PNNL-11122 UC-810

Project Technical Information

Cesium Ion Exchange Using Actual Waste: Column Size Considerations

K. P. Brooks

April 1996

Prepared for the U.S. Department of Energy under Contract DE-AC06-76RLO 1830

Pacific Northwest National Laboratory Richland, Washington 99352

PNNL-11122 UC-8 10

Project Technical Information

Cesium Ion Exchange Using Actual Waste: Column Size Considerations

KP Brooks

April 1996

Prepared for the U.S. Department of Energy under Contract DE-AC06-76RLO 1830

Pacific Northwest National Laboratory Richland, Washington 99352

Reprint of hiitoriul documen! TWRSPP--1. b u d Seplcrnber 1994. Dam. f m l t i n g . and other convtntiom reflect smrduds at the original dalc of printing. Technical peer review a d editorial review, may m have been performed.

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EXECUTIVE SUMMARY

Cesium i o n exchange w i t h actual Hanford tank waste i s being planned t o

v e r i f y p rev ious ly performed simul ant runs. I n order t o reduce cost and

r a d i a t i o n exposure, small e r i o n exchange co l umns are bei ng consi dered . Past

s tud ies have shown t h a t i n many cases, columns can be scaled successfu l ly

based on l i q u i d residence t ime on ly .

The purpose of t h i s study i s t o provide a t h e o r e t i c a l foundat ion f o r

s i z i n g very small columns f o r actual waste t e s t i n g . The study was 1 i m i ted t o

Neutral i zed Current Acid Waste (NCAW) and Doubl e-She1 1 S l u r r y Feed (DSSF)

wastes w i t h Duo1 i ten CS-100 (Rohm and Haas) and r e s o r c i no1 -formaldehyde (R-F!

res ins . Both the column wid th and leng th were considered du r ing scale-down.

The wid th o f t he column was determined t a k i n g i n t o cons idera t ion channel 1 i n g

and f l o w d i s t r i b u t i o n . The length o f t he column was determined consider ing

a x i a l d ispers ion, e n t r y 1 ength, wave shape development, mass t rans fe r

l i m i t a t i o n s , and aspect r a t i o . Rules o f thumb, experimental r e s u l t s ,

co r re la t i ons , and models were used i n t h i s development.

Minimum column dimensions are shown i n Table S.1. I n o rder t o prevent

s i g n i f i c a n t channel l ing and r a d i a l gradients, t he column diameter must be a t

l e a s t 1 cm and 1.9 cm f o r R-F and CS-100 res ins , respec t i ve l y . The minimum

column leng th (aspect r a t i o = 1) w i l l not produce t h e same breakthrough curve

as the 200 mL columns, but w i l l prevent poor feed d i s t r i b u t i o n and channe l l ing

and a1 low mathematical ana lys is o f t he breakthrough curve. Longer co l umns

w i l l be requ i red t.o r e p l i c a t e the performance o f t he 200 mL columns. A 15-cm

column i s suggested f o r a f l ow o f 6 c v l h r w i t h NCAW. Higher f low r a t e s w i l l

no t r e q u i r e as long o f column.

The 200 mL column i n t u r n appears t o produce breakthrough curves very

s i m i l a r t o those t h a t would be produced by t h e Hanford Tank Waste Remediation

System (TWRS) base1 i n e 2000 L i o n exchange columns. However, i f r e s u l t s ident ica l t o t h e 2000 L column are required, a 200 mL column may not be

s u f f i c i e n t s ince there may be elements of f i l m d i f f u s i o n res is tance i n the

200 mL co l umn t h a t are not present i n the 2000 L column. Fur ther s tud ies w i 11

be requ i red t o determine the minimum length t o match t h e breakthrough curve o f

the 2000 L base1 i n e column.

TABLE S. I . Column S i z i n g

CS-100

R- F

CS- 100

R- F

Minimum Column Size

Volume, mL

5.4

0 . 8

Diameter, cm

1 . 9

1

Length, cm

1 . 9

1

Rep1 i cate Lab-scal e Col umn Performance

42

12

1 .9

1

15

15

CONTENTS

. . . . . . . . . . . . . . . . . . . . . . . . . . . . EXECUTIVE SUMMARY iii

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 :rNTRODUCTION 1

1.1 BACKGROUND . . . . . . . . . . . . . . . . . . . . . . . . . . 1

. . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 PURPOSE 1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 SCOPE 2

. . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 APPROACH 2

2.0 PAST SCALE-UP S T U D I E S . . . . . . . . . . . . . . . . . . . . . . . 4

3.0 COLUMN DIAMETER AND SHAPE . . . . . . . . . . . . . . . . . . . . . 10

3.1 COLUMN DIAMETER . . . . . . . . . . . . . . . . . . . . . . . 10

3.2 BED ASPECT R A T I O . . . . . . . . . . . . . . . . . . . . . . . 11

4.0 COLUMNLENGTH . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 D I S P E R S I O N 12

4.2 ENTRANCE LENGTH . . . . . . . . . . . . . . . . . . . . . . . . 16 4.3 DEVELOPING WAVE SHAPE . . . . . . . . . . . . . . . . . . . . 17

4.4 MASS TRANSFER L I M I T A T I O N S . . . . . . . . . . . . . . . . . . 19

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.0 CONCLUSIONS 24

6.0 RECOMMENDED EXPERIMENTAL WORK . . . . . . . . . . . . . . . . . . . 26

7.0 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

APPENDIX A . COLUMN LOADING AND ELUTION MODEL

FIGURES

Comparison o f t h e Cesium Breakthrough Curves us ing 200 mL Columns w i t h Simulated Waste and 17 mL Columns Using Actual Neu t ra l i zed PUREX Waste a t t he Waste Va l ley Demonstration P ro jec t ( I t z o 1987) . Comparison o f Cesium Breakthrough Curves Using 200 mL Columns w i t h Simulated Waste and t h e Fu l l -Sca le Columns Using Actual Neutra l i zed PUREX Waste a t t he West Val l e y Demonstrati on P r o j e c t (Kurat h 1989) . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison o f Cesium Breakthrough Curves w i t h SRS Simulant Using a 2 mL a t 3 c v l h r and several 200 mL Columns a t 2 c v l h r . ( B i b l e r e t a l . 1990 and Bray e t a l . 1990) . . . . . . . . . . . . . . . . . . . Comparison o f Cesium Breakthrough Curves Performed w i t h 2 and 10 mL Columns and 101-AW Simulant a t 10 c v l h r . (Bi b l e r 1994) . . . . Model Developed Cesium Breakthrough Curves f o r Col umns o f var ious Lengths. The Curves D isp lay the E f f e c t s o f Ax ia l D ispers ion on Column Breakthrough. Data a t 1 c v l h r w i t h NCAW and CS-100 Resin. . Model Developed Cesium E l u t i o n Curve f o r Columns o f Various Lengths. The Curves D isp lay t h e E f f e c t s o f Ax ia l D ispers ion on t h e E l u t i o n Curve. Data a t 1 c v l h r w i t h NCAW and CS-100 Resin. . . Model Developed Cesium Breakthrough Curves f o r 5 Columns i n Series. The Curves D isp lay t h e Effects of Developing Wave Shape on t h e Column Breakthrough f o r 2 cm and 40 cm long Column. Data S h i f t e d Back i n Order t o A l i g n 50% Breakthrough Po in ts f o r A l l Columns. Data a t 6 c v l h r f o r NCAW and CS-100 Resin. NOTE: A x i a l Dispers ion E f f e c t s a re Also Inc luded i n Model. . . . . . . . . . . Model Developed Cesium Breakthrough Curves w i t h CS-100 f o r Columns o f Various Lengths. The Curves D isp lay t h e E f f e c t s o f F i l m D i f f u s i o n Mass Trans fer L i m i t a t i o n s (MTL) as Compared t o Runs w i t h D ispers ive E f f e c t s Only. Data a t 6 c v l h r w i t h NCAW. . . . . . . . Model Developed Cesium Breakthrough Curves w i t h R-F f o r Columns o f Various Lengths. The Curves D isp lay the Ef fec ts of F i l m D i f f u s i o n Mass Trans fer L i m i t a t i o n s (M'TL) as Compared t o Runs w i t h D ispers ive E f f e c t s Only. Data a t 6 c v l h r w i t h NCAW. . . . . . . .

