NOVEMBER, 1939
INDUSTRIAL AND EKGINEERING CHEMISTRY
Yield of products on chlorine consumed: Allyl-type monochlorides 78.9 Vinyl-type monochlorides 1.5 14.8 Dichlorides 3.6 Chlorohydrins 1.2 Polymers Yield of tert-amyl chloride on amylene oonsumed 0.0
71.3 2.3 18.6 3.0 4.8
20.1
0.0
0.0
66.0
3.0 13.5
7.4
CHLORINATION OF “TERTIARY AMYLENE”IN COXCENTRIC TUBEREACTOR.Chlorine was mixed with “tertiary amylene” vaporized to 50’ C. and reacted in the zone between two concentric tubes 10 cm. long (outside diameter of inner tube, 0.6 cm.; inside diameter of outer tube, 0.7 cm.; volume, 1.6 cm.). The nature of the reaction products was determined when the outside tube was cooled with tap water, when both the inside and outside tube were cooled, and when no cooling was applied. The conditions and yield of products were as follows: 24.
Experimental conditions: Cooling
External External and internal
3.7 Flow of ohlorine, grams/min. 1.51 Mole ratio, amylene/chlorine 0.043 Reaction time, sec. 96 Temp. at point of mixing, C. 88 Temp. at outlet of reactor, O C. Yield of products on chlorine consumed: Unsatd. monochloride 83.8 12.2 Diohloride 7.9 Polymer Yield~oftert-amyl chloride on amylene consumed 2.2
3.3 1.08 0.044 60-70 (estd.) 60-70 (estd.)
None 4.1
1.50 0 040 115 128
85.9 10.3 6.2
67.5 24.9 9.4
4.5
3.4
Acknowledgment The authors thank E. C. Williams, vice president in charge of research, for his active interest and encouragement.
1419
For their kind permission to include in this publication independent results of their work, thanks are due R. M. Deanesly (experiment 8) and W. E. Vaughan and F. F. Rust (experiments 17 and 18). The authors’ thanks are further due to M. Adams, D. S. La France, G. von Stietz, and A. Redmond, who assisted in the experimental work.
Literature Cited (1) Aschan, Oversikt Finska VeZenskaps-Soc. Fdrh., 58, 122 (1915). (2) Badische Anilin und Soda Fabrik, German Patent 258,555 (May 31, 1912). (3) Chilton and Genereaux, Trans. Am. Inst. Chem. Engrs., 25, 102 (1930). (4) Coffin and Maas, Can. J . Research, 3, 626 (1930). (5) Deanesly and Hearne, U. S. Patent 2,031,938 (Feb. 25, 1936). (6) Engs and Redmond, Ibid., 2,077,382 (April 20, 1937). (7) Hass, McBee, and Hatch, IND. ENQ.CHEM.,29, 1335 (1937). (8) Kondakov, J . Russ. Phys. Chem. SOC.,17, 290 (1885). (9) Ostromislensky, Ibid., 47, 1988 (1915). (10) Pogorshelski, Ibid., 36, 1129 (1904). (11) Schales, Bet-., 70, 116 (1937). (12) Sheshukov, J.Russ. Phys. Chem. SOC.,1 6 , 4 7 8 (1884). (13) Stewart and Weidenbaum, J. Am. Chem. Soc., 57, 2036 (1936). (14) Tishchenko, J. Gen. Chem. (U. S . S . R.), 6 , 116-32, 1549-52 (1936). (15) Vaughan and Rust, private communication. (16) Whitmore, “Organic Chemistry”, p. 97, New York, D. van Nostrand Co., 1937. PRESENTED before the Division of Organic Chemistry at the 97th Meeting of the American Chemical Society. Baltimore, Md.
Fluid Flow through Porous Carbon iM. R. HATFIELD National Carbon Company, Inc., Cleveland, Ohio
A
CONSIDERABLE amount of study has been given to the problems of the flow of fluids through various types of porous media. A great deal of excellent work has been done on flow through consolidated and unconsolidated oil sands (10) and on the flow of gases through packed towers (8). Several theoretical studies have been made on flow through aggregates of spherical particles such as beds formed by lead shot, etc. (2, 16). However, as far as we know, there has been no correlation of flow data to facilitate the application of commerically available porous media such as porous carbon. The general properties of porous carbon have been described elsewhere (6, 21, 24). This material consists of carefully sized carbon particles bonded together with a carbon bond. The particles are selected and the manufacture is controlled to produce several grades of regulated pore size and permeability. The permeability and pore diameters decrease in regular steps from the fastest grade needed in industrial applications through intermediate grades to a fine-pored ultrafilter material. Porous carbon is composed of better than 99 per cent carbon so that its chemical properties are those of the element. It is chemically resistant under all but strong oxidizing conditions. It will withstand strong thermal shock and is an electrical conductor. Although usually supplied in the amorphous form, porous carbon may also be graphitized which greatly increases its electrical conductivity.
