Characterisation of Mixing Patterns in an Anaerobic Digester by Means of Tracer Curve Analysis

7/21/2019 Characterisation of Mixing Patterns in an Anaerobic Digester by Means of Tracer Curve Analysis

http://slidepdf.com/reader/full/characterisation-of-mixing-patterns-in-an-anaerobic-digester-by-means-of-tracer 1/19



26 8 L C SM1TH ET AL

d e t e r m i n e t h e e f fe c ti v el y m i x e d p r o p o r t i o n o f th e r e a c t o r a n d t o a s se ss t h e

v a l u e o f d i ff e r e n t o p e r a t i o n a l p r o c e d u r e s a s a m e a n s o f o p t im i z i n g p r o ce s s

p e r f o r m a n c e .

S e v e ra l m e t h o d s a r e a v a il a bl e f o r m e a s u r i n g t h e d e g r e e o f m i x in g i n a

c o n t i n u o u s f lo w s y s te m , b a s e d o n t h e r e s i d e n c e t i m e d i s t ri b u t i o n R T D ) o f

m a t e r i a l in t h e sy s t e m D a n k w e r t s , 1 9 53 ). T h e R T D is u s u a ll y m e a s u r e d b y

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

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

t h e C c u r v e . I n th i s p a p e r C c u r v e s a re p r e s e n t e d i n t h e ir n o r m a l i s e d f o r m

L e v e n s p i e l , 1 9 6 2 ) f o r c o m p a r a t i v e p u r p o s e s .

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

w h i c h e x h ib i t d i f f e r e n t fl o w r e g i m e s . B i s c h o f f a n d M c C r a c k e n 1 9 6 6) d e -

s c r ib e d t h e i n t en s i t y f u n c t i o n w h i c h p r o v i d e s q u a l i ta t iv e i n f o r m a t i o n o n t h e

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

t h e v o l u m e o f t h is r eg i o n . Z o l t e k a n d G r a m 1 9 75 ) an a l y s e d m i x i n g p a t -

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

b e e n c r i ti c is e d b y S m a r t 1 9 78 ) a n d M o n t e i t h a n d S t e p h e n s o n 1 9 81 ) a s

b e i n g i n a c c u r a t e .

M e t h o d s o f an a l y si n g tr a c e r c u r v e s to d e t e r m i n e m i x in g p a t t e r n s i n a

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

1 95 9 ; L e v e n s p i e l , 1 96 2 ; B i s c h o f f a n d M c C r a c k e n , 1 96 6; T h i r u m u r t h i , 1 9 6 9;

M o n t e i t h a n d S t e p h e n s o n , 1 98 1). T h e y i n c l u d e s i n g le p o i n t in d i ce s ; m o d e l s

w h i c h d e s c r i b e t h e d e g r e e o f d i s p e r s io n i n t h e s y s te m ; a n d d i v is i on o f t h e

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

T h e r a n g e o f m e t h o d s a v ai la b le c r e a t e s c o n f u s i o n w h e n e v a l u a t in g

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

u s i n g d i ff e r e n t m o d e l s . T h e a i m o f th i s p a p e r is to d e s c r i b e t h e c o n v e n -

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

m e t h o d i n t e r m s o f: a ) e a s e o f u s e ; b ) a c c u r ac y ; c ) c o n s i s t e n c y ; a n d d )

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

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

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

m i x i n g p a t t e r n s c a n b e d e s c r i b e d . A c o m p a r i s o n o f m e t h o d s w a s ca r r i ed

o u t u s i n g t h e C c u rv e s f ro m a s er ie s o f t r a c e r s t u d i es p e r f o r m e d o n a n

o p e r a t i n g p i l o t s c a l e c o n t a c t p r o c e s s .

METHO S

racer studies

A s e ri e s o f t r a c e r s t u d i e s w a s c a r r ie d o u t o n t h e S E R C P i lo t - S ca l e

C o n t a c t P r o c e s s a t G l o u c e s t e r t o a s se s s t h e e f fe c t o f im p e l l e r s p e e d u p o n

m i x i n g T a b l e 1 ).



M I X I N G P A T T E R N S I N A N A N A E R O B I C D I G E S T E R

TABLE 1

Contact process tracer studies

269

Criterion Tracer study

1 2 3 4

Impelle r speed rpm) 370 270 370 470

Contents of reactor Water Sludge Sludge Sludge

TSS concn. mg /l ) - 2600 800 3500

VSS concn. mg/1) - 2200 700 2800

Hydraulic ret ent ion time h) 33.4 75.2 53.2 98.0

Recycle : feed rat io 0 1.58 1.06 2.06

Tracer studies were carried out using lithium chloride. A known quantity

was introduced into the feed line of the system over as short a time as

possible. The effluent lithium concentration was analysed using a flame

photometer (Jenway Model PF77).

The C curves were analysed using the following techniques:

oint analyses

The point indices described below are defined in Fig. 1.

tl0

t90

t p

t

time for 10 of the injected tracer to pass out in the effluent

time for 90 of the injected tracer to pass out in the effluent

time to reach peak or maximum tracer concentration (modal

value)

time to reach centroid of curve or actual mean detention time

C

o

o

p

theoretical

retention time

t l t p

C

u r v e

t t ~ t o o

t i m e f t e r i n j ec t i o n

Fig. 1. Definition of point analyses.



