DAVID S.
KOONS and B. E. LAUER
University of Colorado, Boulder, Colo.
Continuous Solids Feed Dense phaseflow techniques offer a solution to the problem of transporting solids uniformly from a common source to multiple fluidized beds W H E N A REACTION involving a granular solid is induced and sustained by elevated temperatures which must be obtained through heat supplied externally to the reaction mass, the fluidized solids technique may be important. T o extend the advantage of the reasonably high heat transfer rates made possible through the use of this technique, large heat transfer surfaces should be provided also. A shell and tube arrangement is a classical method for obtaining a large heat transfer surface. To fluidize solids in a number of parallel beds of small cross sectional areas such as would be formed within the tubes of a vertical shell and tube heat exchanger, the problem of uniform distribution of solids and gas into the many separate beds must be solved. The uniform distribution of a single phase fluid through parallel vertical tubes is brought about by the increasing pressure drop obtained with an increasing flow rate of fluid in the tubes. However, when solids fluidized with a gas are rising in a tube, the pressure drop decreases with an increase in the flow of fluidizing gas, and the flow distribution of solids and gas from a common bed into parallel vertical ’tubes is very nonuniform. Ordinarily, some tubes become packed with nonfluidized solids and the remaining tubes carry all of the gas and solids. Corrigan and Mills (Z), in a series of articles relating to fluidized bed reactors, indicated that the fluidizing gas alone could be distributed uniformly into the tubes of a shell-and-tube type unit by placing restrictive orifices in the bottom of each tube. Their discussions dealt only with fluidized beds preloaded with solids. I n a parallel tube fluidized bed arrangement in which the solids must be transported into the bottom of the tubes for displacement of spent material and to provide fresh material for reaction, the simultaneous and controllable flow of both solids and fluidizing gas to the individual beds must take place. The flow of gas can be completely isolated from the solids flow and the introduction of the latter controlled through the use of a purely mechanical system to move the
Present address, Socony Mobil Oil Co., Field Research Laboratory, Dallas, Tex.
970
solids into the bottom of each tube. However, a nonmechanical flow system employing gas as a driving force should be highly superior if it could be made to operate. I t would seem possible to feed solids and gas together through inlet orifices of the appropriate size, a method suggested by Corrigan and Mills. This possibility was rejected because it was found that the small size of orifice essential for pressure control would make it subject to plugging. There appear to be two methods of moving solids together with fluids in which the essential characteristic of increasing pressure drop us. flow necessary for uniform distribution is obtained. The first method is the movement of solids as a dilute suspension in a high velocity gas stream (pneumatic conveying). The second one is the movement of the solids in dense form with the driving force for the movement being supplied by gas flowing through and with the solids (hyperflow or mass flow). As compared to solids handling in a pneumatic system, the transport of solids in dense phase appears to offer these several superior features for feeding parallel fluidized beds : The pressure drop per unit length is larger. The quantity of transport gas is much smaller. The pressure drop due to the solids acceleration is much less. The rate of increase of pressure drop per unit length with increasing gas velocity is larger. For these reasons, particularly the last one, the dense phase method was selected as the more promising one. An experimental program was undertaken to show that this method would operate to deliver solids uniformly through parallel tubes fed from a common source of solids and transport gas. Theory In dense phase flow, the solids move as a compact mass with the force for movement supplied by the pressure gradient of the carrier gas. According to a patent relating to the dense phase transport of solids in a single tube, the pressure drop per unit length must be greater than the bulk density of the
INDUSTRIAL AND ENGINEERING CHEMISTRY
solids to keep the solids moving ( I ) . Thus, it was indicated that a back force, which could be created by a restriction or other type of resistance to flow, was required a t the outlet of the transport tube to keep the solids from expanding into a fluidized or dilute bed within the tube. Berg presented the following equation for the flow of granular solids in dense phase through a tube of constant cross sectional area :
Additional equations which he found necessary to be used in conjunction with this equation are:
ux
= (1/C) [(dPldL)Il
(Valid for viscous flow only) (3) uy
= (wa~/Aps)
(4)
Equation 1, in the form given, is suitable for design purposes but is very inconvenient for experimental use because (dp/dL)~,u,, and uy cannot be measured directly in an experimental apparatus. T o convert Equation 1 to a more usable form, Equation 3 can be changed to a form of Darcy’s law (7), as follows : uz =
k / v [(dfildL)
- pgl
(5)
Neglect the gravity term (pg) in Darcy’s law because of its small value : uz =
( k / v ) [(dP/dL)11
(6)
Substitute Equations 2, 4, and 6 in Equation 1:
