Acidic

Separation of Thulium and Ytterbium in Acidic Chloride Solutions by Fractional Solvent Extraction Norman E. Thomas, Morton Smuts,' and Lawrence Burkhart Institute for Atomic Research and Department of Chemical Engineering, Iowa State Cniversity, Ames, Iowa 50010

Equilibrium data were obtained for the systems TmCI3-5 M HCI-H20-1 M di(2-ethylhexyl)phosphoricacid (HDEHP) in Amsco odorless mineral spirits and YbC13-TmC13-5 M HCI-H20-1 M HDEHP-Amsco. The separation factor for Yb with respect to Tm was found to be essentially constant with a value of 3.22.An empirical correlation was developed for predicting the total distribution coefficients for the binary lanthanide system YbCl3-TmCI3-5 M HCI-H20-1 M HDEHP-Amsco. A computer program using the distribution correlation and the experimental value of the separation factor was used to predict the operating conditions necessary for the separation of a 90% YbCI,-lO% TmCI3-5 M HCI feed into a 98% Yb extract product at 90% Yb recovery. The predicted conditions were verified experimentally by simulated column runs in the laboratory.

S o l v e n t extraction has become a n important technique for the separation and purification of rare earth mixtures. I n many cases it is more economical than other methods and can easily be adapted to continuous operation. I n this study di(2-ethylhexy1)phosphoric acid (hereafter abbreviated HDEHP) in the diluent, Amsco odorless mineral spirits, was used as solvent to study the separation of thulium and ytlerbium. The purpose of the work was to obtain equilibrium data for the systems TmC13-HCl-H~O-HDEHP-Amsco and YbC1~-TmC13-HC1-H~0-HDEHP-Amsco, to develop a model for the total distribution coefficient in the YbC13TmC13 system, and to use this model to predict the operating conditions necessary to perform a desired separation of Yb and T m , assuming ideal stage behavior in the extractor. Experimental Section

The rare earth oxides used in this study were obt,ained from the Rare-Earth Separations Group of the Ames Laboratory aiid had a purity greater than 99.9% with respect to other rare earth oxides. The H D E H P , obtained from Union Carbide Corp., was mixed with Xmsco odorless mineral spirit's (hydrocarbon diluerit.) as obtained from American Xineral Spirits Co. t,o form a 1 M solution of H D E H P on a monomeric basis (hereafter designat'ed 1 Jf HDEHP). The undilut.ed H D E H P was 98.870 monoacidic. The hydrochloric acid was reagent grade. The rare earth chlorides were prepared by treating the rare earth oxides with an excess amount of hydrochloric acid, evaporatiiig the unreacted HC1, and titrating the solution with 12 -If HC1 to t.he equivalence point,. d known volume of aqueous feed solution \vas equilibrated with an equal volume of the organic solvent (1 -11 HDEHP) in a separatory funnel by shaking the two phases vigorously for 15 min, allowing the phases to separate for 30 min, and then shaking for an additional 15 min. The separatory funnel Present address, College of Engineering, Gniversity of Florida, Gainesville, Fla. 32601.

was then allowed to remain undisturbed for a t least 12 hr before the phases were separated and t,he analysis begun. The organic phase often remained cloudy, probably due t,o entrained aqueous material. T o remove the cloudiness, the organic phase was cent'rifuged for 15 miii in a clinical centrifuge. The extracted thulium was recovered from the organic phase by back-extracting four times with double volumes of 8 JI hydrochloric acid. When ytterbium \I-as present in the organic phase, t8he rare earths were also removed by backextract.ing four times with 8 Jf HC1 but an acid to organic solvent volume ratio of 12.5: 1 was used. The total rare earth concentration of the initial and final aqueous phases and t.he organic back-extract was determined by tit,ration with 0.05 Jf EDTA. drseiiazo was the indicator and pyridine was used as a buffer, follo\ving the analytical procedure described by Fritz, et al. (1958). All equilibrium data were obtained a t a temperature of 25 i 1OC. of the organic strip The titration reaction for the anal) solution was very slow and the color change at' the eiid point was not distinct because of the presence of organic and inorganic phosphates. This difficulty was resolved by acidifying the solution t,o pH 2 by adding a few drops of concentrated HC1. The HC1 dissolved the sparingly soluble material, aiid the titration was contiiiued a t the readjusted pH. The acidity of the aqueous solutions was determined by the ion-eschange resin technique outlined by l d a m s and Campbell (1963). Dower; 50-X8 resin was used. The general spectrophot,ometric method of Banks and Klingmaii (1956) was used to determine the composition of t'he Tm-Yb mixtures from the organic and aqueous phases. Correlation of Total Distribution Coefficients for YbC13-TmCl~-HCl-H10-1 M HDEHP-Amsco