27

L.C. SMITH ET AL

t h m e d i a n t im e o r t i m e fo r 5 0 o f t h e i n j ec t e d t r a c er t o p a s s o u t i n

t h e e f f l u e n t

T t h e o r e t ic a l h y d r a u l i c d e t e n t i o n t i m e

t9o t lo

M o r r i ll I n d e x o f m i x in g

1 t p t g

i n d e x o f s h o r t - c i r c u i t i n g

Dispersion model

T h e d i s p e r s i o n m o d e l d e s c r ib e s a p l u g fl ow m o d e l u p o n w h i c h is s u p e r -

i m p o s e d s o m e d e g r e e o f b a c km i x in g , t h e m a g n i t u d e o f w h i c h i s in d e p e n -

d e n t o f t h e p o s i t i o n w i t h i n t h e v e ss e l. I t is b a s e d o n F i c k ' s L a w o f

m o l e c u l a r d i f f u s i o n ( E q . 1 .1 ).

d C d z C

d--7 = 2 d x 2 ( 1 . 1 )

w h e r e _ 9 = c o e f f i c i e n t o f m o l e c u l a r d i f f u s i o n ; x = d i r e c t i o n o f fl ow ; C =

c o n c e n t r a t i o n o f t r a ce r .

2 is r e p l a c e d b y D i n t h e d i s p e r s io n m o d e l . T h e d i m e n s i o n l e s s g r o u p

u s e d t o c h a r a c t er i s e t h is s y s t e m is t h e d i s p e r s io n n u m b e r

D u L

a nd i t i s

r e l a t e d t o t h e s y s t e m v a r i a n c e i n E q . 1 .2 .

D

o 2 = 2u-- - (1.2 )

w h e r e o . 2 = v a r i a n c e ; u = v e l o c it y t h r o u g h s y s te m ; L = l e n g t h o f s y s t e m ;

D u L = d i s p e r s i o n n u m b e r .

T h i s i s a c c u r a t e a t l o w r a te s o f d i s p e r s i o n , b u t a h i g h r a t e s o f d i s p e r s i o n ,

E q . 1 .3 is m o r e a c c u r a t e ( T o m l i n s o n a n d C h a m b e r s , 1 9 7 9).

2 - - - 2 1 - 1 . 3 )

u L

T h e d i s p e r s i o n n u m b e r v a r ie s f r o m 0 fo r p l u g f lo w to ~ f o r a c o m p l e t e l y

m i x e d r e a c t o r .

A n a l t er n a t iv e a p p r o a c h t o t h e d i s p e r s io n m o d e l is s h o w n i n E q . 1.4,

w h i c h c a l c u l at e s a d i s p e r s i o n c o e ff i ci e n t f r o m t h e v a r ia n c e a n d m e a n

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

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

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

where E = dispersion coefficient; U= mean velocity of flow; o a , t, =

variance and mean retention time of tracer response curve in plug flow



MIXING P TTERNS IN N N EROBIC DIGESTER 27

sys t e m; t r 2 , t = v a r i a n c e a n d m e a n r e t e n t i o n t i m e o f a c t u al t r ac e r r e s p o n s e

c u r v e .

T h e d i s p e r s i o n c o e f f i c i e n t i s i n c o r p o r a t e d i n t o E q . 1 .5 to c a l c u l a t e t h e C

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

g e o m e t r y .

C = A 4vr4~-- ex p 4-Et 1. 5 )

w h e r e C = t r a c e r c o n c e n t r a t i o n ; W = q u a n t i t y o f t r a ce r a d d e d ; A = c r os s

s e c t i o n a l a r e a o f r e a c t o r ; t = t i m e ; x = d i s t a n c e d o w n s t r e a m - t r a v e l l e d r e a c -

t o r l e n g t h .

T a n k s i n s e r i e s m o d e l

T h e v e s s e l i s a s s u m e d t o b e r e p r e s e n t e d b y a s e r i e s o f N e q u a l l y s i z e d ,

c o m p l e t e l y m i x e d v es se ls . N m a y b e c a l c u l a t e d f r o m t h e v a r ia n c e o f t h e C

c u r v e E q . 1 .6 , M o d e l A ) ,

1

- - = t r 2 . 1 .6)

N

E q u a t i n g t h is s o l u t i o n w i t h t h e e q u a t i o n f o r th e d i s p e r s io n m o d e l g iv e s t h e

a n a l y t ic a l s o l u t i o n s h o w n in E q . 1 .7 M o d e l B ) ,

1

N - 1 - t p ( 1 . 7 )

F o r l a rg e v a lu e s o f N , t h e r e s i d e n c e t i m e d i s t r i b u t io n b e c o m e s i n c r ea s in g l y

s y m m e t r ic a l F ig . 2 b) a n d c a n b e c o m p a r e d w i t h t h e d i s p e r s i o n m o d e l F ig .

2 a ). A t l o w v a l u e s o f N , t h e m o d e l s i n c r e a s in g l y d i f f er f r o m e a c h o t h e r .

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

f lo w , w h e r e a s t h e t a n k s -i n - se r ie s m o d e l is p r e f e r a b l e w h e n t h e f lo w p a t t e r n

a p p r o a c h e s a c o m p l e t e l y s t ir re d t a n k r ea c t o r T o m l i n s o n a n d C h a m b e r ,

1979) .

C o m b i n e d m o d e l s

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

v e s s e l i n t e r m s o f d i s t i n c t z o n e s . F l u i d f l o w p a t t e r n s m a y i n c l u d e c o m -

p l e t el y m i x e d z o n e s , p l u g f lo w r e g i o n s a n d c h a n n e l l i n g o r d e a d s p a ce .

