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Experimental and mathematical Modelling of Activated Sludge Process
E X P E R I M E N T A L A N D M A T H E M A T I C A L M O D E L L I N G OF A C T I V A T E D SLUDGE PROCESS P . F A R K A S O V A l , J . DERCO'
and M.
KRALIK'
Department o f E n v i r o n m e n t a l Chemistry and Technology, S l o v a k Technical Univeraity, Bratislava Department o f Organic Technology, Slovak Technical U n i v e r s i t y , Bratislava SUMMARY T h i s p a p e r d e a l s w i t h e x p e r i m e n t a l i n v e s t i g a t i o n a n d m at h em at i c a l m o d e l l i n g o f a c t i v a t e d s l u d g e p r o c e s s . T h r e e m a t h e m a t i c a l mod e l s f o r p r o c e s s d e s c r i p t i o n were d e r i v e d , e x p e r i m e n t a l l y v e r i f i e d f o r a t r a n s i e n t s u b s t r a t e c o n c e n t r a t i o n l o a d a n d t h e r e s u l t s were c o m p a r e d . The f i r a t t w o m o d e l s a r e b a s e d o n s u b s t r a t e a n d b i o m a s s m a t e r i a l b a l a n c e s a r o u n d a n a e r a t e d t a n k . The t h i r d o n e i s a d i s c r e t e s t a t i s t i c a l m o d e l . The b e s t f i t b e t w e e n e x p e r i m e n t a l a n d c s l c u l a t e d v a l u e s was o b t a i n e d u s i n g t h e s t a t i s t i c a l m o d e l . PREFACE C u r r e n t l y , t h e moat economic t r e a t m e n t o f w a s t e w a t e r s c o n t a i n i n g b i o d e g r a d a b l e o r g a n i c c o m p o u n d s i s a c h i e v e d by t h e u t i l i z a t i o n o f b i o c h e m i c a l r e a c t i o n s m e d i a t e d by m i c r o o r g a n i s m s . One o f t h e moat w i d e l y u s e d b i o l o g i c a l t r e a t m e n t methods t h a t r e q u i r e s a n a e r o b i c environment f o r e f f e c t i v e o p e r a t i o n is t h e a c t i v a t e d s l u d g e pro-
cess 1 1 1 . Because o f time v a r i a t i o n a n d c h a n g e i n t h e f l o w r a t e a n d t h e composition of t h e wastewater, t h e process is usually operated under highly variable losding conditions with variability of effluent q u a n t i t y . Many d e s i g n e n g i n e e r s d o n o t a p p r e c i a t e t h e d y n a m i c c h a m r a c t e r of t h e p r o c e s s , and s t e a d y - s t a t e p r o c e d u r e s are used.
Tran-
s i e n t l o a d i n g s t u d i e s o f a c t i v a t e d s l u d g e p r o c e s s e s a r e of i n t e r e s t b o t h t o m i c r o b i o l o g i s t s and e n g i n e e r s . M i c r o b i o l o g i a t s have been i n t e r e s t e d i n t h e dynamics o f m i c r o b i a l r e s p o n s e from t h e p o i n t o f
.
view t h a t i n f o r m a t i o n o b t a i n e d c o u l d b e h e l p f u l t o u n d e r s t a n d i n g t h e mechanisms i n v o l v e d i n m i c r o b i a l growth and r e p r o d u c t i o n .
Practical
i n t e r e s t o f e n g i n e e r s is focussed on d e s i g n and c o n t r o l o f t h e a c t i vated sludge process.
The i n c r e a s i n g a v a i l a b i l i t y o f c o m p u t e r s e n -
c o u r a g e s t h e uae o f m a t h e m a t i c a l models, which are a p p l i c a b l e b o t h
-
-
78
i n d e s i g n and o p e r a t i o n o f w a s t e w a t e r
treatment plants.
A l a r g e amount o f l i t e r a t u r e h a s a p p e a r e d i n t h e l a s t t w e n t y y e a r s on t h e d y n a m i c m o d e l l i n g o f a c t i v a t e d s l u d g e p r o c e s s e s . o f the transient
Many
l o a d i n g s t u d i e s have been p e r f o r m e d u s i n g t h e c o n t i -
nuous f l o w s t i r r e d t a n k r e a c t o r w i t h o u t s l u d g e r e c y c l e s t a t e o f wastewater
t r e a t m e n t system c o n t r o l ,
f2-81.
The
d y n a m i c m o d e l s a n d i-
d e n t i f i c a t i o n a p p l i c a t i o n s h a v e b e e n r e v i e w e d b y Andrews [ 9 1 a n d Olson (101.