Owens and Smuts (1968) and Peterson (1953) found that the t,otal distribution coefficient, E a O , for a binary lanthanide mixture, TmC13-YbC13-H20-HC1-1 Jf HDEHP in Anisco, was a function of t,lie follo~vingparameters a t equilibrium: tot.al concentration of rare eart'h chloride in the aqueous phase, ( X T ) Amolar s ratio (Le., mole fraction 011 a solvent free basis) Ind. Eng. Chem. Fundam., Vol. 10, No. 3, 1971

453

I n differential form, the expression is

Table 1. Equilibrium Data for the System TmC13-HCI-H20-1 M HDEHP in Amsco at Approximately 5.0 M HCI and 25°C

Species

Initial aqueous phase concn, moles/l.

Equilibrium aqueous phase concn, moles/l.

Equilibrium organic phase concn, mole/l.

Predicted organic phase concn, mole/l.

Tm HC1

0.139 4.74

0,072 4.92

0.070

0.076

Tm HC1

0,343 4.62

0,246 4.92

0.095

0.094

Tm HC1

0 599 4.32

0.490 4.77

0.109

0,106

Tm HC1

0.854 4.27

0.741 4.72

0.113

0.113

I

Tm HC1

1.121 4.68

0.986 4.92

0.120

0.119

Tm HCl

1.358 4.68

1.234 4.95

0.125

0.123

Tm HC1

1.615 4.68

1.484 4.93

0.135

0.127

Tm HCl

1 674 4 51

1.537 4 77

0.137

0 128

0

5 0.20

I

I

I

I

I

I

I

I

I

I

I

I

A

SLOPES = 0.168

0.lOr-

,mi "1-

ul

y

2

A Yb- 5 M HCI 0

015

I

I

I

008

Interpretation of

Partial Derivatives of E.40

The first term of eq 1 is the change of the total distribution, with total RECla concentration in the aqueous phase at constant acidit.y aiid molar ratio of ytterbium in the aqueous phase. For this experimental model of t,he ext,raction process, ~ it was assumed that the dependence of E A 0 on ( X T ) would be the same for intermediate values of ( S Y as ~ for ) ~the boundary values of zero and unity. The second term of eq 1 is the change of EA' with molar ratio of yt,terbiuni in the aqueous phase a t constant total RECl3 aqueous concentration aiid a t constant acidity of t.he aqueous phase. For t,his model, the dependence of EaO on ( S y b ) A mas assumed to be the same for different fixed but arbitrary values of ( X T ) A . The third term of eq 1 is the change of E A O with the final acidity of t'he aqueous phase when ( X T ) and ~ (LVYI,)~ are constant. Because of bhe high extract,ability of the heavier rare earth chlorides by HDEHP, it was necessary to have high acidities (5-8 J I ) in the aqueous phase to avoid the formation of an insoluble polymer (Peppard, et al., 1957) in t,he organic phase. However, in the region of 8 JI HC1, it has been shown (Harada and Smutz, 1970a; Nichelsen and Smutz, 1970) that the distribution coefficient's for t'he heavier rare earths-HCl-HzO-HDEHP-.lmsco systems exhibit minimum values with respect to the acidity and t'hat the variation of E A O with (HT),is small in this region. Thus, for this work, the acid dependence of the dist'ribution coefficient was neglected aiid the acidity assumed to be constant a t 5 .I1 HC1. Although these assumptions appear quite reasonable, they can only be justified by comparison of such predict'ed values wit,h observed experimental results. A comparison is shown in t,he Verification of Model section of this paper. EA',

.---; A

016

A study of the variations of EAO with ( X T ) ~( N , Y I , )and ~, (H+)A made it possible to develop an experimental model for E A O in the system YbC13-TmC13-HCI-H20-HDEHPAmsco.