L e v e l s p i e l 1 9 6 2) d e s c r i b e d m i x i n g i n t e r m s o f d i f f e r e n t p o r t i o n s a n d

v o l u m e s o f i d e a l fl o w u n i ts . H e p r o d u c e d a c a ta l o g u e o f C c u r v es re p r e -

s e n t i n g d i f fe r e n t f l u id f lo w p a t t er n s . A n e x a m p l e o f t h e m o d e l u s e d i n t h e

s u b s e q u e n t a n a l y s i s i s i l l u s t r a t e d i n F i g . 3 .

C h o l e t t e a n d C l o u t i e r 1 9 59 ) s p e c i fi e d m i x e d a n d d e a d z o n e s a n d a

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





M I X I N G P A T T E R N S I N A N A N A E R O B I C D I G E S T E R 73

F r a c t i o n o f v e s s e l v o l u m e

/ a c t i v e l y

mixe

_ ~ =v~.. = VvV ,

~ A r e a b e y o n d c u t - o f f p o i n t

= 2 e q u a l to~ ~_

V V V

M e a s u r e d a r e a o n l y s l ig h t ly

t ~ d i f f e r e n t f ro m u n i ty = ~ _

i g h r ~ i ii i: i i i ° i e il~ b eR ei ° ° n P ~ e ~ n ~ d ~ e d n ° °n

II ( • k L . . ~ r - - '~ S h i f t o f O f ro m u n i ty

w I ~ [ m e a s u r e s e o d w a te r

r e g i o n

~ A r e o i g n o r e d i n t a i l i s

g = V - Va v L_ v e r ~ s m o l l b u t c o n t ri b u t e s

V v a m u c h in s h i f t in g g f ro m u n i ty

Fig . 3 . Tr ac e r cu rve ana lys i s Lev ensp ie l , 1962).

used was similar to that for other combined models, visualising the vessel

consisting of distinct zones. However, additional features of the model

improve the accuracy with which it described the mixing characteristics of a

vessel.

The basic unit of the model was a completely stirred tank reactor

(CSTR). The mass balance equation for the tracer was solved using a 4th

order Runge-Kutta technique. A flow diagram of the model is shown in

Fig. 6.

In the contact process, three zones may be distinguished. A small initial

mixed zone is included to account for the short delay in the maximum

tracer concentration appearing in the effluent. This has been previously

ignored in conventional methods of analysis. The flow passes from this

initial zone into a large main mixed zone (the effectively mixed volume).

The majority of the influent passes through only the mixed regions.

However, a portion (QD) passes into a dead zone which is represen ted by

a CSTR through which the rat e o f flow is greatly reduced . The delay in the

appea rance of the tracer from this zone accounts for the tail effect often

observed in tracer response curves from mixed vessels (Bischoff and Mc-

Cracken, 1966; Stevens et al., 1986). A dispersion coeff icient is used to

describe the cross boundary mov ement of tracer from the mixed zones into

the dead zone.



74

L C S M I T H E T A L

1

- - - - C o m p l e t e l y m i x e d t a n k

\ T a n k

with sh o r tc i rcu i t in g

~ \ C/Co = ne ''Vmv

\ S lo p e - n / m

\

\

2

N o r m . t i m e

feed shortcircuitinc

= 1

- n

Y

a x i s i n t e r c e p t

= n

= f r a c t i o n o f f e e d

e n t e r i n g m i x e d z o n e

y 9 x i s i n t e r c e p t = m i x e d z o n e v o l u m e

S l o p e

x e d z o n e 1

/ p o g z o n e

I

1

1 - - ~

C o m p l e t e l y m i x e d

t a n k

~ , N ~ , T a n k with partia l p lug f low

I \ C / C o =

e - ' / ~ ( - / ~ - o - m ~

c

0 4 I \ l \

0 2

N o r m . t i m e

F i g . 4 . T r a c e r c u r v e s a n a l ys i s C h o l e t t e a n d C ] o u t i e r , 1 9 5 9 .

1 =

m i x e d z o n e v o l u m e

I n it ia l e s t i m a t e s o f th e z o n e v o l u m e s w e r e m a d e f r o m v a l u e s o f t h e C

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

t h e t a i l r eg i o n o f th e C c u r v e . T h e v a l u e s o f a ll p a r a m e t e r s w e r e c h a n g e d

i n s e q u e n c e t o o b t a i n t h e b e s t - f i t t i n g s i m u l a t e d c u r v e t o t h e a c t u a l d a ta . A n

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

s q u a r e s b e t w e e n a c t u a l a n d s im u l a t e d d a t a .

R E S U L T S A N D D I S C U S S I O N

A t y p ic a l C c u r v e f r o m a t r a c er s t u d y c a rr i ed o u t o n t h e c o n t a c t p r o c e s s

is s h o w n i n F i g . 7 . T h e f o r m o f t h e c u r v e c l o s e l y r e s e m b l e s t h e C c u r v e

e x p e c t e d f r o m a C S T R . A m o r e - d e t a i l e d e v a l u a t i o n o f t h e m i x in g p a t t e r n

in e a c h c a s e w a s o b t a i n e d u s i n g t h e m e t h o d s d e s c r i b e d p r e v i o u sl y . U n f o r -

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

s t u d i e s w e r e c a r r ie d o u t r e s u l t i n g in d i f f e r e n c e s i n f l o w c o n d i t i o n s a n d

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

i n f e r e n c e s m a y b e m a d e f r o m t h e a n a l y si s o f t h e d a ta .



