adsorption of pollutants from wastewater onto activated carbon based on external mass transfer and...

8/8/2019 Adsorption of Pollutants From Wastewater Onto Activated Carbon Based on External Mass Transfer and Pore Diffusi

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Wat. Res. Vo l. 22, No. 3, pp. 279-286 , 1988 0043-1354/88 $3.00+ 0.00Printed in Gr eat Britain Pergamon Press plc

ADSORPTION OF POLLUTANTS FROM WASTEWATERONTO ACTIVATED CARBON BASED ON EXTERNALMASS TRANSFER AND PORE DIFFUSION

G O R D O N M c K A Y * a n d M ~ J . B rN oD ep ar tm en t o f C h em ica l E n g in ee r in g , T h e Q u een ' s U n iv e r s i t y o f B e l f a s t , B e l f a s t B T 9 5 D L , N o r th e rn I r e l an d

(Received September 1985)A b s t r ac t - -T h e ad so rp t io n o f fo u r p o l lu t an t s i n aq u eo u s so lu tio n s o n to ac t iv a t ed ca rb o n h as b een s tud ied .T h e fo l lo w in g so lu te s h av e b een in v es tig a ted , p h en o l , p - ch lo ro p h en o l , so d iu m d o d ecy l su lp h a t e an dmercur ic ions . The k inet ics were s tud ied using an ag i ta ted batch adsorber and a model was p roposed ,based on ex ternal mass t ransfer and pore d i f fusion . The model p resen ted has a rap id analy t ical so lu t ionand is based on the assum ption o f a pseudo-i r revers ib le ( rectangu lar) i so therm.Key words--adsorpt ion , ca rb o n , m ass t r an sp o r t , p h en o l , m ercu r i c i o n s , so d iu m d o d ecy l su lp h a t e ,p - c h l o r o p h e n o l

Aa ~

B i =BC =

co..=co=c,=

C e . c o

C tDe f =D m ~ =

f-~k , =~ ' ( t ) =

Qe =

Q e . !

Q e . ~ o

Q e . tR =r =

N O M E N C L A T U R EOutside su rface area o f par t ic le , 4nR2(cm 2)C o n s t an t i n ev a lu a t io n o f eq u a t io n (2 3 )( l - - C h / C h ) 0"33B io t n u m b er , k/R/Dpo~A cons tan t , [1 - - (1/Bi)], i n S p ah n an d S ch lu n d erm o d e lC o n cen t r a t i o n o f so lu t e i n aq u eo u s p h ase(m g d in - 3)C o n cen t r a t i o n o f so lu t e a t eq u i l i b r iu m , i n aq u e -ous phase ( rag dm -3 )C o n ce n t r a t i o n o f so lu t e a t eq u i l ib r iu m o n th eso l id p h ase (m g d m -3)C o n cen t r a t i o n o f so lu t io n l i q u id a t t h e o u te rsu rface o f par t ic le ( rag dm -3 )C ap ac i ty f ac to r i n S p ah n an d S ch lu n d er m o d e l ,( YhW/Co V)E q u i l i b r iu m l iq u id p h ase co n cen t r a t i o n in b a t chco n tac t w h en sy s t em h as r each ed eq u i l i b r iu m(m g d m -3)L iq u id p h ase co n cen t r a t i o n a t t im e t (m g d m -3 )Effec tive diffusio n coefficient (cm 2 s -~)Pore diffusion coefficient (cm 2 s - I )P a r t i c le d i am e te r ( cm )Liqu id pha se m ass t rans fer coeffic ien t ( cm s - I )Ma ss t ransfe r coeff ic ien t in the so l id phase, ins ing le res is tance m odel (cm s - I )A d so rp t io n r a t e a t t im e t (m g s -1 )T h e am o u n t o f so lu t e ad so rb ed p e r u n i t w e ig h t o fad so rb en t i n fo rm in g a co m p le t e m o n o lay e r o nth e su r f ace fo r t h e L an g rn u i r i so th e rm ex p res s io n( m g g - l )M e a n v a l u e o f c o n c e nt r a t io n o f ad s o r b at e o na d s o r b e n t ( r a g - l )C o n c e n t r a t i o n o f a d s o r b a t e a t s u r f a c e o f a d -s o r b e n t a t e q u i li b r i u m ( m g g - ' )C o n c e n t r a t i o n o f a d s o r b a t e o n a d s o r b e n t a ti n f in i t e i m e ( r a g - l )S o l i d p h a s e c o n c e n t r a t i o n t i m e t ( m g g - ~ )R a d i u s o f p a r t ic l e ( c m )R a d i a l d i s t a n c e f r o m t h e c e n t r e o f p a rt i c l e ( c m )

* T o w h o m a l l co r r e sp o n d en ce sh o u ld b e ad d res sed .

r r = R ad iu s o f co n cen t r a t i o n f ro n t ( cm )g [ i = M o d i f i ed th eo re t i ca l S h e rw o o d n u m b erS h = S h e rw o o d n u m b er , (krR)/Dmot = T ime (s)V = V olum e o f eff luen t (dm 3)W = W eig h t o f ad so rb en t (g)x = V ariab le o f in teg rat ion in equa t ion (23) , (1 -~ /)3Y~* = Hy po thet ic al so l id phas e conce n trat ion , in th isw o rk i t t ak en to b e t h e sa tu ra t ed m o n o lay e rco v e rag e ( r ag g - i )

Greek lettersr /= D im en s io n les s so l id p h ase co n cen t r a t i o n= D im en s io n les s l i q u id p h ase co n cen t r a t i o n ,(c,/co)n = G eo m et r i ca l co n s t an tp , = Bu lk dens i ty o f ad sorba te par t ic le , g d ry ad -so rb en t p e r cm 3 o f b ed . v o lu m e= Dim ension less t ime, po re d i f fusion m odel(D,o~tCo/A~p. r~) .

