Ion Exchange of Trace Components

in beakers, and the two phases n'erc sep:irat,ed by dec,mtation. The somewhat8 ... The cyclic operations required tno feed solutions, a satui~ant and ...
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ENGINEERING AND PROCESS DEVELOPMENT

Ion Exchange of Trace Components In a Countercurrent Equilibrium Stage Contactoa NEVIN K. HIESTER, RUSSELL C. PHILLIPS, EARL F. FIELDSi, RAYMOND K. COHEN, AND SHIRLEY

B.

RADDING

Sfanford Research Institofe, Sfanford, Calif.

M

ULTISTAGE mixer-settler units are i n common use for liquid-liquid and solid-liquid extraction operations t o provide improved extraction efficiency over single-stage contactors. In a n investigation of countercurrent ion exchange, Stanford Research Institute has developed design theories and equipment for the analogous multistage contact between ion exchange resins and solutions t o be treated. The method provides a different approach to the removal and separation of ionic components than the traditional chromatographic, fixed-bed technique. Much of the background for the present work on the mixersettler was reported in a companion paper ( 1 ) .

The separation of ions by ion exchange operates by the transfer of ions between a solid resin phase and a fluid solution phase. The differences in affinities of the resin for the ions to be separated, say ions A and B , lead to a n enrichment of one, say A , i n the fluid phase and of the other in the solid phase. I n order to recover both ions in solution, it is necessary t h a t ion B in the resin phase be re-exchanged. This requires a third component, say ion G, to elute or remove B from the resin. Thus, in the simplest ion exchange separation SJ stem, three components (ions A, B , and G j and two phases (resin and solution) are involved. The only design theory t h a t is available to handle this complex system is the trace theory. Trace exchange is the case in which ion exchange occurs between a gross component, G, with which a resin is saturated and a trace component, A , present in the solution in a very small concentration, along with a very large concentration of component G. Vermeulen and Hiester (6) have defined the relative concentrations of A and G which lead t o this case. Under trace conditions, a linear relationship exists between the concentration of the trace component on the resin and its concentration in the solution. This exchange may be represented as

+ G . resin k Gf + A . resin

(1)

The mass action equilibrium constant, KAG,for this reaction has been defined ( 1 ) as

KAG =

7J; =

(3)

.1f2iZ.4

and (4)

where the asterisks denote equilibrium, and MA

=

KAOUG.

~

ZG

Trace Theory of Design Simplifies Ion Exchange

A+

with respect to cz, the total ionic coiicentration of the solution per unit volume, and X G / ~ Gis a constant under trace conditions, (For other than univalent systems, t'he use of equivalent fractions would be necessary.) Expressed as mole fractions, the equilibrium concent,rationsare

YAXQ

The slope of the equilibrium line, M A , is a constant for a given trace ion exchange; so these are then Henry's law (or linear isotherm) forms. I n Figure 1 , countercurrent contact between ion exch'tnge resin and an ionic solution is represented diagrammatically. Fol the purposes of the theoretical discussion, continuous flow of thp tm-o phases has been assumed. The effect of intrrmittcnt 0pc.1.1tion is considered i n the section on equipment. Resin of a constant molal composition, ( y ~ ) ~is~fed t ~into , one end of the contactoi a t a constant weight rate, R p p p , as the effluent resin of composition ( ~ . & ~ t is removed a t the same rate. Simultaneis ously, the solution of constant molal composition, (zA)enti, introduced countercurrently into the contactor at a constant volume rate, RF,and is removed a t the corresponding rate at a composition of ( ~ & ~ t . There are two methods for predicting the compositions of the effluents. One, which is based on the statistical residence contact time of a resin particle i n the countercurrent section and the kinetics of the process, was discussed and experimentally evaluated in another paper ( 1 ) . The second method is based on the assumption that the section is composed of a finite number of equilibrium stages. For such continuous countercurrent contact in discrete equilibrium stages, the design relations of Kremser (6)for the absorption of lean components, as given in the Souders and Brown (4) form, were adapted to ion exchange. I n ion exchange nomenclature, the relation between the degree of approach to equilibrium transfer in the solution phase and the countercurrent operation factors is

where YA and 2 1 are ~ the mole fractions of components A and G with respect to &, the total ionic capacity of the resin per unit weight, ZA and X G are the mole fractions of components A and G 1

Present addresa, William Wallace Co., Belmont, Calif.

2402

where EA,the product of the equilibrium isotherm constant and

I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY

Vol. 45, No. 11

ENGINEERING AND PROCESS DEVELOPMENT the ratio of the total molal flow rates in the resin and solution phases, is defined as

EA =

M A RPPPQ RFCZ

I n Equation 5 , N e i s the number of equilibrium contacts between the two phases or the contact number counted from the solution inlet end, and ?A, the approach t o equilibrium transfer of component A in the solution, is defined as

desired purity and/or recovery of one of the separated components. The ratio of component A to component B in a given ali. quot haa been termed the concentration factor for A , 4 ~ The concentration factor for A in the spent feed would thus be (9)

where U denotes the upper product. The purity of a Component, say A , in an aliquot is the fraction of that component i n a mixture of several, say A and B , and is related to the concentration factor. Thus

d

It can be seen from the above relation that the degree of approach to equilibrium transfer for the resin phase is given by

?ADA.

P

Rearrangement of Equation 5 gives a more convenient form for the determination of N , from y and E.

Separations in Two-Section Unit. A complete unit for separating ions into two fluid streams would have at least two sections of the type shown in Figure 1. SOLUTION IN VOLUMETRIC RATE COMPOSITION- (xA)

SOLUTION OUT VOLUMETRIC RATE RF COMPOSITION ( xA) E X , T

- RF

-

-

Likewise, the recovery of A , RA,is the fraction of component A i n a given product with respect t o the amount in the feed, over the same time interval, as follows:

where subscripts F and L denote the feed and lower product streams. The last expression results from a consideration of the over-all material balance. For A this is

+

F ( z A ) F = u(ZA)U L(XA)L (12) Obviously, concentration factors and recoveries are somewhat ~ specified, then related. For instance, if (+AB)U and ( R A )are

and

RESIN OUT WEIGHT RATE-RpPp COMPOSITION ( y A )

-

RESIN IN WEIGHT RATE RpPp COMPOSITION- (yA)

-

EXIT

Figure 1,

ENTR

Countercurrent Ion Exchange

SECTION

SATURATED RESIN

LOWER PRODUCT,

L

Figure 2.

