C.L THICKNING

8/8/2019 C.L THICKNING

http://slidepdf.com/reader/full/cl-thickning 1/9

Wat. Res. Vo l. 25, No. 10, pp. 1263-1271, 1991 0043-1354/91 $3.0 0+0 .00Printed in Great Britain. All rights reserved Copyright © 1991 Pergam onPress plc

A D Y N A M I C M O D E L O F T H E

C L A R I F IC A T I O N - T H I C K E N I N G P R O CE S S

I . T A KA C S , G . G . P A T R Y I O a n d D . N O LA SC O

IH y d ro m a n t i s In c . , 1 6 8 5 M a in S t W. , Su i t e 3 02 , H a mi l to n , O n ta r io , Ca n a d a LSS IG 5 a n d2 CH 2 M H i l l En g in e e r in g L td , 1 80 K in g S tree t S o u th , Wa te r lo o , O n ta r io , Ca n a d a N 2 J IP8

(First received M ay 1990; accepted in revised orm March 1991)

A b s t ra c t - -A d y n a m ic mo d e l o f t h e c l a r if i c a t io n - th i c k e n in gprocess is presented. Based o n the solids fluxc o n c e p t a n d o n a ma ss b a l a n c e a ro u n d e a c h l a y e r o f a o n e -d ime n s io n a l set tl er , t h is mo d e l c a n s imu la tethe so l ids prof i le th roug hou t the s e t t l ing colum n, inc luding the und erf low and e ffluent suspended so l idsc o n c e n t ra t io n s u n d e r s t e a d y -st a te a n d d y n a m ic c o n d i ti o n s . Th e mo d e l m a k e s u se o f a sp ec ia l se t t l in gve loc ity equ a t ion designed to s im ula te the se t t ling ve loc ity o f d i lu te and mo re conce ntra ted suspensions.Th e m o d e l c a n b e a p p l i e d to b o th p r im a ry a n d se c o n d a ry se tt le rs t o s imu la t e d y n a mic a n d s t e a d y -s ta t econdi t ion s. Examples based o n fu l l-sca le and p i lo t -sca le exper imenta l da ta taken from the l i te ra ture se rve

to i l lust ra te the appl ica t ion of the m odel to second ary se tt le rs. Resul ts of the ana lysis confi rm tha t themod el can se rve to predic t the e ff luent and underf low suspended so l ids co ncentra t ions under a var ie ty ofc o n d i t i o n s .

Key words--clarifications, dyn amic m odel l ing , h indered se t t ling, s teady-sta te ana lysis , sol ids f lux ana lysis ,t h i c k e n in g

NOMENCLATURE

Ac = surface area of th e clarifier (m )Jd , = downward so l ids f lux due to the bulk move-

me n t o f t h e l i q u id (g /m-d )Jj = dow nwa rd so l ids f lux in layer j (g /m-d)J~ = so l ids f lux due to gravi ty se t t l ing (g /m-d)

-/up = up ward so lids f lux due to the b ulk m ovem ento f t h e l i q u id (g/m-d )

ra in(B, C) = B i f B < C; C i f B > CQi = inf luent flow ra te to the p lant (m3/d)

QR = recycle and w astage flow ra te (m3/d)Xin = inf luent suspended so lids co ncen tra t ion (g /m 3)

X ~n = m in im u m a t t a in a b le su sp e n d e d sol id s c o n c e n -t ra t ion in the e ff luent (g /m 3)

X1= lower suspended so l ids concentra t ion l imi t ofregion II I (g /m 3)

Xu = upper suspend ed so l ids con centra t ion l imi t ofre g io n I I I (g /m 3)

Xt = thres hold suspended so l ids conc entra t io n g /m 3)

~= su sp e n d e d sol id s c o n c e n t ra t io n in l a y e r j (g /m3)

~= non-se t t leable f rac t ion o f the inf luent sus-pended so l ids

rp = se t t l ing param eter associa ted wi th the lowc o n c e n t ra t io n a n d s lo w ly se t t l i n g c o m p o n e n to f t h e su sp e n s io n (m3/g)

r h = se t t l ing param eter assoc ia ted wi th the h inderedse t t l ing component of se t t l ing ve loc i tyequa t ion (m3/g)

Vo = max imu m theore t ica l se t t l ing ve loci ty (m/d)v~ = max imu m prac t ica l se t t l ing veloci ty (m/d)v~ = settl in g velocity (m/d )~, = se t t l ing param eter (m3/g)

INTRODUCTION

T h e s e p a r a t i o n o f s o l id s f r o m w a t e r b y g r a v i t y

s e d i m e n t a t i o n is o n e o f th e m o s t i m p o r t a n t

p h y s i c a l p ro c e s s e s i n a w a s t e w a t e r t r e a t m e n t p l a n t .

S o l i d s - l i q u i d s e p a r a ti o n i s a v i t a l c o m p o n e n t o f e v e r y

b i o l o g i c a l w a s t e w a t e r t r e a t m e n t s y s t e m . I n t h e

p r i m a r y c l a r i fi e r, s e t t le a b l e o r g a n i c m a t t e r i s r e m o v e d

b y g r a v i t y p r i o r t o r e a c h i n g t h e b i o l o g i c a l r e a c t o r . B y

d e s i g n , a c t i v a t e d s l u d g e p l a n t s t r a n s f o r m s o l u b l e

o r g a n i c m a t t e r i n t o b i o m a s s ; t h e e f f e c t i v e o p e r a t i o n

o f t h e p ro c e s s r e q u i r e s t h a t t h e b i o m a s s b e r e m o v e d

f r o m t h e l i q u i d s t r e a m ( i n t h e s e c o n d a r y s e t tl e r) p r i o r

t o b e i n g d i s c h a r g e d i n t h e r e c e i v i n g w a t e r s . P a r t o f

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

r e t u r n e d t o t h e b i o l o g i c a l r e a c t o r t o m a i n t a i n t h e

a p p r o p r i a t e s u b s t r a t e - to - b i o m a s s r a t i o .

N o t w i t h s t a n d i n g t h e i m p o r t a n c e o f t h e s o l i d s -

l i q u i d s e p a r a t i o n p r o c e s s , f e w i n v e s t i g a t o r s h a v e

p r o p o s e d a u n i f i e d s e t t l in g m o d e l d e s i g n e d t o a d d r e s s

t h e c l a r i f i c a t io n a n d t h i c k e n i n g f u n c t i o n s o f s e t tl e rs .

A c c o r d i n g l y , t h e p u r p o s e o f t h is p a p e r i s t o s u g g e s t

a n a l t e r n a t e f o r m o f t h e s e t t l i n g v e l o c i t y m o d e l ,

a l l o w i n g fo r t h e d e v e l o p m e n t o f a u n i f i e d a p p r o a c h

t o d y n a m i c m o d e l l i n g o f t h e c l a r i fi c a ti o n a n d t h i c ke n -

i n g f u n c t i o n s o f s e tt le r s.

THE SOLID-LIQUID SEPARATION PROCESS

D e p e n d i n g o n t h e n a t u r e a n d c o n c e n t r a t i o n o f t he

s o l i d p a r t i c l e s , f o u r t y p e s o f s e t t l i n g c h a r a c t e r i s t i c s

a r e n o r m a l l y e n c o u n t e r e d i n a w a s t ew a t e r t r e a t m e n tp l a n t .

Di scre t e par t i c l e se t t l i ng . A s s o c i a t e d w i t h t h e r e -

m o v a l o f g r it a n d s a n d p a r t i c l e s , d is c r e te p a r t i c l e

s e t t l i n g is c h a r a c t e r i z e d b y s o l i d s w h i c h s e t t l e a s

1263



1264 I. TAKJ,CS et al.

i n d i v i d u a l e n t i t i e s w i t h l i t t l e o r n o i n t e r a c t i o n w i t h

o t h e r p a r t i c l e s .