Dynamic b e h a v i o u r o f a c t i v a t e d s l u d g e has been s t u d i e d
u s i n g c o m p u t e r s i m u l a t i o n b y B u s b y 1111. A t t i r
1 1 2 1 has d e s c r i b e d
t h e r e s u l t s o f a s i m u l a t i o n s t u d y o f t h e dynamics and c o n t r o l o f t h e a c t i v a t e d sludge process,
u s i n g a model o f dynamics o f c o n t i n u o u s
s e d i m e n t a t i o n t h a t a c c o u n t s f o r s e v e r a l d i s t i n c t models o f operation.
A dynamic model o f n i t r i f i c a t i o n i n 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 has been developed,
a n d an e x p e r i m e n t a l a n d s i m u l a t i o n s t u d y
h a s b e e n p r e s e n t e d b y P o d u s k a 1131.
T h k r i e n I 1 4 1 h a s p r e s e n t e d a mo-
d e l f o r p r e d i c t i n g t h e dynamics o f oxygen u t i l i z a t i o n i n t h e a c t i v a t e d sludge process.
M o d e l s m e n t i o n e d above u s e u s u a l l y f o r p r o c e s s
d e s c r i p t i o n Monod t y p e k i n e t i c e q u a t i o n s f o r a m i c r o b i a l g r o w t h a n d Michaelis-Menten type k i n e t i c equations f o r t h e b i o l o g i c a l o x i d a t i o n o f organic substrate.
These t y p e s o f m o d e l s c o n t a i n a l a r g e s e t o f
d i f f e r e n t i a l e q u a t i o n s i n which t h e k i n e t i c c o n s t a n t s appear.
The
v a l u e o f t h e s e k i n e t i c parameters i s sometimes d i f f i c u l t t o d e t e r m i ne w i t h p r e c i s i o n .
From t h e p r a c t i c a l p o i n t o f view t h e s t a t i s t i c a l
model c o u l d a l s o be a v a i l a b l e f o r 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 control.
Berthouex
1151 h a s d e v e l o p e d s t a t i s t i c a l t e c h n i q u e s t o s t u d y
t h e d a t a from m u n i c i p a l wastewater
treatment plants.
died the impact o f operating conditions,
Hansen I 1 6 1 s t u -
waste c o n t r i b u t i o n s ,
e n v i r o n m e n t a l f a c t o r s on t r e a t m e n t o f i n d u s t r i a l wastewater
and
evaluated
using a s t a t i s t i c a l technique. The p u r p o s e o f t h i s w o r k was t o i n v e s t i g a t e t h e r e s p o n s e t o quantitative
s h o c k l o a d i m p o s s e d u p o n t h e p r o c e s s a n d t o e x a m i n e a-
v a i l a b i l i t y o f t h r e e d e r i v e d m a t h e m a t i c a l models f o r p r o c e s s desc r i p t i o n under t r a n s i e n t
conditions.
MATHEMATICAL MODEL DESCRIPTION
F o r t h e m a t h e m a t i c a l p r o c e s s d e s c r i p t i o n we d e r i v e d t h r e e models.
The f i r s t two a r e k i n e t i c models,
t h e t h i r d one i s a s t a t i s t i -
c a l model. The s u b s t r a t e a n d b i o m a s s m a t e r i a l b a l a n c e f o r a c o m p l e t e l y m i x e d b i o r e a c t o r i n k i n e t i c m o d e l s may be d e s c r i b e d i n e q u a t i o n s (1, 2 ) .
-
79
-
Substrate balance
(Symbols a r e e x p l a i n e d a t t h e end o f t h i s p a p e r ) . Biomass b a l a n c e dX R9
-
= dt
qx
Michaelis-Menten
(2)
'a
t y p e r e l a t i o n s h i p was u s e d f o r d e s c r i p t i o n
o f s u b s t r a t e u t i l i z a t i o n r a t e rs
r
x.5
= - - pmax
8
K~
'obs
+
Monod r e l a t i o n s h i p was u s e d f o r d e s c r i p t i o n o f maximum m i c r o o r g a n i s m s g r o w t h r a t e pmax
5 "max Model No.
KS
(4)
+
2 i s b a s e d on t h e same p r i n c i p l e s ,
l a t i o n s h i p i s extended,
b u t t h e Monod r e -
and s l s o t a k e s i n t o a c c o u n t t h e decay o f
which can be d e s c r i b e d as
microorganisms,
S
p
=
%ax
Ks
+
The e x p l i c i t f o u r t h - o r d e r
S
-
(5)
kd.X
Runge-Kutta-Merson
m e t h o d [ 1 7 1 was
used f o r s o l v i n g t h e s e t o f d i f f e r e n t i a l equations.