UPPER PRODUCT, 0

ELUTED RESIN

SECTION

The term [M(z),nt2./(~)entr]sat can now be eliminated between these two equations to give

E LUTA NT,

E

Two-Section Separation Unit

A feed stream containing a mixture of A and ,l? ions would be introduced between the two sections, as indicated in Figure 2. The least strongly held ion, say A , would remain largely in the solution phase traveling to the right throu$h the saturating section. Thus the effluent solution from this section (the upper product) would be enriched in ion A , while the effluent resin wou!d be enriched in ion B. The transfer: of the trace ions from the resin to the solution phase would require another exchange step. I n the eluting section, the resin would come in contact with a n elutant free of ions A and B . The spent elutant from this section would be enriched in B and would be considered the lower product. The eluted resin would be returned to the saturating section to complete the cycle. This two-section unit is the most simple arrangement of groups of countercurrent contacting devices that will separate ions A and B. I t s main drawback is that, although nearly pure A can be obtained in the spent feed solution, there is a much lower limit t o the -purity - in which B can be obtained in the spent elutant. The design theory applying t o a two-section-unit is based on the relations among N o , y,and E presented earlier and also on the November 1953

The relations between 7, the degree of approach t o equilibrium transfer in the solution phase, and the recovery, ( R ) v , are of importance in any design considerations. From the definitions given in Equations 7 and 11 several relations can be obtained:

But also, analogous to 16,

as in most cases the elutant is free of the ion to be stripped. From Figure 2 it is obvious that the exit resin from the saturating section is the entrance resin t o the eluting section, and vice versa, SO

This latter term can now be eliminated from Equation 17, through Equation 18, to obtain a completely general relation between (?)sat and ( R ) U involving the degree of approach t o equilibrium removal in the resin phase during elution:

-

(YLt

(R)U = 1

+ [(-t)adE)Bstl{ [E/rlerut - 1)

INDUSTRIAL AND ENGINEERING CHEMISTRY

(19)

2403

ENGINEERING AND PROCESS DEVELOPMENT In those cases where the resin is nearly completely eluted, [y/E],i,t N 1, Equation 19 reduces to the approximate form

1

-

(R)u 2

(~1s.t

For specific ions A and B this gives 1 - (RAIL,= ( Y A ) ~ ~ ~

(20)

and 1

(RA)U - (RB)u = (YB)sat = (RB)L= 1 - (+AB) u(+ B A ) F

9 s complete removal of B from the resin would require an infinite number of contacts in the elution section, a small amount of leakage must be permitted t o obtain a finite contactor. I t may be assumed that, if almost none, or say 0.5y0,of the B ion entering in the resin stays on, the resin can be recycled without affecting the accuracy of the simplified design equations (20 and 21). This may be expressed mathematically from Equation 18, when the elutant is free of B , as

(21)

where Equation 14 is used to obtain the final form. Design Procedure Is Sfraighfforward

Under the simplifying assumption that the resin from the eluting section of the two-section unit shown in Figure 2 is essentially free of ions A and B, the design procedure is straightforward and the simple relations, Equations 20 and 21, can be used. Since the elutant is free of ions A and B, it is possible to elute (strip) the resin almost completely to this point by operating with an EA and EBin this section of less than unity and a large number of equilibrium contacts. This is apparent from Equation 5, as under these conditions of E < l and + m y approaches E. Equation 18 then shows that, as e/ approaches E, gexit must approach zero. The significance of E less than 1 is a higher total equilibrium molal flow rate in the solution than in the resin. For any one section, the difference between the values of E for ions B and B is in the equilibrium isotherm, so that ~

122)

where 6 is the separation factor between components A and B. As it has been assumed that B is held more strongly by the resin than A , then EB > EA,or 6 > 1. Thus the only operating requirement for the eluting section is that Eg be less than 1, since then EAwill necessarily be less than 1. The values of y obtained by Equations 20 and 21 can then be used to determine the number of equilibrium contacts and the values of EAand EBfrom Equation 8. K h e n equilibrium is attained in each contact, the number of equilibrium contacts ehould be identical for both d and B , 01

Tlierefore, (ra/E~),i,t may be taken as 0.995, or essentiallj, unity, when design Equation 8 is applied to the elution section. Sormally, certain of the items considered would be fixed in any design problem, such as ( Z A ) ~ ,( Z B ) P , F j ( C Z ) F , KA, K B , and Q. Of the remaining seven items usually considered-Rppp, E, ( m ) ~( @, A B ) c , (RAIv, ( S o ) s a t , and (S,),l,t-the choice of any four, subject to the limitation that ( E B ) ~ < ~ "1~when t,he simplified design equations are used, immediately fixes the other ~ ~ three. The four chosen [these usually include a t least ( + A ~ )and (RA),] can be subjected to an economic balance t'o determine the optimum choice. Theoretical Limits of Separation in Two-Section Unit. It is of interest a t this point to consider the ultimate enrichments and recoverips that can be obtained in this two-section unit. For values of Eg less than 1 (Le., EA < 1/6) y will approach E a t a large number of contacts-that is, as -+ a , -(A EA, and - i ~ -+ Eg with the limitation that EA (and thus EB) must be greater t h m zero. For infinite contacts then 67.4 = -,B, since 6E.d = EB, and from Equations 20 and 21

-

Rearranging

since from Equation 22, EB = EA. Thus there is only one value of EA (or EB) and the number of contacts, S,, which will satisfy a given set of */A and [or ( R A )and ~ (PA)U]values. The value of EA obtained in this manner for the saturating section can now be used in the design of the eluting section. The relation between the EA values in the two sections will depend only upon the relative solution flow rates and total solution ionic levels, since the resin flow rate and the total resin ionic level will remain constant throughout the entire unit in steady-state operation. Thus

and from Equation 22 PURITY OF A I N U P P E R

PRODUCT

(p,,),~

Figure 3. Relation between Theoretical Recovery and Purity at Various Values of

where E is the flow rate of the elutant. 2404

N, and EA

INDUSTRIAL AND ENGINEERING CHEMISTRY

Vol. 45, No. 11

ENGINEERING AND PROCESS DEVELOPMENT (27)

(@AB)U (@AB)F

-

(RA)U

1

(%a')

- 6[1 - (RA)u]