TABLES

S.1. ColumnSiz ing . . . . . . . . . . . . . . . . . . . . . . . . . . . i v 1. Column Dimensions Studied . . . . . . . . . . . . . . . . . . . . . 14 2. Mass Transfer C o e f f i c i e n t s . . . . . . . . . . . . . . . . . . . . 23

1.0 INTRODUCTION

1.1 BACKGROUND

It i s p resen t l y planned t o remove cesium from Hanford tank waste

supernates and sludge wash s o l u t i o n s us ing i o n exchange. To suppor t t h e

development o f a cesium i o n exchange process, l a b o r a t o r y experiments produced

column breakthrough curves us ing wastes s imulants i n 200 mL columns. 'These

t e s t s p rov ided an understanding o f t h e process r a t e and t o a l i m i t e d e x t e n t

t h e e q u i l i b r i u m behavior. To v e r i f y t h e v a l i d i t y o f t h e s imu lan t t e s t s ,

co l umn runs w i t h ac tua l supernatants a r e being p l anned.

S i g n i f i c a n t cos ts a re associated w i t h ob ta in ing , t r a n s p o r t i n g , and

t e s t i n g r a d i o a c t i v e waste samples. Use o f t h e minimum poss ib le column s i z e

requ i r e s 1 ess r a d i oact i ve waste, fewer s a f e t y and dose consi de ra t i ons , and

fewer waste-disposal concerns. However, i f t h e t e s t - c o l umns a r e t o o smal l , t h e da ta obta ined cannot be f u l l y u t i l i z e d and cannot u l t i m a t e l y be used t o

sca le up t o p roduc t ion sca le columns.

1.2 PURPOSE

The purpose o f these ac tua l waste t e s t s i s two- fo ld . F i r s t , t h e t e s t s

w i 11 v e r i f y t h a t use o f t h e simul an t accura te ly r e f l e c t s t h e equi 1 i br ium and

r a t e behavior o f t h e r e s i n compared t o ac tua l wastes. Batch t e s t s and column

t e s t s w i 11 be used t o compare equi 1 i br ium behaviors and r a t e behaviors,

r e s p e c t i v e l y . Second, t h e t e s t s w i l l a s s i s t i n c l a r i f y i n g t h e negat ive

i n t e r a c t i o n s between t h e ac tua l waste and t h e i o n exchange r e s i n , which cannot

be e f f e c t i v e l y t es ted w i t h simul an t . Such i n t e r a c t i o n s i n c l u d e organ ic f o u l i n g o f t h e r e s i n and s a l t p r e c i p i t a t i o n i n t h e column. These e f f e c t s may a f f e c t t h e shape o f t h e column breakthrough curve. The r e d u c t i o n i n column

s i z e a l s o may change t h e shape o f t h e curve, making t h e i n d i v i d u a l e f f e c t s

even more d i f f i c u l t t o s o r t ou t . To simp1 i f y t h e eva lua t ion , t h e changes due t o column s i z e must be e i t h e r understood o r e l im ina ted .

Th is r e p o r t descr ibes t h e de termina t ion of t h e column s i z e f o r ac tua l

waste t e s t i n g t h a t best minimizes t h e e f f e c t of scale-down. Th is eva lua t i on

w i l l p rov ide a t h e o r e t i c a l basis f o r t he dimensions o f t he column.

Experimental t e s t i n g i s s t i l l requ i red before the f i n a l dec i s ion can be made.

1.3 SCOPE

This eva lua t ion w i l l be conf ined t o the study o f CS-100 and R-F r e s i n s

w i t h NCAW simulant and t o a l i m i t e d ex ten t DSSF waste s imulant . Only t h e

cesium load ing phase has been considered.

1.4 APPROACH

To determine the minimum s i z e o f column appropr ia te f o r cesium i o n

exchange, several avenues w i 1 1 be pursued. F i r s t , past experimental work w i t h

var ious s ized columns w i l l be discussed. Both successful and unsuccessful

co l umn scal e-down attempts w i 1 1 be i nves t i gated. Theoret i cal work w i 1 1 then

be presented f o r t h e system i n quest ion here. To determine the minimum column

s ize, two dimensions must be considered: column wid th and column length . The

minimum column w id th w i l l be chosen such t h a t the ef fects of r a d i a l v e l o c i t y

and concent ra t ion grad ien ts become negl i g i b le . The r a t i o n a l e behind t h e

var ious r u l e s o f thumb f o r length t o diameter r a t i o (aspect r a t i o ) w i l l be

i nves t i ga ted i n t h e context o f small-column systems.

The minimum column leng th w i l l be chosen such t h a t t h e e f fec t o f

d ispers ion , entrance 1 engths, and f i lm d i f f u s i o n mass t r a n s f e r become

n e g l i g i b l e . The model o f column opera t ion used t o i n v e s t i g a t e these e f f e c t s

inc ludes d i spe rs ion and mass t r a n s f e r terms. I t s parameters are based on work

done by Kurath and col leagues (1994) t o exper imenta l l y f it the l abo ra to ry -

sca le 200 mL columns (See Appendix f o r d e s c r i p t i o n ) . F i n a l l y , a t e s t p lan

w i l l be proposed t o v a l i d a t e the conclusions o f t h i s t h e o r e t i c a l approach.