The flow of fluids through porous carbon follows the wellknown laws of flow through porous media. The flow of all types of fluids under widely differing conditions and through all grades of porous carbon may be correlated by means of Reynolds criterion and the corresponding friction factors.
Types of Flow The flow of fluids through porous media is known to be of two types. At low rates the flow is streamline or viscous and is governed by Darcy’s law (9). As the velocity is increased beyond a critical value, the streamline flow changes to turbulent flow characterized by fluctuating eddies with resultant mixing of the fluid. The velocity a t which transition from one type to the other occurs is governed by the size and nature of the pores and the density and viscosity of the fluid. The transition was qualitatively observed by Fancher and Lewis (10) by means of filaments of fluorescein solution injected into water flowing past shot in a glass tube. The resistance to flow varies linearly with the velocity during viscous flow and approximately as the square of the velocity during turbulent flow. The similarity of the flow conditions and the methods of analysis have led many to draw rather close analogies between fluid flow through porous media and flow of ordinary hydrodynamics through open vessels, such as pipes. Several investigators (2, 11) have pointed out the dangers of this, since the flow resistance through porous media is caused
1420
INDUSTRIAL AND ENGINEERING CHEMISTRY
VOL. 31, NO. 11
Courtesy, Chicago Pump Company
POROUS CARBON DIFFUSER INSTALLATION IN ACTIVATED SLUDGE SEWAGE TREATMENT TANKS,LAKECHARLES, LA.
by different conditions. The individual pores are made up of relatively large cavities connected by smaller openings. The flow of the fluid is not uniform; it is characterized by sudden accelerations caused by enlargements and contractions of pore cross section and the twistings of the paths. The divergence of the paths through the interconnecting pore spaces of porous carbon was observed while water was passing upward through it by means of a filament of colored liquid (potassium permanganate solution). In traversing a halfinch thickness of 10-grade porous carbon stock, the area of the path increased fifty fold. The flow resistance is caused predominantly by inertia effects rather than tangential shearing effects. The fundamental difference (16) between viscous flow through porous media as governed by Darcy’s law and viscous flow through tubes as governed by Poiseuille’s law lies in the fact that the macroscopic velocity of the former is uniform over the cross section whereas the velocity traverse across the latter is essentially parabolic, falling to zero a t the walls. Therefore the total flow through uniform porous media a t constant pressure drop is proportional to the cross section instead of varying as the square of the cross section according to Poiseuille’s law. Undoubtedly, the individual pores exhibit minute velocity traverses, but the average velocity is uniform across the medium. A similar distinction may be drawn for turbulent flow. Another difference between fluid flow through open vessels and porous media is manifested by the slower transition from viscous to turbulent flow through porous media. The tremendous wall surface presented by the latter gives rise to a viscous drag on the fluid. The larger pores or sections of pores assume turbulence first, and this condition gradually disseminates throughout the medium. The usual method of correlating flow data through porous media is by means of the familiar flow chart formed by plot-
ting Reynolds criterion, DVap/p, against a friction factor on logarithmic paper. The friction factor, which is obtained from the general equation of fluid flow as derived from dimensional analysis, is of the form DgAP/2pLVs2. It is a unique function of DV8p/pin that, if one is plotted against the other, a single curve will result, no matter how widely the independent variables may vary. By use of the dimensionless Reynolds criterion, both types of flow may be correlated by a single curve. The relation is linear for viscous flow but becomes exponential with the advent of turbulence. Flow charts of this type have been used by many investigators (2, 7, 8, IO, 16) in analyzing flow data through all types of porous media.