Thus, a t any given purity the calculated recovery is the highest that can be achieved, and for each recovery there is a n ulti6-1

mate purity [for values of (R& less than __ this ultimate 6 purity is unity]. a

An example may clarify this. If an absolutely ure stream of A so that is desired for the top product-Le., (@AB)LJ/(+AB?$ = ( P A ) U = 1-then the highest possible recovery 1s

(28) *

Also, for the second cascade

But because the bottom product from cascade 1is used as the feed to cascade 2 [(@B)F]Z

=

[($B)Ll2 [($B)F11

6-

[(@B)L]I [(@B)Fl1

62

(35)

Thus for the M'th cascade [($B)LlM

= 6~

[(@B)Fl1

(36)

beThe recovery of A in the top product from the first cascade will

Under these same conditions, using Equations 13 and 14, (@BA)L/(@BA)R

[($B)Ll1

then

(37) (29)

= 6

However, although the recovery of the.A from' its feed will be identical in the second cascade, there 18 less to recover, as an amount [ ( R A ) U ] t has already been recovered. Thus, based on the original feed,

or

with

( R B ) L= 1

(30)

By a similar procedure, the ultimate enrichments and recoveries, with-an infinite number of contacts, a t other values of EA, are found t o be 1

1 > EA >/ g, (@AB)u/(@AB)F

EA

= a ,( R A ) u=

1, ( @ A B ) u / ( + A B ) F =

m,

1

( R A ) u= 0

- Ea

(31) (32)

The effects of other values of N , and of EA are shown in Figure 3. For the particular case illustrated, a feed solution containing equal amounts of ions A and B with a separation factor of 3.79 (and complete removal of the trace ions from the resin in the elution section) have been assumed. It is apparent that a t a recovery of 0.50, one contact would yield a solution of 0.70 purity while 10 countercurrent contacts would give 0.99 purity, and a n infinite number would produce a pure solution. The EA values show that, for a given feed rate, ten contacts would require one half as much resin per contact as the single contact, and thus a total of only five times as much resin in the saturating unit. As can be seen, it is not possible t o obtain purity-recovery curve i n a simple two-section combinations above the No = unit. T o obtain such combinations, these units must be ca& caded, as discussed below. Effect of Cascading Separate Two-Section Units. I n a single two-section unit, the enrichment of B in the bottom product can never exceed the value of 6, no matter how many equilibrium contacts are used. ( I t is apparent that for isotopes, where 6 is slightly greater than unity, a single two-section unit will not provide satisfactory separations.) However, it may be possible t o attain further enrichment of B by using this bottom product stream as the feed t o another two-section unit. This second cascade would then remove more A from the feed, thus leaving the new bottom product more pure in B. The effect of the number of cascades can best be shown by considering the highest possible enrichment per cascade-Le., the case of infinite contacts in the saturating section.

-

%

a .

Consider, a8 a n example, that the original enrichment factor of [ ( + ) P I , and that the enrichment of B in the lower product from the f i s t cascade (or two-section unit) is [ ( $ B ) L ] l . Then, from Equation 29, under conditions of complete purity of A in all the top products-Le., ( + A ) u i= m and ( R B ) L= 1

B in the feed is

(33)

November 1953

and for the M'th cascade

The sum of all the recoveries, through a given cascade, can be obtained from Equation 39

For any reasonable value of 6, high purities of B in the bottom product and high recoveries of A in the top product can be achieved with only a small number of cascades. However, the elutant flow rate is usually greater than the saturant flow rate. The effect is that each succeeding unit i n a cascade will require a still larger quantity of resin and elutant t o process the elutant from the previous unit. Thus the increase in purity of B in t h e bottom product is usually obtained a t the expense of pyramiding, resin and elutant requirements. Automatic Mixer-Settler Assembly Separates Phases

Ion exchange in a countercurrent column implies t h a t the resin enters one end of the unit at a constant rate and leavee the other end a t the same rate. Feed solution enters and leavea the unit a t the same rate but travels i n the opposite direction with respect to the resin. This countercurrent contact may, of course, be obtained by either a continuous moving-bed type of unit ( 1 ) or in a n equilibrium-stage unit analogous to a plate distillation column. I n this latter type of unit, mechanical difficulties in transferring resin from one p18 te to the next, in a n even stream and without solution entrainment, led t o the consideration of a batch mixer-settler type of unit. In intermittent countercurrent operations, the resin and solution aliquots are agitated batchwise in a number of individual stages where equilibrium between the two phases is approached. Following mixing, the resin and solution are separated; then one phase is transferred t o the adjoining stage where the two phases are brought in intimate contact again. Then, after separation, the other phase is transferred countercurrently t o the next ad-

INDUSTRIAL AND ENGINEERING CHEMISTRY

2405

ENGINEERING AND PROCESS DEVELOPMENT

Figure

4.

Intermittent Mixer-Settler Assembly

jacent stage, and the i ~ s i nand solution we ag:iiii niixcd. This met,hotl of' operation has Ileen clescrilied I)?. Stephenson (6). In the initial studies, this sequence of operations wiis c:ii,rietlout in beakers, and the two phases n'erc sep:irat,ed by dec,mtation. The somewhat8erratic results indicated that l x d ~ c r scould not be manually manipulat~edn-ith enough finesse to :issure stalile operating conditions. Moreover, the sepnr:ttion by simplc tl(mnt,:ttion left a n appreciable quantity ol solution in the cxtern:rl void volume of the wsin aliquot, ivliich cont,:lminnieil the n e x t solution in contact with the resin. The volume of this interstiti:il solution could have been reduced by filtering under :rir pressure, Iiut this \r-ould hRve inJ,olved still more inanigulntions. A large ~ i i i i l i l ~ofc ~ . t,hese tedious transfei.~W'RR required i o est:ihlish the steady state. Consequently, a mech:mic:il devicc Ir-liich mould simul:it,c: t,he bezilcer operations hut offer greritei precision v a s consitlei~edncccssarj- for an adequate investigation of intermittent operations. I n the ideal mechanical app:rrat,us, operations ~voultlhe a u h matic, transfers vc~oulcl be simultaneous, a n d the inte~stitinl solution would be filtered from the resin under air pressure. Intermittent Mixer-Settler. The autoiiiatic intermittent mixersettler shown in Figure 4 was designed to satisfy these requirements. I n tjhis assembly a complete cycle of saturation of wsin with metal ions and subsequent elution with hydrogcn ions is carried out continually until the steady state is attninctl. This cycle is represent'ed by Figure 2. In effect, the resin is :iltei~nately saturated and eluted. The assembly contnined 10 misers and 10 reservoirs. I h c h resin aliquot was retained in its respective miser for t,he tiunition of a run, and trhe solutions were transferred from one miser t,o the nest by way of the reservoirs in such a manner that the operations were truly countercurrent. Both the mising and transicr steps were accomplished with air pressure applied to the t,op of the approprkte vessel. It was possible by proper msnifolding to operate half these misers and settlers a.s a unit, while the other half was operated as a n independent unit in which duplicate riiiis were made. It, was also possible to interconnect :ill 10 misers and settlers into one unit. The cyclic operations required t n o feed solutions, a satui~ant and an elutant. The relat,ive positions of these two feed solutions were sepamted by the number of misers being used for thc siituration step. Figure 5 is a flow diagram of this appitratus shon-ing only five mixers and five reservoim. The feed posilioiis nioved in a elocliwise direction, with the elutant feed precmlinp ilic wtumnt feed b>- one stage. Under t,he conditions indic:itetl. nt, :in). one time, some one miser wits devoted to saturation, lvhile the other four were used for elution. The reservoirs consisted of vertical glass cylinders of about 250nil. capacity, t,apered at the bottom to a 6-mm. tube and tapered to a t u l x h t u r e a t the top for a stoppered outlet. Also near the