In fo rmat ion der ived from the above approach suggests th ree s izes o f

co l umns: 1) the smal lest from which equi 1 i brium and mass t r a n s f e r in fo rmat ion

can be der ived w i thout being skewed by such ef fects as channel ing and r a d i a l

g rad ien ts t h a t cannot be model l e d e a s i l y , 2) t he s i z e requ i red t o o b t a i n

r e s u l t s w i t h i n experimental e r r o r o f those produced w i t h the 200 mL co l umn,

and 3) t he s i z e requ i red t o ob ta in r e s u l t s i d e n t i c a l t o t he 2000 L TWRS

base l ine column. I n Case 1, the breakthrough curves would t o be used i n

con junc t ion w i t h a model t o compare w i t h t h e 200 mL column simul an t runs. The

curves can a l so be used t o understand column e q u i l i b r i u m behavior . I n Case 2,

breakthrough curves can be compared d i r e c t l y between t h e ac tua l waste column

and t h e 200 rr~L column and w i 11 p rov ide mass t r a n s f e r d i f f e rences between t h e

s imulated and ac tua l waste. I n Case 3, d i r e c t scale-up t o t h e f u l l s i zed

column i s poss ib le i f both a re run a t t h e same res idence t ime ( c v l h r ) .

2.0 PAST SCALE-UP STUDIES

Small columns have been used success fu l l y i n t h e past t o p r e d i c t t h e

behavior o f l a r g e r sca le columns f o r t h e West Val l e y Demonstration P ro jec t .

Removing cesium from a waste t h a t i s s imi 1 a r t o NCAW, researchers produced

breakthrough curves from a 200 mL s imulant column and a 17 mL ac tua l waste

column ( I t z o 1987). Since the waste composit ion d i f f e r e d s l i g h t l y between t h e

two columns, t he re a s h i f t i n t h e l o c a t i o n o f t he breakthrough curves,

however, t h e i r slopes a re nea r l y i d e n t i c a l (F igure 1) . S i m i l a r i t y i n s lope

i nd i ca tes t h a t t he columns have s i m i l a r mass t r a n s f e r c h a r a c t e r i s t i c s and

column scale-down was successful . When these same 200 mL column runs were -

compared t o the f u l l sca le 1700 L column, t h e r e s u l t s were nea r l y i d e n t i c a l

(F igure 2) . Therefore, even a 17 mL column could have been used t o sca le up

the co l umns (Kurath 1989) . Another example o f successful use o f small i o n exchangers t o p r e d i c t

breakthrough curves was w i t h Savannah R iver S i t e (SRS) simul an t (Bi b l e r ,

Wall ace and Bray 1990). This waste i s a1 so very s imi 1 a r t o NCAW. A 2 mL

column (0.9 cm diameter) was loaded a t 3 c v l h r us ing R-F r e s i n . The

breakthrough curve f o r t h i s co l umn i s s imi 1 a r t o - those p red i c ted

t h e o r e t i c a l l y . Using an i d e n t i c a l waste composit ion and 2 c v l h r , Bray (1990)

produced 11 breakthrough curves w i t h a 200 mL of column. These curves a r e

compared i n F igure 3. Some o f t he 200 mL column breakthrough curves e x h i b i t e d

poor r e s u l t s . The reason has no t been i d e n t i f i e d , b u t could be due t o

channel l ing. Those curves have n o t been inc luded here. Although t h e r e i s s i g n i f i c a n t v a r i a b i l i t y between Bray's and B i b l e r ' s data, t h e breakthrough

curve from 2 mL column i s very s i m i l a r t o t he breakthrough o f t h e - l a r g e r

columns and i n some cases i s more i dea l . This r e s u l t s suggests once again

t h a t a small column can prov ide acceptable r e s u l t s .

B i b l e r a1 so s tud ied the much more concentrated 101-AW simul an t (1994).

Un l ike t h e o the r experiments run, t h i s simulant i s a concentrated form o f

DSSF. Columns 2 and 10 mL i n volume were operated a t 10 c v l h r us ing R-F r e s i n

(F igure 4) . Unl i ke the o the r exampl es shown, t he 2 mL co l umn experienced a

much e a r l i e r breakthrough than t h e 10 mL columns and appears t o have a lower

d i s t r i b u t i o n c o e f f i c i e n t . Since both columns were run a t t h e same f l o w r a t e

L

WNS.8g1 g " . .

Experimental Conditions ................. . . ............. . .. ............... . ... ....... 0.2 cvlhr - - - - - - - .- -

25°C 1.3~10-3M CS

' + 17mL, actual waste 95 L ........... . .......... .. .- ... -. - . - .- ....... --+- 2OOmL, simulant .- .- -. -. - -

West Valley Alkaline Supernate -.- ............. . - . - . - ............ - . - - . - .. .- .. - .. - ...... - . -. -. - ............ -. - .- .- . - ...... .- ... -. - . - . - ...............- .- .-. - ................ - .. ...............

Column Volumes FIGURE 1. Comparison o f t h e Cesium Breakthrough Curves us ing 200 mL Columns w i t h Simulated Waste and 17 mL

. Columns Using Actual Neut ra l i zed PUREX Waste a t t h e Waste Val 1 ey ,Demonstration P r o j e c t ( I t z o 1987)

Bed Volumes of Feed

Fiqure 2. Comparison o f Cesium Breakthrough Curves Using 200 mL Columns w i t h Simulated Waste and t h e F u l l -Scale Col umns Using Actual Neut ra l i zed PUREX Waste a t the West Va l ley Demonstration P r o j e c t (Kurath 1989)

4th Run: 200 mL Column

--+I---. 6th Run: 200 mL Column - 7th Run: 200 mL Column + 8th Run: 200 mL Column

e Column in Series

three columns in series 7th-11th Run: Single Resin

A - - -

Column Volumes Fiqure 3. Comparison of Cesium Breakthrough Curves w i t h SRS ~ i r n u l a n t Using a 2 mL a t 3 c v / h r and several

200 mL Columns a t 2 cv /hr . (Bi b l e r e t a1 . 1990 and Bray e t a1 . 1990)

and w i t h t h e same s imulant , t h e . d i f f e r e n c e must be t h e r e s u l t o f some

n o n i d e a l i t y assoc ia ted w i t h scale-down o r channe l l i ng . The h i g h f l o w r a t e may

be respons ib l e f o r these e f f e c t s . I n any case, scale-up may be d i f f i c u l t w i t h

a 2 mL column under these cond i t i ons .

3.0 COLUMN DIAMETER AND SHAPE

Col umn' diameter and shape are important considerat ions i n p revent ing

channel 1 i ng and r a d i a1 concentrat i on and vel oc i t y g rad ien ts . Col umn d i ameter

and shape w i l l a l so impact t he feed d i s t r i b u t i o n i n t he column.

3 .1 COLLIMN DIAMETER

Column diameters o f 20 t o 30 p a r t i c l e diameters have been used as a

standard f o r determin ing t h e minimum s i z e f o r packed beds ( H e l f f e r i c h 1962;

Smith 1981). These suggestions o r i g i n a l l y came from Schwartz and Smith (1953)

and Fahi en and Smith (1955) . I n a study t o measure v e l o c i t y v a r i a t i o n s i n a

packed bed, Schwartz and Smith found t h a t t he peak v e l o c i t y occurs

approximately 1 pa r t i c l e -d iamete r away from t h e p ipe w a l l , due t o increased

vo id f r a c t i o n near t h e w a l l . For columns o f l e s s than 30 p a r t i c l e diameters,

t he peak v e l o c i t y i s 30 t o 100% higher than the v e l o c i t y a t t h e center o f t he

column. Fahien and Smith s tud ied r a d i a l v a r i a t i o n s i n CO, concent ra t ion i n

packed beds. They found t h a t t h e Peclet number1 increases from t h e center

towards the column w a l l . This increase i s s i g n i f i c a n t f o r columns l e s s than

20 p a r t i c l e diameters.

