gasoline is used for fuel. A motor fuel having a high benzene content will give results varying somewhat from the values given above. The vertical line in Figure 2 shows the average carburetor adjustment for automobiles and trucks. The area of inflammability does not extend to this line, so that the exhaust gas liberated by the average motor vehicle is non-inflammable when admixed with air at ordinary temperatures. Caution in Using Exhaust Gas
I n view of the fact that automobile exhaust gases have inflammable limits under certain conditions, care should be taken when using these gases for killing animals or for other similar uses. If the exhaust from an engine running on a rich carburetor adjustment is introduced into a closed space, then electric sparks, arcs, or flames should be absent from the area into which the exhaust gas is introduced; otherwise a serious accident may result. 7
T h e results of these investigations have been prepared for publication
as a U. S. Bureau of Mines Technical Paper entitled “The Explosibility of
Agreement between Calculated and Determined Values
Complex Gases.”
A large number of mixtures containing various proportions of hydrogen, carbon monoxide, methane, nitrogen, and carbon dioxide have been prepared; the limits of inflammability have been calculated by the method previously outlined, and then experimentally determined. With one exception, the calculated and determined values have checked fairly closely, the average variations ranging from 0 to 3 per cent. I n this connection, mixtures representing mine-fire gases, detonation
Lignite Gas Works for Germany-Deutsche Erdol -4.G., Berlin, Braunkohlen und Brikettindustrie A. G., Berlin, Julius Pintsch, A. G., Berlin, and two other concerns have formed a company entitled, “Lignite Gas Co., Ltd.” (Braunkohlen Gas G. m. b. H., Berlin), to construct gas works for the gasification of lignite in various German citiea A contract was recently concluded with the city of Kassel, providing that lignite gas works having a daily capacity of 360,000 cubic feet be constructed there.
