1206
INDUSTRIAL AND ENGINEERING CHEMISTRY
rounded off and weak particles eliminated. The attrition causes a rounding off of sharp edges of particles similar to that occurring i n a commercial fluid catalytic cracking unit. The attrition resistance of ground catalysts increases rapidly during operation in a commercial unit. Mechanical erosion of particles is the primary cause of this increase. With a ground silica-magnesia catalyst the effect of process temperatures is significant. The presence of fine particles in a catalyst reduces the attrition rate of the coarser particles, and a correction to a fines-free charge basis helps to compensate for this effect. The most valid comparisons of attritiori resistance are obtained when the catalyat samples have comparable fines contents. The particle size of the fine material produced during the attrition of a catalyst in the laboratory test is predominantly less than 10 microns with the exception of some agglomerated catalysts. The particle-size distribution resulting from the attrition of an agglomerated catalyst depends on the size of the individual particles in the agglomerates.
Vol. 41, No. 6
ACKNOWLEDGMENT
It is desired to acknowledge the development of this general test method by J. T. Clapp and J. B. Gray. Appreciation is also expressed for many helpful suggestions bir .4.L. Conn and J. 0. Howe. LITERATURE CITED
(1) Innes, W. B., and iishley, K. D., Proc. Am Petroleum I r ~ s l . , 27, [111], 9-17 (1947). (2) Matheson, G. L., Ibid.,pp. 18-22. (3) Murphree, E. V., Brown, C . L., Gohr, E. J., Jahnig, C. E., Martin, H. Z., and Tyson, C. W., Trans. Am. Inst. Chem. Engra., 41, 19-33 (1945). (4) Roller, P.S.,J . Am. Cerum. S o c . , 20, 167 (1937). ( 5 ) Roller, P. S., Trans. Am. SOC.Testing Materials, 32, 607 (1932). (6) Roller, P. S..U. S. Bur. Mines, Tech. Paper 490, 46 (1931). (7) Webb, G. M., Petroleum Processing, 2 ( 7 ) , 497 (1947). R%CUIT E D January 3, 1940.
id G e n e r a l fluidizatiom principles are reviewed briefly, and t h e natureof earlier data isdiscussed. New data, observed during t h e fluidization of an anthracite coai in a glass c o l u m n 4 inches in diameter, are described. T h e matorials investigated were mixtures of m a n y sizes, ranging from 325- t o 32-mesh and larger. Because of t h e appreciable internal porosity of t h e coal, it is n o longer justifiable %o consider t h e percentage voids, determined by water
immersion, as wholly effective during fluidization. A more satisfactory correlation resulted from alp estimation of t h e shape factor of t h e Coal particles by comparison with materials of known shape factor and from a subseq u e n t estimation of percentage of effective voids through application of a suitable pressure drop correlation. T h e data are used in an effort t o demonstrate a more general approach to t h e solution of problems in fluidization.
M A X LEVA, MURRAY WEINT AUB, MILTON c3 IS PCpLLCHliK OFFICE OF S Y N T H E T I C LIQUID FUELS, B U R E A U
I
O F M I N E S , BRUCETDN,
PA,
N R E C E N T years, fluidization has received considerable
The validity of this expression was tested by many workers
attention as an improved method of achieving gas-solid contact in industrial catmalysis. The early literat,ure (12, 14, 16) dealt with the subject only descriptively arid in a general way. Quantitative fundamental relationships backed by experimental work have only recently become availablc (Q-1'1, 13, 16). The present paper I e v i e ~ st'he fundamentals of fluidization of nonporous materials and, by means of new data observed during fluidization of an anthracite coal, demonstrates a more general approach toward the solution of fluidization problems when the material possesses considerable internal porosity.
(6, 9, 13, 1 6 ) and found to be independent of such system proper-
REVIEW
Fluidization as now applied to catalysis is characterized by eountergravity flow of gaseous fluids through beds of fine, solid particles. I n an analysis of pressure drop-fluid velocity relations of such systems, it has been observed by various investigat'ors (6, 9, 13, 15, 1'6) that the bed begins to expand a t a definite fluid velocity. Although t,he pressure drop increases steadily with the fluid velocity for flow through unexpanded solids, it remains essentially constant for flow through expanded materials. Mathematically, this may be expressed by the simple relation :
The symbols of this and all subsequent correlations are defined in the table of nomenclature.