Both these experiments were performed a t Reynolds numbers between 10 and

1000; t h e actual waste columns w i l l have Reynolds numbers o f 0.001 t o 0.1.

This d i f f e r e n c e may impact t h e use o f 20-30 p a r t i c l e diameters as a method o f

determin ing column diameter. This i s e s p e c i a l l y t r u e s ince the l i t e r a t u r e

work was performed i n t r a n s i t i o n f l o w (10 < Re < 1000) and t h e small column

work w i l l be done i n laminar f l o w (Re < 10). The appl i c a b i l i t y o f these

suggested diameters should be inves t iga ted .

I f 3 0 - p a r t i c l e-diameter columns are a c t u a l l y acceptable, a 1.0 cm

diameter column could be used f o r the R-F r e s i n (0.34 mm mass-average

diameter) and 1.9 cm i n diameter column could be used f o r t h e CS-100 r e s i n

(0.63 mm mass-average d i ameter) .

1 Defined as d,u,/D, where d, i s t he p a r t i c l e diameter, u, i s t h e i n t e r s t i t i a l v e l o c i t y , and D, i s the r a d i a l d ispers ion .

3.2 BED ASPECT RATIO

A " r u l e o f thumb" developed by He l f f e r i ch e t a1 . (1987) s t a t e s t h a t bed

aspect r a t i o s (1ength:diameter) should be 2 t o 7. For l a r g e columns, t h e

aspect r a t i o may be as low as 1. Columns w i t h aspect r a t i o s <1 tend t o

per form poo r l y because i t i s d i f f i c u l t t o d i s t r i b u t e t h e feed evenly over t h e

area o f t h e bed when t h e r a t i o i s low. The tendency o f feed t o channel,

e s p e c i a l l y down t h e middle of t h e column, w i l l r e s u l t i n an u n d e r - u t i l i z e d

bed. For t h e smal le r columns t h a t w i l l be used t o process ac tua l waste, a

channel may c o n s t i t u t e on l y a few p o o r l y packed r e s i n beads. Therefore, these

c o r r e l a t i o n s should cont inue t o ho ld f o r t h e smal le r columns and t h e minimum

aspect r a t i o f o r t h e columns should be 1.

The upper 1 i m i t o f t h e aspect r a t i o i s c o n t r o l l e d by t h e minimum column

diameter, pressure drop, and s t r u c t u r a l cons idera t ions . As discussed above,

t he column diameter should no t be l e s s than 30 p a r t i c l e diameters. The

maximum aspect r a t i o i s a l s o l i m i t e d by . the a b i l i t y t o cons t ruc t a s t u r d y

column which i s very t a l l . Furthermore, as t h e bed aspect r a t i o increases,

t h e pressure drop i n t h e column a l s o increases.

4.0 COLUMN LENGTH

Four fac to rs must be considered i n determin ing t h e minimum column

leng th : 1) cesium d i spe rs ion i n t he sho r te r column must no t s i g n i f i c a n t l y

change t h e shape o f t h e breakthrough curves, 2) t h e column l e n g t h must be

s u f f i c i e n t t o p rov ide adequate mass t rans fe r and hydrodynamic entrance 1 ength,

3) t h e column s i z e should no t a f f e c t t h e r a t e of formation o f t h e constant

wave shape, and (4) t h e v e l o c i t y i n t h e column must be l a r g e enough t h a t

1 i m i t i n g s tep o f t h e mass t r a n s f e r does no t change du r i ng scal e-down.

4.1 DISPERSION

Dispers ion i n a column i s a combination o f molecular d i f f u s i o n and

convect ive d i f f u s i v i t y . Both molecular and convec t ive d i f f u s i o n w i 11 cause a

spread i n t h e cesium concent ra t ion g rad ien t as i t moves through t h e r e s i n

beads. D ispers ion w i l l r e s u l t i n e a r l i e r breakthrough and a widening o f t h e

breakthrough curve. I n t h e case o f d ispers ion , t h e l e n g t h o f t h e columns i s

t h e s i g n i f i c a n t parameter; column w id th has no e f f e c t . I t i s g e n e r a l l y

s i g n i f i c a n t i n very s h o r t columns w i t h sharp breakthrough curves. Many

i n v e s t i g a t o r s have s tud ied d i spe rs ion i n packed beds.' A c o r r e l a t i o n was

devel dped f o r d i spers i on us ing spher ica l p a r t i c l e s a t Reynol ds numbers down t o

0.003 (Chung and Wen, 1968) :

where D, = t h e a x i a l d ispers ion , E = t h e bed p o r o s i t y , d~ = t h e p a r t i c l e diameter, u o = t h e i n t e r s t i t i a l v e l o c i t y , and Rep = t h e Reynolds number i n terms o f t he r e s i n p a r t i c l e s .

The breakthrough curve f o r CS-100 r e s i n and NCAW s imulant a t 1 c v l h r and var ious column lengths (see Table 1) were compared t o t h e 2000 L TWRS base1 i n e

column. The breakthrough curves f o r 15, 20, 40 cm long columns were very

s imi 1 a r t o t ha t - o f t h e 2000-L (136 cm) co l umn (see F igure 5) . The s h o r t e r columns (1, 3, 5, and 10 cm) successive ly deviated f rom t h e l onge r columns

w i t h t h e 1 cm column showing t h e g rea tes t dev ia t i on .

Flow r a t e , r e s i n type, and waste t ype were v a r i e d t o e l u c i d a t e t h e i r

e f f ec t on d i spe rs ion . Those v a r i a b l e s have much l e s s e f f e c t than column

1 ength on d i spers ion- i nduced spreading o f t h e breakthrough curve. Decreasing

f l o w r a t e increased t h e e f f e c t o f d i spe rs ion . S i m i l a r l y , l o a d i n g waste w i t h

CS-100 increased t h e e f f e c t o f d i spe rs ion over t h a t found w i t h R-F r e s i n .

Al though t h e breakthrough curves f o r R-F and CS-100 w i t h DSSF were much l e s s

sharp than those w i t h NCAW t h e e f fec ts o f d i spe rs ion as t hey re1 a t e t o column

scal e-down were s im i 1 a r .

TABLE 1. Column Dimensions S tud ied

D ispers ion was a l s o s tud ied as i t r e l a t e s t o e l u t i o n . S ince cesium r e t e n t i o n i s no t favored du r i ng e l u t i o n , t h e cesium concen t ra t i qn curve

spreads as i t moves down t h e c o l umn (a "non-sharpeni ng" behav io r ) . Therefore,

t h e a d d i t i o n a l curve spreading due t o d i s p e r s i o n i s i n s i g n i f i c a n t d u r i n g

e l u t i o n (See F igure 6 ) . Carberry and Wendel (1963) i n v e s t i g a t e d t h e e f f e c t s

o f a x i a l m ix i ng . T h e i r work suggests t h a t a x i a l d i s p e r s i o n should be

n e g l i g i b l e f o r a a x i a l Pec le t number o f 2 as l ong as t h e bed depth exceeds 50

p a r t i c l e diameters. Lower Pecl e t numbers requ i r e 1 onger beds. The a x i a1

Pec le t number f o r NCAW i s between 0.2 and 0.6 a t t h e column c o n d i t i o n s

desc r i bed here.