Except for the permeability (k), Equation 7 now contains only quantities which can be readily measured in an experimental apparatus. Therefore, it can be used to determine the permeability of the moving solids. Berg implied that the permeability of the moving solids was constant and the same as the permeability of a fixed bed of the same material. Equation 7 applies only to tubes of uniform cross sectional area. I t does not cover flow conditions through restrictions which might be used to control the solids flow rate in the tubes. A search of the literature revealed no data on the effect of the gas flow rate on the solids flow rate in the case of simultaneous flow of solids and gas through orifices. The flow of solids alone by gravity through orifices has been reported to obey the following type of equation ( 5 ) :
hogany Ledge of the deposits in Western Colorado. This oil shale was ground and that fraction passing a 28-mesh Tyler screen and retained on a 65-mesh Tyler screen was used for this work. Screen analysis of the material was as follows:
wt. %
of Sample Trace 7.9 17.2 44.8 28.6
Total
1.0 -
A -
A
Retained on Screen, Mesh Size
-
32 35 40 48 65 65
* DISK-
99.5
Average particle diameter of this shale was calculated to be 0.0122 inch ( 4 ) . Other physical properties of the shale were : SECTION
W.
= CD"
(8)
Several figures, between 2.5 and 3.0, have been reported as the value of n in this equation (7, 3, 5). Experimental
Several more or less distinct areas were explored :
1. Flow in six parallel tubes was studied to determine if it was possible to transfer solids uniformly from a common source through several parallel tubes by the dense phase flow mechanism. Once it was established that this could be done, the various elements of such a system were studied in detail. 2. Three types of outlet restrictions were compared when discharging into the air without further flow restraint. 3. Effect of immersion of the outlet restrictions in fluidized beds was tested. 4. Variations in the flow characteristics created by variations in the length, size, and configuration of the transfer tubes were determined. 5. Design equations were developed. Materials
The solid used in all of these experiments was oil shale mined in the Ma-
ROTAMETER
REGULATING
Schematic arrangement of feed vessel and tubes assembled to study the delivery of solids simultaneously through six delivery tubes
Bulk density, Ib./cu. ft. Actual density, Ib./cu. ft. Fraction voids
64
103 0.38
Study of Flow in Parallel Tubes. The apparatus used for this segment of the work is shown in a schematic drawing (bottom, col. 1). A more detailed drawing of the six parallel tubes is also shown (top, col. 3). The feed vessel was a gas-tight sheet iron tank of 1-cubic foot capacity capable of withstanding a pressure of 15 p.s.i.g. The bottom of the vessel was an assymetrical cone to which was attached one part of an ordinary 2-inch pipe union. The inlet ends of the feed tubes were soldered into holes in a plate which could be clamped firmly into the pipe union to form a pressure-tight attachment of the tubes to the vessel. Six tubes, 0.375 inch O.D. by 0.30 inch I.D. and 31.5 inches long, were arranged so that the outlet end of each tube would be at the same level as the inlet. They were formed to long radius return bends, the radii of the return bends being 2.5, 4.5, and 8 inches. The outlet restriction on each tube consisted of a cap of the design shown in Figure 1A. The outlet orifice in each cap was 0.25 inch in diameter. Solids discharged freely into the atmosphere. Air flow into the feed vessel was controlled by a pressure regulator and measured with a rotameter. Other measurement and control devices included a mercury manometer for measuring the pressure in the feed vessel and a means for collecting and weighing the quantity of solids discharged from each tube. I n this procedure, the solids were charged to the feed vessel. A piece of 100-mesh screen was clamped over each outlet orifice to prevent the solids from flowing through the port. The air pressure in the feed vessel was established a t the desired level. The screens then
A A
This parallel tube assembly moves solids from a storage vessel to six different delivery points
were removed from the outlet orifices to allow the solids to flow. After a 2minute period, during which a steady state flow of solids and gas was established, the solids expelled from the tubes during two or more successive 1minute intervals were collected and weighed. This process was repeated a t each of three different driving pressures, 3.6, 3.5, and 1 5 . 5 p.s.i.g. Following this set of experiments, each of the six tubes was tested in the same manner when operating individually, with the five nonoperational tubes being plugged. Measurements of the pressure drop in the bed of solids held in the feed vessel and of the pressure drop in the outlet orifice showed that the pressure drops in these two segments of the system were negligible. Hence, the pressure drop in the transfer tube was taken as the difference between the pressure in the top of the feed vessel and that a t the outlet of the orifice cap (atmospheric). Results of these several experiments demonstrated that there was no significant difference in the solids flow rate in a tube when it was operating individually or when it was operating as one of a set of six in parallel. The method of transporting solids as a dense moving mass appears, therefore, suitable for delivering uniformly and simultaneously solids and gas from a single source to multiple delivery points. Comparison of Restrictive Devices. Three types of outlet restriction devices were studied to determine their relative suitability and to establish the relationships between the mass velocity of the solids, the superficial velocity of the gas, and the size of the opening in the restrictive device. VOL. 53,
NO.