I

1

I

T m - S M HCI

l

l

1

I

0.6 0.7 0.80910 12 MOLES RARE EARTH CHLORIDE/LITER, AQUEOUS

02

0.3

0.5

0.4

I l l

1.4

1.6

Figure 1. Dependency of extractability on aqueous REC13 concentration for the systems YbCI3-5 M HCI-H201 M HDEHP and TmC13-5 M HCI-H20-1 M HDEHP in Amsco at 25°C 0.0 3 I

Equilibrium Data SLOPEzTAN 35O.0.699

0.01

0.2

0.3

I

0.4

MOLAR RATIO

I

0.9 1.0

0.5 0.6 0.7

Yb/RE,AOUEOUS

Figure 2. Dependency of total organic concentration of rare earth on aqueous molar ratio of Yb: (H*)A = 5.0 M, ( X T ) A = 0.24 M, 25°C

of ytterbiuin in the aqueous phaze, (&\7kb)A, aiid acidity of the aqueou- phase, I n general mathematical form this may be stated a. EA' 454

=

~ [ ( X T ) (.YI~~)A, ,. (H+)A] =

Ind. Eng. Chem. Fundam., Vol. 10, No. 3, 1971

(E'TIO ~

(XT ) A

It should be noted that the extraction chemistry of the rare earth ion and the chloride ion in the HDEHP phase is not well understood (Harada and Smutz, 197Ob). Hence, only rare earth conceiitrat,ions were given for the H D E H P phase while rare earth chloride concentrat,ions were given for the aqueous phase. The equilibrium data used in t,his study are given in Figures 1 and 2 anti Tables I a i d 11. Figure 1 is a log-log plot of the data reported by Owens and Sniutz (1968) for t'he system YbCI3-5 J T HC1-H20-1 J f HDEHP-Ahnsco and the data of this work for the system TmC13-5 JI HCI-HeO-1 Jf HDEHP-,Imsco. Figure 2 is a log-log plot of the equilibrium data for the system TniCI3-YbC13-5 JT HCI-H?O-l JI H D E H P in Almsco.From a study of Figures 1 and 2, it

Table II. Equilibrium Data for the System YbCI3-TmCla-HCI-H20-1 Approximately 5.0 M HCI and 25°C

Species

Initial aqueous phase concn, moles/l.

RE Yb Tm H C1 RE Yb Tm HC1

Equilibrium aqueous phase concn, moles/l.

0.357 0.205 0.152 4.62 0.360 0.286 0.074 4.59 0.365 0.336 0.029 4.58 1.561 0.166 1,395 4.97 0.138 0.000 0.138 4.95

RE Yb Tm HCl

RE Yb Tm HC1

RE Yb Tm HC1

Equilibrium organic phase concn, mole/l.

0.245 0.120 0.125 4.89 0.243 0.179 0.064 4.92 0.244 0.218 0.026 4.99 1.426 0.134 1.292 5.24 0,177 0,013 0.164 4.83

Initial organic concn, mole/l.

Initial aqueous phase molar ratio, moIe/moIe

Equilibrium aqueous phase molar ratio, mole/mole

Equilibrium organic phose molar ratio, mole/mole

Predicted total distribution coefficient> moIe/moIe

0.112 0.084 0,028

0.00

1.0000 0.5748 0.4252

1. 0000 0.4884 0.5116

1.oooo 0.7554 0.2446

0.455

0.117 0.106 0.011

0.00

1.0000 0.7946 0.2054

1. 0000 0.7381 0.2619

1. 0000 0.9051 0,0949

0.481

0.121 0.116 0.005

0 .oo

1. 0000 0.9213 0.0787

1. 0000 0.8948 0.1052

1. 0000 0.9628 0.0372

0.493

0.135 0.032 0.103

0.00

1. 0000 0.1063 0,8937

1. 0000 0.0939 0.9061

1. 0000 0.2371 0,7629

0.094

0.095 0.019 0.076

0.135 0.032 0.103

1. 0000 0~0000 1. 0000

1,0000 0.0733 0.9267

1. 0000 0.1994 0,8005

0.530

was found that the data for the single-component lanthanide systems could be represented in the form 0.155(X~b)A~."~; (H+)A= 5.0 Jf

Yyb

=

YTm

= 0.120(XTm)A0"68;(H+)A= 5.0

A ? f

+ 0 . 0 2 8 ( N y 1 , ) A ~ (XT)A . ~ ~ ~ ; = 0.24 ilI

Differentiating and eliminating k

(2) (3)

and that the dependency of extractability on molar ratio was

(YT)= ~ 0.095

(4)

