AUGUST, 1939
INDUSTRIAL AND ENGINEERING CHEMISTRY
I n the activated sludge process it is reasonable to assume that the nitrogen pentoxide and the sulfur trioxide liberated in this oxidation would react with the water to form nitric and sulfuric acids. This would result in a change of the p H of the mixture, which would be resisted by the buffering effect of the bicarbonates and the organic matter of the mixture with the formation of an approximately equivalent quantity of carbon dioxide as shown in the following equations:
+ 9 HzO = 18 H + + 18 NOS+ HzO = 2 H + + SO4--
9 N2Os SO8
Considering all buffering due to bicarbonates : 20 HCOa20 H + = 20 Ha0 20 CO,
+
+
The addition of this amount of carbon dioxide to the amount indicated in Equation 4,illustrating the oxidation of protein by activated sludge, would increase the total amount from 72 to 92 and result in a higher R. Q.:
R.Q. = COz/Og
92/113
=i
0.81
I n consideration of the theoretical R. Q. values for the various classes of food materials, it seems reasonable that the R. Q. of an activated sludge-sewage mixture can be varied by adding different food materials; also, since sewage itself is of such variable composition, we cannot necessarily expect different samples to give the same results. I n the matter of the variation of R. Q. values obtained by treating like samples of sewage with different activated sludges, we must look for another explanation of the difference since the available food material is the same except for those food substances stored in the different sludges. Aside from this slight difference in food supply, the variation in biological life composing the sludges seems to be the deciding factor.
1047
Experiments conducted in this laboratory have shown that the nature of the oxidation produced by two different activated sludges when fed the same sewage may be radically dissimilar. The nature of these experiments is too extensive to present here but will be given in a later publication. I n the measurement of carbon dioxide production over a particular period of time, it must be remembered that the carbon dioxide evolved is not necessarily a true indication of the amount being produced a t that particular interval of time. The high solubility a t ordinary temperatures and the danger of incomplete removal by underaeration coupled with the tendency to decomposition of the bicarbonates present in the sewage by overventilation makes the exact determination of the rate of production extremely difficult. Since the respiratory quotient varies so widely for different sludges and sludge-sewage mixtures, the authors doubt whether carbon dioxide measurements as a means for the determination of oxidation rates can be justified. They do believe, however, that further studies involving the simultaneous determination of both oxygen used and carbon dioxide produced under the same environmental conditions may show interrelations between the respiratory quotient and such sludge characteristics as activity, biological composition, ash content, bulking, and dewatering. Such relations will be of value in developing a better understanding of the mechanism of the activated sludge process of sewage treatment.
Literature Cited (1) Heukelekian, H., Sewage Works J., 8, 210 (1936). (2) Heukelekian a n d Ingols, Ibid., 9, 717 (1937). (3) Wooldridge and Standfast, Biochem. J., 30, 156 (1936). P R E S E N Tbefore ~ D the Division of Water, Sewage, and Sanitation Chemistry a t the 96th Meeting of the American Chemioal Society, Milwaukee, Wis.
The Action of Filter Aids This paper shows quantitatively that, when kieselguhr is added as a filter aid to a filter cake consisting of rigid quartz particles, the resulting increase in permeability is due solely to the corresponding change in the porosity of the cake. The changes i n resistance on adding different proportions of filter aid are similar to those observed on adding kieselguhr to compressible cakes and substantiate the theory that, i n these cases too, the main function of the filter is to increase porosity. It foHows that the most important property of a filter aid is its high porosity, and that this should not be sacrificed by seeking high adsorptive or high coagulating power.
T
HE paper is presented to amplify the conclusions drawn in a previous article ( I ) . It was there stated that the chief function of a filter aid such as diatomaceous earth was to give a filter cake a highly porous texture and hence a high permeability. The experimental data also indicated that positively charged colloidal particles are probably ad-
P. C. CARMAN University of Cape Town, Rondebosch. South Africa sorbed on the negatively charged surface of siliceous filter aids such as kieselguhr; but that, even though this effect increased the efficiency of the kieselguhr, its contribution appeared to be of minor importance compared with the purely mechanical effect of the change in texture. If we assume that the action of kieselguhr is essentially mechanical, it should be possible to substantiate this assumption quantitatively and mathematically in the case of ideal cakes, provided we can find the correct relation between cake permeability and cake porosity. Recently this has become possible, owing to advances in the theory of the permeability of beds of rigid particles ( 2 ) .