I NTRODUCTION

A c t i v a t e d c a r b o n i s w i d e l y u s e d f o r t h e a d s o r p t i o n o fs o l u t e s f r o m g a s e s a n d l i q u i d s ( M a n t e l l , 1 9 6 8 ; H a s s -l e r , 1 9 7 4 ; P e r r i c h , 1 9 8 1 ; A l l e n e t a l . , 1 9 6 7 ) . I t i sg a i n i n g p r o m i n e n c e i n t he r e m o v a l o f o rg a n i c s f r o md r i n k i n g w a t e r s a n d w a s t e w a t e r s ( B u r k e e t a l . , 1980 ;W u , 1 9 7 8 ; R a m a l h o , 1 9 77 ). V a r i o u s c o n t a c t i n g d e -v i c e s a r e a v a i l a b l e f o r a d s o r p t i o n s y s t e m s , s u c h a sb a t c h a d s o r b e r s a n d f i x e d b e d a d s o r b e r s . T h e a c c u -r a t e d e s i g n o f s u c h s y s t e m s i s a c h i e v e d b y d e v e l o p i n gm a s s t r a n s f e r m o d e l s w h i c h a d e q u a t e l y d e s c r i b e t h ek i n et i c s a n d m e c h a n i s m s o f t h e a d s o r p t i o n p r o c e s s .T h i s p a p e r p r e s e n t s a m a s s t r a n s f e r m o d e l b a s e d o ne x t e r n a l m a s s t r a n s f e r a n d p o r e d i f f u s i o n t o d e s c r i b et h e a d s o r p t i o n o f v a r i o u s p o l l u t a n t s o n t o a c t i v a t e dc a r b o n i n a w e l l a g i t a t e d b a t c h a d s o r b e r . T h e p o l l u t -a n t s u n d e r i n v e s t i g a ti o n a r e p h e n o l , p - c h l o r o p h e n o l ,

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280 GORDON McKAY and MURAD J. BINO

sodium dodecyl sulphate and mercuric ions. Ad-sorpti0n isotherms have been determined and contacttime studies undertak en to assess the effect of systemvariables such as adso rbent mass and initial polluta ntconcentration.

A review of two-resistance mass transfer modelsprior to 1974 has been presented (Weber and Chak-ravorti, 1974). Other two-resistance models have beendeveloped for liquid phase adsorption, some incor-porated a numerical solution (Furusawa and Smith,1974; Neretnieks, 1976) for ads orpti on in batch ves-sels. A limited number of analytical techniques havealso been reported (Neretnieks, 1974; Spahn a ndSchlunder , 1975; Weber, 1978; Ditl e t a l . , 1978; Fritze t a l . , 1981), however, they involved either graphicaldifferentiation or the solution to a series of complexequations. Obviously, for practical design purposes,the more mathematically simple the model the moreamenable it is to designers of wastewater treatmentplants.

In this investigation the adsorption rate is devel-oped as an analytical function which can be solvedrapidly on a computer, based on the a ssumption of anirreversible isotherm, t hat is, where the opera ting andtie lines terminate on the monolayer.

EX PER IMENTALM a t e r i a l s

The solutes used, namely, phenol, p-chlorophenol, so-dium dodecyl sulphate and mercuric chloride, were of analargrade as supplied by B.D.H. The carbon was Filtrasorb 400as supplied by Chemviron.A n a l y s i s

Phenol and p-chlorophenol concentrations were deter-mined by absorption spectrophotometry at wavelengths of270 and 280 nm respectively, corresponding to the maxi-mum absorption values. Sodium dodecyl sulphate wasanalysed using a Beckman Model 915-B Total OrganicCarbon Analyser. Mercuric ion concentrations were meas-ured by the sodium borohydrate flameless technique on anatomic absorption spectrophotometer.E q u i p m e n t

The agitated batch adsorber is shown in Fig. 1 andcomprises a 1.7 dm3 vessel. The impeller agitation rate canbe carefully controlled using a Heidolph motor. For theagitation runs using mercuric ions the system was entirelyglass but aluminium was used for the impeller and baffles inthe other experiments. The relative dimensions are shown onthe figure.THEORY

E x t e r n a l m a s s t r a n s fe r a n d p o r e d i f fu s i o n m o d e l f o rb a t c h a d s o r b e r s

It is assumed that the adsorption rate is controlledby an external and internal mass transfer resistance.This linked transport mechanism may be describedusing mass transfer coefficients defined as follows:mass transfer in the external layer,

N = X k r ( C ' - C,); (1)

VariabLe peedRubber support I I ~ motor

/ I I. ,i i ,i .

D

Fig. I. Agitation unit. Z = height of liquid in vessel = D;B = baffle width = 0.075D; b = height of impeller blade =0.1D; diameter of impeller blade = 0.5D; distance betweenimpeller blade and vessel bottom = 0.5D.

mass transfer in the particle,~ V = A p , k , ( Q , . , - O .o ). (2)

It is assumed that the concentration s at the gran ularsurface (C, and Qs) remain in equilib rium as de-scribed by the adsorp tion isotherm during the entireperiod o f adsorp tion. The mass t ransfer coefficients krand k, are generally functions of all system param-eters. They can be determined from batch testevaluations.

At time t -- 0 a prepared wetted quan tity of acti-vated carbon W of uniform particle size was broughttogether with a qu antity of water V of initial ad-sorbate concentration Co in a well agitated beaker.Changes of adsorbate concentration C were meas-ured with a spectrophotometer while those in theadsorbent ~., were calculated from mass balance.