2406

top was an outlet for connection to the outer, or reservoir, air manifold. The mixers had similar external characteristics, hut within the bottom taper was a horizontal fritted-glass disk which ret,ainetl the resin. The mixers Iyere connected t o the inner, or mixer, air manifold a t the top v i t h rubber tubing. At the bottom, the misers were connected to the solution manifold with standard -spherical joints, so they could be removed from the a,pparatus Tor replac-ement of resin when necessary. The solution manifold of glass and rubber t,ubing intoi~connectcd all the misers and reservoirs in a unit, Check valves are indicated o n the diagram as it means of controlling the direction of Ron-, RS i t vas desired that each solution aliquot should f l o ~cloclirr-ise from a reservoir into the next mixer, then from that mixer int,o the adjoining reservoir and so on around the circle. Although tapered ground-glass check valves were initially tried to control the direction of flow, they failed t o seat securely, and they were supplemented with mechanical pinch valves, which consisted of sheet metal yokes around thin-\l-alled rubber tubing. hsf otivated by solenoids, the yokes pinched the ruhber tubing against a fiscd surface and provided a poaitive seal. There were two groups of these eolenoid pincli valves in the solution manifold system: One group cont,rolled the flow from the reservoirs to the mixers, whjle the other set controlled the flow from the mixers to the reservoirs. Solution transfers n-ere made by applying air pressure o n the containers which were to be emptied of solution. T h e air pressure was indicated by a manomet'er and was adjusted with a diaphragm valve. To minimize loss of water from the solutions Isy saturalion of the ]om--humidity a,ir used for transferring, the air \vas firpt passed through a saturator: a vert,ical glass cylinder Pome 7.5 cni. in diameter and 90 em. long. Air was dispersed through a sparger into the water retained in the saturator. Contact, betn.een air a,nd water \vas aided by passage through a bed of glass n-ool. -4t the upper end o€ the saturator, there n-as a disengaging zone in which entrained Tvater n-as removed. -4utoniatic control of the sequence of operations in the mixersettler 'iT'as achieved with a motor-driven multicam mechanism. T h e x cams actuated mercury sn-itches, n-hit) in turn cont'rolled the electrical circuits involved in the operation-. The principal circuits xere those controlling each group of solution valves and those controlling the nmgnctic, valves for supplying air pressure to or for venting the air mnnifoldu. A Selsyn transmitter was also geared directly t o the cam mechanism drive shaft. The associated Selsyn receiver was mounted at the center of the top board on the miser-&tler. The receiver motivated an indicator, which at the proper time pointed to the reservoirs that must be drained and then fillet1 with fresh feed solutions. Operation of Mixer-Settler. The operation of t'he unit ca,n be understood best by folloir-ingthe sequence of events that occurred during an operating cycle. A t the beginning of a. cycle, the solution aliquots Kere all in reservoirs and the resin aliquots were in the mixers. When the

K'

FEED IN

S P E N T H'

OUT

c.(

TO"ILlb*,l,OII

SPENT K'

0

F L I T * Y O T I K L O F r Poi", T l l V E L I " L L F OF D I I I I H C E I Z . i l L I * R L l E R V O I l D FOR 116" ZQiilLillATlO"

Figure

5 . Flow D i a g r a m of Intermittent Mixer-Settler

INDUSTRIAL AND ENGINEERING CHEMISTRY

Vol. 45, No. 11

ENGINEERING AND PROCESS DEVELOPMENT cam mechanism was started, air pressure was applied in the top of all the solution reservoirs through the outer air manifold. Simultaneously, the proper group of solenoid pinch valves opened to permit the solutions t o transfer in a clockwise direction from the reservoirs to the mixers. Simultaneously, the inner air manifold, connected to the mixers, was vented to the atmosphere. Air flow was continued into the bottom of the mixers for the duration of the desired equilibration period. This air flow served two purposes: t o keep the solution in the mixer, and by its dispersion through the fritted disk, t o provide turbulence for keeping the slurry well agitated. At the end of this predetermined contact period, the cam mechanism caused the air flow to reverm, so t h a t pressure was applied to the mixers and the reservoirs were vented. At the same time, the reservoir-to-mixer pinch valvw mere closed and thofie permitting flow from the mixers t o the reservoirs opened. This combination of events caused the solutions in the mixers to flow through the fritted-glass disks into the reservoirs in a clockwise direction. Air flow was continued through the resin retained on the fritted disks long enough to assure adequate removal of free solution from the resin. Then all the pinch valves and air valves were closed, leaving the apparatus in a momentary quiescent condition. Then the cam mechanism repeated the cycle. At the end of the second cycle, the drive motor shut off and a buzzer sounded to indicate the end of this cycle. At the end of this second cycle, the Selsyn-driven indicators pointed to the reservoirs which contained the spent saturant and elutant samples to be removed and replaced with fresh feed solutions. This solution replacement was done manually, although an automatic selector valve arrangement for removing the exhausted samples and filling the empty reservoirs with fresh feed could have been provided.

d

84

.

a

Ty

b V

b C

d

VI

a

b

VI1

a

b C

d

-

42"