Experiments on Permeability I n the present experiments the substances to be removed by filtration were two finely divided quartz powders, consisting of particles in the size range 2 to 10 microns, since they are rigid and not small enough to introduce colloidal phenomena. To these were added as filter aid a special grade of kieselguhr sold commercially as Celite 503, which contains particles in the same size range and is completely free from colloidal matter.
'
1048
INDUSTRIAL AND ENGINEERING CHEMISTRY
The permeabilities were not obtained from time-discharge filtration curves but by direct measurement on a preformed cake. The essential parts of the apparatus are shown in Figure 1: Tube a is of uniform and accurately known cross-sectional area ( A sq. em.), connected by a standard ground joint, b, and bent tube, c, to the receiving vessel, d. Tube e connects to a vacuum receiver, fitted with pressure regulator and manometer so that a constant and known vacuum can be produced in d. At j is a piece of Monel metal filter cloth, carefully cut t o fit tube a and supported horiaontally by a loosely wound spiral, g. Spiral g is made from a rectangular piece of c o p p e r sheet and, owing to its tendency t o expand, fits neatly into a. The duty of j is to support cake k. This duty was fulfilled in the case of Celite, but in the case of the quartz powders or mixtures containing them, the particles were too fine, so that some escaped through j . To prevent this, f was precoated with about 0.5 to 1 mm. of k i e s e l g u h r , colored black with carbon t o make clear the boundary between it and the white cake. I n all cases the resistance of the support, with or without its layer of kieselguhr acFIGURE 1. ESSENTIAL PARTS OF THE cording t o the exAPPARATUS FOR MEASURING PERME- periment, was deABILITY termined before the cake was formed, and this was afterwards subtracted from the total resistance of cake and support. This correction never exceeded 1or 2 per cent of the cake resistance and was usually negligible. To maintain a constant head in a, the measuring cylinder, m, was fitted with a wide tube, n, and placed as shown. The rates of percolation were sufficiently low to allow of simultaneous movement of air bubbles upward and liquid downward in n. When rates of percolation were very slow, evaporation during the experiment was prevented by fitting a with a cork containing a large hole through which passed n, and a small one to connect to the atmosphere. The total pressure difference across the cake was obtained by adding the pressure due t o the head of liquid hl to that observed on the manometer.
This is D'Arcy's law for porous media, modified by introduction of a term for viscosity, q poises. That K1 is a constant, typical of the porous medium and independent of the liquid used, has been proved by many workers for a great many types of porous medium (4) and hardly needs further justification. A few experiments, however, were carried out using water (q = 0.0102 poise) and ethyl alcohol (q = 0.0121 poise) as well as acetone ( q = 0.00325 poise); the latter was chosen as the main liquid because of its low viscosity and the readiness with which i t wets fine powders. Typical figures are K1 = 1.81 X with acetone and 1.75 X low6with ethyl alcohol for the 10micron powder (e = 0.47); K1 = 1.74 X lo-' with acetone and 1.83 x lo-' with water for the 3-micron powder ( E = 0.485); K1 = 1.76 X with acetone and 1.68 X with alcohol for Celite (e = 0.849). The values of K I for the various mixtures, using acetone, are reproduced in Table I. The composition of each mixture is given both as 3,the volume fraction of Celite