Floc c u le n t par t i c l e se t t l i ng . T y p i c a l o f t h e t y p e o f

s e t t l i n g f o u n d i n p r i m a r y c l a r i fi e r s , a n d t h e u p p e r

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

s e t t l i n g i s c h a r a c t e r i z e d b y t h e f l o c c u l a t i o n o f s o l i d

p a r t i c l e s a s t h e y s e t t l e t h r o u g h t h e w a t e r c o l u m n .H i n d e r e d s e t t l i n g . S u s p e n s i o n i n w h i c h i n t e r - p a r -

t i c l e f o r c e s h i n d e r t h e s e t t l i n g p r o c e s s . T h e m a s s o f

p a r t i c l e s s e t t l e s a s a u n i t .

C om pre ss ion se t t l i ng . " S e t t l i n g " i s a c h i e v e d b y

c o m p r e s s i o n o f t h e m a s s o f p a r t i c l e s . C o m p r e s s i o n

r e s u l t s f r o m t h e w e i g h t o f p a r t i c l e s a d d e d t o t h e

s y s t e m .

Clari f icat ion

T h e t h e o r y o f d i s c r e t e p a r t i c l e s e t t l i n g h a s b e e n

r i g o r o u s l y a d d r e s s e d ( C a m p , 1 94 5) . G i v e n t h e f a c t

t h a t t h e s o l i ds c o n c e n t r a t i o n i n t h e u p p e r l a y e rs o f t h ec la r i f ie r is su f f ic ien t ly lo w t o r esu l t in d i s c r e te p ar -

t i c le s , o n e w o u l d t h i n k t h a t t h i s t h e o r y c a n r e a d i l y b e

e x t e n d e d t o t h e c l a ri f i ca t i o n c o m p o n e n t o f p r i m a r y

a n d s e c o n d a r y s e t t l in g b a si n s . H o w e v e r , t h e p r o b l e m

d o e s n o t l i e w i t h t h e s e t t l i n g v e l o c i t y t h e o r y , b u t w i t h

t h e f l o c c u l e n t n a t u r e o f t h e s e p a r t i c l e s w h i c h a f f e c t s

t h e p a r t i c l e s iz e d i s t r i b u t i o n f r o m o n e l a y e r t o

a n o t h e r . L i a n d G a n c z a r c z y k (1 98 7) h a v e f o u n d t h e

s e t t l i n g v e l o c i t y o f a c t i v a t e d s l u d g e f l o c p a r t i c l e s t o b e

a l i n e a r f u n c t i o n o f t h e i r c r o s s - s e c t i o n a l d i a m e t e r .

H o w e v e r , l i t t l e e f f o r t h a s b e e n m a d e s o f a r t o p r e d i c t

t h e s i z e d i s t r i b u t i o n o f t h e s o l i d s p a r t i c l e s i n t h e u p p e rl a y e r s o f a s e c o n d a r y c l a r i f i e r a s a f u n c t i o n o f t h e

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

p r o c e ss . R o t h a n d P i n n o w ( 19 8 1) a r e a m o n g t h e f ew

i n v e s t i g a t o r s t h a t h a v e e x a m i n e d t h e p a r t i c l e s i z e

d i s t r i b u t i o n o f s e c o n d a r y c l a r i f i e r e f f l u e n t f r o m

a c t i v a t e d s l u d g e p l a n t s . C o n s e q u e n t l y , a d i r e c t

a p p l i c a t i o n o f t h e d i s c re t e p a r t i c l e s e tt l i ng t h e o r y t o

t h e p r i m a r y a n d s e c o n d a r y c l a r i f ic a t i o n f u n c t i on s i s

p r e m a t u r e .

M o s t o f t he c l a r i f i c a ti o n m o d e l s r e p o r t e d i n t h e

l i t e r a t u r e a r e b a s e d o n a s t a t i s t i c a l a n a l y s i s o f

f u l l -s c a l e p l a n t d a t a , r e l a t i n g t h e e f f l u e nt s u s p e n d e ds o l id s c o n c e n t r a t i o n t o a n u m b e r o f p ro c e s s

p a r a m e t e r s s u c h a s m i x e d - l i q u o r s u s p e n d e d s o l i d s

( M L S S ) , r e c y c l e f l o w r a t e , o v e r f l o w r a t e , c h a n g e i n

o v e r f l o w r a t e , d e t e n t i o n t i m e , a i r f l o w r a t e i n t h e

b i o l o g i c a l r e a c t o r , e t c . C h a p m a n ( 19 84 ) a n d H i l l

( 19 85 ) p r o v i d e a g o o d r e v i e w o f t h e m o r e p o p u l a r

m o d e l s .

T h i c k e n i n g

A s t h e c o n c e n t r a t i o n o f s o l id s i n cr e a s e s, t h e m a s s

o f s o l i d s t e n d s t o s e t t l e a s a u n i t . T h e s e t t l i n g v e l o c i t y

o f th e s l u d g e b l a n k e t h a s b e e n f o u n d t o b e a n o n l i n -e a r f u n c t i o n o f t h e s o l i d s c o n c e n t r a t i o n . H i l l ( 1 98 5 )

p r o v i d e s a c o m p r e h e n s i v e r e vi e w o f t h e m a n y s e t t li n g

v e l o c i ty m o d e l s a p p l i c a b l e to t h e t h i c k e n i n g f u n c t i o n

o f t h e s e t t l e r .

T h e s o l id s h a n d l i n g c a p a c i t y o f a s e t t le r c an b e

a s s e s s e d b y p e r f o r m i n g a l i m i t i n g s o l i d s f l u x a n a l y s i s

( K e i n a t h e t a l . , 1 9 77 ). I n a co n t in u o u s f lo w se t t le r , th e

d o w n w a r d s o l id s fl u x is t h e s u m o f t h e g r a v i t y s e t t l in g

f l u x ( J s ) a n d t h e s o l i d s f l u x d u e t o t h e b u l k m o v e m e n t

o f t h e l i q u i d ( J d n ) , n a m e l y t h e u n d e r f l o w :

J = J ~ + J d n (1 )

E = L Y e , + ~ v , ( 2 )

w h e r e J j - = d o w n w a r d s o l id s fl u x i n l a y e r j ;

J~ = g rav i ty se t t l in g f lu x ; Ja , = s e t t l i n g f l u x d u e t o t h e

b u l k m o v e m e n t o f t h e l i q u i d ; ~ = s o l id s c o n c e n -

t r a t i o n i n l a y e r j ; % = s e t t l i n g v e l o c i t y o f t h e s o l i d s

i n l a y e r . /; v , = u n d e r f l o w v e l o c i t y . D i c k a n d E w i n g

(1 9 6 7 ) , Ves i l in d (19 6 8) an d K ein a t h e t a l . (1 9 7 7 ) h av e

d e s c r i b e d i n d e t a i l t h e t h i c k e n i n g t h e o r i e s u n d e r

s t e a d y - s t a t e c o n d i t i o n s .

D y n a m i c s o f t h e s o l i d s - l i q u i d s e p a r a t i o n p r o c e s s e s

B r y a n t ( 1 9 7 2 ) w a s o n e o f t h e f i r s t t o d e v e l o p a

d y n a m i c m o d e l o f t h e a c t i v a t e d s l u d g e p r o c e s s , i n -

e l u d i n g s o l i d s - l i q u i d s e p a r a t i o n m o d e l s f o r b o t h t h e

p r i m a r y a n d s e c o n d a r y s e t t l e r s . B a s e d o n a v a r i a b l e

t h i c k n e s s / v a r i a b l e n u m b e r o f l a y e r s c o n c e p t , B r y a n t

d e v e l o p e d a c o m p l e x s e t o f h e u r i s t i c s t o g o v e r n t h e

f a t e o f t h e p h y s i c a l d i m e n s i o n s o f a l a y e r w i t h i n t h e

s e c o n d a r y c l a r i f i e r ( i . e . t h e l a y e r ' s a p p e a r a n c e a n d

d i s a p p e a r a n c e d e p e n d i n g o n i t s t h i c k n e s s ) . B r y a n t ' s

m o d e l o f t h e p r i m a r y s e t t l e r w a s n o t a s s o p h i s t i c a t e d

a n d w a s b a s e d o n a s e q u e n c e o f fi v e c o n t i n u o u s f l o w

s t i r re d t a n k r e a c t o r s ( C F S T R ) , s e l e ct e d i n s u c h a w a y

a s t o r e p l i c a t e t h e a p p r o p r i a t e d e t e n t i o n t i m e f o r t h e

sy s tem (e .g . 1 .5 -2 .0 h in h i s case) .