Therefore, t he bed depth must be s i g n i f i c a n t l y g rea te r than 50 p a r t i c l e

diameters, which agrees w i t h the work presented above.

4.2 ENTRANCE LENGTH

The hydrodynamic and d i f f u s i o n entrance leng th must be much smal le r than

t h e bed leng th i n a column. I n the f u l l scale column t h i s i s undoubtedly

t rue . I n order f o r t he smal ler column t o dup l i ca te t h e r e s u l t s o f t h e 1 arger ,

t he entrance length o f t he smal ler column must a l s o be completely developed

w i t h i n a shor t d is tance i n t o the column. I f the Schmidt number2 i s l a r g e

(approximately lo3 f o r t h e wastes studied here), t he hydrodynamics impact t h e

cesi um p r o f i l e much more profoundly than does molecular d i f f u s i o n . Therefore,

t h e hydrodynamic entrance 1 ength shoul d determi ne t h e r a t e o f devel opment f o r

both t h e v e l o c i t y ) and the concentrat ion p r o f i l e . To determine t h e

hydrodynamic entrance length f o r laminar f l o w i n a tube, t h e f o l l o w i n g

equation was developed (Incropera and DeWi tt 1985) :

where Re = t h e Reynolds number o f t h e c i r c u l a r tube, D = i t s diameter, and x = i s t h e e n t r y length.

Since t h i s expres'sion was not developed f o r a packed bed, two approaches

can be taken: assume t h e e n t i r e column i s t h e diameter f o r t h e entrance

leng th (D) o r assume t h a t the i n t e r p a r t i c l e spacing i s t h e diameter f o r

c a l c u l a t i n g the entrance length . The most reasonable approach would be t o

assume t h a t the entrance length i s c o n t r o l l e d by i n t e r p a r t i c l e spacing.

Assuming a 0.06 cm diameter spacing, NCAW v i s c o s i t y o f 2.6 cent is tokes, a 1 cm

long column, and 12 cv /hr f low ra te , t he entrance leng th i s ca l cu la ted t o be

approximately 3 microns. This i s much smal ler than the column leng th and

- -

2 The Schmidt number i s def ined as p/pD where p i s t h e v i s c o s i t y , p i s t h e densi ty , and D i s t he d i f f u s i v i t y . I t i s t h e r a t i o o f v i scous and d i f f u s i v e forces.

would be even more i n s i g n i f i c a n t f o r l a r g e r columns. Therefore, t h e e n t r y

l e n g t h i s n o t impor tant i n determin ing t h e l e n g t h o f t he t e s t columns.

4.3 DEVELOPING WAVE SHAPE

As cesium loads on an i o n exchange column, a concent ra t ion g rad ien t

forms i n t he column. Th is concent ra t ion g rad ien t wave i s o r i g i n a l l y sharp,

bu t tends t o spread as i t moves down the column. I f equi 1 i br ium favors t h e

l oad ing o f cesium onto t h e res in , once t h i s wave i s es tab l i shed, i t w i l l n o t

change i n w id th o r shape. If t h e iso therm i s very favorable, t h e curve w i l l

approach a constant wave shape very q u i c k l y . I f however, t h e separa t ion

f a c t o r i s n o t la rge , t h e exchanger mass t rans fe r i s q u i t e slow, o r t h e f l o w

r a t e i s h igh, t h e constant wave shape w i l l develop more s lowly . I t may n o t

develop before e x i t i n g the f i r s t column, and i t i n f a c t may r e q u i r e severa l

columns i n se r i es ( o r one very l ong column) t o reach t h e constant wave shape.

To determine i f t h e sca le of t h e column a f f e c t s t h i s development o f a

constant wave shape, t h e model was run f o r 5 ion-exchange columns i n s e r i e s t o

t r a c k t h e changing shape o f t h e breakthrough curve. A 2 cm long column s e r i e s

was compared t o a 40 cm long column se r i es . CS-100 r e s i n and NCAW s imu lan t

were used a t a f low r a t e of 6 c v l h r . I n o rde r t o comp'are these column se r i es ,

a l l t h e breakthrough curves were s h i f t e d back i n t ime so t h a t t h e 50%

breakthrough p o i n t f o r each column i s a l igned.

As shown i n F igure 7, n e i t h e r t h e 2 cm nor t h e 40 cm long column has

complete ly reached e q u i l i b r i u m a f t e r t h e f i r s t column. I n fac t , t h e columns

approach equi 1 i br ium o n l y a f t e r > 5 columns. Both t h e l a r g e and small column

se r i es show s i m i l a r t rends, i n d i c a t i n g t h a t t h e formation of a constant wave

shape i s independent o f column s i ze . The small d i f fe rence between t h e two

s izes o f column i s be1 ieved t o be o n l y a f u n c t i o n of d ispers ion . Therefore, t h e at ta inment o f t h e constant wave shape i s no t a concern w i t h regard t o

scale-down. A t t h i s f low r a t e , even t h e f u l l -sca le column w i 11 r e q u i r e

mu1 t i p l e columns t o reach a constant wave shape.

100

Time (min)

FIGURE 7 . Model Developed Cesium Breakthrough Curves f o r 5 Columns i n Ser ies. The Curves D isp lay the Ef fec ts o f Developing Wave Shape on t h e Column Breakthrough f o r 2 cm and 40 cm long Column. Data Sh i f t ed Back i n Order t o A l i g n 50% Breakthrough Po in ts f o r A l l Columns. Data a t 6 cv/hr f o r NCAW and CS-100 Resin. NOTE: A x i a l D ispers ion E f f e c t s a re Also ' Inc luded i n Model.

4.4 MASS TRANSFER LIMITATIONS

A t h i gh f l u i d v e l o c i t i e s , t h e r a t e o f i o n exchange i n a column i s

c o n t r o l l e d by d i f f u s i o n o f cesium i n t h e p a r t i c l e phase. As a column i s

scaled down a t constant residence t ime, s u p e r f i c i a l v e l o c i t y i s reduced. When

t h e v e l o c i t y surrounding t h e p a r t i c l e s i s reduced, t h e concent ra t ion boundary

l a y e r around t h e p a r t i c l e s increases and i o n i c d i f f u s i o n f rom t h e bu l k

so l u t i o n t o t h e p a r t i c l e surface becomes i ncreasi n g l y more impor tan t . A t very

low v e l o c i t i e s , t h e mass t r a n s f e r due t o f i l m d i f f u s i o n may c o n t r o l t h e r a t e

o f i o n exchange. To determine t h e in f luence o f these two f a c t o r s , t h e mass

t r a n s f e r c o e f f i c i e n t f o r f i l m and p a r t i c l e d i f f u s i o n , r e s p e c t i v e l y were

ca l cu l a ted u s i ng t h e f o l 1 owi ng c o r r e l a t i ons :

I n these c o r r e l a t i ons,

D = t h e d i f f u s i v i t y i n t he l i q u i d , D~ = t h e d i f f u s i v i t y i n t h e s o l i d phase, v = t h e s u p e r f i c i a l v e l o c i t y , and 4 = t h e p a r t i c l e diameter (Perry and Chi 1 ton, 1973).