Application to Porous Carbon As shown above, the character of flow is determined by the Reynolds criterion, DVap/p. Of the four factors involved, the one that characterizes the porous medium itself is the pore diameter, D. To be truly definitive, this factor should also take into consideration the shape of the pores, the roughness of the pore walls, etc. It seems obvious that a bed of rough-grained sand particles will present a different resistance to flow than that offered by an aggregation of smooth spheres such as metal shot, even though the conditions of porosity and average pore size are identical. Fortunately, the pore characteristics for all grades of porous carbon are the same so that a definition of pore size is sufficient for complete correlation of the various grades, and a “shape” factor is not necessary. The determination of actual pore diameters is often difficult, and many investigators have substituted in its place the size of the particles making up the granular medium with the idea that this represents a value equal to or proportional to the actual pore size (10, 12). This substitution has been
NOVEMBER, 1939
INDUSTRIAL AND ENGINEERING CHEMISTRY
successful in the case of unconsolidated materials. However, for bonded material, where the amount and distribution of bond is an important factor, a more precise definition and measurement of pore size is necessary. It has been found that actual determination of the mean effectivepore diameter is a necessity for correlating the various grades of porous carbon.
1421
of thickness d under a pressure head p . The mean effective pore diameter is then calculated from the relation,
+p 20
Kpt
where K represents the void space in the sample, and all values are expressed in the proper metric units. The mean effective pore diameters for all grades of porous carbon are as follows; it should he understood that during filtration the porous carbon structure will retain particles considerably smaller than the mean effective pore diameter of any given grade: Grade
c
X* 50A’ 40 30 20 10
Xesn Pore Diam.
Cm. 0.000s 0.0031 0.0007 0.0086 0.0102 0.0141 0.0204
Effwtive POrositY
Inch
%
0.0002 0.0012 0.0020 0.0034 0.0040 0.0056 0.0080
42 48 4s 4s 48 4s
30
Erperimentd grade. PORTION OF
MULTIPLE DIFFUSERFOB ELECTEOLYTIC TANKIN ACTION
The method employed in determining the mean pore diameter is that described by Ruoss and others (18, 22). I t depends on measuring streamline flow through porous carbon and calculating the diameter from Poiseuille’s law. The resulting value is a statistical average. The conception of Chalmers, Taliaferro, and Rawlins (7) is that this represents the “equivalent diameter of a straight tube of capillary dimensions which will flow the same amount of gas under the same pressure conditions as will flow through the tortuous paths of a single series of interconnected pores that extend to the limits of the same”. Our experiments check those of Wilde and Moore (26) who shon,ed that the mean effective pore diameter is independent of the type of fluid, as it should he from the theory of viscous Row. 13artell and his co-workers (4) considered this subject critically. They believe that in applying Poiseuille’s law it is necessary to correct for (a) the real path in such a system as compared to the apparent path, ( 6 ) deviation of the cross section of the average pore from circular, (e) the larger pressure gradient necessary for flow through curvilinear or sinuous pores, and (d) the added energy consumption due to many alternate enlargements and contractions of the cross-sectional area in the average flow path. Hitchcock (15) states that for spherical grains the length of the capillaries ought to he greater than the thickness of the sand membranes in tho ratio of r/Z. Bartell feels that this correction is somewhat large for the length of pore alone. This latter view is upheld hy Carman (6) who concludes that the path of the fluid through a granular bed is & times the depth of the bed. Bartell believes, however, that the other indeterminate factors may he compensated by using the factor r / 2 . Chilton and Colhurn (8) object to this correction from theoretical considerations and claim that the correction factor should be no less than twice the above. However, Bartell checked his correction against the diameter measured by the capillary rise method. The mean pore diameters of porous carbon as measured by this method are reasonahle in magnitude and certainly represent the relative pore sizes for the various grades. Therefore, the mean effectivepore diameters are calculated from measurements using viscous liquids to ensure streamline flow. The timet is recorded for the flow of a given volume Q of a liquid of viscosity z through a sample of porous carbon
A knowledge of porosity is necessary for determining pore sizes, and the percentage porosities of the various grades are included in the above table. With the exception of grades C and X, which are specially made fine-grained stock, the porosity is constant for all grades of porous carbon even though the pore sizes and the permeahility vary over a wide range. This indicates uniform compacting of spherical particles with the proper amount of hinder in each instance. I
REPRESENTATIYE POROUS CARBON SHAPES I n other words, the less permeable grades contain many small pores; the more permeable grades contain a fewer number of large pores. The result is constant porosity. Porosity plays a role in fluid flow correlation as well as being a necessary step in computing pore sizes. Even when identical spheres are packed into the same space under identical conditions, variations in porosity arise that affect the flow. R i t h open continuous pores of this type, porosity corrections may be made as was done recently by Meyer and Work (16) and Baclimeteff and Feodoroff (2). General corrections of this type cannot he applied indiscriminately t o bonded materials. It is obviously possible to have a highly porous medium containing many closed and blind end pores a i t h little permeahility, as contrasted to another material of lower porosity which contains continuous pores allowing the easy