B u s b y (1 9 73 ), S te n s t ro m (1 9 7 6 ) an d H i l l ( 1 9 8 5 )

h a v e a l l m a d e s i g n i f i c a n t e f f o r ts t o i m p r o v e o u r

u n d e r s t a n d i n g o f t h e d y n a m i c s o f t h e t h ic k e n i n g

p r o c e s s u s i n g t h e s o l i d s fl u x t h e o r y i n a o n e - d i m e n -

s i o n a l la y e r e d s e tt l e r. W h i l e B r y a n t a n d B u s b y m a d e

u s e o f a v a r i a b l e n u m b e r o f l a y e r s o f t i m e - v a r y i n g

t h i c k n es s , S t e n s t r o m a n d H i l l us e d a f i xe d n u m b e r o f

l a y e r s o f c o n s t a n t t h i c k n e ss t o d e s c r i b e t h e t h i c k e n i n g

f u n c t i o n o f s e t t l e r s .

R e c e n t l y , V i t a s o v i c (1 98 6, 1 98 9) d e v e l o p e d a m o r e

r i g o r o u s a n a l y s i s o f t h e d y n a m i c s o f s e c o n d a r y s e t -

t i er s , th a t i n c l u d e d c o n s i d e r a t i o n o f t h e u p w a r d b u l k

m o v e m e n t o f t h e l i q u id i n t h e l a y e r s a b o v e t h e f e e d

p o i n t . O u r a p p r o a c h , d e s c r i b e d b ri e fl y i n t h e n e x t

s e c t i o n , i s b a s e d o n t h e w o r k o f V i t a s o v i c ( 1 9 8 6 ) .

H o w e v e r , b e f o r e f o c u s i n g o n t h e d e v e l o p m e n t o f

t h e m o d e l , i t s h o u l d b e e m p h a s i z e d t h a t a l l o f th e

s o l i d s - l i q u i d s e p a r a t o r m o d e l s r e f e r e n ce d s o f a r h a v e

f a i le d to p r o v i d e a u n i f i e d f ra m e w o r k t o p r e d i c t t h e

s u s p e n d e d s o l i d s i n t h e e f f lu e n t o f t h e c l a r i f i e r. I n a l l

c a s es , a u t h o r s h a v e m a d e u s e o f s t a t is t i c a l l y -b a s e d

m o d e l s t o p r e d i c t t h e e f fl u e n t s u s p e n d e d s o l i d s . W h i l et h i s a p p r o a c h m i g h t s e e m l o g i c a l , i t f a il s t o a c c o u n t

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

p r o b l e m c a n b e p a r t i c u l a r l y i m p o r t a n t a s s e t tl e r s

r e a c h f a i l u r e .



M odellin g of settling velocity 1265

Top layer

Feed ayer

Bottom layer

(Qi+Qr )Xin

7

8

9

lO

Qr Xlo= Qr Xrecycle

Fig . 1 . Layered set t ler model.

Qi x 1 =Qi x cfliucnt

I

LAYERED SETTLER M ODEL

V i t a s o v i c ' s (1 9 86 ) m o d e l p r e d i c t s t h e s o l i d s c o n c e n -

t r a t i o n p r o f i l e i n t h e s e t t l e r b y d i v i d i n g t h e s e t t l e r i n t o

a n u m b e r o f l a y e r s ( 10 ) o f c o n s t a n t t h i c k n e s s a s

s h o w n i n F i g . 1 , a n d b y p e r f o r m i n g a s o l i d s b a l a n c e

a r o u n d e a c h l a y e r . V i t a s o v i c ' s m o d e l f a l l s i n t h e s a m e

c l a s s o f o n e - d i m e n s i o n a l m o d e l s a s t h o s e o f B r y a n t

( 1 9 7 2 ) , B u s b y ( 1 9 7 3 ) , S t e n s t r o m ( 1 9 7 6 ) a n d H i l l

( 19 8 5) . A l l o f t h e m , i n c l u d i n g t h e o n e p r e s e n t e d i n

t h i s p a p e r , a r e b a s e d o n t h e f o l l o w i n g a s s u m p t i o n s :

• i n c o m i n g s o l id s a r e d i s t r i b u t e d i n s t a n t a n e o u s l y

a n d u n i f o r m l y a c r o s s t h e e n t i r e c r o s s - s e c t i o n a l

a r e a o f t h e c l a r i f i e r l a y e r ; a n d

• o n l y v e r t i c a l f l o w i s c o n s i d e r e d i n t h e m o d e l .

V i t a s o v i c ' s m o d e l d o e s n o t i n c l u d e a c l a r i f ic a t i o n

c o m p o n e n t . C o n s e q u e n t l y , e f f l u e n t s u s p e n d e d s o l i d s

a r e n o t p r e d i c t e d d u r i n g n o r m a l o p e r a t i n g c o n -

d i t i o n s . H o w e v e r , w h e n t h e s e t t l e r ' s t h i c k e n i n g

a n d / o r s t o r a g e f u n c t i o n f a i l s , t h e m o d e l w i l l p r e d i c t

l a r g e q u a n t i t i e s o f e ff l u e n t s u s p e n d e d s o l i d s . V i t a s o -

v i c ( 1 9 86 ) a r b i t r a r i l y d e f i n e s t h e s l u d g e b l a n k e t h e i g h t

a s t h e h e i g h t o f t h e f i r s t l a y e r w i t h a s o l i d s c o n c e n -

t r a t i o n g r e a t e r t h a n 3 0 00 m g / l .

F i v e d i f f e r e n t g r o u p s o f l a y e r s a r e p r e s e n t i n t h e

p r o p o s e d m o d e l , d e p e n d i n g o n t h e i r p o s i t i o n r e la t i v e

t o t h e f e e d p o i n t . T a b l e 1 s u m m a r i z e s t h e in p u t a n d

o u t p u t o f s o l i d s t o e a c h g r o u p o f l a y e r s , w h i l e t h e

s o l i d s b a l a n c e a r o u n d e a c h t y p e o f l a y e r i s s u m m a r -

i z e d i n F i g . 2 .

V i t a s o v i c ' s m o d e l i s b a s e d o n t h e t r a d i t i o n a l s o l i d s

f l u x a n a l y s i s , w i t h t h e e x c e p t i o n o f t h e t h r e s h o l d

c o n c e n t r a t i o n ( X t ) d e s i g n e d t o l i m i t t h e d o w n w a r d

f l u x o f s o l i d s t o t h a t w h i c h c a n b e h a n d l e d b y t h el a y e r b e l o w . F o r e x a m p l e , a b o v e t h e f e e d l a y e r t h e

f l ux o u t o f l a y e r " j " i s re s t r ic t e d , i f t h e c o n c e n t r a t i o n

i n l a y e r " j + 1 " i s g r e a t e r o r e q u a l t h a n s o m e

t h r e s h o l d v a l u e ( X t ) , i n w h i c h c a s e t h e f l u x o u t o f

l a y e r " j " i s s e t e q u a l t o t h e m i n [ J ( j ) , J(j + 1 ) ] . Th e

s p e ci fi c s o f t h e a l g o r i t h m a r e s u m m a r i z e d i n F i g . 2 .

T h e s o l i d s f lu x d u e t o t h e b u l k m o v e m e n t o f th e

l i q u i d i s s t r a i g h t f o r w a r d t o a s s e s s , b e i n g e q u a l t o t h e

p r o d u c t o f th e c o n c e n t r a t i o n ( X ) a n d t h e b u l k v e l-

o c i t y o f t h e l i q u i d ( V b ), w h i c h c a n b e u p o r d o w n

d e p e n d i n g o n t h e p o s i t i o n o f t h e l a y e r w i t h r e s p e c t t o

t h e f e e d p o i n t .T h e s o l i d s f l ux d u e t o g r a v i t y s e t t l i n g o f t h e s o l i d s

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

( X ) a n d t h e s e t t l i n g v e l o c i t y o f t h e s o l i d s p a r t i c l e s

( v s ) . A s i n d i c a t e d p r e v i o u s l y , s e v e r a l m o d e l s h a v e

b e e n s u g g e s t e d t o d e s c r i b e t h e s e t t li n g v e l o c i ty o f a

m i x e d - l i q u o r . O n e o f t h e m o r e w i d e l y a c c e p t e d

s e t t l i n g v e l o c i t y m o d e l i s t h a t o f V e s i l i n d ( 1 96 8 ):

vs = v0e-~X (3)

w h e r e v ~ = s e t t l i n g v e l o c i t y o f t h e s u s p e n s i o n ;

v0 = m a x i m u m s e t t l i n g v e l o c i ty ; X - - s o l i d s c o n c e n -

t r a t i o n ; a n d • = m o d e l p a r a m e t e r . T h i s m o d e l w a s

u s e d s u c c e s s f u l l y b y H i l l ( 19 8 5 ) a n d V i t a s o v i c ( 1 98 6 ).