Using t h e sum o f t h e i r res is tances, an o v e r a l l mass t r a n s f e r c o e f f i c i e n t can

be determi ned . The d i f f u s i v i t y o f cesium i n t he l i q u i d and s o l i d phase a r e two

parameters t h a t must be determined. The l i q u i d d i f f u s i v i t y was assumed t o ' b e

constant w i t h respec t t o i o n i c concent ra t ion . A va lue o f 1.2 x cmtlmin

was used based on t h e s e l f - d i f f u s i v i t y o f potassium i n a 4M_ s o l u t i o n o f KC1

(Bru ins 1929). The par t i c le -phase d i f f u s i v i t y of t h e r e s i n s was determined i n

one o f two ways: 1) batch k i n e t i c t e s t s performed a t Sandia Nat iona l

Laboratory (SNL) and PNL (unpubl ished data) and 2) f i t t i n g column t e s t s

performed a t PNL (Kurath e t a l . 1994). I n both cases i t must be assumed t h a t

p a r t i c l e d i f f u s i o n l i m i t s mass t r a n s f e r . Values of 2 x 10" cm2/min and

1.4 x 10'~ cm2/min were used f o r NCAW s imulant on R-F and CS-100, r e s p e c t i v e l y .

The mass t r a n s f e r c o e f f i c i e n t f o r f i l m , p a r t i c l e and o v e r a l l mass

t r a n s f e r c o e f f i c i e n t were ca l cu la ted f o r CS-100 and R-F r e s i n s w i t h NCAW

s imulant (Table 2) . These r e s u l t s shown t h a t t h e importance o f f i l m d i f f u s i o n

v a r i e s i n v e r s e l y w i t h column s i ze . The 2000 L column has no f i l m d i f f u s i o n

in f luences w h i l e f i l m d i f f u s i o n l i m i t a t i o n s s i g n i f i c a n t l y impact t h e mass

t r a n s f e r i n t he small column. Breakthrough curves model l e d f rom these mass .

t r a n s f e r c o e f f i c i e n t s a r e compared t o t he cond i t i ons w i thou t f i l m d i f f u s i o n

l i m i t a t i o n s (dev ia t i on i s caused o n l y by d ispers ion) . F igure 8 shows t h e

breakthrough curve f o r CS-100 w i t h NCAW a t a f l o w r a t e o f 6 c v l h r . F igure 9

shows t h e breakthrough curve f o r R-F r e s i n (a l so 6 c v l h r ) . Because t h e

e f f e c t s of d i spe rs ion and mass t r a n s f e r on the curves a re s i m i l a r (s teeper

breakthrough curve w i t h i nc reas ing column leng th ) , they w i l l be d i f f i c u l t t o

separate. I n both cases, d i spe rs ion appears t o have a l a r g e r e f f e c t on t h e

s lope o f t he breakthrough curve than f i l m d i f f u s i o n 1 i m i t a t i o n s . I f these c a l c u l a t i o n s a r e co r rec t , a 15 cm long column w i 11 produce

breakthrough curves t h a t a re probably w i t h i n experimental e r r o r o f t h e f u l l -

sca le column. I f r e s u l t s i d e n t i c a l t o t h e f u l l sca le column a r e requ i red ,

even t h e 40 cm column (200 rnL) used i n prev ious s tud ies would n o t be

s u f f i c i e n t s i nce both d i spe rs ion and mass t r a n s f e r cont inues t o a f f e c t t h e

shape o f t h e breakthrough curve.

I t n o t c l e a r what impact DSSF w i l l have on t h e requ i red s i z e o f t h e i o n

exchange column. As mentioned prev ious ly , t he e f f e c t s o f d i spe rs ion should be

s i m i l a r f o r both DSSF and NCAW. Pre l im inary r e s u l t s f o r Kurath (1994) seem t o

i n d i c a t e t h a t f i l m d i f f u s i o n could be more s i g n i f i c a n t than p a r t i c l e d i f f u s i o n

f o r DSSF. T h e o r e t i c a l l y , t h i s should n o t be t h e case s ince t h e chemical and

phys ica l p rope r t i es o f DSSF a re no t very d i f f e r e n t f rom those o f NCAW. I f

DSSF i s indeed l i m i t e d by f i l m d i f f u s i o n , l a r g e r columns would be requ i red f o r

DSSF than NCAW i n o rder t o o b t a i n r e s u l t s s i m i l a r t o t h e f u l l sca le column.

Fur ther experimental work should be performed t o address t h i s d i screpancy .

Time (min)

FIGURE 8. Model Developed Cesium Breakthrough Curves w i t h CS-100 f o r Columns o f Var ious Lengths. The Curves D i s p l a y t h e E f f e c t s o f F i l m D i f f u s i o n Mass T r a n s f e r L i m i t a t i o n s (MTL) as Compared t o Runs w i t h D i s p e r s i v e E f f e c t s Only . Data a t 6 c v l h r w i t h NCAW.

Time (min)

FIGURE 9. Model Developed Cesium Breakthrough Curves wi th R-F f o r Columns o f Various Lengths. The Curves Display the Effects of F i lm D i f fus ion Mass Transfer L imi ta t ions (MTL) as Compared t o Runs w i th . - Dispersive Ef fects Only. Data a t 6cv lhr w i t h NCAW.

TABLE 2 . Mass Transfer C o e f f i c i e n t s

r

136 cm

40 cm

15 cm

2 cm

1 cm

Kpa (mi n-')

* For 6 cv/hr, NCAW simulant.

0.010

0.010

0.010

0.010

0.010

K,a/4 (mi n- Overal l K (mi n- )

% Fi lm D i f f usi on

2.46

0.127

0.079

0.045

0.032

0.010

0.0096

0.0092

0.0084

0.0079

0

8

12

19

2 4

5.0 CONCLUSIONS

Based on the above ana lys is , ob ta in ing a breakthrough curve f rom which

equi 1 i br ium and 1 im i t ed mass t r a n s f e r i n fo rma t i on can be der ived requ i res t h a t

t h e w id th o f t h e column should be a t l e a s t 30 p a r t i c l e diameters. Th is

diameter should prevent channel 1 i n g and reduce the r a d i a1 concent ra t ion and

v e l o c i t y g rad ien ts . To prevent s i g n i f i c a n t impact due t o poor feed

d i s t r i b u t i o n , t he column aspect r a t i o should be approx imate ly 1. Thus t h e

minimum column diameter and he igh t a re 1 cm (0.78 mL) f o r R-F r e s i n and 1.9 cm

(5.4 mL) f o r CS-100.