-

-a-

From this point on, the operations described above were repeated, starting with the transfer of solutions into the mixers. The experimental runs made with this apparatus required t h a t a large number of cycles be completed before dynamic equilibrium could be assured. Figure 6 outlines the physical transfers of solutions for a run in a five-stage unit with one saturation stage and four elution stages. One might imagine t h a t this figure was shaped as a cylinder, with mixer 5 adjacent t o and just preceding reservoir 1 to complete the cycle. Initially, equal, predetermined quantities of hydrogen resin were placed in the mixers. Approximately equal quantities of distilled water were placed in all but two reservoirs. Into one of the empty reservoirs, R-1, the first elutant sample, E-1, was transferred volumetrically. Reservoir R-5 was filled with the first saturant, F-1. F-1 subsequently came in contact with resin in two mixers, and was then removed from the system. Similarly, the elutant, E-1, came in contact with resin in eight stages before removal. Thus two equilibrium contacts were attained per stage in a given cycle. 'This follows Ravenscroft's ( 3 ) reasoning with regard to batch countercurrent operations. The outline of operations given in Figure 6 is practically selfexplanatory. Samples were withdrawn and feed solutions were introduced only every other cycle. As a consequence, the position of the saturant feed, for instance, moves one reservoir while the saturant solution is transferred through two stages. Specifically, the initial saturant feed, F-1, was placed in R-5; the next saturant feed, F-2, was placed in R-1, the adjacent reservoir.

b IX

0

b c

d X

a

b XI

a

b C

d

XI1

a

b

XI11

a

b C

d i

XN

a

b

xv

* b

e

C

td

kn

Figure 6.

a

WII

Intermittent Mixer-Settler Operations

For 5 mixers and 5 reservoirs, 1 mixer on saturation, 4 mixers

b

on elution Elutant feed F. Saturant feed M. Mixer R. Reservoir

*

E.

b C

Sequence a.

Transfer into mixer and agitate Transfer out of mixer C. Empty proper reservoir d. Fill this reservoir Solution out $ Feed in f Resin originally in mixer 1 remains in mixer 1 throughout all operations, etc.

b.

hU1

h ne 1 Cycle farRnS

b

F-15

November 1953

E 15

E-14

E-13

E-12

INDUSTRIAL A N D ENGINEERING CHEMISTRY

2407

*

ENGINEERING AND PROCESS DEVELOPMENT Meanwhile, F-1, after two contacts, had passed to R-2, from which it was withdrawn. The lower dashed line across the figure indicates that the same physical situation existed a t cycle XVIII, sequence a, as a t the upper dashed line, cycle VIII, sequence a. Cycle XVIII is the first one which duplicated a previous cycle after all the reservoirs had been filled with active solutions. I n other words, it may be assumed that dynamic equilibrium existed no earlier than at the lower dashed line. The experimental runs were usually carried even further t o assure a steady state. The locations of solutions a t the end of an early run, for instance, are shown on the last line of the diagram.

The proper identification of the entering and exiting solutione and resins is more difficult with the intermittent contactor than it would be for a continuous unit. This identification is important, as the value of y , the degree of approach to equilibrium transfer in the solution phase, depends on the compositions of these streams. For the ssturating section, the entering solution concentration is obviously that of the feed and, at t,he steady state, the exiting concentration can be obtained from the spent feed leaving the unit. The resin compositions must be obtained from those aliquots that have received the proper number of contacts. In the case of the five-stage unit outlined in Figure 6, tmheexiting (or saturated) resin aliquot would be that which had just completed two contacts with feed , solutions and the entering (or eluted) resin End of would be t'hat which had just gone through Cycle sequence R - l u.1 1-3 A-4 L 4 R.s M-5 R" m-s R" \1-7 R-s M-8 R-9 M-9 M-IO eight equilibrations wibh elutant aliquots. XLY e The position of these resin aliquots will depend on the cycle, since the feed position changes every two cycles. For instance, a t cycle XVI b (on Figure 6) %vl a the resin in mixer M-2 has just finished its second equilibration with feed solution w411 * -Le., it had been in contact only with E'-7 and F-8 since its last elution. Likewise the resin in mixer M-3 has just had Figure 7. intermittent Mixer-Settler Operations eight elutions, with E-1 to E-8. Resins For 10 mixers and 10 reservoirs, 1 mixer on saturation, 9 mixers on elution 31-2 and M-3 would then be exiting and E. Elutant f e e d entering resins, respectively, for the satuF. Saturant feed rating section. M. Mixer R. Reservoir of the short cycles-i.e., cycles not Sequence involving solution removal and addition Transfer into mixer and agitate a. --will exhibit a similar behavior after t h e b. Transfer out of mixer c. Empty proper reservoir steady state is reached-for example, in d. Fill this reservoir the case of cycle XVIII the proper aliSolution out 4 quots would be M-3 and M-4, respecFeed in t tively. As these resin aliquots cannot b e obtained during a run, it would be necessary, after the unit has reached the steady state, to shut Although net indicated on the diagram, it is obvious that the down a t such a short cycle. ,it this shutdown point, none of t h e distilled water initially present in the system was replaced with solutions in the reservoirs correspond to encering or exiting aliactive solutions as the run progressed. The water served only t o quots. This is not important, however, as such solutions wilB prevent dehydration, by air, of the resin aliquots which were not have been obtained from the previous long cj-cles and, a t t h e all in contact with active solutions during the filling cycles. steady state, their compositions would not change. Operations in a ten-stage unit were substantially identical with The proper aliquots involved in calculating -( from Equation 7 those in the five-stage unit, except that a larger number of concan now be identified in terms of the operating program. For the. tacts was made. The essence of operations with the ten-stage case outlined in Figure 6, the compositions would be those €or the. unit is outlined in Figure 7, which shows only the last few cycles, samples indicated: ending with conditions existing a t the end of the first run of this type. [(zlentrlsat = = [(5)R--31XYII d I n the case of the ten-stage unit, again two equilibrium contacts [(Z)exltlsat = = [(Z)R--IIXVII b were attained per stage. I n terms of the number of actual phys[(!/)entr]s%t = [ ( v ) e i i t ! e l u t = [(?//)M--3]XVI 6 [(!/)exit sat [ ( l / ) e n t r l e l u t = [(2/).M-ZlXYI b ical stages, N , , then, the Kremser relation, Equation 8, must be = [(Z)R--4lXVII d [(s),ntr1 elut = modified as follows: [(Z)ex*tlelut = = [(Z)R--IIXVII b