H o w e v e r , i t s h o u l d b e r e c o g n i z e d t h a t V e s i l i n d ' s

s e t t l in g v e l o c i ty e q u a t i o n a p p l i e s o n l y t o h i n d e r e d

s e t t l in g c o n d i t i o n s . A s t h e s o l i d s c o n c e n t r a t i o n i n t h e

u p p e r l a y e r s o f t h e c l a r i f ie r d e c r e a s e s b e l o w t h e

h i n d e r e d s e t t l i n g c o n c e n t r a t i o n , s e t t l i n g v e l o c i t i e s

p r e d i c t e d b y V e s i l i n d ' s e q u a t i o n w i l l e x c e e d t h e a c t u a l

s e t t l i n g v e l o c i t y o f t h e f l o c p a r t i c l e s a s p r e d i c t e d b y

L i a n d G a n c z a r e z y k ( 1 9 8 7 ) .

I n a w e l l o p e r a t i n g s e t t l e r , t h e c o n c e n t r a t i o n o f

s o l i d s in t h e u p p e r l a y e r s o f a c l a r i f i e r i n c r e a s e s w i t h

d e p t h . B e c a u s e o f t h e d y n a m i c f o r c e s a c t i n g o n t h e

f l o c p a r t i c l e s a b o v e t h e f e e d p o i n t , t h e p a r t i c l e s i z e

d i s t r i b u t i o n o f t h e f lo c p a r t ic l e s c h a n g e s f r o m o n e

l a y e r to a n o t h e r . I n t h e i r s t u d y o n p a r t i c l e si z e

d i s t r i b u t i o n , R o t h a n d P i n n o w ( 19 8 1) f o u n d t h a t f lo c

p a r t i c l e s i n t h e e f f l u e n t o f s e c o n d a r y c l a r i f i e r s f r o m

a c t i v a t e d s l u d g e p l a n t s , f o l l o w e d a l o g - n o r m a l d i s t r i-

b u t i o n . M o r e r e c e n t l y , P a r r y a n d T a k f i c s ( 1 9 9 1 ) h a v e

Table 1. Layeredsettler model: input-output summary

Layer

I n p u t Output

B u l k l i q u i d B u l k l i q u i d

F e e d S e t t l in g f l u x S e t t l in g f l u x

Top layer - - Up + UpLayers above feed point - + Up + UpFeed layer + + -- + Up-downLayers below feed point - + Down + D o w n

B o t t o m l a y e r - + Down - Down

Note: + = phenomenon considered; - = phenomenon not considered.



1266 I. TAKACS t a l .

J u p, 2 = - -

L a y e r sa b o v e t h ef e e d l a y e r

B u l k G r a v i t ym o v e m e n t _ ~ Q i X l S e l t li n ~

/

T o p Il a y e r

+ Js,l = min(Vs,l Xl ' or Vs,2 X 2

Qi X2 orAC + r Js,l = Vs,l X1 ' i f X2-< Xt

• - - ' rJs,2 = min(Vs,2 X2 ' or V, 3 X 3Qi X 3 or

Jup.3 = - -A C Js,2 = V s,2 X2 ' if X3< X~

J s , 3 = m n(Vs,3 X 3 ' o r \ : 4 X 4

j Q i X 4 d o r

F e e d u p 'n = - - ~ : ~ - " ~ J s , 3 = V s ,3 X ~, ' i f X 4 < X I

l a y e r - ~ ~ , . ~ - f~.:.-.

(Q i + Qr ) Xi n ~ ' :-'~"~

ACQ = min(Vs,4 X 4 , or V~,5 X5)

J d n , 4 -

L a y e r sb e l o w

f e e d l a y e r

B o t t o ml a y e r

Q

J d n , 5 -AC

I

Q r X 9 IJdn,9 -

= min(Vs,5 X 5 , oi vs,6 X6)

= min(Vs,9 X 9 , or VaAoXI0

Fig. 2. Solids balance across set t ler layers.

d e r i v e d a r e l a t i o n s h i p b e t w e e n p a r t i c l e s i z e d i s t r i -

b u t i o n , d e s c r i b e d b y t h e m e a n a n d v a r i a n c e o f t h e l o g

o f th e p a r t ic l e d i a m e t e r s , a n d t h e i r c o n c e n t r a t i o n . A

s i m i l a r e x p r e s s i o n w a s a l s o d e r i v e d f o r t h e a v e r a g e

s e t t l i n g v e l o c i t y o f a f l o c c u l e n t s u s p e n s i o n i n t h e

u p p e r l a y e rs o f a s e c o n d a r y c l a ri f ie r . F i n a l ly , b e c a u s e

o f t h e o p e r a t i o n a l c o n s t r a i n t s o f a s e c o n d a r y c l a ri f ie r ,

P a t r y a n d T a k h c s h a v e s h o w n t h a t t h e a v e r a g e

s e t t l i n g v e l o c i t y o f s o l i d s i n t h e u p p e r l a y e r s o f a

s e c o n d a r y c l a r if i e r c o u l d b e r e l a t e d t o i ts c o n c e n -

t r a t i o n . C o n s i d e r f o r e x a m p l e a l a y e r i n t h e u p p e r

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

p a r t i c l e s i z e d i s t r i b u t i o n . A s t h e o v e r f l o w r a t e

i n c r e a s e s , p a r t i c l e s w i t h a h i g h e r s e t t l i n g v e l o c i t y

( i . e . l a r g e r p a r t i c l e d i a m e t e r ) w i l l b e f l u i d i z e d a n d

c a r r i e d u p w a r d . B e c a u s e p a r t i c le s iz e i s b o u n d e d a t

z e r o , t h i s w i l l r e s u l t i n a l a r g e r m e a n a n d v a r i a n c e i n

t h e l o g o f t h e p a r ti c l e d i a m e t e r s . B a s e d o n t h e

r e l a t i o n s h i p d e r i v e d b y P a t r y a n d T a k :~ c s ( 1 9 9 1 ), t h e

i n c r e a s e i n o v e r f l o w r a t e w i l l r e s u l t i n a l a r g e r s o l i d sc o n c e n t r a ti o n , a s w o u l d h a v e n o r m a l l y b e e n e x p e c t e d

f r o m a n i n c r e as e i n o v e r f lo w r a te . H o w e v e r , a n

i n c r e as e i n t h e m e a n a n d v a r i a n c e o f th e l o g o f t h e

p a r t i c l e d i a m e t e r s w i l l a l s o r e s u l t i n a n i n c r e a s e i n t h e

a v e r a g e s e t t li n g v e l o c i t y o f t h e s u s p e n s i o n a s d e p i c t e d

i n r e g i o n I I o f F i g . 3 .

F r o m a p r a c ti c a l s ta n d p o i n t , t h e c o r r e l a t i o n

b e t w e e n a v e r a g e s e t t l in g v e l o c i t y a n d s o l id s c o n c e n -

t r a t i o n ( r e g i o n I I , F i g . 3 ) i s v a l i d f o r l o w s o l i d s

>

v~

\\

\\

\\

\

X m i n X 1 X u

Concentration (X)

Fig. 3. Sett l ing velocity mo del.



