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