ties as material density, shape and size of particles, weight-size distribution of the charge, geometry of the vessel, fluid density, and viscosity. Particle size ranges supporting Equation 1 extend from 600-mesh or finer (13) through fine-grained sands and iron Fischer-Tropsch catalgst,s (9-11) up t o particles 0.23 inch in diameter (16). Various gases as well as water were used as fluids, and vessel diameters varied between 1 arid 6 inches. Experimental data observed with sands (9, I O ) and iron Fischer-Tropsch catalyst particlcs (11) showed that before a bed of solid pa,rtieles could pass into the fluidized state-Le., exhibit internal particle motion-a definite amount of bed expansion was required in order to disengage the particles sufficiently from each other. The fraction of voids associated with this condition, tlefined as minimum fluid voidage, was found characteristic of the shape and the size of the particles. In general, small and irregular particles required a higher minimum fluid voidage than more regular and largcr shapes. For the nonfluidized range, the pressure drop is related to other system variables by the equation: Ap =
2fG2LX(3-n) (1.__,)(S-n) I__ DngcPFea
(2)
This equation, proposed earlier (Y), is relat,ed t o similar forms developed by Blake ( l ) , Kozeny (Y), Burke and Plummer (Z), Fair and Hatch (4,and Carman (S), and its validity has been
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1949
Figure 1.
thoroughly demonstrated. ized by values of
N ~ e m
Modified Friction Factors vs. Modified Reynolds Number
For the viscous flow range character100 .f = ---* N~etn For N ~ c m> 2oo and
175 smooth particles, f = -L, whereas with particles of appreciable N R ~ ~ ~ surface roughness, friction factors are considerably higher (8). In the transitional range of flow as indicated in Figure 1, the state-of-flow factor, n, is a function of the modified Reynolds number. Equation 2 applies to this range after n has been properly evaluated from the inset in Figure 1. Combining Equations 1 and 2, substituting emf for e, and solving for the mass velocity yields :
a general expression which may be used to estimate the necessary mass flow for the beginning of fluidization. Inasmuch as the pressure drop remains essentially constant for the fluidixation range, it follows that, if Equation 2 applies, a plot of log
1207
Figure 2.
- .)S-n GnP2-"R us. log (I 7 should yield a straight line of slope PF
Use of this analysis indicated that particles of comparatively large diameter obeyed Equation 2; whereas, with small materials, deviations were observed that became progressively more significant as the particle diameter d e creased. I n addition, it appeared that the smaller the particles, the more intense was the state of agitation. Interpretation of 7%
= -1 for any t i p e of bed.
Weight-Size Distribution of Beds Investigated
1208
INDUSTRIAL AND ENGINEERING CHEMISTRY
Figure 3.
Anthracite Coal Fluidization Data
the data led to the concept of Huidizatioii efficiency. Thus 7 = (G, - G J / G j . A knowledge of the percentage voids in the bed is indispensable for the application of the above relationships. For nonporous materials, representative void determinations are readily possible from the dimensions of the apparatus, the weight of the charge, and the pycnometric density. Holvever, in dealing with materials such as coal or coke which have an appreciable internal porosity, the voidage, as obtained from the pycnometric density, will include the crevices inside the particles and, therefore, does not represent the truly effective voidage as far as fluid Holy is concerned. For this reason, a mole gencral approach to the solution of the probkm is necessary. EXPERIMENTAL DATA
Materials. The coal used in these experiments mas prepared by egg-sized lulnps to pieces of approsimately0,25 inch. The fragments 1vej-e reduced still further in a ball mill and passed through standard sieves. Plates a to h in Figure 4 show the various cuts sufficiently enlarged to permit recognitiori of the characteristic shape or most particles. Densities determined by immerwere 2.37 alld grams per ml,, sion in water and respectively. Assuming that the water fills all the internal crevices and that the mercury does not penet'rate into tjhe particles a t 2.37-1.97 all, an average internal porosity of ~ - X -100 = 16.9% 2.37 based on the apparent solid volume of the particles is calculat,ed. Cumulative size distributions of the materials fluidized are indicated in Figure 2. The uniformitfly coefficient, a concept frequently used in size classificat,ion, is defiiried as cu = ds8,/dlo where d~~arid r l , ~are sieve openings permitting passage of 60 and lo%, respectively, by weight of a sample to be sieved. It is a oonvenieiit, though approximate, index for expressing the degree of homogeneity of a mixture of particles. Figure 2 reveals that all beds were mixtures containing a greater ot' ledser number of separate components. The average particle diameter of t,he
(xdp)z-, a rule
mixtures was calculated according t o D, ==
Vol. 41, No. 6
ble differences were observed. There was a greater degree of bed consolidation, as indicated by the considerable bed expansion which preceded the onset of fluidization (internal motion). It is probable that this observation is not an inherent characteristic of small coal particles as such but may instead be associated with the much larger size distribution of the small partkle beds, as is indicated bp the c, values in Table I. The coal particles exhibited marked channeling tendencies which became more pronounced as the particle diameter decreased. I n some cases, channeling was severe enough to prevent completely observation of the onset of fluidization. For the sizes recorded in Table I, channeling was most prevalent in the bottom portion of the bed. In all cases, the pressure drops across the channeling beds were observed to be considerably lower than values suggested by Equation 1. n'ith increasing_ gas _ flow, the line of demarcation (not necessarily horizontal) between the channeling portion and the upper fluidized section of the bed was observed to move downward, indicating participation of a la.rger portion of t,he bed in the fluidization. This improved operat,ion wa,s always associated with a pressure drop recovery to a point where, a t comparatively high flows, the observed pressure drop corresponded essentially to that ca'lculated from Equation 1.