Modelling of settling velocity 1267

c o n c e n t r a t i o n . A s t h e s o l i d s c o n c e n t r a t i o n i n c r e a s e s ,

a r e g i o n e x i s t s ( r e g i o n I I I , F i g . 3 ) w h e r e t h e a v e r a g e

s e t tl i n g v e l o c it y o f t h e s u s p e n s i o n r e a c h e s a m a x i -

m u m u p p e r l i m i t. T h i s c o r r e s p o n d s t o t h e t r a n s i t io n

z o n e b e t w e e n t h e l o w s o l i d s c o n c e n t r a t i o n r e g i o n

( r e g i o n I I ) a n d h i n d e r e d s e t tl i n g c o n d i t i o n s ( r e g i o n

I V ) . O s s e n b r u g g e n a n d M c I n t i r e ( 1 9 9 0 ) h a v e a l s os u g g e s t e d t h a t a m a x i m u m p r a c t i c a l s e t t l i n g v e l o c i t y

b e u s e d b e l o w t h e h i n d e r e d s e t t l i n g c o n c e n t r a t i o n .

A s s u m i n g m a x i m u m f lo c p a r ti c le d i a m e t e r s o f

1 - 2 m m i n th i s c o n c e n t r a t i o n r a n g e w o u l d r e s u l t i n

f l o c p a r t i c l e s e t t l i n g v e l o c i t i e s i n t h e r a n g e o f

1 7 5 - 4 0 0 m d - ~ ( L i a n d G a n c z a r c z y k , 1 9 87 ).

M a t h e m a t i c a l l y , t h e g e n e r a l i z e d s e t t l i n g v e l o c i t y

m o d e l c a n b e r e p re s e n te d a s t h e s u m o f t w o e x p o n e n -

t i a l t e r m s :

v~ j = Vo e - ' hx ; - Voe - ' ~ x ; (4 )

0 ~< v,j ~< v ~ (5 )

w h e r e v . j = s e t t i n g v e l o c i t y o f t h e s o l i d s p a r t i c l e s i n

l a y e r / ( m / d ) ; v o = m a x i m u m s e t tl in g v e l o c i t y ( m / d ) ;

r h = s e tt l in g p a r a m e t e r c h a r a c t e r i s t ic o f t h e h i n d e r e d

s e t t li n g z o n e ( m 3 /g ); r p f fi s e t t li n g p a r a m e t e r c h a r a c -

e r i s t ic o f l o w s o l i d s c o n c e n t r a t i o n ( m 3 /g );

X j* = X j - X m m ; X j = s u s p e n d e d s o l id s c o n c e n t r a t i o n

i n l a y e r j (g / m 3 ) ; X i = m i n i m u m a t t ai n a b l e s u s-p e n d e d s o l i d s c o n c e n t r a t i o n ( g/ m 3) ; X ~ = f ~ , ~ m ;

X io = m i x e d - l i q u o r s u s p e n d e d s o l i d s e n t e r i n g t h e s e t -

t l e r ( g / m 3 ) ; f ~ = n o n - s e t t l e a b le f r a c t i o n o f X ~ . A s

d e p i c t e d i n F i g . 3 , v ,j r e a c h e s a m a x i m u m v a l u e o f v ~

i n t h e r a n g e o f X I - X ~ , w h e r e X I a n d X ~ r e p r e s e n t

t h e lo w e r a n d u p p e r c o n c e n t r a t i o n s o f re g i o n I I I ,

r e s p e c t i v e l y .

T h e f i r s t t e r m (vo e -~hx~ ) i n e q u a t i o n ( 4 ) r e fl e c ts t h e

s e t t l i n g v e l o c i t y o f t h e l a r g e , w e l l f l o c c u l a t i n g p a r -

t i c l e s . O n t h e o t h e r h a n d , t h e s e c o n d t e r m ( v 0e - ' p x ] )

o f e q u a t i o n ( 4 ) is a v e l o c i ty c o r r e c t i o n f a c t o r t o

a c c o u n t f o r t h e s m a l l e r , s l o w l y s e t t l i n g p a r t i c l e s .

100000

]o o

io

1.r,0000

10G00

1000

100

10

100000

10000

I(X)O ,

1(30,

l • Data- - e -- - Mode l

r

!

2

10 ,

0

(a) Low Load Experiment

Layer number

( b ) M e d i u m L o a d E x p e r i m e n t

/

~ le_ Data- Model

r . . . ~ , . - . - ~4

o a t . iModol

(c)Hi

. . . . . , f

JJ

/ /

Layer number

~h Lo ad Ex periment

/

6

Layernumber

Fig. 4. Observed and simulated concentration profiles.

.- 4

__ ,d

8 10

WR 25/IO--H



1268 1. TAKJ~CS t al.

F o u r r e g i o n s a r e o f i n t e re s t i n e q u a t i o n ( 4) :

X < Xmj~

I n t h i s r e g i o n , t h e s e t t l i n g v e l o c i t y i s s e t e q u a l t o

z e r o , a s t h e s u s p e n d e d s o l i d s c o n c e n t r a t i o n r e a c h e s

t h e m i n i m u m a t t a i n a b l e c o n c e n t r a t i o n .

Xmin < X <~ Xl ]

I n t h i s r e g i o n , t h e s e t t l i n g v e l o c i t y i s d o m i n a t e d b y

th e s lo wly se t t l in g p ar t ic les ; in th i s case , v s i s mo s t

sen s i t iv e to rp .

x,<x<xoj

I n t h i s c o n c e n t r a t i o n r a n g e ( t y p i c a l l y b e t w e e n

2 0 0 - 2 0 0 0 g / m 3) th e s e t t l i n g v e l o c i t y i s i n d e p e n d e n t

o f c o n c e n t r a t i o n . F l o c p a r t i c l e s re a c h t h e i r m a x i -

m u m s i z e r e s u l t i n g i n a n a v e r a g e s e t t l i n g v e l o c i t yt h a t i s m o r e o r l e s s i n d e p e n d e n t o f c o n c e n t r a t i o n

( v ~ ) .

X > X u l

I n t h i s r e g i o n , t h e e f f e c t ( c o r r e c t i o n f a c t o r ) o f t h e

s l o w l y s e t t l i n g p a r t i c l e s i s s m a l l i n c o m p a r i s o n t o

t h e t o t a l s e t t l i n g v e l o c i t y . T h e s e t t l i n g v e l o c i t y i s

m o s t s e n s i t iv e t o r h a n d t h e m o d e l e f f e c ti v e l y

r e d u c e s t o V e s i l i n d ' s e q u a t i o n .

T h i s s e t t l in g v e lo c i t y m o d e l w a s f o u n d t o p r o d u c e

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

p e n d e d s o l i d s c o n c e n t r a t i o n u n d e r b o t h s t e a d y - s t a t e

a n d d y n a m i c c o n d i t i o n s .

A s s e s si n g m o d e l p a r a m e t e r s

I n t h i s s t u d y m o d e l p a r a m e t e r s w e r e a s s e ss e d b a s e d

o n a n a n a l y s i s o f fi e ld a n d p i l o t - sc a l e e x p e r i m e n t a l

d a t a . I n a l l c a s e s, S I M U S O L V ( S t e i n e r e t a l . , 1987),

a n o n - l i n e a r d y n a m i c o p t i m i z a t i o n p a c k a g e w a s u s e d

f o r m o d e l p a r a m e t e r i d e n t i f i c a t i o n .

A l t e r n a t i v e l y , m o d e l p a r a m e t e r s o f t h e p r o p o s e d

s e t tl i n g ve l o c i ty m o d e l c o u l d b e a s s e s s ed t h r o u g h a

c o m b i n a t i o n o f l a b o r a t o r y e x p e ri m e n t s a n d n o n -

l i n e a r o p t i m i z a t i o n t e c h n i q u e s ( K e n n e d y , 1 99 1) . F o r

e x a m p l e , f n s, t h e m i n i m u m e f f lu e n t s u s p e n d e d s o l i d s

c a n r e a d i l y be m e a s u r e d i n a s e t t l in g c o l u m n a n a l y s is .