12
DECEMBER 1961
971
superficial gas velocity which offers an additional driving force, a generalized equation of the form G, =
SECTIOH LiA
SECTION BB
DIMENSIONS
I
Q+
+ b)D"
(9)
may be obtained. The line which represents the correlation of these data (Figure 2) fits the equation:
Figure 1. These several devices (orifices) are built for studying the effect of type of restriction on flow of granularsolids through tubes leading to the orifice
SEOTlOH CC
DIMEN810NS
(au
+ 1300
G,/D = 125u
(10)
All results obtained for the flow of solids and air upward through the constrictive device, consisting of a simple circular orifice (Figure lC), are shown in Figure 3 . The equation which describes the line representing the average of these data is:
D
G8/D'J2= 250 ul/*- 200
The apparatus for this study was the same as that described above (bottom, p. 971), except that a single tube replaced the multiple tube arrangement. Tubes of several sizes and lengths were used to obtain a wide range of solid delivery to the outlet devices under study. Tube dimensions used in this and subsequent work are given in the table (at right). The outlet caps shown in Figure 1 were used in these experiments. The procedure used in this section of the work was identical to that described in the previous section. Results of the solids flow rate through the type of cap with the outlet orifice consisting of the narrow slit (Figure 1B) were erratic; and therefore unsatisfactory in this type of system. The slit, when reduced to the width necessary for control, was so narrow that it was subject to plugging. 3300
I
I
l
I
I
I
I
Dimensions and Configuration of Tubes Used in Studying Dense Phase Flow of Granular Solids
Transfer Tube Dimensions, Inches Radius of Net Inside return vertical Length diameter bend lift
l
,
ORIFICE MAMETER. 0 3100'
.
0-
2sm.
a-
t
tr
0
D = 7/32 IN
0
D: 1/4 IN
A
0:19/64
3 0
3.5 11 11 11 4.5 3 1 3 26
0 0
0 18 29 26 0
1
!?44' .
./'
IN.
,.,in
.
I
8 Po
-
0
0.402 0.30 0.402 0.75 0.30 0.75 0.402 0.75 0.402
/
2700. rn 0;5/16 IN A DE 11/32 IN. 2500 0 0 : 3 / 6 IN 2300,
Solid Discharge through Restrictive Devices i n a Fluidized Bed. The next step in the study of the individual elements of the transport system was to investigate the flow of solids and gas through the restrictive devices submerged in fluidized beds. The apparatus for this study was a modification of that used in the previous section. The transport tube outlet for this experiment was fitted to the bottom of a glass fluidization column, 4 feet long and 1.4 inches inside diameter. Several transfer tubes and all outlet caps (Figures 1A and C) used in the previous experiments were used also for this work. However, the transfer tube, 0.75 inch in diameter, was provided only with an outlet orifice which allowed the solids to discharge upward into the fluidized bed (Figure 1C). The downward discharge outlet caps (Figure 1A) for the 0.75-inch diameter transfer tube were too large to fit into the fluidizing tube. Fluidizing air was supplied to the bottom of the fluidizing tube through a separate inlet tube. A rotameter was used to measure its quantity. The pressure in the fluidized bed at the level of the outlet orifice was measured with a manometer.