The s i m p l e x o p -
t i m i z a t i o n t e c h n i q u e 1 1 8 1 waa u s e d t o d e t e r m i n e t h e v a l u e o f b i o k i n e t i c p a r a m e t e r s by m i n i m i z a t i o n o f t h e f u n c t i o n
To r e d u c e t h e c o m p u t a t i o n a l t i m e , r i z a t i o n u s i n g t h e T a y l o r s e r i e s 1191.
we u s e d t h e m e t h o d o f l i n e a -
-
80
-
The t h i r d m o d e l i s a d i s c r e t e s t a t i s t i c a l m o d e l w i t h one i n p u t a n d one o u t p u t ,
and c a n b e d e s c r i b e d a s
... an,
The p a r a m e t e r s al
...
bo
bm w e r e e s t i m a t e d u s i n g l i n e a r
[ 19 1 .
regression
EXPERIMENTAL The e x p e r i m e n t s w e r e c a r r i e d o u t i n l a b o r a t o r y a p p a r a t u s c o n s i s t i n g o f a c o m p l e t e l y m i x e d b i o r e a c t o r and s e t t l e r . had a volume o f a p p r o x i m a t e l y f e e d f l o w r a t e o f 3.06
4.4
ml.min-l.
The b i o r e a c t o r
1 and was s u p p l i e d w i t h a c o n s t a n t T h r e e a i r d i f f u s e r s a t r i g h t an-
g l e s a t the bottom o f the bioreactor provided aeration o f the biomass.
S l u d g e was c o n d i t i o n e d t o a f e e d c o n t a i n i n g c y c l o h e x a n o l e
( c = 0.56 (c
=
0.33
dehyde ( c
k ~ j . m - ~ ) c, y c l o h e x a n o n e ( c
= 0.56
k g . n ~ - ~ ) ,p e n t a e r y t r i t o l
k g . ~ n - ~ ) ,h e x a m e t y l e n e t e t r a a m i n e ( c
=
0.0375
0.48
k g . ~ n - ~ ) ,as s o u r c e s o f c a r b o n ,
a m o u n t s o f m i n e r a l s a l t s a c c o r d i n g t o t h e r a t i o C:N:'P The a v e r a g e COD v a l u e was 3.894
k g . n ~ - ~ ) ,f o r m a l -
besides the proper o f 100:5:1.
k g . ~ n - ~ .The b i o d e g r a d a b l e p o r t i o n
o f s u b s t r a t e corresponds t o 0.5.
The s e t t l e d s l u d g e was r e c y c l e d t o
t h e b i o r e a c t o r u s i n g a p e r i s t a l t i c pump a n d t h e s l u d g e was w a s t e d f r o m t h e a e r a t i o n t a n k i n o r d e r t o m a i n t a i n t h e mean s l u d g e age Qx
= 10
days.COD,
suspended s o l i d s ,
NH;
and f o r m a l d e h y d e c o n c e n t r a -
t i o n a n a l y s i s were p e r f o r m e d f o l l o w i n g s t a n d a r d m e t h o d s b y 1201. pH and d i s s o l v e d o x y g e n m e a s u r e m e n t s w e r e p e r f o r m e d u s i n g a R a d e l k i s Aquacheck. R E S U L T S AND D I S C U S S I O N
Before s t a r t i n g t h e s t e p shock l o a d , under steady-state
conditions.
t h e s y s t e m was o p e r a t e d
A f t e r reaching the steady-state,
( o u t p u t C O O and M L S S v a l u e s were o s c i l a t i n g a r r o u n d s t a t i o n a r y
va-
l u e s ) t h e s t e p t w o f o l d d e c r e a s e i n s u b s t r a t e c o n c e n t r a t i o n was i m possed t o t h e system.
The d i s s o l v e d o x y g e n c o n c e n t r a t i o n
r e a c t o r was a l w a y s m a i n t a i n e d a b o v e t h e g r o w t h - l i m i t i n g i.e. the
above 2 m g . 1 - l .
i n the bio-
conditions,
The a v e r a g e C O D s u b s t r a t e c o n c e n t r a t i o n a f t e r
s t e p c h a n g e was 1 8 0 0 m g . 1 - l .
The C O O c o n c e n t r a t i o n r e s p o n s e o f
t h e a c t i v a t e d s l u d g e r e a c t o r i s shown i n F i g .
1. One c a n o b s e r v e
oscillations
COO v a l u e s .