A n e s t i m a t e o f t h e m a x i m u m p r a c t i c a l se t t li n g v e l-

o c i t y , v 6, c a n b e o b t a i n e d b y d i l u t i n g t h e m i x e d l i q u o r

t o 1 - 2 g / l , a n d m e a s u r i n g t h e s e t t l i n g v e l o c i t y o f t h e

l a r g e i n d i v i d u a l f l o c p a r t i c l e s . V e s i l i n d ' s h i n d e r e d

s e t t li n g v e l o ci t y m o d e l p a r a m e t e r s , v0 an d r h , can b e

m e a s u r e d t h r o u g h a s e r i es o f c o l u m n s e t tl i n g t e s ts

( V e s i l i n d , 1 9 6 8 ; K e i n a t h e t a l . , 1977) . Finally , rp is

b e s t a s s e ss e d u s i ng a n o n - l i n e a r o p t i m i z a t i o n s e a r c h

t e c h n i q u e , s u c h a s t h e o n e c o n s i d e r e d i n t h i s s t u d y .

A P P L I C A T I O N O F T H E M O D E L

T W O e x a m p l e s w i l l s e r v e t o i l l u s t r a t e t h e a p p l i -

c a t i o n o f t h e s e t t l i n g v e l o c i t y m o d e l . I n t h e f i r s t

e x a m p l e , t h e m o d e l w i l l b e a p p l i e d t o f u l l- s c a le d a t a

c o l l e c t e d b y P f l a n z ( 19 69 ) a s s u m i n g t h a t s t e a d y - s t a t e

c o n d i t i o n s p r e v a i l e d a t t h e t i m e o f t h e e x p e r i m e n t s .

I n t h e s e c o n d e x a m p l e , d y n a m i c d a t a c o l l e c t e d a t

p i l o t s c a l e ( T h o m p s o n , 1 98 8) w i l l b e u s e d t o a s s e s s

t h e p o t e n t i a l o f t h e m o d e l u n d e r t r a n s i e n t c o n d i t i o n s.

P f l a n z f u l l - s c a l e d a t a

P f l a n z (1 96 9) c a r r i e d o u t e x p e r i m e n t s t o d e t e r m i n et h e s e t t l i n g c h a r a c t e r i s t i c s o f s l u d g e s u n d e r d i f f e r e n t

c o n d i t i o n s . I n o n e o f h i s e x p e r i m e n t s a t C e l l e , h e

p r o v i d e d s o l i d s p r o fi l e s i n a f i n a l s e t t l i n g t a n k w i t h

s u f fi c i e n t d e t a i l t o c a l i b r a t e t h e m o d e l p r e s e n t e d

e a r l i e r .

T h e h i g h - r a t e a c t i v a t e d s l u d g e t r e a t m e n t p l a n t

r e c e i v e d m a i n l y d o m e s t i c w a s t e w a t e r . P f l a n z

m e a s u r e d t h e s u s p e n d e d s o l i d s c o n c e n t r a t i o n s a t

s e v e n p o i n t s a l o n g t h e r a d i u s o f t h e c i r c u l a r s e c -

o n d a r y s e t t l e r a n d a t t e n p o i n t s a l o n g i t s d e p t h . F o r

t h e p u r p o s e o f t h i s a n a l y s i s , t h e t w o - d i m e n s i o n a l

s u s p e n d e d s o l i ds c o n c e n t r a t i o n d a t a b a s e w a s f i l te r e d

a n d t h e d a t a w e i g h t e d w i t h r e s p e c t t o t h e c r o s s - s e c -

t i o n a l a r e a o f t h e c l a r i f i e r p r i o r t o b e i n g r e d u c e d t o

o n e - d i m e n s i o n a l s o l i d s p ro f il e s. A s u m m a r y o f t h e

c h a r a c t e r i s t i c s o f t h e t h r e e e x p e r i m e n t a l c o n d i t i o n s

c o n d u c t e d b y P f l a n z i s p r e s e n t e d i n T a b l e 2 .

T h e s e tt le r m o d e l w a s c o d e d i n A C S L ( A d v a n c e d

C o n t i n u o u s S i m u l a t i o n L a n g u a g e ) , a c o n t i n u o u s

s i m u l a t i o n l a n g u a g e d e v e l o p e d b y M i t c h e l l & G a u -

t h i e r ( 1 9 8 6 ) . M o d e l p a r a m e t e r s w e r e e s t i m a t e d u s i n g

S I M U S O L V , a n i n t e g r a t e d m u l t i - f u n c t i o n a l p a r -

a m e t e r e s t i m a t i o n a n d o p t i m i z a t i o n p a c k a g e c o u p l e d

t o A C S L ( S t e i n e r e t a l . , 1 98 7). S I M U S O L V w a s u s e d

t o i d e n t i f y a c o n s i s t e n t s e t o f m o d e l p a r a m e t e r s f o r

e a c h o f t h e t h r e e d a t a s e ts .

R e s u l t s o f t h e a n a l y s i s a r e p r e s e n t e d i n F i g . 4 ( a - c ) ,

w h e r e t h e l o g a r i t h m o f t h e s o l i d s c o n c e n t r a t i o n i s

p l o t t e d a s a f u n c t i o n o f d e p t h . A l o g a r i t h m i c s c a le

w a s c h o s e n f o r t h e s o l id s c o n c e n t r a t i o n t o p r o v i d e

m o r e d e t a i l a t l o w e r c o n c e n t r a t i o n s . M o d e l p a r -

a m e t e r s f o r e a c h o f t h e t h r e e e v e n t s a r e s h o w n i n

Table 2. Sum mary of the experimentalcond itions Pflanz, 1969)

Suspended solids Mass of SS

Detention SludgeF lo w time r eturn In p u t R ec y c le Lo ad in g Ou tp u tEx perim ent (m3 /h) (h) (m3/h) (g/I) (g]l) (t/d) (t/d)

Low lo ad 360 5.0 300 5.62 12.87 89.0 92.8Mediu m lo ad 450 4.0 300 5.52 12.80 99.4 92.3High lo ad 600 3.0 300 5.10 14.72 110.2 106.2



Modelling o f settling velocity

T a b l e 3 . M o d e l p a r a m e t e r s f i t te d t o P f l a n z f u ll - s ca l e d a t a s e t s

P a r a m e t e r L o w l o a d M e d i u m l o a d H i g h l o a d

v0 (m / d ) 2 1 4 . 2 3 7 0 . 0 1 7 2 . 8

v ~ (m / d ) 1 5 0 . 2 1 4 2 . 9 1 1 2. 1

rp (m3/g) 5 .71 x 10 -3 2 .86 x 10 3 2 .70 × 10 3

r h (m 3 / g ) 3 . 6 4 x 1 0 -4 3 . 7 8 x 1 0 4 2 . 9 3 × 1 0 -4

f , ~ ( - - ) 1 . 2 3 × 1 0 3 2 . 2 8 × 1 0 -3 2 . 5 9 x 1 0 -3

i n p ( 6 ) ( - - ) 0 . 0 0 0 . 11 0 . 2 4

i n p ( 7 ) ( - - ) 1 . 0 0 0 . 8 9 0 . 7 6

N o t e : i n p ( 6 ) a n d i n p ( 7 ) r e p r e s e n t t h e f r a c t i o n o f t h e f e e d d i s t r i b u t e d

t o t h e s i x t h a n d s e v e n t h l a y e r s , r e s p e c t i v e l y , w i t h

i n p (6 ) = 1 - i n p (7 ) .

Tab le 3 wh ile resu lt s o f the s imu la t ion a re p resen ted

i n Ta b l e 4 .

Based o n the resu l t s o f the ana lys i s , it is appar en t

tha t the e f f luen t suspended so l id s p red ic t ions a re

e x c e l l e n t - -d e v i a t i n g f ro m t h e r e c o rd e d v a l u e s b y

appro x . 1% ( i.e. a max im um of 0 .1 g/m3). In genera l ,

the underf low concen t ra t ion i s a l so very wel l s imu-

la ted by the model . D ev ia t ion s o f 1 .1 , 13 .8 and 18 .2%

f ro m t h e o b s e rv e d u n d e r f l o w c o n c e n t r a t i o n s h a v e

b e e n r e c o rd e d fo r t h e lo w , m e d i u m a n d h i g h l o a d

cond i t ions , respec t ive ly . The la rges t d i sc repancies

b e t w e e n o b s e rv e d a n d s i m u l a t e d s o l i d s c o n c e n -

t r a t i o n s a r e fo u n d a ro u n d t h e f e e d l a y e r .