The variation of ( Y T ) ~with the equilibrium molar ratio of Yb in the aqueous phase, when the tot,al aqueous concentration was constant and when the aqueous acidity was constant, was shown to conform to eq 4. I n general

(H+)A = 5.0 M

(YT)o

The separation factor of Yb with respect to Tm, P Y b , T m , was found to be essentially constant with a value of 3.22. A Model for the Total Distribution Function

The total distribution function has been described in differential form by eq 1. If the variation of E A O with acidity is neglected, as mentioned earlier, the differential equation becomes

The equilibrium distributions of Yb and Tm, at constant aqueous molar ratios of YbC13 and a t a constant aqueous acidity of 5 &TI HCl, have been shown to conform to eq 2 and 3, respectively. I n general

(YT)o = ~ ( X T ) A ~ , '(NYb)A ~*; (H+)A

M HDEHP in Amsco at

=

constant

=

5.0 JI

=

A

+ B ( N Y ~ ) ~(XT)A ~ . ~=~ constant ~;

(9)

(H+)A= constant where A and B are constants. From the definition of A , it follows that

A

=

(EA')Tm(XT)A

(10)

T o simplify eq 9 and to facilitate the solution of the differential equation (eq 5 ) , a new variable, 7, was defined as

where ( X T )and ~ concomitantly ( E A O ) ~ are , , , fixed. Thus, from eq 9, 10, and 11 (YT)O

=

B1

and

(6)

(H+)A= constant

where k is a constant. Thus Therefore

Ind. Eng. Chem. Fundam., Vol. 10, No. 3, 1971

455

Recasting the last term of eq 5 in terms of q = q[(NYb)A]

Substituting for the partial derivatives

Separating variables and integrating gives

where R* is a constant of integration. Using eq 12, the expression for 7 was rearranged to give (14) Substituting eq 14 in eq 13 and simplifying gives

From eq 3, it follows that

Combining eq 15 and 16 EA'

=

0.120

+R*(NY~).~~'~~~ (XT)Ao'u32

Using the boundary condition (eq 2)

when (NYb)A

=

EA'

1.00. Thus R* = 0.035 and eq 17 becomes =

0.120

extraction of a 90% YbC&-lO% TmC&-5 M HC1 feed into 8 98% Yb extract product a t 90% Yb recovery, a computer simulation and a laboratory simulation of the process were carried out. A modification of the digital computer program developed by Sebenik (1965) for the system La(N0&-Pr(NOs)3S ~ ( N O & - H N O ~ - H Z O - T B P (tri-n-butyl phosphate) was used to simulate the extraction of the TmCla-YbC13-H20HC1-HDEHP system. Briefly, Sebenik's technique is a stage-by-stage calculation of all stream compositions for a fractional extraction cascade, assuming ideal stage behavior. The equilibrium data are stored directly in the computer memory in tabular form. I n modifying Sebenik's computer program, eq 18 and 19 were used, rather than direct data input. The predicted results of the computer simulation of the process are shown in Figure 3 in a fashion analogous to the McCabe-Thiele method of distillation calculations. The predicted multicomponent equilibrium data lie inside the equilibrium curves for the pure components, Yb and Tm. Under the same conditions (see Figure 4) as the computer simulation, a laboratory simulation of the process was carried out using a simulated column technique. A simulated column experiment is a batchwise approximation to a continuous, steady-state extraction process. As the number of experimental cycles increases, steady state is approached asymptotically. The mechanics and mathematical derivations involved are well accepted and have been discussed extensively by Scheibel (1951, 1952, 1954a, 195413). I n carrying out equilibrations, both phases, contained in 500-ml separatory funnels, were shaken for 5 min and allowed to stand for 30 min. The temperature was 25 1°C. Fifteen cycles were required for the total rare earth concentration of the extract and the raffinate to reach steady state. A complete compilation of the experimental-predicted comparisons are given in Figures 5 and 6 and Table 111. I n all stages except for the first, the experimental and predicted results agree quite well. For the first stage, the extract concentration was significantly less than that predicted by