M I X I N G P A T T E R N S I N A N A N A E R O B I C D I G E S T E R

o

L

C / C o = ( v m , V / v 2 ) e x p - t / t m + v z / v - - V m

0 I

N o r m . t i m e

1 m ) e x p ( - ~ / ~ m • O

Y a x i s i n t e r c e p t = v m * V ~ s 9 p e

v

1 : m i x e d z o n e HRT

osr ~

Vm = vm

Y a x i s i n t e r c e p t =_ Y._

V m

I

= t * V m

0 1 ~ V

Norm t ime

F i g . 5 . T r a c e r c u r v e a na ly sis M o n t e i t h a n d S t e p h e n s o n , 1 9 8 1 ).

2 7 5

Q R

ini t ia l mixed

zone I

I I~ k [ ma i n m i xed

\

j zon

,,~Q~ + Q Q

d i S :d l i° n d b V D e e n \ \ ~ /

' 1 °

Q

dead zone

F i g . 6 . F l o w d i a g r a m o f s i m u l a t i o n m o d e l .

-- QF



76 L .C . S M I T H E T A L

• 1 . 0

t

C

0

U

E

=

0 5

t -

. . J

0

z 0 . 0

0 1 2 3 4

N o r m o l i s e d t i m e

F i g . 7 . T y p i c a l C c u r v e f r o m c o n t a c t p r o c e s s .

Poi n t ana lyses an d ana ly t ica l m odels

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

m o d e l s i s s h o w n i n F i g . 8 . S e v e r a l o f t h e p o i n t v a l u e s i n d i c a t e t h a t a s t h e

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

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

t 9 o / t l o I n c o n t r a s t a d e c r e a s e i n t T a n d i n t h e n u m b e r o f t a n k s i n s e ri e s

0.110

E

0.105

o

0 100

0 . 0 9 5

2 .80

~ 2 . 6 0

2.40

2.20

0 . 0 0 6

v 0.004

0.002

0 .9

E

0 .8

o

v

0 . 6

170

I I I

Y = - O . O 0 0 8 1 9 X + 2 . 8 2 2

I i i

y = - g E - 6 X + O . O 0 8 7 9

275 -~

o 25.0

o

2 0 0

17.5

C.

.__. -~

I ~

1.2

~_E 1.0

0 . 8

•~ 1 . ~

~ 0

Y = - O , 0 1 8 4 X + 3 0 . 6 9 3

Y = O . O 0 1 3 9 X + 0 . 7 0 1 7

r - - - -

Y = - 5 . 0 0 0 2 3 E - ~ + 1 .0 0 7 5

F i g . 8. E f f e c t o f i m p e l l e r s p e e d o n p o i n t a n a l y s i s v a l u e s d u r i n g p i lo t s c a l e c o n t a c t p r o c e s s

t r ac e r s t u d ie s .

E

i i i 1 , ~ i i i

~ 3 . 0 0

Y = O . O O O 4 4 5 X + 0 . 5 4 9 7 ~ ~

1 7 0

I I 7 ¸ . ¸ ~ I I

270 .370 470 270 370 470

I m p e l l e r s p e e d ( r . p . m . ) I m p e l l e r s p e e d

( r . p . m . )



MIXING P TFERNS IN N N E ROBIC DIGESTER 77

(Model B) suggest that mixing is enhanced by an increase in impeller

speed.

These contradictory result suggest that point analyses are inad equat e for

distinguishing small differences betw een flow patte rns in a vessel. It ma y be

argue d that if the change in the flow pat ter n is small, accurate characterisa -

tion of the flow patt ern is unnecessa ry. However, small differe nces which

occur at one scale of reactor may be more important at a larger scale. Pilot

scale reactors are often operated for the purpose of determining the

controlling factors in the process.

The effect of the presence of sludge on the mixing patterns is shown by

comparing studies 1 and 3, both performed at an impeller speed of 370

rpm. The point analyses again show contra dictory results. The higher

tp

value when water was present indicates a reduced degree of mixing. This is

supported by an increase in the Morrill Index and the numbe r of tanks and

a decrease in the dispersion number. In contrast, the dead zone volume

(described by t g / T is smallest in the study with water present, indicating

that the presence of sludge increases the amount of dead space and

the ref ore reduces the effectively mixed volume.

C o m b i n e d m o d e l s

The results of the tracer curve analysis using the various combined

models are shown in Table 2. Applying the model described by Levenspiel

(1962) indicates that the vessel was least well mixed when only water was

TABLE 2

Results from pilot-scale contact process tracer studies using combined models

Impeller speed (rpm)

Method

Tracer study

2 3 4

370 270 370 470

volume volume volume volume

Levenspiel

(1962)

Monteith and

Stephenson

(1981)

Cholette and

Cloutier

(1959)

Vm 4912 82 6295 86 6227 85 6617 91

Vd 1088 18 1005 14 1073 15 683 9

vm 2.54 85 1.13 85 1.58 84 0.87 85

Vm 2934 49 6697 92 7113 97 1190 16

Vd 3066 51 603 8 187 3 6110 84

vm 1.97 66 1.33 100 1.88 100 0.18 18

tm 1489 74 5009 91 3780 97 1287 18

Vm 5796 97 6919 95 6604 90 6803 93

fm 88 98 100 91

Vm = mixed volume (1); Vd = dead volume (1); vm = mixed zone tlowrate (1/min); tm =

mixed zone retention time (min); fm = fraction of feed passing through mixed zone.