H o w e v e r , i n a s s e s s in g t h e r e s u lt s o f t h e s i m u l a t i o n

i t s h o u l d b e e m p h a s i z e d t h a t t h e d e t a i l s s u r ro u n d i n g

P f l a n z ' s e x p e r i m e n t s w e re n o t a v a i l a b l e f ro m t h e

p u b l i s h e d r e p o r t s . F o r e x a m p l e , i n s i m u l a t i n g t h e

l o w , m e d i u m a n d h i g h l o a d c o n d i t i o n s , s t e a d y - s t a t e

c o n d i t i o n s h a d t o b e a s s u m e d fo r e a c h o f t h e t h r e e

even ts . I t i s easy to ver i fy tha t th i s as sumpt ion i s no t

s t r i c t ly va l id fo r the exper ime n ts , as the m ass o f so lid s

en ter ing the c la r i f i e r i s l a rger than the mass o f so l id s

leav ing the se t t l e r (i .e . 3 -7 tonn es /d ) . A ccord ing ly , fo r

t h e m e d i u m a n d h i g h l o a d c o n d i t i o n s , t h e m o d e l w a s

fo rc e d t o o v e rp re d i c t t h e u n d e r f l o w c o n c e n t r a t i o n s

because th i s was necessary to reach s teady-s ta te .

N o t w i t h s t a n d i n g t h i s d i s c r e p a n c y , t h e m o d e l w a s

a b l e t o r e p l ic a t e t h e g e n e ra l b e h a v i o u r o f t h e s o l id s

p ro f i l e fo r a l l th ree exper imen ts . In add i t ion , the

m o d e l w a s a b l e t o p r e d i c t th e d e p t h o f t h e s l u d g e

b l a n k e t m e a s u re d b y P f l a n z .

W h i l e m o d e l p a r a m e t e r s v a r ie d f r o m o n e c o n d i t i o n

to ano ther , the range o f va lues is no t un rea l i s t i ca l lyla rge g iven the l imi ted da ta ava i lab le .

F eed dis tr ibut ion to the c lari fier . In h i s paper , P f lanz

d id no t p rov ide su f f ic ien t de ta i l s abou t the phys ica l

T a b l e 4 . O b s e r v e d a n d s i m u l a t e d

S u s p e n d e d s o l i d s c o n c e n t r a t i o n ( g / m 3 )

1269

charac te r i s t i cs o f the se t t l e r to p roper ly as sess the

feed d i s t r ibu t ion to the se t t l e r . However , an ana lys i s

o f t h e c o n c e n t r a t i o n p ro f il e s r ev e a l s t h a t t h e f e e d

l a y e r m u s t h a v e b e e n a b o v e t h e e i g h t h l a y e r w h e re

zone se t t l ing cond i t ions p reva i led . S imi la r ly , the feed

l a y e r h a d t o b e b e l o w t h e f i ft h l a y e r b e c a u se o f t h e

l o w s o l i ds c o n c e n t r a t i o n i n a n d a b o v e t h e f i ft h la y e r .A c c o rd i n g l y , t h e s i x t h a n d s e v e n t h l a y e r s w e re c o n -

s idered as po ten t ia l fee d po in t l ayers . The feed d is t r i -

b u t i o n b e t w e e n l a y e r s is a f u n c t i o n o f th e h y d ra u l i c

r e g i m e . W h i l e t h e p ro p o s e d m o d e l d o e s n o t p r e t e n d

t o s i m u l a t e t h e d y n a m i c s o f f e ed p o i n t d i s t r i b u t i o n ,

i t does a l low the f l ex ib i l i ty to hand le mul t ip le feed

layer cond i t ions , to re f lec t more c lose ly f i e ld con-

d i t ions . Op t imized resu l t s a re shown in Tab le 3 . As

i t t u rn s o u t , m o s t o f th e f e e d h a d t o b e d i s t r i b u te d t o

l a y e r 7 . H o w e v e r , a s t h e h y d ra u l i c l o a d i n c r e a s e d , a

l a rg e r f r a c t i o n o f th e f e e d h a d t o b e d i s t r ib u t e d t o

layer 6 .

P i l o t - s c a l e e x p e r i m e n t s

Th o m p s o n (1 9 8 8 ) in v e s t ig a t e d t h e b e n e fi ts o f s t e p

fe e d i n r e d u c i n g t h e i m p a c t o f s t o rm f lo w s , u s in g t h e

2 8 8 m 3 / d p i l o t p l a n t l o c a t e d a t t h e W a s t e w a t e r Te c h -

n o l o g y C e n t r e i n B u r l i n g t o n (O n t a r i o , C a n a d a ) .

U s i n g h i s d a t a , e f fo r t s w e re m a d e t o c a l i b r a t e t h e

s e t t l i n g v e l o c i t y m o d e l u n d e r d y n a m i c c o n d i t i o n s .

Th e p i l o t p l a n t c o n s i s ts o f t h r e e a e r a t i o n t a n k - i n -

series fo l low ed by a f inal sett ler . Set t led sew age

e n t e r i n g t h e p l a n t c a n b e f e d t o a n y o f th e t h r e e

r e a c t o r s . Th e s e c o n d a ry s e tt le r h a s a s i d e w a t e r d e p t h

o f 2 .7 m, wh i le the overf low ra te to the se t t l e r was se t

to 27 .6 m/d . A con s tan t recyc le was used in the s tudy .

Th e c h a ra c t e ri s t ic s o f t h e p l a n t a r e s u m m a r i z e d i n

m o re d e t a i l b y Th o m p s o n (1 9 8 8 ) .

A m a t h e m a t i c a l m o d e l o f th e p i l ot p l a n t w a s

c o n s t ru c t e d u s i n g a l i b r a ry o f d y n a m i c m o d e l s d e v e l -

ope d by Pa t ry a nd T akf ics (1990). T he b io log ica l

r e a c t o r s w e r e m o d e l l e d u s i n g t h e I A W P R C T a s k

G r o u p m o d e l o f th e a c t i v a t e d s l u d ge p ro ce s s . D e t a i ls

o f t h e m o d e l a r e g i v en e l s ew h e re (H e n z e e t a l . , 1987).

Th e s e tt le r m o d e l d e s c r ib e d e a r l ie r w a s c o u p l e d t o t h e

a c t i v a t e d s l u d g e m o d e l p ro v i d i n g a c o m p l e t e r e p -resen ta t ion o f the p ilo t p lan t .

N o m a j o r c a l i b r a t i o n w a s n e e d e d fo r t h e a c t i v a t e d

s l u dg e p o r t i o n o f th e m o d e l , h o w e v e r p a r a m e t e r s o f

s u s p e n d e d s o l i d s c o n c e n t r a t i o n s ( g / m 3)

L o w l o a d M e d i u m l o a d H i g h l o a d

L a y e r s O b s e r v e d S i m u l a t e d % D i f f . O b s e r v e d S i m u l a t e d % D i f f . O b s e r v e d S i m u l a t e d % D i f f .

l 9 .0 9 .1 I . I 15 .6 15 .7 0 .6 30 .7 30 .8 0 .3

2 10 .7 11 .2 4 .7 14 .8 18 .9 27 .7 41 .4 42 .9 3 .6

3 13 .6 14 .1 3 .7 21 .8 23 .6 8 .3 59 .4 58 .5 1 .5

4 2 3 . 8 1 9 . 5 1 8 .1 2 9 . 9 3 2 . 9 1 0 .0 8 8 . 6 8 7 . 4 1 .4

5 3 5 . 0 3 3 . 8 3 . 4 5 8 .8 5 9 . 2 0 . 7 1 3 5 . 5 1 6 3 . 5 2 0 . 76 6 6 . 6 9 6 . 6 4 5 . 0 2 7 4 . 2 1 8 7 . 4 2 4 . 2 5 6 7 . 7 4 8 1 . 1 1 5 .3

7 7 8 7 . 1 7 0 6 . 7 1 0 . 2 9 3 3 . 0 8 2 6 . 0 1 1 . 5 1 2 7 3 . 6 1 3 7 7 . 6 8 . 2

8 5 2 8 0 . 8 4 6 1 8 . 9 1 2 . 5 5 2 6 3 . 6 6 1 3 0 . 3 1 6 . 5 6 9 9 9 . 4 8 3 0 8 . 6 1 8 .7

9 1 0 0 2 1 . 5 9 1 2 4 . 4 9 . 0 1 0 4 8 1 . 9 1 0 6 9 9 . 6 2 .1 1 0 6 1 3 . 5 1 1 9 0 1 . 0 1 2 .1

10 12487.2 12353.1 1 .1 12100.1 1376 6.5 13 .8 1289 3.0 1523 8.4 18 .2



1270 I. TAK.kCS t al.

the settling velocity model were adjusted to reflect

more closely the actual behaviour of the secondary

clarifier. The calibrated set of model parameters are:

v0 = 712.0 m/d;

v~ = 340.0 m/d;

r h = 4.26 x 10 -~ m3/g;

rp = 5.0 x 10 -3 m3/g;

and fn~ = 1.0 X 10 -~.

