SEPTEMBER, 1940
INDUSTRIAL AND ENGINEERING CHEMISTRY
in increased ionic activity. However, this is counteracted by the decrease in reaction rate since fewer ions are involved as precipitation proceeds, Modern treatment methods involve the use of coagulants to combat slow rates of reaction and resultant colloidal solutions. The calculated solubilities do not indicate appreciable differences in solubilities at equivalent amounts of different types or mixtures of types of alkalinity. The effect of treatment with excess soda ash on the residual hardness is similar to that obtained by treatment with an equivalent of sodium hydroxide. The effect of either is limited by the concentration of the other. It would appear that excess treatment with equal parts of carbonate and hydroxyl (2Na2C03:1CaO) would be more effective than treatment with either alone. However, from the theoretical data and the current cost of lime and soda ash, such treatment would not be economically effective unless an excess of more than 0.75 e. p. m. (equivalents per million parts of water) carbonate alkalinity were added. From the standpoint of residual mineral content, excess treatment increases the mineral content only after a limited concentration of excess has been added. At 25" C. the
1241
figures indicate that excess treatment may be from 0.15 to 0.4 e. p. m. before the mineral content becomes greater than the theoretical limit without excess treatment. As previously stated (4), the data presented do not give values to be expected in softening practice but indicate the limits that may be approached under proper regulation. More complete data on the constants involved would permit further desirable calculations to indicate higher solubility limits a t 18" and lesser limits a t 60" C.
Literature Cited Johnston, J., and Frear, G. L.. J . Am. Chem. Soc., 51, 2082 (1929). Kline, W. D., Zbid.,51, 2093 (1929). Langlier, W. F., J. Am. Water W o r k s Assoc., 28, 1500 (1936). Larson, T. E., a n d Buswell, A. M., IND.ESQ. CHEX, 32, 130 (1940). MacInnes, D. A., "Principles of Electrochemistry", New York, Reinhold Publishing Corp., 1939. MacInnes, D. A., and Belcher, D., J . Am. Chem. Soc., 55, 2630
(1933). P R E ~ E N Tbefore E D the Division of Water, Sewage, and Sanitation Chemistry a t the 99th Meeting of the -4merican Chemical Society, Cincinnati, Ohio.
Factor C in the Performance O f Ejectors a Function of Molecular
.
I
AS
Weights of Vapors
h' AN EARLIER paper1 a conventionalized pattern was
offered to show the effect of vapor density, expressed as molecular weight, on the performance of ejectors. The analysis of self-entrainment cases invo1ved.a factor C; values of C were empirically plotted as lines on a graph having coordinates of pressure ratio P,/P, (boiler pressure to exhaust pressure) and weight ratio w / W (weight of entrained fluid to weight of boiler fluid per unit time), or the molal ratio W/E Factor C was a ratio of the difference between exhaust pressure and entraining pressure and of the difference between exhaust pressure and suction pressure under conditions of no entrainment; that is, C = (P, - P,)/(P, - Po). Thepurpose of this paper is to analyze this constant in terms of some of the variables affecting it. I n this paper the treatment is conventionalized, and it is recognized that certain variations will result for specific cases where the normal boiling point of a fluid differs materially from that of those under test and where the standard ejector is not the best design for the fluid in question. These effects, though noticeable, are not expected to be large. The data upon which this paper is based are in the WorkHaedrich article and involve the use of two ejectors, the form and dimensions of which are shown in Figure 1 somewhat more accurately than in the original sketch in the WorkHaedrich paper. The fluids used varied in chemical and physical properties and their molecular weights covered a range from 18 to 154. There were, however, no high-boiling materials such as mercury or dibutyl phthalate, so that molecular weight and vapor density may be regarded as substantially synonymous. The runs involved both self-entrainment-i. e., the same boiler and evaporator fluids-and two-component entrainment-i. e., a different fluid in the Work and Haedrich, IND. ENQ.CBEM..31, 464 (1939).
LINCOLN T. WORK AND ADOLPH MILLER Columbia University, New York, N. Y
SMHLL EJ€CTOR
FIGURE1.
DETAILSOF EJECTORS,WITH DIMENSIONS IN INCHES
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INDUSTRIAL AND ENGINEERING CHEMISTRY
0.7
a2
0.1
FIGURE3.