(41) or

where the subscripts indicate reservoir or mixer number and cycle. number. Apparatus W a s Evaluated

by Separating Lithium and Potassium The ratio of the solution and resin flow rates used in E must also be expressed in terms of aliquot (or intermittent flow rate) ratios because of the intermittent operation of the units. The value of E is then defined as

(43) where V F is the volume of the solution aliquot and Wp is the weight of the resin aliquot. 2408

The mixer-settler apparatus was evaluated by carrying out the. separation of lithium and potassium ions, in trace concentration^ with respect t o the hydrogen ion carrier (or gross) component, in a feed solution. The resin was also eluted with hydrogen. This ion system was chosen because of the equal valence of t h e three ions, the ease of analysis, and the known feasibility of separating the metal ions. The resin has greater affinity for the potassium than the lithium, so, in reference t o the theoretical discussion, lithium corresponds t o the A ion, potassium t o the B' ion, and hydrogen t o the G ion. The determination of the param-

INDUSTRIAL AND ENGINEERING CHEMISTRY

Vol. 45. No. ll!

I

,$ 0.03

I z

z

i

2

0.02

E

0.01

-

:; EL

-

2s

s

5

DATA FROM M I X E R SETTLER RUNS

-

o=Li+ X.K+

DATA FROM PREVIOUS W O R K ( L Li+

s

.=

K+

I 0

0.01

0.02

0.03

0.04

0.05

I

o 06'

0

E-I SAMPLE

E-5 E-9 NUMBER

E-13

Figure 9. Compositions of Effluent Solutions for Run 19 All samples removed from the apparatus and aliquots of both feed and elutant solutions were analyzed for cation contents. At the end of the run the resin samples and the solutions left in the various reservoirs were removed, and their metal ion contents were determined. The oven-dried weights of the resin samples were also obtained. The weights of the resin aliquots used in separate runs varied from 5 to 35 grams. A run was continued until there was reasonable assurance that the steady state had been attained. This necessitated operation

Q

minute. The saturant feed was composed of hydrochloric acid and approximately equimolar quantities of potassium and lithium ions, in the form of their chlorides. These ions were in trace concentrations (-0.03 N ) with respect to the approximately 1.0 N hydrochloric acid carrier, The elutant was -1.0 N hydrochloric acid. Saturant aliquots varied for different runs from 40 to 100 ml. and elutant aliquots from 150 to 200 ml. All feed and product solutions were measured in graduates. November 1953

rium isotherm, and the average molal aliquot ratio, V F C ~ / W ~ Q , according to Equation 43, Evaluation of Data Shows Method and Equipment Are Satisfactory

The experimental data were obtained in terms of solution concentrations (later converted t o mole fractions) for both the upper

INDUSTRIAL AND ENGINEERING CHEMISTRY

2409

ENGINEERING AND PROCESS DEVELOPMENT and lower products. A typical set of such data (for run 19) is represented in Figure 9. The approach t o steady state a t the end of the run is readily apparent. I n addition, upon completion of the run, data were obtained in terms of resin concentrations for each mixer (say in M-1) along with the concentration of the solution (say R-2) that had just been equilibrated with t h a t resin. These equilibration data, for the later runs, were plotted as shown on Figure 8, and checked the equilibrium isotherms obtained previously (1). The steady-state potassium data for run 19 are shown graphically i n Figure 10. This diagram is a graphical representation of the Kremser relations (Equations 5, 7, and 43), and is similar to the McCabe-Thiele representation of distillation column data. The points along the equilibrium line were obtained a t the end of the run as previously described. I n agreement with the value of MXH,its slope was 3.30. The operating lines express the material balances for the individual sections and have slopes equivalent t o the molal aliquot ratios, Vpcz/WpQ ( = M/E). For the saturating section, this slope is 1.45 ( = 3.30/2.28) and for the eluting section is 3.63 ( = 3.30/0.91). I n the case of the saturating section, the upper end of the operating line was fixed by the composition of the resin leaving the saturating section and the saturant feed composition. The lower end of this line was established by the compositions of the eluted resin entering the saturation section and of the upper product (exhausted saturant). It is apparent from Figure 2 t h a t the eluted resin entering the saturating section is identical with the resin leaving the eluting section. Similarly, the saturated resin leaving the saturating section is also the resin entering the eluting section. Thus, the upper end of the operating line for the eluting section is fixed by the compositions of the saturated resin and of the lower product (exhausted elutant). As the elutant feed contains no potassium, the lower end of this line must fall on the ordinate axis a t a height equivalent t o the composition of the eluted resin. The number of countercurrent equilibrium contacts between the resin and solution phases required for a given ionic transfer may be determined graphically a s shown. For the saturating section, this was 2 contacts and for the eluting section, 18. It will be recalled t h a t 2 contacts were made for each stage and t h a t in the 10-stage unit, one stage was devoted t o saturation and nine to elution. The equilibrium data were obtained for each physical stage and thus for every other contact. I n general it is more convenient t o use the modified Kremser relation, Equation 41, than the graphical method for the determination of the number of physical stages required for a n exchange of ions, but the graphieal approach is more illustrative of the stepwise and cyclic operations involved. Evaluation of Data. Values of y were calculated for both the saturating and eluting sections by use of Equation 7 and the proper steady-state data. Although solution information was

Table II.

available for the upper and lower products a t the end of each two cycles, resin could be obtained only upon completion of the run. For a given section, four values of y were obtained: one based on the change in the fraction of lithium ion in solution, one based on the potassium in solution, and the two corresponding values obtained from the resin concentration information. The two -) values based on lithium were averaged. as were the two y values based on potassium. This was done to compensate for any inaccuracies due to a poor material balance over the section in question. These average values of y are given i n Table 11. The material balance for the unit was checked i n two ways. First, the amount of a given ion (say lithium) entering the contactor per unit time was compared t o the amount leaving over the same period. This was known as the instantaneous outputinput ratio and was calculated from the content of the saturant and elutant feeds and of the two product streams only, since the resin was recirculated internally. il recurring ratio of unitjindicates that none of the component is being accumulated or depleted i n the unit and that steady-state operation is occurring. The second method involved a material balance on the unit over the entire run. The input for a component was calculated from 0.036

-

I

I

I

I

0028-

5

v)

0024-

t

z

0

2

0.020

U

0

z

0 c

OPERATING L I N E TURATING SECTION

0

a E

U -I

0 I

ELUl

"

Figure 1 0.