278 L C SMIT H ET AL

present. This was also shown by the method described by Monteith and

Stephenson (1981). Levenspiel's method indicates that the largest main

mixed zone and the smallest dead zone occurred during the tracer study at

the highest impeller speed. Using Monteith and Stephenson's method, a

large degre e of short-circuiting was pres ent during this study, resulting and

in a very small complete ly mixed zone. This result is due to the dep end enc e

of the me tho d on the value of the Y-axis interce pt for the best fitting line to

the decay portion of the C curve. Above 1.0 the vessel is considered to

comprise a mixed zone and a dead volume. Below 1.0 a fraction of the

influent shortcircuits directly to the effluent. The close approximation of

the influent shortcircuits directly to the effluent. The close approximation

of the study at 470 rpm to a CSTR resulted in an intercept value marginally

below 1.0, resulting in a major change in the interpretation of the flow

pattern. This method is particularly sensitive to the value of the intercept.

Analysis using Chole tte and C loutier's (1959) me tho d showed tha t the

largest mixed zone occurred at the lowest impeller speed (270 rpm) in the

presen ce of sludge. This zone increase d to 97 of the reactor volume in

TABLE 3

Computer simulation results from pilot-scale contact process tracer studies

Tracer study

2 3 4

Impeller speed (rpm) 370 270 370 470

Parameter volume volume volume volume

Mixed zone 1 (VM1) 6

Mixed zone 2 (VM2) 5 200

Dead zone (VD) 794

Feed flowrate (QF) 2.99

Recycle flowrate (QR) 0.00

Total flowrate (Q) 2.99

Dead zone flow

coefficient 0.10

Dispersion coefficient

(KB) 0.14

Flow rate through dead

zone (QD * Q) 0.299

HRT of dead zone 2656

VD/QD 129

VM1/Q (Mixing time) 2.01

0.1 14 0.23 25 0.4 15 0.25

87.0 5956 99.3 5960 99.3 5975 99.6

12.9 30 0.47 15 0.3 10 0.15

1.33 1.88 1.02

2.10 2.00 2.10

3.43 3.88 3.12

0.002 0.001 0.0007

0.2 0.32 0.45

0.0069 0.0039 0.0022

4 373 3 866 4 579

235 300 214

4.08 6.44 4.81

Volumes in 1; flowrates in 1/min; times in min.



M I X I N G P T r E R N S I N N N E R O B I C D I G E S T E R 79

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

z o n e w a s l e a s t in t h e w a t e r - o n l y s t u d y , s u g g e s t i n g a la r g e d e g r e e o f

s h o r t - c i r c u i t i n g . T h e s e r e s u l t s c o n t r a d i c t t h e o b s e r v a t i o n s u s i n g t h e m i x e d

m o d e l s d e s c r i b e d p r e vi o u sl y .

omputer simulation model

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

s i m u l a t i o n m o d e l d e v e l o p e d b y t h e a u t h o r s i s s h o w n i n T a b l e 3 a n d F i g. 9.

A n i m p o r t a n t d i f f e re n c e b e t w e e n t hi s m o d e l a n d t h o s e p r ev i o us ly d e-

s c r ib e d i n th e p r e s e n c e o f a n a d d i t i o n a l m i x e d z o n e ( V M 1 ) t o s i m u l a t e t h e

d e l a y t o t h e p e a k t r a c e r c o n c e n t r a t i o n . T h i s w a s f o u n d t o b e a n i m p o r t a n t

p a r a m e t e r i n d e t e r m i n i n g t h e m i x i n g t i m e o r t h e t i m e t o re a c h u n i f o r m i t y

i n t h e m a i n m i x e d z o n e. V M 1 w a s s m a l le s t in t h e w a t e r s t u d y ( st u d y 1 )

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

m a r g i n a l l y i n c r e a s e d t h is v o l u m e b u t t h e r e w a s n o c l e a r p a t t e r n w i t h

c h a n g i n g i m p e l l e r s p e e d .

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

c h a n g e i n o t h e r m o d e l p a r a m e t e r s : ( a ) t h e m a i n m i x e d z o n e ( V M 2 )

i n c r e a s e d i n v o l u m e ; ( b) t h e d e a d z o n e v o l u m e ( V D ) d e c r e a s e d ; ( c) t h e

d i s p e r s i o n c o e ff i ci e n t ( K B ) i n c re a s e d ; ( d) t h e f l o w r a te t h r o u g h t h e d e a d

v o l u m e d e c r e a s e d .

T h e e f fe c ti v el y m i x e d v o l u m e o f t h e v e s s el i n c r e a s e d a s t h e i m p e l l e r

s p e e d i n c r ea s e d , w h i c h is c o n f i r m e d b y t h e r e d u c t i o n i n t h e d e a d z o n e

v o l u m e a n d t h e i n c r e a se i n th e d e g r e e o f d i sp e r s io n . T h e r e d u c t i o n i n

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

m a y b e d u e t o t h e d i f fi c u l ty o f a c c u r a t e l y m o d e l l i n g t h e t a il r e g i o n o f t h e C

c u r v e (Y o u n g a n d Y o u n g , 1 98 8). A n a d d i t i o n a l f a ct o r a f fe c t in g t h e d e g r e e

o f m i x i n g is t h e s l u d g e c o n c e n t r a t io n . T h e b a c t e ri a l s u s p e n s i o n a l t e rs t h e

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

m e a n s t h a t i t s v i s co s i ty d e c r e a s e s w i t h i n c r e a s i n g s h e a r r a t e ( o r i m p e l l e r

s p e e d ) . T h e s l u d g e c o n c e n t r a t i o n w a s l o w e s t d u r i n g t r a c e r s t u d y 2 (3 7 0

r p m ) . T h e h y d r a u l ic r e t e n t i o n t i m e o f th e d e a d z o n e w a s l o w e s t d u r i n g t h is

s t u d y a n d h i g h e s t d u r i n g t h e s t u d y a t 47 0 r p m w h e n t h e t o t a l s o li d s

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

c o n c e n t r a t i o n c a n h a v e a s i g n i f ic a n t e f f e c t o n t h e m i x i n g c h a r a c t e r i s ti c s o f

t h e v e s s e l .