The model was verified against two sets of exper-

iments: (a) storm flow conditions without step feed;

and (b) storm flow condi tions with step feed to the

second reactor. The analysis focused on the solids

distribution within the settler, the sludge blanket

height, and the effluent suspended solids.

S t orm f l ow cond i ti ons w i t hou t s t ep f eed . Results of

the simulation under storm flow conditions without

step feed are shown in Fig. 5(a) and (b) and compared

with the recorded observations. Storm flow con-

ditions were simulated by an abrupt change in

flowrate from 200 to 500 l/s, while the recycle flowrate

was kept constant. This produced an increase in the

sludge blanket height (H~) and consequently a high

effluent suspended solids value once the sludge blan-

ket reached the weirs [Fig. 5(b)].

As observed by Thompson (1988), the effluent

suspended solids concentration (ESS) is relatively

'9 o

x

~ t

._~

x

,o ( o ) . . . .

i T - ~ . . . . q . . . . . .

i i i

° . . . . . . . ! . . . . . . . . . ! . . . .

4 . . . . 4 : ] J _ i - - ~ - - ~ - _

2 . . . . . . . . . . . . L

o o o 0 2 o 4 o 6 o , 8 1 . 0

Time , days

~ E 8 0

v )

( b ) = ' si

. . . . . . . . . . . . . . . . . . . . . . .

r _ ¢ r

i

l

2 0 . . . . . ~. . . . . I

i • e l •

0 - t - - o

o o 0 2 0 4 0 6 0 . 8 1 0

Time,days

Fig. 6. Storm flow with step feed to second reactor.

1 o ~ T t

i i J

i i i

" : " i r t

8 . . . . . ; - - T . . . . . i - - - - - - ]

~ o i r k i

~ 6 _ ~ . . . . . . L _ _ , _ _ _ J . . . . . . . .= i t t0 R e a c t o r # 1 ( ~ ) I

. . . . . / . . . . . . . L . . . . . ~ 1 _ _ ° - _ _ J4I • ~ t - ~ -

t e o e l !

~ i • t i

~ ; t t i t

o f I I I

o o 0 2 0 4 0 . 6 0 8 1 0

Time,day s

~ E 8 O

~ o

0

O 0

n n

( b ) ' , i ',i i t i

i t t

F t

r t tE r i i

= l . . , ~ _ | i il i

t l I I

~ i a i t

. . . . i _ J _

i i

: 2 1 i 1i t i i

i e b t ~* . ,

o 2 0 . 4 0 . 6 0 8

T ime , d a y s

F i g . 5 . S t r o m f l o w w i t h o u t s t e p t e e d .

4

i2

3I

F

0

1 0

independent of the sludge blanket height until the

moment the bl anke t reaches the weir level. The sludge

blanket, as well as the effluent suspended solids

concentration, returned to their normal levels once

normal flow conditions were re-established. The

solids concentration in the reactors was drastically

reduced during storm flow. A 40% reduction in the

MLSS concentrat ion in each reactor was observed in

the model [Fig. 5(a)]. This reduction is in close

agreement with Thompson's results. The mixed-

liquor suspended solids in the first and third reactors

are plotted in Fig. 5(a). The decrease in the MLSS

concent ration is well simul ated-- however the recov-

ery is underestimated by the model. A possible expla-

nation for this discrepancy lies in the fact that the

mass of solids lost from the settler during storm flow

is not known precisely. Accordingly, it is possible that

the actual mass of solids washed out from the pilot

plant could have been significantly smaller than that

predicted by the model.

S t o r m f l o w c o n d it io n s w i t h s te p f e e d t o t h e s e c o n d

reac t or . To prevent a significant loss of solids during

storm flow conditions, Thompson (1988) experi-

mented with a n umbe r of step feed control measures.

In this particula r set of experiments, the opera tionalstrategy was to step feed the settled sewage to the

second reactor during storm flow conditions. The

simulated and observed results are shown in Fig 6(a)

and (b).



Modelling of settling velocity 1271

A s s h o w n i n F i g . 6 ( a ) , t h e f i r s t r e a c t o r w a s u s e d t o

s t o r e t h e b i o m a s s d u r i n g t h e s t o r m , w h i l e s o l i d s f r o m

t h e t h i r d r e a c t o r w e r e w a s h e d o u t , d e c r e a s i n g t h e

s o l i d s l o a d i n g t o t h e s e t t l e r . I n i t i a l l y , t h e h e i g h t o f t h e

s l u d g e b l a n k e t r o s e s l i g h t l y , h o w e v e r t h i s t e n d e n c y

w a s s o o n r e v e r s e d [ F i g . 6 ( b) ] . S i m u l a t e d a n d

m e a s u r e d e f fl u en t s u s p e n d e d s o l i d s a r e i n c l o s e a g r e e -m e n t .

I n g e n e r a l , t h e m o d e l w a s a b l e t o r e p l i c a t e f a i r l y

c l o s e ly t h e t r e n d s i n M L S S , e f f lu e n t s u s p e n d e d s o l i d s ,

a n d s l u d g e b l a n k e t h e i g h t u n d e r a v a r i e t y o f d y n a m i c

e v e n t s. T h e d i s c r e p a n c i e s b e t w e e n t h e o b s e r v e d a n d

s i m u l a t e d r e s u l t s f a ll w i t h i n t h e e x p e c t e d r a n g e o f

a c c u r a c y f o r s u c h c o m p l e x m o d e l s . I t s h o u l d b e

n o t e d , t h a t T h o m p s o n ' s e x p e r i m e n t s w e r e n o t

i n i t i a ll y d e s i g n e d f o r d y n a m i c m o d e l l i n g p u r p o s e s .

A c c o r d i n g l y , a f u l l s o l i d s p r o f i le a n d b a l a n c e w e r e n o t

a v a i l a b l e f o r t h i s i n v e s t i g a t i o n .

CONCLUSIONS

A m u l t i - l a y e r d y n a m i c m o d e l o f t h e c l a ri f ic a -

t i o n / t h i c k e n i n g p r o c e s s w a s p r e s e n t e d . B a s e d o n t h e

s o l i d s f l ux c o n c e p t a n d a m a s s b a l a n c e a r o u n d e a c h

l a y e r o f a o n e - d i m e n s i o n a l s e t t l e r , t h e m o d e l i s d e -

s i g n e d t o p r e d i c t t h e s o l i d s p r o f i le a l o n g t h e s e t t l in g

c o l u m n , i n c l u d i n g t h e e ff lu e n t a n d u n d e r t o w s u s -

p e n d e d s o l i d s . T h e m o d e l p r o v i d e s a u n i f i e d f r a m e -

w o r k f o r t h e s i m u l a t i o n o f t h e c l a r i f i c a ti o n a n d

t h i c k e n i n g p r o c e s s e s u n d e r b o t h s t e a d y - s t a t e a n d

d y n a m i c c o n d i t i o n s . T h e m o d e l w a s a p p l i e d t o b o t hp i l o t s c a le a n d f u ll s c al e e x p e r i m e n t a l d a t a w i t h v e r y

g o o d r e s u l t s .

A c k n o w l e d g e m e n t s - - T h e authors would l ike to acknowl-edge the f inancial suppor t received f rom the NaturalSciences and Engineering Research Council o f Ca nad a,Environment Cana da, Supply and Services Cana da, Ly on-naise des Eaux (Par is) and la Socir t6 Qurbrcoised 'Assain issem ent (Qurbec).

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