Graphical differentiation of C t t I gives d C / d t whichis proportional to the adsorption rate .N(t), since thedifferential mass balance is given by:

N(t) = - V dC W d~'c. (3)-~= d tFrom the adsorption rate N(t) the equilibrium con-centr ation s Cs and Qc can be determined as a functionof the concentrations C, and ~.c as shown in Fig. 2,provided the external mass transfer coefficient kr isknown.

At time t = 0 all the mass transfer resistance isrestricted to the external layer on the particle.

v ( d Ck r = - A C o " \ '~-} t -o ' (4)

Hence the external mass transfer coefficient can bereadily determined (Spahn and Schlunder, 1975; Fur-usawa an d Smith, 1973; McKa y and Allen, 1980).


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Adsorption of pollutants 281

O,

Fig. 2. Connection between bulk and surface concentration

Reacted r *C ] c C t"N / -/ Tie n, ~ i 0. ~- . . . . ./ ..... \ o ....

/ \Co Co Unreocted / " ~ i

anectiolL be:ween b u l k m ql s u rf ; "e co x p o r h cl , e ~ ' ~ C e n ~ ntra tio n f ro n tdur in g the adsorption in batch tests,On ce k r i s kno wn , t he e qua t ions (1 ) and (3 ) can beu s e d t o d e t er m i n e t h e c o n c e n t r a t i o n o f th e a d s o r b a t e

in the l iqu id ph ase C~ a t t he g ra nu la r su r face . Th i sg ives the va lue o f t he concen t ra t ion Q~0 in the so l idphase which i s a ssum ed to be in equ i l i b r ium wi th C~ .These equ i l i b r i a a re desc r ibed fo r bo th h igh and lowa d s o r b a t e c o n c e n t r a t i o n s i n w a t e r b y t h e e q u i li b r iu miso the rms.T h e a d s o r b e n t p a r t i c l e i s r e g a r d e d a s a p o r o u ss o l i d . T h e s u b s e q u e n t d e s c r i p t i o n o f t h e a d s o r p t i o nra t e wi l l t he re fore be based on the fo l lowing a ssump-t ions:( i ) The adsorba te i s t r ansfe r red wi th in the pores o ft h e a d s o r b a t e s o l e l y b y m e a n s o f m o l e c u l a r

di ffusion.( i i ) A d s o r p t i o n e q u i l i b r i u m a c c o r d i n g t o t h e i s o -t h e r m i s p r e s u m e d b e t w e e n t h e p o r e w a t e r a n dt h e a d s o r b e n t t h r o u g h o u t a d s o r p t i o n p r o c e s s .I n o t h e r w o r d s , t h e d e p o s i t i o n r a t e o f t h ea d s o r b a t e m o l e c u l e s i n t h e p o r e w a t e r o n t h ea d s o r b e n t s u r f a c e i s t a k e n t o b e m u c h h i g h e rthan the i r r a t e o f d i f fus ion .( i i i ) T h e a d s o r b a t e c o n c e n t r a t i o n i n t h e c a r b o n i sindep ende n t o f t ha t i n t he wa te r , i . e. t he ad-sorpt ion is i r reversible .( i v ) T h e q u a n t i t y o f a b s o r b a t e i n t h e p o o r e w a t e ri s m u c h l o w e r t h a n t h a t o n t h e a d s o r b e n t p e ru n i t v o l u m e a n d c a n t h e r e f o r e b e n e g l e c t e d .

Because o f t he ex te rna l mass t r ansfe r r e s i s t ance ,t h e c o n c e n t r a t i o n o f a d s o r b a t e i n t h e w a t e r d r o p sf ro m va lue C0~ in the bu lk to t he eq u i l i b r ium va lueC ~tl a t t h e s u r f a c e . T h e c o n c e n t r a t i o n o f a d s o r b a t e i nthe pore wa te r , t he re fore , dec reases f rom C~0 to ze roa t r t . T h e a d s o r b a t e i n t h e p o r e s i s a d s o r b e d i n aw e l l - d e f i n e d c o n c e n t r a t i o n f r o n t , m o v i n g w i t h v a r y -ing ve loc i ty f rom the pa r t i c l e su r face inwards . Aconcen t ra t ion curve in t he pa r t i c l e i s shown in F ig . 3 .T h e e q u i l i b r i u m c o n c e n t r a t i o n s C , a n d Q , w e r ed e t e r m i n e d a s a f u n c t i o n o f t h e c o n c e n t r a t i o n Cto a n d~ b y s u b s t i tu t i n g t h e v a lu e o f kf f r o m e q u a t i o n ( 4 )and the adsorp t ion ra t e .~ ' ( t ) a t d i f fe ren t t imes in :+Z.(dqC~t) = C,) A k r \ d t ]" (5 )

Fig. 3. Concentration profile in particle.E a c h C a o w a s p l o t t e d o n t h e i s o t h e r m a n d t h ec o r r e s p o n d i n g e q u i l i b r i u m v a l u e Q ~ 0 w a s o b t a i n e d .T h e o p e r a t i n g l i n e f o r t h e a b o v e p r o c e s s w a s a l s od r a w n b y p l o t t i n g t h e Cto, Q ,~o va lues , de t e rminedf r o m t h e b a t c h c o n t a c t e x p e r i m e n t , a n d C , . ~ a n dQ, . ~ va lues were de t e rm ined by ex tend ing the ope r -a t ing l i ne to cu t t he i so the rm (Fig . 2 ) . Knowing thecon cen t ra t ions Ct0 , Q~0 , C , and Q, a t any t ime , t het ime dependen t i n t e rna l mass t r ansfe r coe f fc ien t , k ,va lues , were ca l cu la t ed by u t i l i z ing equa t ions (1 ) and(2) i n t he fo rm,

k f ( C , - C , )k, = (6)p , (Q , , , -O , )T h e r a t e o f a d s o r p t i o n o n a c a r b o n p a r t ic l e c a n b ede te rmined a s fo l lows:

( i ) Mass t r ansfe r f rom the ex te rna l wa te r phase := 4rrR 2kr(C - C,). (7)

( i i ) Di f fus ion in t he pore wa te r accord ing to F i ck ' sl aw:47rDeer C= ~ ~,~ (8 )

\ r r R ]wh ere D,fr i s the effect ive di ffusio n c oeff ic ient int h e p o r e w a t e r .( i i i ) The ve loc i ty o f t he concen t ra t ion- f ron t i s ob-t a i n e d f r o m t h e m a s s b a l a n c e o n a s p h e r i c a le l ement :N = - 4 n r ~ Y ~ p , ( d r r ~ . (9 )\ a t )

( iv ) Th e ave rag e conc en t ra t ion in t he pa r t i c l e i sg iven by :

I n t r o d u c i n g d i m e n s i o n l e s s p a r a m e t e r s :C o D , ~ tP, Yg' R2 (11)

W ,R. .2/3.--B


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282 GORDON M cK Av and M uaA o J. BINO

r/ = y-~ (12)__Ce (13)Co

B i = k f R . (14)D drT h e a d s o r p t i o n r a t e f o r a s i n g l e p a r t i c l e fo l l o w s

f r o m e q u a t i o n s ( 7 ) , ( 8 ) , ( 9 ) a n d ( 1 0 ) :dr/ ~ 3(1 - q),/3- - = ( 1 5 )d t 1 - - [1 - - ( 1 / B i ) ] ( l - - q)1/3"

T h i s e q u a t i o n i s o f t h e t y p e ,dr/d - z = ~ f ( r / ) B i . ( 1 6 )

T h e a d s o r p t i o n r a t e t o t h e i n d i v i d u a l p a r t i c l e i st h u s a f u n c t i o n o f a d s o r b a t e c o n c e n t r a t i o n s i n t h ew a t e r p h a s e ~ , i n t h e c a r b o n p h a s e r / a n d o f t h e B i o tn u m b e r .

T h e c o e f f i c ie n t s k st t) d e t e r m i n e d e x p e r i m e n t a l l yw e r e c o m p a r e d i n t h e f o r m o f a m o d i f i e d S h e r w o o dn u m b e r . T h i s S h - n u m b e r i s p r o p o r t i o n a l t o t h e a d -s o r p t i o n r a t e , w h i c h f o l l o w s f r o m e q u a t i o n s ( 2 ) a n d(3).

S---h= _ _ 1 d r/ ( 1 7)3 (1 - r / ) d rw i t h t h e a d s o r p t i o n r a t e d r / / d ~ f r o m t h e b a t c h t e s t so n e o b t a i n s t h e e x p e r i m e n t a l v a lu e s o f S h w h i l e f r o mt h e r e a r r a n g e d e q u a t i o n ( 1 5 )

dr/ 3(1 - Chr/)(1 -- r/)~/3d--~ = 1 -- [1 -- ( l /B i)] (1 - r / )u3 (18)

t h e t h e o r e t i c a l v a l u e s S h c a n b e p r e d i c t e d . T h e r e b yt h e c o n c e n t r a t i o n i n e q u a t i o n ( 1 5 ) w a s r e p l a c e d b y( 1 - C h r/ ) w h i c h f o l l o w s f r o m t h e t o t a l m a s s b a l a n c ef o r t h e v e s s el . H e r e C h = W Y ~ / L C o i s t h e c a p a c i t yf a c t o r f o r t h e i n d i v i d u a l t e s t . T h e v a l u e o f t h ee f fe c ti v e d i f f u si v i ty i n t h e p o r e s D ~ h a s b e e n a d o p t e dt o g i v e th e b e s t f it b e t w e e n e x p e r i m e n t a l a n d t h e o r -e t i c a l d a t a .F r o m a d s o r p t i o n t e s t s p r e s e n t e d i n t h i s p a p e r i tf o l l o w s t h a t t h e e x p e r i m e n t a l a n d t h e o r e t i c a l v a l u e so f a n y g i v e n s y s t e m c a n b e f i t t e d w i t h s u f f i c i e n ta c c u r a c y i n t r o d u c i n g a c o n s t a n t d i f f u s io n c o e ff i ci e n tD en f o r m a s s t r a n s f e r i n s i d e th e p o r o u s c a r b o np a r t i c l e .Com parison of experimental and theoret ical resul tsbased on the assumption o f a pseudo-irreversib le iso-therm

T h e c o e f f i ci e n ts k , ( t ) o b t a i n e d f r o m b a t c h t e s ts a r en o w c o m p a r e d i n t h e f o r m o f a m o d i f ie d S h e r w o o dn u m b e r , S h . T h i s S h i s p r o p o r t i o n a l t o th e

l t ' d r /= (19)

p r o v i d e d t h e o p e r a t i n g l i n e t e r m i n a t e s a t t h e m o n o -

l a y e r c o v e r a g e t h e s y s t e m c a n b e t r e a t e d w i t h a" p s e u d o - i r re v e r s i b le " i s o th e r m a p p r o x i m a t i o n , s ot h a t ,

Q , - Oe = Y~' - Oe. (20 )T h i s a s s u m p t i o n a l l o w s a n a n a l y t i c a l s o l u t i o n o fe q u a t i o n ( 1 8) in t h e f o l l o w i n g m a n n e r . L e t ,

1B = 1 - - - ( 2 1)B ia n d

x = (1 - 1 7 ) 0 . 3 3 . (22)S u b s t i t u t i n g e q u a t i o n s ( 2 1 ) a n d ( 22 ) a n d r e a r r a n g i n g ,e q u a t i o n ( 1 8 ) b e c o m e s ,

x ( l - B x )dz = [1 - Ch(1 -- x3)] dx (23)a n d i f

T h u s

a _ _ f l -\ Ch ,] " (24 )

1dr =--~h x3 + a3 j dx (25)a n d t h i s c a n b e i n t e g r a t e d u s i n g p a r t i a l f r a c t i o n sa c c o r d i n g t o t h e f o l l o w i n g f o r m ,. + , o F ( x .