The results obtained for the flow of solids and air through the cap illustrated as Figure 1A are shown in Figure 2. Applying the general form of the orifice equation for gravity flow (Equation 8) and adding a term, u, for the
31.5 31.5 39.4 39.4 31.5 31.5 39.4 39.4 78.8
A
D: 7/16 IN IN
SPA 0
A d '
4 D- 1/2
~
1400
I200
cd
. s
-
looo-
.2t;
O O I I ~ ORIFICE MAYETE R , D
$ 0
1100
o
I
I
I
I
I
I
I
I
I
I
z
3
4
12
Figure 2. These data relate the mass velocity of solids, orifice diameter, and superficial gas velocity in an orifice of Type 3a in which the solids are discharged downward into open air
972
INDUSTRIAL AND ENGINEERING CHEMISTRY
I
I
600-
I
I
A D : 5/16 W .
1 /'
,v'
L
":
A 0: 3/8 IN. m D : 3A6 IN.
4'
' b
,k*
200-
-200
I
I
4 /
/"
m D : 11/32IN. 000-
I
e D: ?/3e IN.
e$";"
"*
I
5 R 7 e s IO I I SUPERFICIAL GAS VELOCITY IN THE ORIFICE, FTISEC.
I
I
o D: 1/4 IN.
400-
a
(11)
"40
'
1
'
'
I
'
'
'
-
CONTINUOUS S O L I D S FEED loosely fluidizing after being discharged and the orifice no longer controlled the solids flow rate in the transfer tube, When using the 0.75-inch I.D. transfer tube at the maximum pressure in the feed vessel (15.5 p.s.i.g.), the supplementary fluidization air to the bottom of the tube could be cut off. The carrier air rate was sufficient in quantity to fluidize the solids in the fluidizing tube. The solids flow could be entirely stopped and restarted in this case by controlling the pressure in the feed vessel. Variations in Flow Characteristics. As the last step in the program, experiments were carried out to test the effect caused by variations in the equipment size, configuration, and length of the transport tube. The permeability was the criterion for comparing the flow characteristics in the tube. The apparatus used to study the permeability of the flowing solids was the same as that described under restrictive devices. The solids were allowed to flow freely into the atmosphere. All of the several transport tubes listed in the table were used in this experiment. The procedure used in this part of the work was identical to that used to study the flow of solids through the restrictive devices. The solids flow rate, the carrier gas flow rate, and the pressure in the feed vessel were recorded for two or more successive 1-minute intervals after steady state flow was established. The permeability of the fixed bed was necessary in these calculations and was obtained through the application of Equation 12 (6). The values in this case relate to air flow rate and pressure drop at zero solid movement.
The basic procedure was identical to that used in the preceding experiments. In addition, the pressure in the fluidized bed a t the level of solids discharge and the quantity of fluidizing air to the bottom of the fluidized bed were recorded during the solids collection intervals. Stopping and restarting the flow of solids in the transport tube could be effected by cutting off or reintroducing the fluidizing gas to the fluidized bed. In one series of experiments the supplementary fluidization air rate was held constant a t 0.36 C.F.M. (12.2 p.s.i.a., 70' F.), and the pressure in the feed vessel was held at values in the range of 2 to 15.5 p.s.i.g. In the other series of experiments the pressure in the feed vessel was held constant at 9.5 p.s.i.g. and the superficial gas velocity in the fluidized bed varied from 1.5 to 2.5 times the minimum fluidization velocity. The solids flow rate through the orifice became erratic if the superficial air velocity in the fluidized bed was below 1.5 times the minimum fluidization velocity. Results of the flow through orifices downward (orifice, 1A) and upward (orifice, 1B) into a fluidized bed are shown in Figures 4 and 5 . The dotted lines in each of these two plots have been transferred from the corresponding data plots in Figures 2 and 3 describing the free discharge from the two orifices. Since the data of this series of experiments fall near these lines, it is evident that the flow of solids into the beds was quite similar in quantity to the flow into the open air. At solids flow rates greater than 1.5 lb./min., it was difficult to maintain a loosely fluidized bed under the tube of the restrictive cap which allowed solids to flow downward into the fluidized bed (orifice, 1A). The restriction developed in the fluidizing tube surrounding the cap prevented the solids from
2500 U c:
I
I
I
-
/
> 2300 -
:
A
0
2100
U
a
o /
I
7/32
IN.
A D:19/64
IN.