in the mixture, and as y, the weight fraction. The two are not identical, since Celite was found to have a specific gravity of 2.25, whereas that of quartz was 2.65. I n referring to filtration problems, i t has become customary to speak in terms of a specific resistance instead of a permeability coefficient. I n some cases the specific resistance per unit cube of cake is used-i. e., l c i n which case, K1 = l/r. I n dealing with filter aids, it is better to use the specific resistance per gram per sq. em. of the substance to be removed from suspension-in this case, quartz. Then
Porosity and Permeability Measurement T o measure porosity and permeability of a given powder, a known weight is taken and introduced into a to form cake L. Tube a is tapped gently until the cake settles as closely as possible, and then the cake thickness, L em., is measured. Since the cross-sectional area, A sq. em., and the density of the powder are known, the porosity or fractional void, e, is readily calculated. The range of variation of E for the mixtures of Celite and quartz powders employed is shown both in Figure 2 and in Table I. The permeability is obtained by measuring the volume, V cc., leaving the measuring cylinder, a, in 0 seconds, when the pressure difference across the cake is P grams per sq. em. Then the permeability coefficient, K1, can be calculated from the equation:
VOL. 31, NO. 8
x FIGURE 2 . POROSITY OF MIXTURES OF CELITEAND OF QUARTZ POWDERS, PLOTTED AGAINST FRACTIONAL VOG UME, 2, OF CELITEIN THE MIXTURE
where o = grams of quartz per sq. em. and hence is equal to (1 - x ) ( l - e ) p ~ Lif, p1 is the densityof quartz-i. e., 2.65 grams per cc. By substituting this value of w in Equation 2 and comparing with Equation 1, we obtain l / = ~ 2.65 (1
- 2)(1 - E ) K ~
(3)
and the values of l/rl so calculated are included in Table I. The graphs of l / r l us. y are shown in Figure 3 and, in general trend, are similar t o those obtained in the earlier investigation (1). Thus, in terms of 1 gram per sq. em. of quartz, the rate of filtration first rises to a maximum and then falls to zero as
AUGUST, 1939
1049
INDUSTRIAL AKD ENGINEERING CHEMISTRY
the increase in cake thickness counterbalances the increase in porosity. The relative increase in I/Q for the second quartz powder is much greater than for the first, and a higher proportion of filter aid is required to attain the maximum. This is due to a difference in particle size for the two powders; that of the second is about 3 microns compared with about 10 microns for the first quartz powder. In other words, the greater the resistance of the powder, the greater is the benefit to be obtained by adding a filter aid. In this respect it is of value to compare Figure 2 of the previous paper (1) with Figure 3 or 4, in which approximately the same grade of kieselguhr was added to substances differing widely in filtering properties. AND POROSITIES OF MIXTURES OF TABLEI. PERMEABILITIES QUARTZPOWDERS AND CELITE
OF CALCULATED AND OBSERVEDVALUES TABLE11. COMPARISON OF Kt
Volume Fraction of Celite, x
Porosity
Porosity Function
-
-K1
0.044 0.123 0.262 0.400 0.495 0.740 0.900 1.00
Observed 10-Micron Quartz Pciwder 1.81 0.470 0.37 2.03 0.485 0.43 2.99 0.530 0.675 4.62 0.607 1.45 6.31 0.670 2.76 7.62 0.721 4.82 8.95 0.761 6.74 13.1 0.806 13.9 14.9 20.1 0.831 17.6 26.6 0.849
0.00 0.225 0.437 0.638 0.731 0.825 1.00
0 485 0.580 0.688 0.761 0.779 0.807 0.849
0.00 0.020
€
4/(l
€)*
3-Micron Quartz Powder 0.43 0.174 1.11 0.46 3.34 1.45 7.71 4.3 9.7 5.85 14.1 8.95 26.6 17.6
X 106Calculated
...
1.96 2.82 4.84 6.45 8.3 9.7 13.3 15.3
...
0.48 1.62 4.17 5.52 8.5
...
-Permeabilitv----.