L \ 1 + a)aJJI f I - ( 2 - a ) -I+ ~ l a r c t a n L ~ j

(26)T h e l i m i t s o f i n t e g r a t i o n i n e q u a t i o n ( 2 6) a r e r = 0 ,r / = 0 , a t x = l a n d r = z , r / = q a n d x = xr = ~ - ~ . ~ h { l n [ ( x 3 + a S ) ( 2 B - - ! ) ]+ l n [ (x + a ) ~ ] }

1 f [ - ( 2 - a ) - ]+ ~ l a r c t a n L a--~-~a r , t a o [ l l (27)T h e r e f o r e , b y c o n v e r t i n g d i m e n s i o n l e s s t i m e , r ,

i n t o r e a l t im e i t i s p o s s i b l e t o c o m p a r e e x p e r i m e n t a la n d t h e o r e t i c a l c o n c e n t r a t i o n d e c a y c u r v e s .

D I S C U S S I O N

A d s o r p t i o n i s o t h e r m s w e r e d e t e r m i n e d t o a s s es s' t h e c a p a c i t y o f a c t iv a t e d c a r b o n f o r t h e f o u r p o l l u t -a n t s . T h e m o n o l a y e r a d s o r p t i o n c a p a c i t i e s a r e 2 06 ,4 1 0 , 3 35 a n d 1 30 m g g - l f o r p h e n o l , p - c h l o r o p h e n o l ,s o d i u m d o d e c y l s u l p h a t e a n d m e r c u r i c i o n s r e -s p e c ti v e l y. F o r t h e k i n e t i c m o d e l t o b e a p p l i c a b l e t h e


5/8

Adsorption of pollutants 283C i , t , Q I , t

- - " 200- - ~

v 1 0 0 -~;

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0C o ( mg dm ~ )

Fig. 4. Equilibrium relation sho wing operating lin e and tielines for phenol.t i c l i ne s and ope ra t ing l i ne s mus t t e rmina t e a t t hes a t u r a t i o n c a p a c i t y m o n o l a y e r l i n e . F i g u r e 4 s h o w sva r ious t i e l i ne s and an ope ra t ing l i ne fo r t he ad-s o r p t i o n o f p h e n o l o n t o c a r b o n u s i n g a n i ni ti a lc o n c e n t r a ti o n o f 5 00 m g d m -3 .

T h e o p e r a t i n g l i n e i s c o n s t r u c t e d f r o m a p o i n t o nt h e C a x is o f t h e e q u i l ib r i u m c u r v e , h a v i n g c o o r d i -na t e s C= = Co and Q = 0 . The o pe ra t ing f ine is d .r awnf r o m t h i s p o i n t , h a v i n g a s l o p e - s o l u t i o n v o l u m e /a d s o r b e n t m a s s , t o t h e e q u i l i b r i u m c u r v e t h u s p r e -d i c t i ng the f i na l l i qu id phase concen t ra t i on and so l idload ing . The t i e o r t ime l i nes mus t f a l l be tween theo p e r a t i n g l i n e a n d t h e e q u i l i b r i u m c u r v e . T h e l o w e rp o i n t i s l o c a t e d b y t h e e x p e r i m e n t a l l y m e a s u r e d C tv a l u e a n d t h e p a r t ic l e s u r f a c e c o n c e n t r a t i o n i s c a lc u -l a t e d f r o m e q u a t i o n ( 5 ) .

I n a p r e v i o u s m o d e l i t w a s a s s u m e d t h a t t h e s o l u tec o n c e n t r a t i o n i n t h e p a r i ie l e i s i n d e p e n d e n t o f t h a t i nthe wa te r , t ha t i s , t he adsorp t ion i s comple t e ly i r r e -ve r s ib l e . Consequen t ly , t he equ i l i b r ium concen-t ra t i on , Q e .= can be rep l aced by a hypo the t i ca le q u i l ib r i u m c o n s t a n t , Y ~' = c o n s t a n t . I t w a s f o u n dt h a t t h i s h y p o t h e t i c a l e q u i l i b r i u m c o n s t a n t d i d n o tg ive t he bes t f it be tween expe r im enta l a nd theore t i ca ld a t a . I n f a c t , i n c e r t a i n c a s e s S p a h n a n d S c h l u n d e r(1975) were unab le t o use Y* to f i t expe r imenta l andt h e o r et i c al d a t a a n d s e le c te d a v a l u e o f Y * = 0 . 5 .

I n t h e p r e s e n t w o r k t h i s m o d e l w a s t e s t e d e x t e n -s iv e ly f o r th e a d s o r p t i o n o f p h e n o l o n t o c a r b o n a n di t w a s f o u n d t o g i v e a v e r y g o o d c o r r e l a t i o n b e t w e e nexpe r imenta l and theore t i ca l da t a . I t was a l so t e s t edf o r p - c h l o r o p h e n o l , S D S a n d H g 2 + a d s o r p t i o n o n t oc a r b o n . T h e v a l u e o f Y * a d o p t e d i n t h e s e c a s e s w a st h a t o f t h e s a t u r a t io n m o n o l a y e r c o v e r a g e o f t here l evan t i so the rm. The va r i ab l e s s tud i ed were : ( a )in it ia l c o n c e n t r a t i o n a n d ( b ) m a s s o f c a r b o n .