0.016 0.020 0.024 MOL F R A C T I O N OF K C I N S O L U T I O N , x

0.004 0.008 0012

(

Graphical Representation of Potassium Data for Run 19

Comparison of Experimental and Predicted Results Average Ratio Output t o I n p u t of Solutions Li + K+

Over-All Material Approach to Equilibriuiiia Balance, % ~ _ Predicted ____ _-__ -Run No. (YLi)sat (7Li)elut (7K)sat (7K)elut (*/Li)aat (YLi)elut (?Idsat (Y1Oelut Li + K+ 0.56 0.30 0.84 0.75 107 96 0.68 0.87 1.06 0.87 0.54 0.86 4 0.31 0.35 0.67 0.79 95 0.95 0.96 99 0.20 0.98 0.28 0.60 5 Flfi 0.38 0 21 0 . 8 2 0.83 94 0.94 1.00 1.20 0.30 0.35 0.65 6 1.11 0.42 97 0 24 0.85 0.92 92 1.06 1.12 0.24 0.82 0.47 7 0.22 1.21 0 62 0.47 94 0 12 106 0.58 1.09 0.14 0.14 0.61 8 1.00 104 0.84 0.79 0.98 0.56 95 0.95 1.35 1.00 0.77 0.92 9 0.48 0.74 92 0.20 95 0.75 0.88 0.96 0.95 0.19 0.86 0.48 10 0.96 89 0.18 0.70 0.69 94 0.93 0.94 0.69 0.84 0.17 11 0.60 0.89 0.50 95 95 0.86 0.53 12 o:i1 0:?8 0.88 0:;2 0:91 i:i4 0.48 90 96 0.88 o:i1 0.44 13 0.47 96 0 . 2 5 0.92 98 0.87 0.97 1.11 0.82 0.25 1.00 0.46 14 92 0.31 87 0.13 0 51 .~ 0.74 0.96 0.55 1.13 0.70 0.12 0.35 15 0.88 0.48 97 0.24 0 89 98 0.97 0.89 1.02 0.89 0.47 0.23 19 0.35 90 100 0.68 0.67 0.31 20 0.46 96 0:25 0'91 104 0.87 O:Q5 0.'97 1.'ii 0.86 0.42 21 0:26 0 Based on one stage in saturation zone and nine in elution (except for runs 4 and 5, which had 4 elution stages) and values of E actually existing during run. Average Approach t o Equilibrium

2410

INDUSTRIAL AND ENGINEERING CHEMISTRY

Vol. 45, No, l l

ENGINEERING AND PROCESS DEVELOPMENT Reproducibility of EiBuent Resin Compositions. One possible source of uncertainty in the calculation of the experimental values of y is in the composition of the saturated and eluted resins. Only one sample of each, obtained at the end of the run, is available, whereas the steady-state compositions for solutions are based on several product samples. There was thus some question as t o the accuracy of the values obtained from the single resin samples. A run (No. 12) was therefore made to check on the range of deviations encountered on duplicate samples. Each of the ten mixers of the unit was filled with similar aliquots of an eluted resin and all but the first resin sample received two counter-

1

-

ELUTING SECTION

o!2

* YPREDICTED

Figure 1 1.

d4 & YPREDICTED

Comparison of Experimental and Predicted y Values

the amount fed in the saturant and elutant solutions and the amount in the initial resin aliquots. The output was based on the upper and lower products and on the amounts i n the resin and solution aliquots left in the contactor a t the end of the run. The over-all material balance was then expressed as the per cent of the input t h a t was found in the output. Both the instantane ous output-input ratio and the over-all material balance are presented i n Table 11. Comparison with Predicted Data. The known number of physical stages in a given section, along with the E values for t h a t section, were used in Equation 42 t o predict theoretical y valuea. I n the majority of the runs there were one saturation stage and nine elution stages. For a given run, four values of y were predicted: one for lithium in the saturating section, one for the eluting section, and the two corresponding values for potassium. This information is also indicated in Table I1 and has been plotted against the pertinent experimental values of y i n Figure 11. Over-all, the agreement between predicted and experimental results was satisfactory. I n general, those points showing the greatest deviations from the norm were from the earlier runs (4 through 8). These runs were made before the analytical techniques reported here were fully refined, and the generally poor material balances for these runs probably reflect the analytical inaccuracies, especially for potassium. For this reason also, the equilibrium data for these runs were not represented in Figure 8. In addition t o possible analytical problems, 'runs 4, 5, and 6 were not entirely satisfactory. Plots of product composition, similar t o Figure 9, revealed t h a t run 4 had not yet reached the steady state at the end of the run. Runs 5 and 6 were inadvertently terminated at the improper cycle-Le., after the resin in the saturating section had received only one contact with saturant. It was thus necessary t o extrapolate the concentrations on the resin aliquots a t the end of the run to obtain estimated concentrations of the resin out of the saturating section after 2 contacts and that out of the eluting section after 18 contacts. These estimated values were used to calculate the approaches t o equilibrium transfer for these runs and the results must therefore be viewed with reserve. I n Table 11, it will be noted t h a t there is a large discrepancy between the experimental and predicted ( Y ~ ) ~ i for * t run 9. I n fact, this point could not be plotted on Figure 11. In this run, the steady state was never attained, for potassium a t least, and therefore the experimental value of y has n o meaning. Because the EK was more than 1, potassium accumulated on the recycled resin, and i t had not reached a stable concentration at the end of the run. The most important point about run 9 is t h a t incomplete elution and thus slower attainment of the steady state could have been anticipated from the EK value. November 1953

current contacts with saturant solution according t o the usual operating procedure. However, after receiving its two contacts, each resin aliquot was removed from the rather than out

a n elution in the i n i t . Although the fik three samples were in contact with either the improper number of times or with solutions which had received the improper number of prior equilibrations, the last six or seven samples should be indicative of steady-state operations in a saturation section. The actual compositions of the effluent solution and resin samples for this run are plotted in Figure 12. The predicted values of the compositions, based on the average E values and two equilibrium contacts, are also indicated. Although the resin compositions are relatively constant, deviations of 5 t o 10% exist between samples. This variation may be partially responsible for the cases of disagreement between predicted and experimental values of y and for the somewhat unsatisfactory over-all material balances. r,

20.040

I

X

vi

I

Figure 12.

l

I

I

I

I

--PREDICTED V A L U E S -EXPERIMENTAL VALUES

SAMPLE NUMBER

Reproducibility of Data for Run 12

. Effect of Equilibration Time on Results. As can be seen from Table 11,there appears t o be no effect of equilibration time on the agreement between predicted and experimental results, at least for times of 1.5 minutes or greater. However, because of minor differences i n conditions between the runs, this conclusion could only be tentative. I n order t o check this factor further, a special run (No. 20) was made. Again each of the 10 mixers of the unit was filled with similar aliquots of an eluted resin. The first two

I N D U S T R I A L A N D E N G I N E ,ER I N G C H E M I S T R Y

2411

ENGINEERING AND PROCESS DEVELOPMENT

~

Nomenclature

c

i

0.8

I

I

I

I

I

1I

w

E 0 U IL I8 RAT I O N TIME (MI N UTES)

Figure 13.