T h e d e a d z o n e d u r i n g t h e w a t e r s t u d y w a s u n e x p e c t ed l y l ar ge c o m p a r e d

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

t h e f l o w r a t e t h r o u g h t h i s z o n e w a s h i g h , r e s u lt i n g in a d e a d z o n e r e t e n t i o n

t i m e m u c h l o w e r t h a n d u r i n g t h e s l u d g e tr a c e r s t u d ie s . T h e n a t u r e o f t h e

f lu i d b e in g m i x e d a f f e c te d t h e m i x i n g p a t t e r n s w h i c h d e v e l o p e d .



280 L C SMITH ET AL

1 O 0 -

= 9 9

-6

>

0

• 9 8

E

9 7

E 0 . 6

6

o 0.3

0

0.0

E

.~-

0 . 0 0 9

0

= 0 . 0 0 6

t -

O

0 . 0 0 3

0

0

0 . 0 0 0

~

0 . 5

~

o

0 . 3

U

0.0

Y = O . O O 1 4 9 X + 9 8 . 8 4 5

y = x - Z ~ , 6 7 7 . 6 3

- - 7

Y = O . O 0 1 2 5 X - 0 . 1 3 9 2 ~ , , I ~ *

I I I

1 7 0 2 7 0 3 7 0 4 7 0

I m p e l l e r s p e e d ( r , p . m . )

Fig. 9. Effect of i m p e l l e r s p e e d o n c o m p u t e r s i m u l a t i o n m o d e l p a r a m e t e r s f o r p i l o t - s c a l e

c o n t a c t p r o c e s s t r a c e r s t u d i e s .

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

s h o w e d n o c o r re la t io n w i t h i m p e l l er s p e e d M i x in g t im e i s d e p e n d e n t u p o n

t h e v a lu e o f V M 1 T h e d i s c o n ti n u i ty o f s a m p l in g d u r i n g t h e t ra c er s t u d y

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

w h i c h th e v o l u m e o f V M 1 d e p e n d s T h e i n c r e as e d m i x in g t im e s c o m p a r e d



MIXING P TTERNS IN N N E ROBIC DIGESTER

281

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

s ion .

COMPARISON OF MODELS

T a b l e 4 s u m m a r i s e s t h e c o n c l u s i o n s a b o u t m i x in g p a t t e r n i n t h e c o n t a c t

process using different methods.

These results illustrate the problem of evaluating the mixing characteris-

tics of a stirred vessel using point analyses or combined models based on

division of the C curve. Use of a single method can produce erroneous

results, while comparing a variety of methods can give confusing and

contradictory results. It is essential when using a certain method of analysis

that the user is aware of the basis of the model and the meaning of the

result.

The point analyses are based on single values from the C curve which

attempt to describe the degree of mixing in the reactor. The limitation of

the point analyses is that they cannot take into account changing conditions

such as flowrate through the vessel or the ratio of recycle:feed flowrates.

Their use is therefore limited to studies where all conditions except the

parameter being studied are unchanged.

TABLE 4

Summary of results from different methods of tracer curve analysis

Increased impeller speed implies increased Increasing impeller speed implies decreased

mixing mixing

t

1 tp / tg

Tanks in series Model B)

Levenspiel 1962)

Computer simulation model-larger VM2

-smaller VD

Morrill Index

Tanks in series Model A)

Monteith and Stephenson 1981)

Cholette and Cloutier 1959)

Water is more completely mixed than sludge Sludge s more completely mixed than water

t g / T

Morrill Index

Cholette and Cloutier 1959)

Computer simulation model-shorter

retention time

dead zone

t

1 t p / t g

Tanks in series Models A and B)

Dispersion number

Levenspiel 1962)

Monteith and Stephenson 1981)

Computer simulation model-larger main

mixed volume

VM2)



8 L C S M I T H E T A L

T h e d i s p e r s i o n s a n d t a n k s - i n - s e r i e s m o d e l s h a v e b e e n c r i t i c i z e d b y

N a u m a n n a n d B u f f h a m ( 19 83 ) f o r b e i n g t o o g e n e r a l is e d o v e r t h e w h o l e

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

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

T h e c o n t r a d i c t o r y re s u lt s u s i n g t h e c o m b i n e d m o d e l s (1 9 81 ) a re d u e t o

t h e s e ns it iv i ty o f th e s e m o d e l s t o t h e s h a p e o f th e C c u rv e . M o n t e i t h a n d

S t e p h e n s o n s (1 9 81 ) m e t h o d a s s u m e s t h a t t h e f ir st p o i n t is in t h e h i g h e s t

t r a c e r c o n c e n t r a t io n . T h i s w a s n o t t r u e i n t h e p r e s e n t s e r ie s o f t ra c e r

r e s p o n s e c u r v e s a n d t h e r e w a s a d e g r e e o f s u b je c ti v it y i n e v a l u a t i n g t h e

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

c a n r e s u l t i n a l a rg e d i f f e r e n c e in t h e e s t i m a t e d v o l u m e s o f z o n e s a n d t h e

e x t e n t o f s h o r t c i r c u i ti n g .