Vol. Fraceion Wt. Fraction Porosity, of Celite, z. of Celite, ?J e K1 X 106 10-Micron Quarrs Powder 0.470 1.81 0.00 0.00 2.03 0.485 0.017 0.020 0.530 2.99 0.038 0.044 4.62 0.607 0.107 0.123 6.31 0.670 0.231 0.262 0.721 7.62 0.362 0.400 0.751 8.95 0.454 0.495 13.1 0.806 0.706 0.740 14.9 0.831 0.885 0.900 0.849 1.00 17.6 1.00 0.00 0 225 I
0.437 0.638 0.731 0.825 1.00
3-Mioron Quarts Powder 0.00 0.486 0.174 0.198 0.580 0.46 0.397 0.688 1.45 0.601 0.761 4.30 0.70 0.779 5.85 0,799 0.807 8.95 1.00 0.849 17.6
1-rl x
lo6
2.56 2.72 3.57 4.25 4.10 3.39 3.01 1.76 0.67 0.00 0.238 0.398 0.675 0.985 0.921 0.801 0.00
In the foregoing experiments, as the size and type of particles were carefully chosen to exclude colloidal phenomena, the action of the filter aid must have been restricted to its effect on the porosity. This is borne out by the quantitative agreement between calculated and experimental values of Kl, as shown in the section on “Calculation of Permeabilities,” and in Table 11. At the same time the curves in Figure 3 are similar in type to those obtained when kieselguhr was added to colloidal and gelatinous materials. It follows that the increase in porosity effected by adding kieselguhr is adequate to explain the whole or a t least the greater part of its action, whether it is added t o rigid or to compressible cakes. Thus, only substances which give highly porous cakes and, preferably, consist of rigid particles are likely to be useful as filter aids. The porosity of a filter aid is one of the most important properties by which its possible usefulness may be evaluated. Although adsorption and other chemical effects tend to increase the efficiencyof a filter aid, they are relatively small and, further, are marked only in kieselguhrs of small particle size and relatively low porosity. In fact, it is best not t o confuse the chemical effect of a coagulating agent, which is most properly used for assisting settling and thickening processes, with the mechanical action of a filter aid, which is useful only for filtration. In some cases the best results may be achieved by adding a good coagulating agent for thickening followed by a good filter aid for filtration; but it is not to be expected that a single substance will combine such widely divergent properties without a loss of efficiency on both.
Calculation of Permeabilities In the study of the permeability of beds of rigid particles, the writer showed (2) that the theoretical treatment first
advanced by Kozeny (S),modified to a certain extent, gives an extremely valuable and accurate correlation of a wide range of data. The equation resulting from the modified treatment for the permeability, &, is given by k 1=
& k
€8
(4)
within an accuracy of *6-8 per cent. In Equation 4, g is gravitational acceleration, 980 cm. per second per second; k is a dimensionless constant with the empirical value 5.0; and SOis the specific surface of the particles in sq. cm. per cc. Then 196 (4-4) K l = p ( m From this equation, we can calculate either K1 from a known value of SO,or SOfrom K I . Thus, substituting the appropriate values of K1 and of E from Table I, we find that values of SOfor the quartz powders are 6340 and 22,400 sq. cm. per cc., respectively; for the Celite the value is 17,200 sq. cm.
-IF-
0.0 0
I
0.2
04
0.6
I
0
0.8
Y FIGURE 3. PERMEABILITIES, I/n, OF FILTER CAKEOF THICKNESS ADEQUATE TO CONTAIN 1 GRAnr OF QUARTZ PER SQ. CM, FOR VARYINGFRACTIONAL PROPORTIONS BY WEIGHT, y, OF CELITEIX THE CAKE
1050
INDUSTRIAL AND ENGINEERING CHEMISTRY
per cc. Then, for a mixture containing a fraction, 2, by volume of Celite, SO= 6340 (1 - z) 17,2002 = (6340 10,7702) sq. cm. per cc. in the first case and, similarly, So = (22,400 - 5200%)in the second case. From these values of 80,the corresponding values of K I can be calculated. The calculated values are compared with the observed values of K1 in Table 11, the agreement being within the limits of experimental error. Corresponding values of the porosity function, e3/(l - E ) ~ ,are also included, since it is the rapid variation of this function for relatively small changes of porosity, e, that explains the power of a filter aid t o make startling changes in rate of filtration.