0 D:
1000 -
-
A Dz11132 IN D = 5 / 1 6 IN
O/
d a: 1500 /'
4 /
/
//
-
A
13001
I
1
"
'
2
3
4
5
I
6
I
7
8
'
"
I
9
1
0
SUPERFICIAL GAS VELOCITY IN THE ORIFICE,
1
I
1 1 FT/SEC.
f 61.5 X 10 -lO(G./Ap/L)
(13)
of Combined Results
Maximum Solids Flow Rate. I n studying the.various phases of this problem, orifice diameters were limited in range size both by the driving force of the transport fluid and the size of the transport tube. There was found to be a maximum solids flow rate for a given system beyond which dense phase flow could not be maintained in the system. This maximum solids flow rate was measured experimentally. I t also was calculated ( 4 ) by analysis of the measured flow in the transfer tube, the flow being broken into three segments-the movement through the inlet of the pipe (considered as flow downward through an
D:5/16
A
h
Discussion
I
I
I
I
I
I
I
I
l
l
I
2
4.
IN.
0: 3/16 IN.
1200
4
1700
I
10-10
1400 -
@
P
O//A
1900-
0
/
I
I
/c
-
m _I
I O . ' / l
I
k = 8 X
Results of this segment of the study demonstrated conclusively that the flow 1600
2700
characteristics of the solids flowing in dense phase were not affected by either the size or the configuration of the transfer tube within the range of sizes and configurations making up the basis for this experiment. Further, the solids could be transported through tubes to points higher, lower, or a t the same level as the inlet of the transfer tube without affecting the design of the system. The radius of the return bend did not appear to be important as long as the area of the tube was not reduced by the bend. The permeability of the flowing solids as calculated from the data obtained in this and previous experimental work was not constant as had been suggested by Berg. Some typical results of the calculations are plotted in Figure 6 . I t was found that instead of being constant, the permeability of the flowing solids was a function of the solids mass velocity and the pressure drop per unit length, and could be calculated with reasonable accuracy by Equation 13 derived from the line describing the average values plotted in Figure 7.
m
Dm 11/32 IN.
0
D: 1/4
-
IN.
soo-
c ln U
600 -
2
400-
i
4 /
J
e
-
0
0-
/
/
/.-
/'
-
/'
//
Figure 4. These data relate the mass velocity of solids flowing in dense phase through a tube and orifice (Type 3a orifice) with the diameter of the orifice and the velocity of the transport gas. The orifice was arranged to discharge into a bed of fluidized solids
Figure 5. Data relate the flow of solids, orifice diameter, and velocity of transport gas when an orifice of Type 3 c is arranged to deliver solids to the bottom of a fluidized bed
Dotted line is transcribed from Figure 2
Dotted line is transcribed from Figure 3
-11
OSQUARE ,do,
OF
suLicw
0,"s VELwiT;
VOL. 53, NO. 12
0
IN O R ~ ~ , J E Z G ~
DECEMBER 1961
973
TUBE 1.R 0.30 IN. TUBE 1.0. 0.402 IN
0
K
CIRCLED POINTS ARE AT A P I L Z 4 I S LB./FT2/FT
0
0 0
5
IO
IS
SOLIDS w s s
90
25
VELOCITY
30
m
TE
35
40
45
50
55
60
TVBE, L ~ . / S ~ . F T S E C .
Figure 6 . Relationship between permeability of a dense bed of moving solids and mass velocity of the solids when transported through tube. Tube length; 39.4 inches
orifice), the dense phase flow in the transfer tube itself, and the flow upward through the outlet orifice. I n the results of one such calculation, the computed value of the flow capacity of the outlet exceeds that of the inlet (for the 0.375-inch outlet orifice) a t superficial gas velocities a t the inlet greater than 1.8 ft./sec. In this particular system the maximum solids mass velocity was computed to be 57 lb./(sq. ft.) (sec.) By experiment, the maximum solids flow rate for the same system was found also to be exactly the same value, 57 lb./(sq. ft.) (sec.), and the maximum allowable superficial inlet gas velocity was found to be 1.76 ft./sec. Above this flow rate the movement became dilute phase in character. Permeability of Flowing Solids. The equation applied to calculate the permeability of the flowing solids was based on viscous flow of gases through the porous media. The flow range of gases gave modified Reynolds numbers ranging from 4 to 24 with most data falling below that which would give a Reynolds number of 10. According to Leva ( 5 ) , the region from Reynolds number 10 to 100 is the transition region between viscous and turbulent flow. Since the plot of modified friction factor us. the modified Reynolds number did not show large deviations from that of viscous flow u p to Reynolds numbers of 20 to 30, all data developed in this work were treated as if they were in the viscous flow region. Qualitative Bases for Design. Two bases for the design of a system to convey granular solids into parallel fluidized beds are suggested by this work. The first design was to deliver solids through tubes of minimum size for the service required, using a minimum quantity of carrier gas. I n this design, a secondary source of fluidizing gas would be necessary for each fluidized bed. The second design would use sufficient carrier gas both to move the
974
5 10 I5 2 0 25 Jo 35 40 45 50 5 5 SOLIDS MASS VELOCITY IN THE TUBE, LB./SQ.FT. SEC.