These a r e t h e minimum a l lowab le column s izes . The breakthrough f rom

these columns should p rov ide in fo rmat ion about t h e e q u i l i b r i u m behavior o f t h e

a c t ~ ~ a l waste and t h e e f f e c t s o f organics and p r e c i p i t a t i o n i n t h e column feed.

With model i ng and experimental l y determined d i spers ion and d i f f u s i o n

coe f f i c i en ts , these breakthrough curves may be success fu l l y compared t o t h e

r e s u l t s obta ined w i t h t h e 200 mL column and t h e mass t r a n s f e r c o e f f i c i e n t s

determined.

To o b t a i n breakthrough curves t h a t r e p l i c a t e t h e performance of t h e

200 mL column, a s l i g h t l y l a r g e r column would be requ i red . Such a column

would permi t comparison o f t h e r e s i n mass t r a n s f e r us ing ac tua l waste w i t h t he

s imulant , i n a d d i t i o n t o t h e e f f e c t s descr ibed above. Based on t h e r e s u l t s o f

t h i s ana lys is , a 15 cm long column may be s u f f i c i e n t t o p rov ide such data f o r

NCAW a t 6 c v l h r . Higher f l o w r a t e would a l l o w a s l i g h t l y smal le r column, and

lower f low r a t e s would r e q u i r e a s l i g h t l y l a r g e r column. A t t h e minimum

diameter t o prevent channel 1 ing , a 12-mL column can be used w i t h R-F and a

42-mL column w i t h CS-100.

I f a breakthrough curve i s requ i red t h a t i s identical t o t h e 2000 L

column proposed by TWRS, t h e e f f e c t s of d i spe rs ion and f i l m mass t r a n s f e r i n

t h e column must be n e g l i g i b l e . I n t h i s case, even t h e 200 mL column s tud ied

p rev ious l y may n o t be 1 arge enough t o e l i m i n a t e these e f fec ts .

The above work has focused on NCAW. DSSF, a1 though chemical l y q u i t e

s i m i l a r t o NCAW, appears t o have a much slower r a t e o f i o n exchange. To

resolve concerns and correctly propose a column s i z e for DSSF further experimental work i s requi red.

6.0 RECOMMENDED EXPERIMENTAL WORK

The t h e o r e t i c a l t reatment presented here in should p rov ide a s t a r t i n g

p o i n t f o r t h e experimental work t o v e r i f y t h e c o r r e c t column s i ze . S ince most

o f t h e t h e o r e t i c a l work was done w i t h NCAW simulant and s i g n i f i c a n t i o n

exchange data e x i s t s f o r NCAW, t h e i n i t i a l experimental work should use t h i s

s imulant . The i n i t i a l f l o w r a t e should be 6 c v l h r t o correspond t o t h e

r e s u l t s o f t h i s study. A dec i s i on should be made as t o whether t h e column

t e s t s should g i v e a we1 1-formed curve ( s i g n i f i c a n t elements o f f i l m d i f f u s i o n

as t h e r a t e c o n t r o l 1 i n g step), breakthrough s i m i l a r t o a 200 mL column

(elements o f both f i l m and p a r t i c l e c o n t r o l 1 ed mass t r a n s f e r ) , o r a

breakthrough curve i d e n t i c a l t o t h e 2000 L column ( p r i m a r i l y o r e x c l u s i v e l y

p a r t i c l e d i f f u s i o n c o n t r o l l e d mass t r a n s f e r ) . Studies should a1 so be

performed on DSSF s imulant . A s i m i l a r approach t o those used f o r NCAW should.

be taken, a l though t h e f l o w r a t e should be reduced t o 3 c v l h r t o o b t a i n

improved breakthrough curves.

To v e r i f y t he column s i z e requ i red f o r a we1 1 formed breakthrough, t h e

experimental work shoul d i n c l ude the f o l 1 owing:

The column diameter should be a minimum o f 30 p a r t i c l e diameters. Th is corresponds t o > 1 cm f o r R-F r e s i n and > 1.9 cm f o r CS-100. For conservat ism du r i ng i n i t i a l t es t s , l a r g e r diameters can be used t o assure no channe l l i ng i s occur r ing .

Dur ing i n i t i a l t e s t i n g , t h e he igh t of t h e r e s i n i n t h e column should be n o t l e s s than t h e column diameter. To f u r t h e r prevent channel1 ing , t h e r e s i n bed should be as uniform as poss ib le and be backwashed p r i o r t o use.

I f t h e d i s t r i b u t i o n c o e f f i c i e n t s aremuch l o w e r t h a n expected, channel ing i s probably occu r r i ng and diameter and l e n g t h o f t h e column should be increased. I f t h e s lope o f t h e breakthrough curve i s unacceptably 1 ow, t h e co l umn 1 ength shoul d be i ncreased.

I f the breakthrough curve i s i d e n t i c a l t o t h a t o f t h e 200 mL column, t h e c o l umn l e n g t h and diameter should be reduced p r o p o r t i o n a l l y t o determine t h e minimum column s i ze .

To v e r i f y t h e column s i z e requ i red f o r breakthrough t h a t rep1 i c a t e s t h e

performance o f t h e 200 mL column, t h e experimental work should i n c l u d e t h e

f o l 1 owing :

The column diameter should be a minimum of 30 p a r t i c l e diameters. Th is corresponds t o > 1 cm f o r R-F r e s i n and > 1.9 cm f o r CS-100. For conservat ism dur ing i n i t i a l t e s t s , l a r g e r diameters can be used t o assure no channel1 i n g i s occur r ing .

The he igh t o f t h e r e s i n i n t h e column should i n i t i a l l y be t e s t e d a t 15 cm f o r both CS-100 and R-F res ins .

If t h e breakthrough curve i s we l l formed bu t has a lower s lope than t h e 200-mL column curve, use p rog ress i ve l y longer columns up t o t h e bed he igh t of t h e proposed f u l l -scale u n i t t o i d e n t i f y t h e p o i n t a t which t h e r e s u l t s a r e approach those of t h e 200 mL and t h e 2000 L column

I f t h e breakthrough curve i s i d e n t i c a l t o t h a t of t he 200 mL column, reduce t h e 1 ength p rog ress i ve l y t o i d e n t i f y t h e minimum co l umn 1 ength.

7.0 REFERENCES

B i b l e r , J. P., R. M. Wallace, and L. A. Bray, "Test ing a New Cesium-Specif ic I on Exchange Resin f o r Decontamination o f A1 kal i n e H igh -Ac t i v i t y Waste," For p resenta t ion a t t h e 1990 Waste Management Meeting, Tucson, AZ, February 25 -

' March 1, 1990.

B i b l e r , J. P., 1994. "Year-End Report f o r UST: Cesium E x t r a c t i o n Tes t ing P r o j e c t DOE/DT&E TTP No. SR1-03-20-01 (U) , " WSRC-RP-94-146, Westi nghouse Savannah R i ver Company, A i ken, South Carol i na.

Bray, L. A., R. J. Elov ich, K. J. Carson, "Cesium Recovery us ing Savannah R iver Laboratory Resorci no1 Formaldehyde Ion Exchange Resin, " PNL-7273, P a c i f i c Northwest Laboratory, R i ch l and, Washington. .