-
r a n g i n g a b o v e a n d b e l o w new s t e a d y - s t a t e
possed change. steady-state
81
after
an i m -
R e l a t i v e l y s m o o t h t r a n s m i t i o n s w e r e made t o t h e new
i n t h e case o f biomass c o n c e n t r a t i o n i n comparison w i t h
I n l e s s t h a n 1 0 d a y s a f t e r s h o c k was i m p o s e d , c h a n g e s o f
biomass c o l o u r and f l o c s m a c r o s c o p i c appearance were observed. new s t e a d y - s t a t e ved,
was r e a c h e d ,
b u t no changes i n m a g n i t u d e o f
o f the transient
After
t h e i n i t i a l b i o m a s s c o l o u r was o b s e r s l u d g e f l o c s had occured.
Some
r e s p o n s e d a t a were u s e d t o o b t a i n t h e b i o k i n e t i c
parameters f a r t h e m a t h e m a t i c a l models.
The c a l c u l a t e d COD v a l u e s
d u r i n g t h e s t e p s h o c k t e s t u s i n g t h e Monod and m o d i f i e d Monod equat i o n are a l s o p l o t t e d i n F i g .
l. F r o m t h i s F i g . l one c a n s e e t h a t
a b e t t e r f i t b e t w e e n e x p e r i m e n t a l a n d c a l c u l a t e d d a t a was o b t a i n e d
n 0 u
T
O
5
1;
1;
2b
215
o;
3;j
Lb
L; t IDAYSl
F i g . 1. C O O c o n c e n t r a t i o n r e s p o n s e o f a c t i v a t e d s l u d g e p r o c e s s t o twofold decreasing o f feed concentration experimental - - - - - - c a l c u l a t e d u s i n g Monod e q u a t i o n . . . . . . . . . . . c a l c u l a t e d u s i n g m o d i f i e d Monod e q u a t i o n .
-
u s i n g t h e m o d i f i e d Monod e q u a t i o n .
The g r e a t e s t d i f f e r e n c e s between
e x p e r i m e n t a l a n d c a l c u l a t e d v a l u e s w e r e o b s e r v e d i n t h e c a s e o f COD d u r i n g t h e f i r s t stage o f t h e experimental run.
One c a n c o n c l u d e t h a t
an i n s t a n t a n e o u s c h a n g e i n e p e c i f i c g r o w t h r a t e d i d n o t o c c u r a s p r e d i c t e d b y t h e Monod e q u a t i o n . w o r k o f Mor 1 2 1 1 .
These r e s u l t s a r e c o n s i s t e n t w i t h t h e
I t was o b s e r v e d t h a t t h e t i m e d e l a y f o r t h e s y s t e m
t o r e s p o n d t o t h e s h o c k was d e p e n d e n t o n t h e m a g n i t u d e o f t h e s p e c i f i c growth rate.
I t s h o u l d be n o t e d t h a t s a t u r a t i o n c o n s t a n t s c a l c u -
l a t e d ( f o r t h e Monod m o d e l
-
82
K s = 0 . 7 8 4 kg.m-3
a n d f o r m o d i f i e d Monod
K s = 0.786 k g . ~ n - ~ )a r e s i g n i f i c a n t l y h i g h e r t h a n t h o s e p u b l i s h e d e l s e w h e r e 1 2 2 1 . We assume t h a t t h i s i s b e c a u s e o f a r e l a t i v e l y h i g h p o r t i o n o f b i o l o g i c a l l y r e s i s t e n t HMT compound i n t h e f e e d 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 o p e r a t e d u n d e r pH v a l u e s a b o u t 7 .
Comparing
c a l c u l a t e d a n d e x p e r i m e n t a l v a l u e s one c a n s e e t h a t t h e M o n o d - t y p e k i n e t i c e q u a t i o n i s n o t adequate f o r t h e p r e d i c t i o n o f t r a n s i e n t b e h a v i o u r o f an a c t i v a t e d s l u d g e p r o c e s s . S i m i l a r r e s u l t s w e r e o b t a i n e d a l s o u s i n g l i n e a r i z e d Monod a n d m o d i f i e d Monod e q u a t i o n s . E x p e r i m e n t a l a n d c a l c u l a t e d v a l u e s o f COD c o n c e n t r a t i o n u s i n g s t a t i s t i c a l m o d e l s a r e shown i n F i g .
2.
2 one c a n c o n f i r m
From F i g .
t h a t t h e d i s c r e t e s t a t i s t i c a l m o d e l i s more s u i t a b l e f o r d e s c r i b i n g a c t i v a t e d sludge process dynamics.