L e v e n s p i e l s m e t h o d i ll u s tr a te s t h e f ac t t h a t i f t h e p e a k t r a c e r c o n c e n t r a -

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

t i m e , t h e s y s t e m is u su a l ly a s s u m e d t o b e c o m p l e t e l y m i x e d . T h i s o v e r si m -

p l i fi e s t h e t r u e m i x i n g c h a r a c te r i s ti c s o f t h e s y s te m .

T h e c o m p u t e r s i m u l a ti o n m o d e l r es u l t s s h o w e d a c o n s i s t en t p a t t e r n o f

i n c r e a s e d m i x i n g w i t h a n i n c r e a s e d i m p e l l e r s p e e d . S e v e r al o f th e m o d e l

p a r a m e t e r s c o n f i r m e d th i s tr e n d , d e s p i t e t h e d i f f e r e n t so l id s c o n c e n t r a t i o n s

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

s t u d ie s . T h i s m o d e l h a s s e v er al a d v a n t a g e s o v e r t h e c o n v e n t i o n a l m e t h o d s

o f a na lys i s :

( a) T h e f i n i t e t i m e o v e r w h i c h t h e p u l s e i n j ec t io n o f tr a c e r o c c u r r e d m a y

b e m o d e l l e d p r ec is e ly . ( A n a l y ti c al m e t h o d s o f a n al ys is a s s u m e a n

i n s t a n t a n e o u s i n je c ti o n )

( b) F l u c t u a t i n g f l o w r a te s d u r i n g t h e s t u d y m a y b e a c c u r a te l y s im u l a t e d .

( c) D i f f e r e n t o p e r a t i n g c o n d i t i o n s b e t w e e n s t u d i e s , s u c h as t h e re c y c l e : f e e d

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

( d) A d d i t i o n a l z o n e s w e r e r e a d i l y a c c o m m o d a t e d a n d d i s p e r s io n p r o c es s e s

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

( e) T h e c o n c e p t u a l z o n e s i n th e m o d e l m a y b e r e l a t e d t o p h y s i ca l p r o -

c e s se s .

DISCUSSION

A n a c c u r a t e e v a l u a t i o n o f t h e m i x i n g c h a r a c t e r is t i c s o f b i o l o g i c al s y s t e m s

is r e q u i r e d f o r d e t e c ti n g t h e p r e s e n c e o f d e a d z o n e s , d e t e r m i n i n g t h e

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

c e ss e s a n d o p e r a t i n g c o n d i t io n s . T h e m i x i n g p a t t e r n o f a s y s t em i s o f

p a r t i c u l a r i m p o r t a n c e i n a b i o lo g i c a l s y s t e m ( M u r p h y , 1 97 1; V e r h o f f e t a l.,

1 97 4). E f f ec t iv e s u b s t r a t e c o n v e r s i o n d e p e n d s u p o n b o t h t h e p r e s e n c e o f a

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



MIXING PA Iq ERNS IN AN ANAEROBIC DIGESTER 83

a n d s u b s t r a t e . S m a r t ( 1 9 7 8 ) a n d M o n t e i t h a n d S t e p h e n s o n ( 1 9 8 1 ) f o u n d

t h a t i n a d e q u a t e m i x in g e x p la i n e d t h e p o o r p e r f o r m a n c e o f f ul l- sc a le a n a e r -

o b ic d i g e st e rs . T h e y d e m o n s t r a t e d t h e i m p o r t a n c e o f c o n s i d e r in g m i xi ng

p a t t e r n s i n r e a c t o r d e s i g n .

T h e t h e o r y o f m i x i n g h a s b e e n t h e s u b j e c t o f m a n y t e x t s ( U h l a n d G r a y ,

1 96 6; N a g a t a , 1 97 5; O l d s h u e , 1 98 3). H o w e v e r , b i o l o g i c a l t r e a t m e n t s y s t e m s

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

f l ow type .

F o r e a s e o f u s e , p o i n t i n d i c e s a r e s u p e r i o r t o o t h e r m e t h o d s . T h e y h a v e

b e e n c o n s i d e r e d t o p r o v i d e q u i c k a n d a c c u r a t e i n f o r m a t i o n a b o u t m i x i n g

p a t t e r n s ( T h i r u m u r t h i , 1 9 6 9 ) . T h i r u m u r t h i ( 1 9 6 9 ) c a l c u l a t e d t h e o r d e r o f

r e li a b il it y o f p o i n t v a l u e s a n d s i m p l e m o d e l s ( i n d e c r e a s i n g o r d e r ) :

D i s p e rs io n n u m b e r

D / u L 1

- - t p / t g t g

tp.

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

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

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

o f m i x in g . R e l i a n c e u p o n t h e h y d r a u l i c r e t e n t i o n t i m e ( H R T ) a s a n in d i c a -

t o r o f m i x i ng is a ls o d a n g e r o u s . T h e s a m e H R T m a y e x is t i n a c o m p l e t e l y

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

l a rg e d e a d v o l u m e . S a w y e r a n d K i n g (1 96 9) r e c o m m e n d e d t h e u s e o f

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

d e s c r i p t i v e v a l u e .