+
+
Acknowledgment The writer wishes to thank the Johns-Manville Company, Ltd., for samples of Celite used in the present studies.
VOL. 31, NO. 8
Literature Cited (1) Carman, P. C . , IND.ENG.CHEM., 30, 1163-7 (1938). (2) Carman, P. C., Trans. Inst. Chem. Engrs.. 15, 150-66 (1937); J . SOC.Chem. Ind., 57, 225-341’ (19381, 58, 1-7T (1939). (3) Kozeny, J., Wusserkraft u. Wusserwirtschuft, 22, 67, 86 (1927). (4) Muskat, M., “Flow of Homogeneous Fluids through Porous Media,” pp. 55 et seq., New York, McGraw-Hill Book Co., 1937.
.** Correction In the previous paper on “The Action of Filter Aids,” which appeared in the October, 1938, issue of INDUSTRIAL AND ENGINEERING CHEMISTRY, an error appeared on page 1164. In the
fist column, ninth line from the bottom, the conversion factor should be 1.06 X lo7, not 1.06 X 1010. P. C. CARMAN
Vapor-Liquid Equilibrium in the System Propane-Isobutylene H. W. SCHEELINE AND E. R. GILLILAND Massachusetts Institute of Technology, Cambridge, Mass.
I
‘ N THE design of petroleum refinery equipment, a knowledge of relations between the temperature, pressure, and composition of two coexisting hydrocarbon phases is essential. Not only in the case of distillation and absorption units, but also in heat transfer and fluid flow equipment, where complete or partial vaporization and condensation occurs, phase equilibrium is the basis for design calculations. Present trends toward higher pressure and closer fractionation have increased the need for accurate data in regions of elevated pressure. With the ultimate objective of obtaining a general correlation of vapor-liquid equilibrium relations for any hydrocarbon mixture, several investigators have, during the past decade, published data on a number of simple systems. Sage, Lacey, and Schaafsma (19) investigated the methane-propane system up to a pressure of 100 atmospheres. Cummings (6, 7 , 8 )obtained data on three systems: n-butane-n-hexane, mpentane-n-heptane, and n-hexane-n-octane. Kay ( I S ) recently published his results on the ethane-heptane system. These last two investigators worked at pressures from atmospheric through the critical region of the mixture in question. Less complete data were reported by von Huhn (10) on benzene-toluene and benzene-xylene mixtures up t o 50 atmospheres, and by Nederbragt (17) on dilute solutions of methane in butane up to 40” C. and 30 atmospheres. More complex systems have been investigated by Katz and Hachmuth (18) who worked on crude oil-natural gas mixtures up to 200” F. and 3000 pounds per square inch, and by Boomer, Johnson, and Argue (1) who recently published a preliminary discussion of their work on natural gas-light oil systems up to 370 atmospheres. Although there are a number of ways in which data of this type can be obtained, the investigators mentioned above
An apparatus is described for the rapid determination of phase equilibrium data at high pressure. By constructing the apparatus largely of glass, visual observation of the material under investigation is made possible. Data are presented on the vapor pressures of pure propane and isobutylene up to the critical points, as well as P-T-x-y data on mixtures of these two substances. A comparison is made between data obtained experimentally and those calculated from the Lewis fugacity equation; considerable differences are found, particularly in the critical region.
used, in general, one of the two following methods: In the first method the mixture of hydrocarbons is introduced into a high-pressure bomb, which can be placed bodily in a thermostatically controlled bath of any desired temperature. The apparatus is equipped with a stirring or shaking device, vapor and liquid sampling lines, and temperature and pressure indicators. Agitation is continued until equilibrium between the phases is reached, at which time samples of liquid and vapor are withdrawn and analyzed. The method suffers from a number of drawbacks, which tend to complicate the apparatus. It is essential that two phases be present at equilibrium; therefore the correct amount of each component must be added to the bomb at the beginning of the run, and some level-indicating device is necessary. As critical conditions are approached and vapor and liquid properties become