*

0.18

I

+ 0.035(Nyb)~~.~~~ (xT)A0'8a2

I

I

I

1

I

APURE Yb OPURE Tm

0.16

The region of applicability of this model was the same as that for the experimental eq 2, 3, and 4: (H+)A = 5.0 M ; 0.1 5 (XT)A 5 1.54; and 0.0 5 ( N Y b ) A 5 1.00. The upper limit on (XT)AJ1.54, is the solubility limit of RECl, in the aqueous phase. I n stage-by-stage calculations for an extractor, it was convenient to have EA' expressed in terms of the total organic concentration and the organic molar ratio of Yb. A similar development to the one above gave

90% Yb IN FEED 90.2% Yb EXTRACT

where (H+)A = 5.0 M ; 0.08 5 ( Y T ) O 5 0.176; and 0.00 5 ( N Y ~ ) o5 1.00. The upper limit on (YT)', 0.176, is the solubility limit of the solvent. Verification of Total Distribution Coefficient Model

To test the precision of the total distribution coefficient model by comparison of predicted results with experimental results and to design an extraction process for the fractional 456

Ind. Eng. Chem. Fundam., Vol. 10, No. 3, 1971

RECOVERY

98.2 % Yb IN EXTRACT

0.oov

0.00

Li 0.10

I

0.20

I 0.30

I 0.40

I

0.50

I

0.60

i

i Q70

MOLES RARE EARTH CHLORIDE /LITER, AQUEOUS

Figure 3. Stages for fractional extraction of 90% 1 0% TrnC13-5 M HCI feed

YbC13-

~

~~

~~

Table 111. Comparison of Experimental and Predicted Stagewise Molarities for Simulated Cascade Total RE

Ytterbium concn, mole/l.

concn,

mole/l. Stream

HCI

concn,

concn, mole/l.

mole/l.

Exptl

Pred

Exptl

Pred

Exptl

0.078 0.340 0.518 0.556 0.265 0,193 0.142 0.090 0.000 0.000 0.073 0.121 0.135 0.137 0.127 0.120 0.114

0.080 0.412 0.535 0.564 0.304 0.200 0.135 0.077 0.000 0.000 0.093 0.128 0.136 0.138 0.125 0.117

0,101

0.100 0.796

0.043 0.243 0.439 0.512 0,240 0,178 0.133 0.088 0.000 0 IO00 0,060 0.108 0.127 0.132 0.124 0.119 0.113 0.099 0.725

0.043 0.304 0.452 0.501 0.277 0.185 0.126 0.073 0.000 0.000 0.073 0.115 0.129 0.133 0.122 0.114 0.107 0.098 0.717

0.0362 0.0937 0.0812 0.0583 0.0239 0,0173 0.0096 0.0054 0.0000 0.0000 0,0172 0.0140 0.0083 0.0057 0.0052 0.0033 0.0029 0.0023 0.0775

0.110

0.802

0.701

SIMULATED PATTERN 2

STAGES -I

Thulium

5

4

3

6

7

8

CYCLES

2 0.60

H

R

I

L

t

Pred

0.0373 0.1082 0.0826 0.0631 0.0271 0.0151 0.0087 0.0042 0.0000 0.0000 0.0199 0.0127 0.0073 0.0052 0.0037 0.0029 0.0023 0.0018 0.0796

Exptl

Pred

6.09 5.47 5.05 4.87 4.82 4.95 5.06 5.20 5.45 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 5.03

6.29 5.30 4.93 4.84 4.58 4.90 5.09 5.27 5.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 5.00

I I I I I - - - - -COMPUTER SIMULATION

I

LABORATORY SIMULATION

L H

-H

2

L CONTINUOUS

CASCADE

SIMULATED

Figure 4. Operating conditions for eight-stage, simulated extractor: H = 25.4 ml, I= 200.0 ml, F = 30.7 ml

I

I 0.14-

I

I

I

I

_ _ - COMPUTER SIMULATION -LABORATORY SIMULATION

I

-

2

3

4 5 6 STAGE NUMBER

7

Figure 6. Comparison of stagewise individual rare chloride concentrations in the aqueous phase

8

earth

the model for 5 -If HC1 equilibrium data. This was because the aqueous acidity was much greater than 5 91 (Le., 6.02); the increased acidity reduced the extractability of the rare earths.