Bruins, H. R. 1929. "Coe f f i c i en ts o f D i f f u s i o n i n L iqu ids " I n t e r n a t i o n a l C r i t i c a l Tab1 es o f Numerical Data, Physics, Chemistry, and Techno1 ogy . Edward W. Washburn, ed., Vol . 5, McGraw-Hill Book Company, New York, pp. 63-76.

Carberry, James J. and Mar t i n M. Wendel, 1963. "A Computer Model o f t h e Fixed Bed C a t a l y t i c Reactor: The Ad iabat ic and Quasi -adi aba t i c Cases, " AIChE Journa l . Vol. 9, No. 1, pp. 129-133.

Chung, S. F. and C. Y . Wen, 1968. "Longi tudinal D ispers ion o f L i q u i d Flowing Through Fixed and F lu id i zed Beds." AIChE Journa l . Vol 14, No. 6, pp. 857- 866.

Fahien, R. W. and J. M. Smith, 1955. "Mass Transfer i n Packed Beds," AIChE Journa l . Vol. 1, No. 1, pp. 28

H e l f f e r i c h , F r i e d r i c h G., e t a l . 1987. Text from t h e AIChE Today Series, " I o n Exchange Theory and Prac t ice . " American I n s t i t u t e o f Chemical Engineers . New York.

Incropera, Frank P. and David P. DeWitt, 1985. Fundamentals o f Heat and Mass Transfer . 2nd Ed. John Wiley & Sons. New York.

I t z o , R. F., 1987. " In tegra ted Checkout o f t he Supernatant Treatment System," WVNS-TR-50-001, West Val 1 ey Nuclear Services Company, West Val 1 ey, New York.

Kurath, D. D., L. A. Bray, W. A. Ross, D. K. P loetz, " C o r r e l a t i o n o f Laboratory Test ing and Actual Operations f o r t h e West Val 1 ey Supernatant Treatment System," PNL-SA-16871, P a c i f i c Northwest Laboratory, Richland, Washington.

Kurath, D. E., L. A. Bray, K. P. Brooks, G. N. Brown, S. A. Bryan, C. D. Carlson, K. J. Carson, J. R. DesChane, R. J. Elov ich, A. .Y. K i m , 1994, "Experimental Data and Analys is t o Support t h e Design o f an. I o n Exchange Process f o r t h e Treatment o f Hanford Tank Waste Supernatant L iquids," TWRSPP- 94-010, Paci f i c Northwest Laboratory, R i ch l and, WA.

Perry , R . H., C. H. C h i l t o n , 1973. Chemical Engineers Handbook. F i f t h Ed. McGraw-Hill , I n c . New York, New York.

Schwartz, C. E. and J . M. Smith, 1953. "Flow D i s t r i b u t i o n i n Packed Beds," I n d u s t r i a l and Engineering Chemistry. Vol. 45, No. 6 , pp. 1209-1218.

Smith, J . M., 1981. Chemical Engineering K i n e t i c s . 3 r d Ed. McGraw-Hi 11 , I n c . New York, New York.

APPENDIX A

COLUMN LOADING AND ELUTION MODEL

APPENDIX A

COLUMN LOADING AND ELUTION MODEL

The column load ing model was developed and i n p u t i n t o Simusol v" (Dow

Chemical) code by Dr. R. S. Skeen, PNL. The code was mod i f i ed and used t o

analyze t h e ion-exchange column 1 oadi ng data and i n v e s t i g a t e e l u t i o n behavior .

The assumptions, governing equat ions, and boundary cond i t i ons are surrunarized

be1 ow.

The Simusol vm model t r e a t s t he i on-exchange as an adso rp t i on ldesorp t i on

process charac ter ized by an e q u i l i b r i u m isotherm. For ana l ys i s o f t h e column

load ing data, t he Freund l i ch isotherm was used. The ion-exchange k i n e t i c s a r e

accounted f o r by a l i n e a r d r i v i n g f o r c e between t h e cesium concen t ra t i on i n

t h e s o l i d and t h e e q u i l i b r i u m concent ra t ion o f cesium i n t h e s o l i d . The mass

t r a n s f e r c o e f f i c i e n t and f l o w r a t e a re assumed constant , and temperature

v a r i a t i o n s are assumed negl i g i b l e. The model a1 so incorpora tes d i spe rs i on i n

t h e l i q u i d phase. The d i spe rs ion c o e f f i c i e n t i s c a l c u l a t e d f rom a c o r r e l a t i o n

based on t h e Pec le t number, p a r t i c l e s ize, and f l u i d v e 1 o c i . t ~ (Per rv 's

Chemi ca l .Enqi neers ' Handbook, 6 t h ed. , p. 16-27).

I. Constants and Var iab les

C, = l i q u i d cesium concent ra t ion (mol lml)

C,, = so l i d ces i um concent ra t ion (mol I c c )

t = t i m e ( m i n )

z = d is tance from column entrance (cm)

U, = 1 i q u i d v e l o c i t y (cmls)

. E = v o i d f r a c t i o n

DA = e f f e c t i v e d i spe rs ion c o e f f i c i e n t (cm2/s)

C,, = feed cesium concent ra t ion (mol I m l )

C,,* = e q u i l i b r i u m cesium concent ra t ion i n t h e s o l i d (mol lcc)

C,,,,, = s o l i d cesium concent ra t ion i n e q u i l i b r i u m w i t h C,, (mol lcc) K,a = p a r t i c l e phase mass t r a n s f e r c o e f f i c i e n t (m-i n-')

L = co l umn he igh t (cm)

K = Freundl ich c o e f f i c i e n t

N = Freundl i ch exponent

I I. Mass Bal ance on Cesi um

111. A d s o r ~ t i o n o f Cesium

I V .

C& = K C:

ac, 1. -0, + U,C, = UzCAo a t z = 0 f o r a l l t

2. = 0 a t z = L f o r a l l t az

V I . I n i t i a l Condi t ion

C,, = 0 f o r 0 < z.5 L a t t = 0

V I I . Model Assumoti ons

1. Ion-exchange i s governed by a l i n e a r d r i v i n g f o r c e between t h e cesium concent ra t ion i n t h e s o l i d and t h e e q u i l i b r i u m cesium concentrat ion i n t he sol i d .

2. The mass t r a n s f e r c o e f f i c i e n t i s constant.

3. The f l o w r a t e i s constant.

4. The e q u i l i b r i u m behavior can be descr ibed by t h e Freund l i ch isotherm.

5. D ispers ion c o e f f i c i e n t i s a l i n e a r f u n c t i o n of l i q u i d v e l o c i t y .

6. Temperature v a r i a t i o n s are negl i g i b l e .

V I I I . Parameters Used I n Study

TABLE A. 1. Model Parameters Used

Kp a (min")

DA (cm2/m5 n)

K (mol , mL)

N

c,, ( ~ O I / ~ L I

NCAW

CS-100

0.02

0.1

2.7

0.834

DSSF

R-F

0.01

0.1

3.82

0.734

CS- 100

0.012

0.1

2.3

0.834

5 x 104 I

R-F

0.002

0.1

2.08

0.734

7 x