Effect of Equilibration Time on y

mixers were then brought in contact, for 1 minute, with separatc saturant aliquots, which were then removed. The next two mixers were in contact for 2 minutes with new saturant aliquots, etc., until the last two mixers m-ere in contact for 5 minutes. The average values of */ and over-all material balances for both lithium and potassium were calculated in the usual manner from the quantities and compositions of the solution and resin aliquots, before and after equilibration. The duplicate results, from the two mixers, have been plotted against equilibration time in Figure 13. The predicted values of y, based on the average values of E and one equilibrium contact, are also indicated on the figure. The results agree with the previous observation that equilibration times of 1.5 minutes or longer are sufficient for these ions in the equipment used. An adverse affect on y is apparent a t 1 minute, however. The poorer material balance for lithium, as indicated in Figure 13, is probably responsible for the less satisfactory agreement between the experimental and predicted values of y for lithium.

A , B, G = trace components 8 , B , and gross component G ionic level in the solution phase, meq. per ml., equal ex = total to the ionic concentrations of components A , B, and G ( seo in reference 6 ) D = distribution or partition parameter, dimensionless E = ratio of the slope of the equilibrium line t o the slope of the operating line, dimensionless volumeof elutant solution aliquot introduced to the eauilibrium-stage contactor volume of feed solution aliquot introduced into the equilibrium-stage contactor chemical equilibrium constant for exchange, dimensionless volume of lower product solution aliquot removed from equilibrium-stage contactor slope of the equilibrium line, dimensionless number of equilibrium contacts number of physical stages purity or the fraction of a given trace component in a specific stream with respect to the amount of all trace components in that stream total ionic concentration of the resin or the ultimate capacity, meq. per gram of oven-dried resin recovery or the fraction of a given component in a specific stream with respect to the amount in the incoming feed stream over the same time interval volumetric flow rate of the solution, ml. per second volumetric flow rate of the resin, ml. of actual solids per second ( R P ~isPthp weight flow rate of the reein, gram per second) volume of upper product solution aliquot removed from equilibrium-stage contactor volume of solution aliquot introduced to equilibrium-stage contactor. If the solution is elutant, V P = E, or if feed, I’F = F weight of resin aliquot introduced to equilibrium-stage contactor mole fraction of a component in solution .iiith respect to the total ionic level of the solution, dimensionless mole fraction in the qolution in equilibrium with a given mole fraction 011 the resin, dimensionless. (z*)oxlt= (Y/)entr/lM

y*

-, 6

4 pp

Conclusions

The results all appear to indicate that the present equipment can be used as a satisfactory equilibrium stage contactor for countercurrent ion exchange. Cnder trace conditions, the operation of the unit can be accurately predicted by the modified Kremser equation as long as equilibration times are adequate. The apparatus may also be useful for other unit operations involving fluid-solid contacting, such as leaching, adsorption, and catalysis. This process could easily be expanded to an industrial scale, as mixer-settlers can be obtained in large sizes. The economics of a commercial scale equilibrium-stage unit for the separation of ions will be discussed in a separate paper. Further work is in progress on the equilibrium-stage theory and the use of this contactor for exchange under gross conditions. This will be reported in a later paper. Acknowledgment

The authors wish to express their appreciation for the invaluable technical advice of Theodore Vermeulen, University of California, and Edward R. Tompkins, Naval Radiological Defense Laboratory, San Francisco, and thank Irvin C. Dumas, Stanford Research Institute, who aided in the design and construction of the equipment. Some of the calculations were performed by Lydia Peters of the institute and her assistance is gratefully acknowledged. 2412

mole fraction of a component on the resin with respect to the total capacity of the resin, dimensionless = mole fraction on the resin in equiIibrium with a given mole fraction in the solution, dimensionless. (y*& = M(x)entr = degree of approach to equilibrium transfer for a component in the solution phase, dimensionless. (The degree of approach to equilibrium transfer for a component in the resin phase is ?/E) = separation factor between B and A . 6 = K B G / K A G = concentration factor or the ratio of the concentration of one trace component to that of another in a given stream = density of resin, grams of oven-dried resin per ml. of true resin volume saturated with the carrier component

Subscripts

A , B , G = components A , B,and G E = elutant stream elut entr exit F L sat %’

elution section influent composition effluent composition feed stream lower product or spent elutant st’ream = sat,uration section = upper product or spent feed stream

= = = = =

literature Cited (1) Hiester, N. X., Fields, E. F., Phillips, R. C., and Radding, S. B., Chem. Eng. Progr., in press. ( 2 ) Kremser, A., Nail. Petroleum N e w s , 22, N o . 21, 42 (1930). ( 3 ) Ravenscroft, E. A., IND. ENO.CHEM.,28,851 (1936). (4) Souders, hl., and Brown, G.G., Ibid., 24,519 (1932). (6) Stephenson, R., “Continuous Multistage Ion Exchange,” Minneapolis meeting, I m . Inst. Chem. Engrs., September 1950. (6) S7ermeulen, T., and Hiester, E . X., IND.ENG.CHEM.,44, 636

(1962). ACCEPTED July 24, 1953. RECEIVED for review April 10, 1953. Presented before the Division of Industrial and Engineering Chemistry, .~~ SOCIETY,LOS Angelea, a t the 123rd Meeting of the A M E R I C CHEXICAL Calif. Work performed for the Atomic Energy Commission under Contract AT( 11-1)-110.

INDUSTRIAL AND ENGINEERING CHEMISTRY

Vol. 45, No. 11