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VOL. 31, NO. 11
in determining the velocity of flow through the pores. With the various grades of porous carbon so defined, the flow of widely differIO' ing fluids under a host of conditions may be correlated by means of the familiar flow chart. Figure 1 is such a chart for porous io3 carbon resulting from plotting the Reynolds number, DV,p/p, against a friction factor, FIGURE 1. POROUS CARDgAP/2pLVm2. This curve affords a corBON FLOW CHART ,Oe relation for the flow of such widely varying d: fluids as air, water, corn sirup solutions, 0 + paraffin oil, and glycerol, covering a density range of 1140 fold and a viscosity range of IO 31,000 fold. There is a 5 fold variation in Z thickness and a 40 fold variation in pore diameter of the porous carbon. There is a 0 pressure change of 214 fold which, combined 10 . with the other factors, produces a superficial velocity range of nearly 600,000 fold. Each point on the curve is an average value taken 10' from measurements on several samples. In all they represent the results from nearly two thousand individual determinations. The two types of flow are quite apparent IOZ from the chart. Under viscous flow conditions, the plot 'is a straight line a t 45" having the required slope of -1. As turbulent REYNOLDS' NUMBER- 7 flow commences, the slope gradually changes until it becomes constant again for complete turbulence. This furnishes a simple picture of the passage of fluid. However, if the type of pore is the same for a group of related materials as it is for the various grades frictional resistance of porous carbon as it changes with the of porous carbon, then a common porosity correction may be velocity of flow raised to a variable power. The values of the power may be obtained by inspection of the slope of applied to all. the curve. Under conditions of streamline flow governed The porosity correction found most useful for porous carbon by Darcy's law, the resistance varies directly with velocity is the one used by Chalmers, Taliaferro, and Rawlins (7). If the superficial velocity V , is divided by the porosity, we and the exponent is unity. When turbulence commences, obtain an approximation of the mean velocity through the the resistance increases faster than the velocity. The curved section of the plot represents the gradual dissemination of The assumptions pores which will be designated as V,. involved are open to serious criticism. However, this turbulent flow throughout the porous carbon. The relaporosity correction provides good correlation of grades 10 tionship again becomes constant under complete turbulence, through 50 which have the same porosity, down to the ultraand the resistance varies as the velocity raised t o the 1.8 power. The same exponent was recently obtained for flow filter grade C which has a smaller porosity. The assumptions seem more valid since it is known that the pore structure of through sized shot (9). Average flow data for two fluids, air and water, are shown porous carbon is nearly isotropic. These factors have been considered in correlating the flow in Figure 2 as representative of the type of data used in deriving the flow correlation of Figure 1. These give the of fluids through porous carbon. The porous medium is characterized by a measure of the size of the average pore flow rates, through various grades of porous carbon one inch thick, of water at 70" F. and of air corrected to the volume making up its structure, The porosity is taken into account
p
E
14
r
2 I2
z
i4
ge
lo
Y
34
8
z 2
CUBIC FEET1 MINUTE I SQUARE FOOT
GALLONS/ MINUTE/ SQUARE FOOT
RATES(left) AND AIR RATES(n'ght) FIGURE 2. WATER
THROUGH
INCH-THICK POROUS CARBON
NOVEMBER, 1939
INDUSTRIAL AND ENGINEERING CHEMISTRY
1423
by the Cleveland laboratories of the American Gas Association. This calibration was corroborated in our laboratory by means of a Metric Metal Works meter which had been checked by the East Ohio Gas Company. The immediate upstream pressure at the sample is measured by means of a water or mercury manometer, and the air emerges from the sample against atmospheric pressure. All volumes are corrected to the standard conditions of 70" F. and 30 inches of mercury pressure. The flow of water through any porous medium rapidly diminishes if air is present in the water. For this reason, only distilled water is used in the determination of water rates (Figure 5 ) . To eliminate corrosion and the attendant errors introduced by sediment in the water, all the e uipment is constructed of brass or bronze with the exception o? the storage tank which is galvanized iron. As an added precaution, the water is also filtered through a bed of 35-65 mesh petroleum coke particles supported on a porous carbon under drain. A Viking positivetype pump provides circulation. A by-pass at the pump regulates the pressure at the sample which is measured by a mercury
FIGURE 3. PERMEABILITY TESTING EQUIPMENT
under standard conditions of 70" F. and 30 inches of mercury pressure. Although much of the flow was measured under turbulent conditions, the finer pored grades show the linear relationship characteristic of streamline flow. STORAGE
Permeability The standard permeability ratings of the various grades of porous carbon are determined b y the flow of air or water under specified conditions. Most of the flow data reported in this paper were obtained b y using the testing equipment shown in Figure 3: Severalkpresentative samples are cut from each piece of stock and carefully machined to either 2 or 3 inches in diameter and the proper thickness. After a thorough cleaning, the sample is placed in a closely fitting annular rubber ring for test. A metal band is tightened around the outside of the ring to prevent leaks, and the assembly is clamped into either the water rate or air rate outfit as shown. The air rate sample holder is equipped for testing 12 X 12 inch plates as well as the smaller disks.