0.3
VOL. 32, NO. 9
94
CORRELATION I N
Q6
QS
Q7
0.0
SELF-ENTRAINMENT 11
boiler from that in the evaporator. The former is really only a specific case of the latter. As a first attempt a t correlation, the factors of weight ratio-that is, w/W (weight ratio of evaporator to boiler fluids)-and the ratio of boiler pressure to exhaust pressure were used; for the small ejector (Figure 2) a plot of C against A = (w/W) (P,/Pz)l-syielded a straight line for all cases of self-entrainment, regardless of substance. When the weight and pressure ratios so expressed equal zero, C is obviously equal to one. With increasing values of this factor the value of C decreases, since with increasing entrainment P, moves in the zone between Po to P,. The maximum spread of the points was 10-12 per cent, while most of the points were within 5-7 per cent of the line. The equation for this ejector was found to be C
=
1 - 0.25 ( w / W ) (Pb/P.)'.6
=
1
- 0.254
(1)
The factor 0.25 and the exponent 1.5 are empirical factors determined by the ejector. For the large ejector (Figure 3) a more limited number of points appeared closer to the line, and the corresponding relation was
C
= 1
- 0.313 ( w / W ) (Pb/Pz)0.85
(2)
The ratio of these two exponents is 1.5/0.85 = 1.77 and is approximately equal to the inverse ratio of the maximum ratio of compression of the two ejectors:
(Po/Pz)a/(Po/Pz)~ = 7.3/3.7
= 1.97
It may also be noted that the multiplying constants, or the slopes of the lines, bear a ratio between the small and large ejectors of 0.25/0.313 = 0.80, approximately equal to the ratio of Pb/P, for the respective ejectors for the boiler pressure causing minimum suction pressure-namely, 4.0/5.5 = 0.72. These relations are only approximate, and much more evidence is needed to establish their significance. Two-component entrainment presents a more complex picture than self-entrainment, since a correction must be made for some specific property of the substance involved, if the same type of correlation as that made for self-entrainment is to hold. Two-component entrainment was not found to be a simple function of the molecular weights of the substances used as one might expect from elementary kinetic considerations. I n the case of the small ejector, however, by plotting C against A for different substances, straight lines resulted with a maximum spread in the points of 5 per cent. Figure 4 shows these lines for methanol entraining water, benzene, ethyl ether, and carbon tetrachloride; Figure 5 shows a much greater spread, in this case for trichloroethylene entraining water, methanol, benzene, and carbon tetrachloride. With increase in the ratio Mb/M, (molecular weight of boiler fluid to molecular weight of entrained fluid), the slope of the line becomes increasingly negative. Yet for each case of one substance entraining other substances, a straight line results on a C V S . A plot, regardless of whether any mutual solubility is involved or not. I n Figure 6 the slope of each line is plotted against the ratio Ma/M., and a straight line results. The equation of this line was found to be as follows:
INDUSTRIAL AND ENGINEERING CHEMISTRY
SEPTEMBER, 1940
1243
to establish this relation than were available for the small ejector, it can be seen that the same type of relation held. The final equation obtained was:
The data used to establish the constants of Equations 4 and 6 are presented in tabular form with over-all values for both ejectors and the values for individual boiler fluids for the small ejector:
FIGURE4. TWO-COMPONENT ENTRAINMENT I
-Constantsa Small ejector Over-all Boiler fluid Water Benzene Ethanol Methanol Trichloroethylene Large ejector, over-all
ao
oc
04
06
oe
/o
LP
14
/e
16
20
PP
FIGURE 5. TWO-COMPONENT ENTRAINMENT I1
$
I O
00
3
No; of Points
0.130
0.115
1.5
25
0.140 0.122 0.121 0.120 0,131 0.159
0.114 0.104 0.114 0.118 0.111 0.153
1.5 .1.5
6
1.5 1.5
4 5 5 10
1.5 0.85
5
08
I)
07
8
06
2
n
The analysis of this constant in these terms does not add further insight as t o the mechanism of entrainment but may be useful in the analysis of ejector performance through the simple establishment
&$
#9= %[#'*S
E
b
4 05
$
04
$
03
ti
02
c'
8
c
01
FIGURE 7. TWO-COMPONENT ENTRAINMENT I11
0 0
00
SO 60 70 W T OF PR/MRRY FLU^ TO MOL OF 8ECO"W.W ?LU/D I
EO A A ~ I OOFMOL 10
30
40
BO
wr
FIGURE 6. CORRELATION OF SLOPES
where m
=
m = - 0.13 (Mb/M,) slope of C us. A plot
-
0.115
(3)
For M b / M . = 1, m is 0.245, which compares well with the previously determined slope of the self-entrainment line of 0.250. Hence the results are found to be self-consistent. Combining relation 3 with the C us. A relation 1, the equation
c
= 1
- (0.13 Ma/M. + 0.115)
( w / W ) (Pb/p=)'
(4)
results, or generically,
c
= 1
-
(a Ma/M.
4- b) ( w / w )
(Pb/p,)n
(5)
where a, b, and n are empirical constants that are characteristic of the particular ejector and depend solely on the ejector design and on no characteristic of the substances used. This relation applies to any type of entrainment, whether self- or two-component. The corresponding relations for the large ejector are illustrated in Figures 7 and 8. Although fewer data were available Y
"*
(12
0.4
0.6
0.8
10
12
ng/4
FIGURE 8. CORRELATION OF SLOPES of a characteristic for a particular ejector. It requires only the determination of points from two runs, using a spread of molecular weight ratios, and from these results the constants can be determined. These equations depend only on ejector design and not on the characteristics of the substances used.