Table I . Run NO.
a b 0
d e
f
g-1 8-2
h-1 h-2
Characteristics of Anthracite Coal Particles and Orientation of Experimental Work
p noh 0.03819 0.02795 0.02321 0 01646 0.01211 0.00940 0.00844 0.00844 0.0065853 0.0065863
cu
1.88 1.45 1.18 1.21 3.29 3.27 2.50 2.50 3.53 3.53
Weight, Lh. 9.65 5.56 7.25 4.44 5.96 6.80 4.96 9.56 6.35 6.35
La, Feet 1.605 0.903 1.259 0.778 1.002 1.129 0.862 1.613 1.lOA 1 094
Range of R 1-1.083 1-1.146 1-1.146 1-1.603 1-1.271 1-1.277 1-1.408 1-1.332 1-1.3iiO 1-1,340
Gas
emf
Air Air -4ir Air Air Air Air IIe Air
0.475 0.503 0.616 0.519 0.507
He
0:ii 0.50
... ..I
Z-1
euggested earlier (9). ?'he apparatus used in the investigation has been described in consideia1)le detail (9). Weiglipd quantities of the solid were charged i n t o a glass tube 4 inches in tliaineter fitted with a supporting screw at, its lower end. Properly located marromet,er connections determillation of the pressure drop across admitted ir>t,othe t h e bed, Dcfillite l.ates of air or ilelium unit, and t,he height of the column was ohserved as v y ~ l las the pressure drop and the general behavior during Auitlization. An orientation of the experimental work is yjveii in Table I. The 3,show the pressure drol, in relat,ior,to data, the modified Reynolds number. Observation. The behavior of fluidized beds of large coal particles was general1.y similar to t,hat of sands and iron FischerTropsch catalysts. With the smaller sizes, however, some nota-
Severe channeling difficulties were encountered with particles that xvere slnaller than 250-mesh. at high fiolvs the particks could not be brought into a fluidized state; instead, t'lie air blasted a clear channel through the bed which occasionally underwent a rearrangement. Pressure drop readings were erratic, and the results coulci not be duplicated. Qualitative investigatioiis m r e made to check any possible attrition in the beds. After operation for several hours, a small percentage of fines was usually formed. N o attempt was made to measure the rate of attrition, chiefly because the experiments did not last long enough to be significantly iniluenced by the breakdown.
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1949
1209
d
f
e
h
Figure 4. a.
b.
c.
0.0382 inch 0.028 Inch 0.0232 Inch 0
d. 0.0165 inch e.
1:
0.0121 inch
1. 0.0094 Inch 0.05
0.1
Photographs of Anthracite Coal Fluidized 0.00844 Inch 0.00658 inch
1.0
INCH
.9 CORRELATION A N D COMMENTS
Anthracite Coal. In the review of the earlier correlations, it was stressed that a satisfactory indication of the applicability of Equation 2 t o fluidization data can be made by plotting log p' against log I n an analysis of the anthra-
w
r .0
.%: - -
PF
cite coal data, one must first evaluate the state-of-flow factor, n. Figure 3 shows t h a t the investigations extended over the Reynolds number range 0.002 t o 25, and therefore n = 1, as evaluated from the inset of Figure 1. Inasmuch as determination of the effective voidage in the bed by the water-immersion method will give high porosity values and density measurements bv disulacement in mercury are also in
"
.