THERMOMETER
FLOWMETEE
PRESURE TAP
ED ~RYINC TWE'RS
AIR
FIGURE 4. AIR PERMEABILITY APPARATUS For air permeability tests (Figure 4),compressed air reduced t o the proper pressures by suitable reducing valves is used. A
surge tank in the line tends to remove any fluctuations of pressure and the relative humidity is reduced to about 15 per cent by passing the air through self-draining calcium chloride drying towers and filters. The flow of air is measured by means of a Meriam multiple-orifice flowmeter. This meter was calibrated
I 8
FIGURE 5 . WATERPERMEABILITY APPARATUS
manometer. The water rate of the sample is determined by timing the flow of a definite weight of water. The receptacle in which the water is collected and weighed is provided with a drain for returning the fluid to the storage tank. Before testing, the samples are completely saturated by boiling in water. The same equipment is used for determinations on higheI viscosity fluids by filling the system with corn sirup solutions of various concentrations. Permeability measurements using paraffin oil and-klycerol are made in the apparatus for measuring pore size.
Bulk Volume The determination of the bulk volume of a piece of porous carbon, which is necessary for porosity determination, is difficult because of its rough surface. Direct measurement introduces errors of several per cent. All methods (1, 3, 19) depending on the filling of the pores with a liquid and then determining the volume by weighing or displacement fail with porous carbon because the larger pores will not retain the liquid. The volume cannot be measured by mercury displacement as used b y the United States Bureau of Mines (20) because of penetration with the more permeable grades. Coating of the sample with paraffin or collodion as described by Melcher (14) and Nutting (17) has certain disadvantages. Therefore the method of "surface polishing" was devised. This technique consists of machining the sample while the pores are filled with some material that may be later removed. The impregnant holds the particles in place so that they are cut through rather than being chipped out. Microscopic examination of the surface polish shows a structure characteristic of the interior so that direct measurement is possible.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1424
Porosity Porosity measurements are made by the “general method” of Washburn and Bunting (23). The procedure is well known, and an adaptation of it is used by the Bureau of Mines (20). The method is accurate, rapid, and does not impair the sample for further permeability of pore size determinations. The apparatus consists of a glass flask of volume VI, joined by a capillary tube to a steel vessel of volume V which holds the sample. To the latter vessel is also connected a suitable manometer for measuring pressures. This vessel with the sample is evacuated to a pressure of 10 to 20 mm. of mercury. The glass flask is then filled with dry air a t atmospheric pressure. When thermal equilibrium has been established, the manometer is read (Po). The stopcock connecting the two vessels is then opened, and when equilibrium is again reached the manometer is read (P). The per cent porosity is calculated from the following equation: porosity = 100
(2)
where B is barometric pressure and V Bthe bulk volume of the sample. V B is measured directly on the sample which has been surface-polished by the method previously described. The closed-end manometer is equipped with a mercury reservoir so that the mercury level can be set a t the zero point before pressure readings are taken. Thus the functioning of the manometer does not affect the volume of the vessel to which it is attached. The whole apparatus is kept in a constant-temperature room to avoid temperature fluctuations. Identical results are obtained with hydrogen gas in place of air, which shows the absence of errors that would arise from sorption effects.