0

a

1 0.10

. -1

Conclusions

I

2

3

4 5 STAGE NUMBER

6

7

8

Figure 5. Comparison of stagewise individual rare earth concentrations in the organic phase

The total distribution coefficient, EAO, for the binary lanthanide mixture TmC13-YbCl3-5 M HCl-H20-1 -11 H D E H P conformed to eq 18 and 19. It was possible to write a digital computer program, using the experimental distribution function and the experimental value of the separation factor, to predict the operating conditions necessary for the fractional extraction of a 90% YbC13-10% TmC13-5 -11 HC1 feed into a 98% Yb extract product at 90% Yb recovery, with 1 -1f H D E H P as solvent. A comparison of the results obtained by a simulated column experiment indicated that the technique was valid. Although not demonstrated, for the TmC13-YbC13 system, Ind. Eng. Chem. Fundam., Vol. 10, No. 3, 1971

457

it would be possible to predict accurately the operating conditions necessary to produce a high purity T m raffinate product and to separate feeds with higher total REC13 concentrations and with different compositions than considered in this study. Models for the multicomponent equilibrium data of other binary heavier rare earth systems, such as Er-Lu, can be developed using the procedures of this study. The solvent extraction process described was operated with what appeared to be the highest possible total rare earth concentration in the organic phase without the formation of a n unwanted insoluble polymer (Peppard, et al., 1957; Peppard and Ferraro, 1959). Thus, in an actual industrial process, the total RE organic concentration would probably be reduced to allow for fluctuations from the steady-state concentration. Nomenclature

A

organic concentration of thulium at a fixed but arbitrary value of Xp on a pure T m distribution plot B = difference a t a fixed but arbitrary value of X P between the organic concentrations of Yb and T m on their respective pure distribution plots Eao = total distribution coefficient, total concentration of rare earths in the organic phase divided by the total concentration of rare earths in the aqueous phase at equilibrium F = flow rate of aqueous feed solution, l./unit time H = flow rate of aqueous scrub solvent, l./unit time H = flow rate of aqueous extract side stream, l./unit time (H+) = hydrogen ion concentration in aqueous phase a t equilibrium, moles/l. L = flow rate of organic solvent, l./unit time n = arbitrary ideal stage in a n extraction cascade N = mole fraction of species on a solvent-free basis R = aqueous stream in simulated column runs RE = trivalent rare earth S = organic stream in simulated column runs X = concentration in aqueous phase a t equilibrium, moles/l. =

458 Ind. Eng. Chem. Fundam., Vof. 10, No. 3, 1971

Y

=

concentration in organic phase a t equilibrium, moles/l.

GREEKLETTERS

0

=

7

= composition variable defined by eq 11

separation factor

SUBSCRIPTS AND SUPERSCRIPTS

A n

0 RE

T

aqueous phase extraction stage number organic phase = trivalent rare earth = total = = =

Literature Cited

Adams, J. F., Campbell, M. H., U. S. Atomic Energy Commission Report, HW-76363 (1963). Banks, C. V., Klingman, D. W., Anal. Chim. Acta 15, 356 (1956). Fritz, J. S.,Oliver, R. T., Pietrzyk, D. J., Anal. Chem. 30, 1111 /lO)r;Q> \IYYV,.

Harada, T., Smutz, AI.,J . Inorg. ~l'ucl.Chem. 32, 649 (1970a). Harada, T., Smutz, N., U. S. Atomic Energy Commission Report, IS-2288 (1970b). Michelsen, 0. B., Smutz, AI., U. S.Atomic Energy Commission Report, IS-2289 (1970). Owens, T. C., Smutz, &I.,J . Inorg. iVucl. Chem. 30, 1617 (1968). Peppard, D. F., Ferraro, J. R., J . Inorg. Nucl. Chem. 10, 276 (1959). Peppard, D. F., Mason, G. W., Maier, J. L., Driscoll, W. J., J . Inorg. Xucl. Chem. 4, 334 (1957). Peterson, H. C., Ph.D. Thesis, Iowa State University, Ames, Iowa, 1953. Scheibel, E. G., Ind. Eng. Chem. 43, 242 (1951). Scheibel, E. G., Ind. Eng. Chem. 44, 2942 (1952). Scheibel, E. G., Ind. Eng. Chem. 46, 16 (1954a). Scheibel, E. G., Znd. Eng. Chem. 46, 43 (1954b). Sebenik, R. F., M.S. Thesis, Iowa State University, Ames, Iowa, 1965. RECEIVED for review June 22, 1970 ACCEPTEDMay 6, 1971 Contribution No. 2767. Work performed a t the Ames Laboratory S.Atomic Energy Commission.

of the U.