.7
.6 Dp, INCH
Figure 5.
Effective Voidage in Anthracite Coal Beds
2210
INDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y
ual cuts. The total voidage is practically independent of D, However, both ea and ke pass thiough a maximum near D, = 0.02 inch. On the basis of available data, this is not readily explainable without having to resort to various unsubstantiated hypotheses.
u 2
€3
03
06
2
10
Vol. 41, No. 6
3 4
In view of the considerable variation in sixes as well as the rather wide distribution, these results should be looked upon as being characteristic of the material investigated. Table I1 lists shape factors that would have resulted from accepting either the watcr density or the mercury density as a basis for the calculation of voids. It is readily seen t h a t the values of X suggested for the coal particles are in most cases considerably higher than mould be expected from visual examination. With n and properly evaluated, Figure 6 shows
GPR and log (1 the relation between log PF
I
2
3 4
3
2
6 810
4
uz
6 810
2
for all the data. The correlation is satisfactory, and the slopes, m, of the individual lines have been incorporated in Figure 7, which shous m in relation t o D,. I n addition t o earlier published data ( I O , l l ) , the figure contains the experimental work of several other investigators (6, 13, 16). Their original data are presented in Figure 8 in a manner suggested by the method of correlation discussed earlier. Examination of Figure 7 shows the existence of two separate branches, A-E and A'-B, which merge at
3 4 5
I
B
Figure 6.
Correlation of Anthracite Coal D a t a
doubt because of uncertainties in the extent of penetration of the mercury into the pores, i t was found more practical to proceed as follows: Procurement of k e d - b e d pressure-drop data for definite flaws. Measurement of bed height and weight. Estimation of particle shape factor by comparison with p n r ticles of known shape factor. Application of Equatlon 2 for the calculation of the effective voidage. A comparison of plates a to h in Figure 4 indicated that the particles contained in the individual cuts were all of the same shape. Further comparison of these photographs with those of sands and iron Fischer-Tropsch catalyst -I ( particles previously reported (9, 11) suggested t h a t the shape of the coal fragments was intermediate between t h a t of the sharp sand and the iron catalyst. -2i
As these particles had shape factors of 1.5 and 1.73, respectively, a value of X = 1.6 was assigned t o t h e coal particles. This value of h 1%-asthen used in combination with pressure drops through the unexpanded beds, as recorded in Figure 3, and effective voidages were calculated for all the cuts by solving Equation 2 for e . I n Figure 5 , the total voidage, et (calculated on the basis of t h e water density), the effective voidage, eg, and the proportion of effective voids, k,, are shown in relation to the composite particle diameter of the individ-
Table II. Shape Factors Calculated on Basis ob Water Density and Mercury Density of Coal Packing
DP
n
0.03819
C
0.02321 0.01646 0.01211 0.00940 0.00844 0.00668
b
0.027Q5
d
e f
0-Glass
XHZO 2.23 2.22 1.96 2.15 2.80 4.43
2.71
3.G4 5.47
3.45
beads
E -3.(
@
-Anthracile
c
-4(
PARTICCE DIAMETER DD,INCH
Figure 7.
Values of m i n Relation t o Dp for Various Materials
XHg
1.40 1.36 1.26 1.40 1.70
2.22
June 1949
I o8
1211
INDUSTRIAL AND ENGINEERING CHEMISTRY Material Sea sand----
m
Dp,(inch) 0.0147
HzO-fl'd'n.
Air-fl'd'n.