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

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

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

a c c u r a c y o f th e s e m o d e l s ( B i s c h o f f a n d M c C r a c k e n , 1 9 66 ; S m a r t , 1 97 8).

T h e s i m u l a ti o n m o d e l p r e s e n t e d i n th is p a p e r h a s m a n y a d v a n t a g e s o v e r

o t h e r m e t h o d s . B y u s i n g c o n c e p t u a l z o n e s t o d e s c r i b e t h e m i x i ng p r o c e s s ,

t h e d i f f e r e n t r e g i o n s o f f l o w m a y b e q u a n t i f i e d . E v a l u a t i o n o f t h e v o l u m e

a n d r e t e n t i o n t i m e o f d e a d s p a c e is p a r t i c u l a rl y i m p o r t a n t ( S m a r t , 1 97 8). I n

a d d i t i o n , th e z o n e s m a y b e r e l a t e d t o p h y s i ca l p r o c e s s e s i n t h e v es s el . F o r

e x a m p l e , t h e i m p e l l e r r e g i o n is a z o n e o f t u r b u l e n c e a n d r a p i d m i x in g

( B a t e s e t a l ., 1 96 6; K e a i r n s , 1 9 69 ; O l d s h u e , 1 98 3) w h i c h c o r r e s p o n d s t o t h e

i n it ia l m i x e d z o n e i n t h e m o d e l , V M 1 . T h e p u m p i n g c a p a c i t y o f t h e

i m p e l l e r d e t e r m i n e s t h e v e l o c i ty w i t h w h i c h l iq u i d l e a v es t h a t r e g i o n a n d is

d i s p e r s e d t h r o u g h o u t t h e v e s s e l ( S t e r b a c e k a n d T a u s k , 1 9 6 5 ) . T h e h i g h e r

c i r c u l a t io n r a t e a t a f a s t e r i m p e l l e r s p e e d i n c r e a s e s t h e e f f e ct iv e l y m i x e d

v o l u m e ( V M 2 ) a n d r e d u c e s t h e d e g r e e o f s ta g n a n c y ( V D ) . U n d e r s t a n d i n g

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

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



84 L C SMIT H ET AL

A d i s a d v a n t a g e o f t h is m o d e l i s t h e l a c k o f a f o r m a l m e t h o d o f q u a n t i f y -

i ng m o d e l p a r a m e t e r s e x c e p t b y t ri al a n d e r r o r . H o w e v e r , c e r t a in c o r r e la -

t io n s w e r e e s t a b l i s h e d w h i c h f a c il i ta t e d p a r a m e t e r e s t i m a t i o n . F o r e x a m p l e ,

t h e p e a k p o s i t i o n is c o r r e l a t e d w i t h V M 1 , w h i l e t h e g r a d i e n t o f t h e

d o w n w a r d s l o p e is a f f e ct e d b y t h e p a r a m e t e r s Q D a n d K B S m i th , 1 9 91 ).

T h e t im e r e q u i r e d t o g ai n an u n d e r s t a n d i n g o f t h e m o d e l s t r u c t u r e a n d t h e

e f f e c t o f p a r a m e t e r s o n t h e f o r m o f C c u r v e s is m i n i m a l c o m p a r e d w i t h th e

i m p r o v e m e n t in a c c u ra c y w h ic h i s a c h i e v e d c o m p a r e d w i t h c o n v e n t i o n a l

a n a ly t ic a l m e t h o d s . T h e r e q u i r e m e n t f o r a c c u r a t e i n f o r m a t i o n a b o u t hy -

d r a u l i c c h a r a c t e ri s t ic s w h e n d e s i g n in g a b i o l o g ic a l sy s t e m s e n c o u r a g e s t h e

w i d e s p r e a d u s e o f th is m o d e l .

CONCLUSIONS

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

a c c u r a t e a n d i n f o r m a t i v e m e t h o d o f a n a ly s is . D e s i g n e n g i n e e r s r e q u i r e

i n f o r m a t i o n a b o u t t h e t y p e o f m i x i ng o c c u r r in g u n d e r d i f f e r e n t p h y s ic a l

a n d o p e r a t i o n a l c o n d i t i o n s i n o r d e r t o a c h i e v e m a x i m u m p r o c e s s e ff ic i en c y .

A n a l y t i c a l m o d e l s d o n o t g i v e c o n s i s t e n t ly a c c u r a t e r e s u lt s b e c a u s e t h e y

o v e r s i m p l i fy t h e m i x in g p r o c e s s i n a m i x e d s y s t e m . D i f f e r e n t f l o w r e g i m e s

e x is t w i t h i n o n e v e s s e l a n d t h e s e z o n e s i n t e r a c t w i t h e a c h a n o t h e r . C o m -

b i n e d m o d e l s a r e b a s e d o n t h e c o n c e p t o f d i f f e re n t f l o w r e gi m e s , b u t

d e p e n d u p o n c o n s t a n t o p e r a t i n g c o n d i t i o n s a n d d o n o t a c c o u n t f o r t ra n s -

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

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

o c c u r r i n g i n th e c o n t a c t p r o c e s s . T h e m i x e d a n d d e a d v o l u m e w e r e q u a n t i -

f i e d a n d t h e t r a n s f e r m e c h a n i s m s a l so in c l u d e d i n t h e f lo w p a t t e r n . T h e

m o d e l h a s t h e p o t e n t i a l f o r a d a p t a t i o n t o i n c lu d e h y d r o d y n a m i c a n d k i n et ic

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

s p e c i f i e d s e t o f o p e r a t i n g c o n d i t i o n s .

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