Pore Size The mean effective pore diameters are determined by an adaptation of Poiseuille’s law. The rate of flow is measured for highly viscous %uidspassing through porous carbon under streamline conditions. The samples, whose porosities have been determined, are held in the same type of annular rubber ring used for the air and water rate tests. The samples are thoroughly saturated with the fluid by evacuation before testing. The fluid head is obtained by a vertical glass tube above the sample. The fluid enters the tube through a side arm, and the rate of flow is regulated to maintain any desired head above the sample. Accurate temperature readings are made during the run, and the time is recorded for the flow of a definite quantity of fluid. The mean effective pore diameter may then be calculated from Equation 1. Identical results are obtained with glycerol or paraffin oil. The former is used for the coarser grades; the latter is used on the finer grades with the exception of C. With this fine-grained stock, water gives the required viscous flow. The viscosities of the fluids are measured with a Hoppler viscometer. It is not practical to determine the porosity and pore sizes for each sample. Therefore average values for each grade of
e
VOL. 31. NO. 11
porous carbon were used in the calculations with average permeability figures obtained from several samples. Reynolds numbers and friction factors of those samples whose porosities and pore sizes are known, as well as the permeability data, follow the plot of Figure 1 very well.
Acknowledgment The author is indebted to B. C. York for his measurements of much of the flow data.
Nomenclature A P = pressure drop, lb./sq. in. L = thickness of porous carbon, ft. p
= mean effective pore diameter, ft. = fluid density, Ib./cu. ft.
p
= =
D
absolute viscosity, Centipoise viscosity, Ib./ft.-sec. = 0.000672~ g = acceleration of gravity = 32.2 ft./sec./sec. V8 = superficialvelocity, ft./sec. = rate of flow/cross section Vm = mean velocity, _ .ft./sec. = rate of flow/cross section x porosity R = Reynoldsnumber = D V m p / p f = friction factor = Dg AP/2pLVm2
z
Literature Cited (1) A. S. T. M., Standard Methods, Test C20-33,p. 209 (1936). (2) Bachmeteff, B. A.,and Feodoroff, N. V., J . Applied Mechanics, 4, A97 (1937). (3) Barnes, K. B., Penna. State College, Mineral I n d . Expt. Sta. Bull. 10 (1931). (4) Bartell, F. E.,and Osterhof, H. J., J . Phys. Chem., 32, 1553 (1928). (5) Broadwell, B. E.,and Werking, L. C.,U. 8. Patent 1,988,478 (Jan. 22, 1935). (6) Carman, P. C., Trans. Inst. Chem. Engrs. (London), 15, 150 (1937). (7) Chalmers, J., Taliaferro, D. B., and Rawlins, E. L., Trans. Am. Inst. Mining Met. Engrs., 98,375 (1932). (8) Chilton, T. H., and Colburn, A. P., IND.ENG.CHEM.,23, 913 (1931). (9) Darcy, H., “Les Fontaines Publiques de la Ville de Dijon”, Paris, Victor Dalmon, 1856. (IO) Fancher, G. H., and Lewis, J. A,, IND.ENB. CHEM.,25, 1139 (1933); Fancher, G. H.,Lewis, J. A., and Barnes, K. B., Penna. State College, Mineral I n d . Expt. Sta. Bull. 12, 65 (1933). (11) Forchheimer, P., “Hydraulics”, Teubner, Leipzig, 1914 and 1930. (12) Furnas, C. C., U. S. Bur. Mines, Bull. 307 (1929). (13) Hitchcock, D. I., J. Gen. Physiol., 9,755 (1926). (14) Melcher, A. F., Bull. Am. Assoc. Petroleum Geol., 9,442 (1925). (15) Meyer, W. G., and Work, L. T., Trans. Am. Inst. Chem. Engrs., 33, 13 (1937). (16) Muskat, M., ”Flow of Homogeneous Fluids through Porous Media”, New York, McGraw-Hill Book Co., 1937. (17) Nutting, P. G., Bull. Am. Assoc. Petroleum Geol., 14, 1337 (1930). (18) Ruoss, H., Kolloid-2.. 74, 221 (1936). (19) Russel, W. L., Bull. Am, Assoc. Petroleum Geol., 10,931 (1926). (20) Taliaferro, D. E., Johnson, T. W., and Dewees, E. J., U. 8. Bur. Mines, Rept. Investigations 3352 (1937). (21) Vosburgh, F. J., Chem. & Met. Ew., 45,607 (1938). (22) Washburn, E.W., Proc. Natl. Acad. Sci., 1, 115 (1921). (23) . , Washburn. E.W..and Bunting, E. N., J . Am. Ceram. SOC.,5 , 112 (1922). . (24) Werking, L. C.,Trans. Electrochem. Soc., 74,365 (1938). (25) Wilde, H.D., Jr., and Moore, T. V., Oil Weekly, 67,34 (1932).