A
A
1.00
0.0219
v
'D
1.00
c
0.0393 0.0113
0.205
+ + & e
---
0
6 ---
Reference
I .05 Wilhelm 0.98 and 0.90 Kwauk 1.17
Parent Yagol Sieiner
point B and proceed along a common course to point C. Branch A'-B represents data observed during gas fluidization of a great variety of materials. It appears that, through the choice of a shape factor of A 1.6 and the resulting effective voidages, the coal data are in substantial agreement with the other gas fluidizfttion data. Solid-Gas and Solid-Liquid Deviations. Figure 7 indicates whether or not certain expansion data obey Equation 2. Obviously all the points along A-B-C follow the equation; whereas, for points along A '-B, the deviations from gas expansion behavior become progressively more pronounced with decreasing particle diameter. The consistency of the data suggests, therefore, a fundamental difference between water and gas fluidization of small particles. I n a n effort t o find the cause of this interesting behavior, a series of experiments was made using very fine sand as the dispersed phase and water as the fluid. The initial voidage of the sand in water was very close t o the initial voidage in air, and particular emphasis was placed on the investigation of the ex an sion range 1 < R < 2, the region that comprised all the gas &id:
ization data. Observation showed t h a t the degree of agitation and turnover of the solids during water fluidization was insignificant in comparison to the rapid rate of circulation and mixing in a solid-gas system of the same particle diameter. Qualitatively, i t appeared that the solid-gas system exhibits considerably more internal agitation and turnover than a corresponding solid-liquid system. The deviations observed along branch A'-B have led to the definition of the previously discussed concept of fluidization efficiency. D a t a regarding bed turnover, as yet unpublished by the authors, and pertaining to fluidization of a variety of materials, give support to a direct relationship between fluidization efficiency and the mixing velocity in fluidized beds, thus explaining the deviation reported in Figure 7 . Minimum Fluid Voidage. The minimum fluid voidage of a bed of solids may be determined by observing either the onset of internal motion due t o increasing fluid flow or the cessation of motion as a consequence of reduction of flow. With substances such as sand or iron catalyst particles, these observations were comparatively easy. Attempts to evaluate emf for the coal were less successful, however, chiefly owing to exoessive channeling.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1212
value in combination with suitable pressure drop data and Equation 2 for the calculation of the effective voids in the bed.
0.E
NOMENCLATURE
I
W
E
Vol. 41, No. 6
.4
1
11
d - Iron Fischer-Tropsch c o t o l y s t , h = 173e- Anthrocite cool, A = I 6 0 I
1
(F) = force ( L ) = length pound, feet, hour system used if not otherwise ( M ) = mass specified (8) = time J
7
c,,
= uniformity coefficient of a mixture of particlea (no
d,
= effective diameter of a component particle in
dimension)
Figure9. M i n i m u m Fluid Voidage, emfr for Various Materials in Relation t o Effective Particle Diameter, Dp
Reliable data could be collected only with sizes larger than 0.01 inch. For these particles, Figure 9 shows the values of em, in relation t o the particle diameter. From the other data recorded in the figure, the increase in ern, with increasing is readily observed. The emf values for the coal agreed with this finding and were intermediate between those of the sharp sand and the iron catalyst, which had, respectively, smaller and larger shape factors than the coal fragments. This agreement may serve as an indirect check for the rather close estimation of A for the coal. Application and Limitations. The application of fluidization principles t o coal for the purpose of gasification is considerably more involved than application to ordinary catalysis. The added difficulties are due primarily t o the size reduction which the coal particles experience as a consequence of the combustion process. Obviously, one of the major problems is to select operating conditions that will maintain a low rate of carry-over of fines. Calculations defining such conditions must coordinate fluidization principles with the thermodynamics and kinetics of the reactions. Before such calculations are possible, more information on the dynamics of small particles in the dilute phase of fluidization is required. The data and calculations have shown t h a t the correlations developed previously are applicable t o porous materials. They permit calculation of the minimum flow required for fluidization, as well as the extent of bed expansion resulting from flows higher than Gmf. Although no data could be provided to demonstrate the validity of the relationship with porous particles smaller than 0.00658 inch, it is believed t h a t the correlations will apply to particles of this size, if channeling tendencies are not too severe. Prediction of bed expansion ratios becomes progressively less accurate n i t h increasing flow rates. For operation with gases, expansion ratios of 1.6 to 1.8 may be estimated with good results; with liquids considerably higher expansions may be predicted. SUMMARY
The paper reviews briefly the more important fluidization principles and concepts t h a t are based on data with nonporous materials. I n an effort to show how the correlations apply to materials possessing internal porosity, new d a t a pertaining to fluidization of an anthracite coal are presented, and the general approach toward the solution of fluidization problems is discussed. For the solution of problems in fluidization, one must know the rate of flow, density and viscosity of fluid, effective particle diameter, particle shape factor, and minimum fluid voidage The first three factors are usually available from process specifications. For this reason, the solution of the problem requires estimation of the shape factor and the minimum fluid yoidage. I n dealing with nonporous materials, the voidage 111 the bed may be estimated from a knowledge of the pycnometric density. From pressure drop data across a fixed bed and by means of Equation 2, the shape factor value may be calculated. From the knowledge of the shape factor and the effective particle diameter, the minimum fluid voidage may be obtained. If no facilities are available for securing pressure drop data, i t will suffice for most engineering work to estimate the shape factor. This estimated value may then be used for obtaining values of the minimum fluid voidage. When the particles are porous, the pycnometric density cannot be used for void determinations. At present, the best way to arrive a t e,,, is t o estimate thc shape factor of the particles by comparison with other particles of known shape and to use this
( L ) d,
=
a mixture adja-
ddldz,where dl and d, are oprnings of
cent sieve sizes.