T h e e f fe c t o f v a r y i n g t h e i n i ti a l c o n c e n t r a t i o n i ss h o w n i n F i g . 5 f o r p h e n o l . I t c a n b e s e e n t h a t f o rs t e e p o p e r a t i n g l i n e s t e r m i n a t i n g a t t h e a d s o r p t i o ni s o t h e r m m o n o l a y e r t h e a g r e e m e n t b e t w e e n t h e o r -e ti ca l a n d e x p e r i m e n t a l d a t a is v e ry g o o d a n d e x t e n d sf o r u p t o 5 0 r a i n o f c o n t a c t t i m e , b u t a s t h e o p e r a t i n g

1 .0

0 8 .

0 . 6

0 . , ~ I I2 0 4 0 6 0T i m e ( r a i n )

Fig . 5 . Concentrat ion decay curves showing the e f fec t o fa d s o r b e n t m a s s f or t h e a d s o r p t io n o f p h e n o l o n c a r b o n . $ ,wt = 0 .85 g ; & , wt = 1 .7 g ; C) , wt = 2 .66 g ; - - - , theoret ical .

l in e a p p r o a c h e s t h e c u r v e d r e g i o n o f t h e i s o t h e r m t h ea g r e e m e n t i s n o t a s a c c u r a t e .T h e e f fe c t o f v a r y i n g t h e m a s s o f a d s o r b e n t i ss h o w n i n F i g . 6 f o r t h e a d s o r p t i o n o f p h e n o l . T h em o d e l g i v e s g o o d p r e d i c t i o n o f e x p e r im e n t a l r e s u lt sus ing a co ns t an t e f fec tive pore d i f fus iv i ty and a s ing l econs t an t ex t e rna l mass t r ansfe r coe f f i c i en t . The e f fec to f i n it ia l c o n c e n t r a t i o n o n t h e a d s o r p t i o n o f p -c h l o r o p h e n o l o n t o c a r b o n i s s h o w n i n F i g . 6 . C o r -re l a t i on be tween expe r imenta l and theore t i ca l r e su l t sis a c h i e v e d f o r o n l y 1 0 - 2 0 m i n , a f t e r t h i s p e r i o d t h etheore t i ca l equa t ion dec reases a t a g rea t e r r a t e t hanthe expe r imenta l r e su l t s . The dev ia t i on f rom thetheory i s p robab ly due to a change in t he e f fec t ivep o r e d i f f u s i v i t y . A b r a n c h e d p o r e t h e o r y w a s p r o -posed (Pee l e t a l . , 1981) which invo lves a change inD a r w i t h v a r y i n g e x t e n ts o f a d s o r p t i o n . T h i s e x t e n t o fa d s o r p t i o n i s a f u n c t i o n o f p o r e s i z e d i s t r ib u t i o nwi th in t he pa r t i c l e and the re l a t i ve s ize o f t he so lu t em o l e c u l e. A d e t ai le d d e s c r i p t i o n o f th e b r a n c h e d p o r emode l i s g iven by Pee l e t a l . (1981) . F igure s 7 and 8

5 0 0

4 0 0

IE"D= " 3 C ; 0E

2 0 0

\ ,

I I I I II G O C) 5 1 0 1 5 2 0 2 5T i m e ( r a i n ) i.F i g . 6 . C o n c e n t r a t i o n d e c a y c u r ve s s h o w i n g t h e e f fe c t o fi n i t i a l c o n c e n t r a t i o n f o r t h e a d s o r p t i o n o f p - c h l o r o p h e n o lo n c a r b o n . , T h e o r e t i c a l ,


6/8

2 8 4 GORDON McKAY and M u ~ D J . BINO1 .0

~ 0 . 8

Co 200 mg drn -3w t 1.0gd~: 605 pmo ~ - - Theoret icoL

0 . 6 I I I1 0 0 2 0 0 3 0 0T i m e (m i n )

F i g . 7 . C o n c e n t r a t i o n d e c a y c u r v e f o r t h e a d s o r p t i o n o f S D Son ca rbon .f o r S D S a n d H g 2+ a d s o r p t i o n s h o w a t r e n d c o n s i s t e n tw i t h t h e p o r e d i f f u s i o n m a s s t r a n s f e r p r o c e s s b e i n gr a t e c o n t r o l l i n g . T h e v a l u e s o f k r a n d D c fr a r e s h o w ni n T a b l e 1 f o r a l l t h e r u n s .Est imat ion o f exper imental k , va lues

E q u a t i o n ( 2 8) d e s c ri b e s t h e r a t e o f m a s s t r a n s p o r ti n t e r m s o f a r a t e o f c h a n g e o f a s o l u t e i n t h e l i q u ido r t h e s o l i d p h a s e f o r t h e s y s t e m a s a w h o l e .

d x tN ( t ) = - - V---~- -= W d dQe (28 /b y c a r r y i n g o u t g r a p h i c a l d i f f e r e n t i a t i o n ( d x / d t ) o r

1.o0.8 ~ T h e o r e t i c a t

~ , 0 6

0.4I I I I Io 20 4 0 6 0 an l o o

T i m e ( r a i n )Fig. 8 . Concentra t ion decay curve for the adsorpt ion ofH g2+ on carbon.

( d C t / d t ) c a n b e c a l c u l a t e d . F i g u r e 9 s h o w s t h i sp r o c e s s f o r a p h e n o l - - c a r b o n s y s t e m . O n c e / ~ ' ( t ) i sk n o w n a t f i x e d v a l u e s o f C t , e q u a t i o n s ( 4 ), (5 ) a n d ( 6 )c a n b e u s e d t o d e t e r m i n e k s . , .