Figure 7. These data relate the permeabilities of solids in moving and fixed beds, the drop in pressure of the driving gas, and the movement Of solids in dense phase
solids through the transfer tube and to fluidize them once they are discharged into the fluidized bed: The additional carrier gas is provided by increasing the diameter of the transfer tube and by increasing the pressure in the feed vessel. T o limit the solids flow rate, however, the diameter of the outlet orifice in this design must be small compared to the diameter of the transfer tube and appreciably smaller than when the minimum quantity of carrier gas is supplied as required in the first of these two situations. I t is quite possible that the design of the outlet orifice size might be so critical that operating problems would result from this design. Design Equations. The several equations were applicable to the design of a system for moving oil shale in the size range indicated (-28 to f 6 5 mesh). The permeability of the flowing solids has been shown to be a function of the solids mass velocity and the pressure drop per unit length; and was of such nature that it could be calculated with reasonable accuracy from Equation 13, derived from the line describing the average of the points in Figure 7. The flow of solids downward through the orifices was similar to the flow of solids by gravity alone, and the relationships reported for gravity flow through orifices were used as a guide for developing mathematical relationships between the solids mass velocity and the superficial gas velocity through the orifice and the orifice diameter. Equation 10 was the empirical equation which was developed to describe these flow characteristics. The empirical equation for the line which best fits the data developed for flow upward through orifices is Equation 11. The minimum diameter of the tubes designed for the delivery of a desired quantity of solids may be calculated from Equation 10. Use in this case, the size of the inside diameter of the pipe is the orifice diameter.
INDUSTRIAL AND ENGINEERING CHEMISTRY
60
Nomenclafure = fraction voids A = cross sectional area, sq. ft. b = constant C = proportionality factor, sq. ft./(lb.) (sec.) D = diameter, ft. g = acceleration due to gravity G = mass velocity, lb./(sec.) (sq. ft.) k = permeability of flowing solids, sq. ft. k, = permeability of fixed bed of solids, sq. ft. L = length, ft. p = pressure, lb./sq. ft. u = superficial velocity, ft./sec. uz = partial air velocity due to the pressure gradient in the porous media, ft./sec. uz, = partial air velocity due to the motion of the porous media, ft./sec. zet = solids flow rate, lb./sec. Z = pressure ratio, pZ/jl p = density, lb./cu. ft. Y = viscosity, (lb.) (sec.)/sq. ft.
a
Subscripts 1 = a t inlet of tube 2 = at outlet of tube = solids
s
literature Cited (1) Berg, Clyde (to Union Oil Co. of California), U. S. Patent 2,684,873 fJulv 27. 1954). (2)’ Corrigan, T: E., Mills, W. C., Chem. Eng. 63, 197-202 (April 1956); 203-6
(May 1956) ; 253-6 (June 1956). ( 3 ) Gregory, S. A,, J. Apfil. Chem. (London) 2, Suppl. Issue 1, 5117 (1952). (4). Koons, David S., Ph.D. thesis, University of Colorado, Boulder, Colo., 1960. (5) Leva, M., “Fluidization,” McGrawHill, New York, 1959. (6) Othmer, D. F., “Fluidization,” Reinhold, New York, 1956. (7) Scheidegger, A. E., “The Physics of Flow through Porous Media,” MacMillan, New York, 1957.
RECEIVED for review March 2, 1961 ACCEPTED July 10, 1961
. .
Division of Industrial and Engineering Chemistry, 139th Meeting, ACS, St. Louis, Mo., March 1961.