f gc
= modified friction factor (no dimension) = conversion factor in Sewton's law of motion (4.18
108)
x
= proportion of effective voids (no dimension) = expansion ratio (no dimension)
exponent (no dimension) state-of-flow factor (no dimension) = number of components in a mixture (no dimensiori) = surface area of an individual packing element ( L z ) = cross-s~ctionalarea of fluidization vessel (L2) = composite particle diameter ( L ) = inside vessel diameter ( L ) = mass velocity based on open vessel cross sectiori (Me-x-2) = mass velocity required for bed expansion ( M W L - 2 ) = inass velocity required for minimum fluidization = =
( M B -11,- -2'1 \ - -
Q L
mass velocity required for fluidiza.tion (Me-'L-2) = height of dumped bed ( L ) L,, = height of bed at minimum fluid voidage ( L ) L, = height of static bed ( L ) . V R= ~~ modified ~ Reynolds number DpG/,u (no dimension) V = volume of a n individual packing element (La) T'r = volume of packing material in column as dumped (Le) x' = fraction of component in a mixture of sizes A p = t'heoretical pressure drop ( F L - 2 ) E = voidage in a dumped bed (no dimension) t. = effective voidage in a bed of porous solids (no dimension) tlril = minimum fluid voidage in a bed of solids (no dimension) et = total voidage in a bed of porous solids (no dimension; q = fluidization efficiency (no dimension) A X = particle shape factor (no dimension) A = 0.203 F?va Os' = 1 / x p = fluid viscosity (M8-iL-1) PF = fluid density (ML-3) pa = solid density ( X L - 3 ) =
L I T E R A T U R E CITED
(1) Blake, I?. C., Trans. Am. Inst. Chem. Engrs., 14, 415 (1922). (2) Burke, S. P., and Pluniiner, W.B., IND. ENQ.CHEM., 20, 1195 (1928). (3) Carman, P. C., Trans. Inst. Chem. Eng. (London), 15, 150-68 (1937). (4) Fair, G. M., and Hatch. L. P., J . Am,. Water Works Assoc., 25, 1551 (1933). (5) Friend, L., et al., Chem. Eng. News, 27, 686 (1949). (6) Hatch, L. P., Trans. Am. Geophys. U n i o n , 1943, 536-47. (7) Kozeiiy, J., B e y . Wien.A k a d . , 1927, 136a, 271. (8) Leva, M., and Grummer, M., Chem. Eng. Progress, 43, 11, 633-8 (1947). (9) Leva, M., Grummer, A I . , Weintraub, M . , and Pollohik, M., I b i d . , 44, NO.7 , 511-20 (1948). (10) Ibid., 44, No. 8, 619-26 (1948). (11) Leva, >I., Grummer, M., Weintraub, hl.,and Storch, H. N., I b i d . , 44, No. 9,707-16 (1948). (12) Murphree, E. Ti., Brown, C. L., Gohr, E. J., Jahnig, C. E., Martin, H. Z., and Tyson, C. W., Trans. Am. Inst. Chem. Engrs., 41, 19 (1945). (13) Parent, J. D., Yagol, N.,and Steiner, C. S., Chem. Eng. Progress, 43, No. 8, 429 (1947). (14) Thomas, C . L., and Hoekstra, J., I N D . EXQ. C H E M . , 37, 332 (1945) (15) W-ickham, H. P., Petroleum Refiner, 24, 263-6 (July 1945). (16) Wilhelm, R. H., and Kwauk, hI.,Chem. Eng. Progress, 44, No. 3. 201 (1948). a
i*;OVc?mher 30, 1948. Symbol in accord with nomenolaturr snggestad in Chem. Ens. Wews (6).
RECEIVED 1