S i n c e k r i s e x t r a c t e d f r o m t h e s l o p e o f c o n c e n -t r a t i o n d e c a y c u r v e a t t = 0 . F r o m t h e a p p r o p r i a t ev a l u e o f C t . Q t c a n b e r e a d f r o m t h e r e l e v a n t i s o -t h e r m , a n d a l s o Q e c a n b e l o c a t e d o n t h e i s o t h e r ms i n c e i t e x i s t s i n e q u i l i b r i u m w i t h C s .

I f k s. , i s c a l c u l a t e d u n d e r t h e a s s u m p t i o n o fd i f f u s i o n i n a h o m o g e n e o u s p a r t i c l e t h e f o l l o w i n ge q u a t i o n i s v a l i d f o r t h e b o u n d a r y c o n d i t i o n s o fc o n s t a n t p a r t i c l e s u r f ac e c o n c e n t r a t i o n Q . ..

(Dpo re 7~2"~ ( 4 R2 ~ (29 )k s ' t = \ R 3 ] + \ n D p o ~ t J "

I f t h is d i f f u si o n p r o c e s s o c c u r s w i t h t h e b o u n d a r yc o n d i t i o n o f c o n s t a n t s u r f a c e p a r t i c le c o n c e n t r a t i o n ,t h e n a p l o t o f ( k s . t )2 v s ( I / t ) s h o u l d h a v e a s t r a i g h tr e l a t io n s h i p . F i g u r e s 1 0 a n d 11 s h o w t h e p l o t o f lo g k ,v s l o g t f o r S D S a n d p h e n o l s y s t em s r e s p e c t i v el y . A sw a s s u g g e s t e d b y S p a h n a n d S c h l u n d e r ( 1 9 7 5 ) t h e~ / t - l aw i s i n d e ed o b e y e d.

A c o m p a r i s o n o f e x p e r i m e n t a l a n d t h e o r e t ic a l p a r -t i c le i n t e r n a l m a s s t r a n s f e r m a s s t r a n s f e r c o e f f i c ie n t sa r e s h o w n i n T a b l e 2 . F i v e v a l u e s o f k, ., a r e p r e s e n t e df o r t h e t w o s y s t e m s a t t h e f o l l o w i n g t i m e v a l u e s ; 1 0 ,2 5 , 3 6, 4 9 a n d 6 4 m i n . I t i s o b s e r v e d t h a t t h e s e v a l u e sd o n o t c o m p a r e p a r t i c u l a r l y w e ll i n t h e c a se o f p h e n o lb u t a r e w e l l w i t h i n t h e r a n g e o f a c c u r a c y e x p e c t e d f o rt h e e x p e r i m e n t a l c a l c u l a t io n i n t h e c a s e o f S D S . I t i sn o t i c e d t h a t w h e n t h e c o n c e n t r a t i o n d e c a y c u r v e s a r es t e e p a t t h e i n i t i a l f e w m i n u t e s o f c o n t a c t t i m e ,e x p e r i m e n t a l a n d t h e o r e t i c a l v a l u e s d o n o t m a t c h .B u t f o r s y s te m s s u c h a s S D S t h e c o n c e n t r a t i o n d e c a yc u r v e s a r e m u c h l es s s t e e p t h a n t h o s e o f p h e n o ls y s t e m s a t s i m i l a r e x p e r i m e n t a l c o n d i t i o n s .

T h e f o l l o w i n g o b s e r v a t i o n s c a n b e m a d e f r o m t h ere s u l t s .

( i) E x p e r i m e n t a l a n d t h e o r e t i c a l v a lu e s o f a g i v e ns y s t e m c a n b e f i t t e d w i t h s u f f i c i e n t a c c u r a c y b yi n t r o d u c i n g a c o n s t a n t d i f f u s i o n c o e f f ic i e n t D ,~ rf o r m a s s t r a n s f e r i n s i d e p o r o u s p a r t i c l e s .

T a b l e I. Fil m ma ss transfer and effectivep o r e d i f f u s i o n coefficients or the adsorption of d i f f e r e n tp o l l u t a n t s

C o W d p k r D ~ Y tR u n P o l l u t a n t ( m g d m - 3 ) ( g ) ( m ) C h ( 1 0 - 4 ) ( 1 0 - ~ ) ( m g g - I )I P h e n o l 2 0 0 0 . 8 5 4 2 8 0 . 5 1 5 1 .0 2 . 0 2 0 62 P h e n o l 3 0 0 0 . 8 5 4 2 8 0 . 3 4 3 1 .0 2 . 0 2 0 63 P h e n o l 4 0 0 0 . 8 5 4 2 8 0 . 2 5 7 1 .0 2 . 0 2 0 64 P h e n o l 2 0 0 1 . 7 0 4 2 8 0 . 9 4 1 I .O 2 . 0 2 0 65 P h e n o l 3 0 0 1 . 7 0 4 2 8 0 . 6 8 7 1 .0 2 . 0 2 0 66 P h e n o l 4 0 0 1 . 7 0 4 2 8 0 . 5 1 5 1 . 0 2 . 0 2 0 67 P h e n o l 5 0 0 1 . 7 0 4 2 8 0 . 4 9 5 1 . 0 2 . 0 2 0 68 P h e n o l 6 0 0 1 . 70 4 2 8 0 . 3 4 3 1 . 0 2 . 0 2 0 69 P h e n o l 3 0 0 1 . 70 6 0 5 0 . 6 2 5 1 . 0 2 . 0 2 0 01 0 P h e n o l 5 0 0 3 . 4 0 ' 6 0 5 0 . 7 8 6 1 .0 2 . 0 2 0 0I I P h e n o l 3 2 6 1 . 7 0 3 0 3 0 . 6 4 4 1 .0 2 . 0 2 1 0

1 2 P h e n o l 5 0 9 3 . 4 0 3 0 3 0 . 8 2 5 1 .0 2 . 0 2 1 01 3 p - C h l o r o p h e n o l 5 0 0 1 . 0 0 4 2 8 0 . 4 8 2 1 .2 0 1 0 .0 4 1 01 4 p - C h l o r o p h e n o l 4 0 0 1 . 00 4 2 8 0 . 6 0 3 1 .2 0 1 0 .0 4 1 01 5 p - C h l o r o p h e n o l 3 0 0 1 . 0 0 4 2 8 0 . 8 0 4 1 .2 0 1 0 .0 4 1 0


7/8

Adsorpti on of pollutants 2855 0 0 -

Phenot.4 5 0 C O = 5 0 0 m g d m 3~'~ wt : 1 .79 gE d p = 4 2 8 F m'1o

E 4 0 0 .

350I

o 5 0 l o o 1 5 o 2 0 0T i m e ( r a i n )

Fig. 9. Graphical differentiation of concentration-time curve.

I2 . 5 0

( i i) T h e d i f f u s i v i t y v a l u e m a y b e e i t h e r s m a l l e r o rl a r g e r t h a n m o l e c u l a r d i f f u s i o n c o e f f i c ie n t s i nt h e w a t e r p h a s e .

( i ii ) T h e p o r o s i t y h a s n o r e c o g n i z a b l e e ff e c t o n t h et r a n s f e r m e c h a n i s m .

( iv ) T h e a d s o r p t i o n r a t e ( d n / d T ) c a n b e p r e d i c t e dw i t h a c o n s t a n t d i f f u s i o n c o e f f i c ie n t , Dc ~, w h i c hd e p e n d s s o l e ly o n t h e t e s t sy s t e m a n d c a n b ed e t e r m i n e d i n a s t r a i g h t f o r w a r d b a t c h t e s t s .

( v ) T h e e q u i l i b r i u m i s o t h e r m i s v e r y i m p o r t a n ta n d a c o n s t a n t v a l u e o f a m o n o l a y e r c o v e r a g e ,Y * , c a n b e u s e d t o f i t e x p e r i m e n t a l a n dt h e o r e t i c a l r e s u l t s .

Table 2. Comparison of experimental and theoreticalparticle mass transfer coefficients for SDS and phenolsystemsExperimental TheoreticalPollutant k,, t (m s- i) k,,~ (m s-J )

Phenol 1.5 x 10 -s I.I x 10 -s0.88 x I 0 - 5 0.88 x I 0 - 50.40 x 10 -5 0.63 x 10 -50 .28 x 10 -5 0 .35 x I 0 -50 .12 x 10 -5 0 .23 x 10 -5

S D S 7 . 6 9 x I 0 - 7 9 . 0 0 x I 0 - 75 .00 x 10 -7 6 .92 x 10 -74.1 x 10 -7 5.69 x 10 -73.31 x 10 -7 4.82 x 10 -72.75 x 10 -7 4.10 x 10 -7

- 6 . 1- 6 . 2n- 6 . 3-6.4-6.5

I2 . 3 2 . 4 2 . 5 2 . 6 2 . 7 2 . 8L o g t i m e

Fig. 10. Log particle mass transfer vs log time for SDS.

- 4

- 6 I I I I1.0 1.3 1.5 1.7l o g t i m e

Fig. 1 I. Lo g particle ma ss trans fer vs log time for p henoladsorption.

CONCLUSIONA t w o - r e s i s t a n c e m a s s t r a n s f e r m o d e l h a s b e e n

d e v e l o p e d f o r t h e a d s o r p t i o n o f p o l l u t a n ts o n t oc a r b o n . T h e o r e t i c a l c o n c e n t r a t i o n d e c a y c u r v es w e r eg e n e r a t e d u s i n g a n e x t e r n a l m a s s t r a n s f e r c o e ff i ci e n ta n d a p o r e d i f f u s i o n c o e f f i c ie n t a n d t h e s e w e r e c o r -r e l a t e d , u s i n g a b e s t f i t t e c h n i q u e , a g a i n s t t h e e x p e r i -m e n t a l c u r v e s . I t w a s p o s s i b l e t o c o r r e l a t e a l l t h ee x p e r i m e n t a l c u r v e s , w i t h r e a s o n a b l e a c c u r a c y u s i n ga s i n g l e c o n s t a n t e x t e r n a l m a s s t r a n s f e r c o e f f i c ie n ta n d a s i n g l e c o n s t a n t p o r e d i f f u s i o n c o e f fi c i e n t f o re a c h s o l u t e / c a r b o n s y s te m . A r a p i d a n a l y t i c a l s o l u -t i o n h a s b e e n d e v e l o p e d f o r a d s o r p t i o n s y s te m s i nw h i c h t h e o p e r a t i n g f in e s a n d t i e l in e s t e r m i n a t e o nt h e s a t u r a t i o n m o n o l a y e r o f t h e i s o t h er m .

R E F E R E N C E S

Allen J. B., Joyce R. S. and Kasch R. H. 0967) Meas-urement o f organics in water. 3". Wa t. Pollut . C ontr ol Fed.39, 217-230.Burke T., Hyde R. A. and Zabel T. F. (I980) Performanceand costs of activated carbon for control of organics.I .W .E .S . S e m i n a r - - T r a c e O r g a n i c s , London Institute ofMarine Ensinccrs.


8/8

2 86 G O R D O N M C K A V a n d M U R A D J. B IN O

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adsorption of pollutants from wastewater onto activated carbon based on external mass transfer and...

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