The c o m p u t a t i o n s 1 t i m e f o r t h e
m o d e l p a r a m e t e r s e s t i m a t i o n was s i g n i f i c a n t l y s h o r t e r i n c o m p a r i s o n t o b o t h n o n l i n e a r and l i n e a r i z e d k i n e t i c models.
mL
l5
0.6
Y
I
0
0
0.5
OA
0.3
0.2
(
5
10
15
20
25
30
35
40
45 t [ OAYSl
F i g . 2. C O D c o n c e n t r a t i o n r e s p o n s e o f a c t i v a t e d s l u d g e p r o c e s s t o twofold decreasing o f feed concentration experimental ------ c a l c u l a t e d u s i n g d e s c r e t e s t a t i s t i c a l model. CONCL US I ON5 The m a j o r o b j e c t i v e o f t h i s w o r k was t o e x a m i n e t h e e x p e r i m e n t a l l y dynamic b e h a v i o u r o f a c t i v a t e d s l u d g e process.
Previously the
-
83
-
o b t a i n e d e x p e r i m e n t a l d a t a was u s e d f o r v e r i f i c a t i o n o f t h r e e d e r i ved m a t h e m a t i c a l models.
From c a l c u l a t i o n s we c a n assume,
that the
Monod-type k i n e t i c models a r e n o t a c c u r a t e i n t h e p r e d i c t i o n o f t r a n s i e n t behaviour o f t h e a c t i v a t e d sludge process. r i f i e d model
-
d i s c r e t e s t a t i s t i c a l model
-
The t h i r d ve-
provides a better f i t
between e x p e r i m e n t a l and c a l c u l a t e d v a l u e s . The n e x t s t e p o f o u r work i s t o v e r i f y a s t a t i s t i c a l m o d e l u s i n g more i n p u t s . SYMBOLS ai, COD kd KS
bi
J
parameters o f d i s c r e t e s t a t i s t i c a l model c h e m i c a l o x y g e n demand endogenous decay c o e f f i c i e n t substrate saturation constant
M
number o f m e a s u r e m e n t s
m
number o f p a r a m e t e r s b .
n
number o f p a r a m e t e r s a
9
feed flow r a t e
qX
rs
R
9
RS
S
=o t
J
i
biomass wastage r a t e substrate u t i l i z a t i o n rate microbial growth r a t e substrate removal r a t e e f f l u e n t substrate concentration feed substrate concentration time
A t
time
U
i n p u t i n s t a t i s t i c a l model
Ut "a
X
'obs Y
yY
L1
Pmax
interval
value o f u i n time t a e r a t i o n t a n k volume mixed l i q u o r suspended s o l i d s ( M L S S ) observed y i e l d c o e f f i c i e n t o u t p u t i n s t a t i s t i c a l model value o f y i n time t s p e c i f i c growth r a t e maximum s p e c i f i c g r o w t h r a t e
w
minimization
e
s l u d g e age
function
-
84
-
REFERENCES
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21 22
M e t c a l f Eddy, W a s t e w a t e r E n g i n e e r i n g , T r e a t m e n t , d i s p o s a l , r e u s e , M c G r a w - H i l l I n c . , New Y o r k , 1972. K . K o m o l r i t a n d A.F. Gaudy, J o u r n a l WPCF, 3 8 , 85, 1 9 6 6 . K. K o m o l r i t a n d A.F. Gaudy, J o u r n a l WPCF, 3 8 , 1 2 5 9 , 1 9 6 6 . J.R. M o r a n d A. F i e c h t e r , B i o t e c h . a n d B i o e n g . , X , 7 8 7 , 1968. J.W. G i l l e y a n d H.R. Bungay, B i o t e c h . a n d B i o e n g . , I X , 6 1 7 , 1967. J.W. G i l l e y a n d H.R. Bungay, B i o t e c h . a n d B i o e n g . , X, 99, 1968. T.B. Young e t a l , B i o t e c h . a n d B i o e n g . , X I I , 747, 1970. S. Koga a n d A.F. Humprey, B i o t e c h . a n d B i o e n g . , I X , 3 7 5 , 1 9 6 7 . J.F. Andrews, W a t e r Res., 8, 261, 1974. G. O l s o n , A I C h E Symp. S e r . N. 1 5 9 , 72, 52, 1976. J.B. B u s b y a n d J.F. Andrews, J o u r n a l WPCF, 47, 1055, 1 9 7 5 . V . A t t i r a n d M.M. Denn, A I C h E J . 24,, 6 9 3 , 1978. R.A. P o d u s k a , J.F. Andrews, J o u r n a l WPCF, 4 7 , 2599, 1 9 7 5 . N. T h 6 r i e n a n d S. P e r d i e u x , J o u r n a l WPCF, 53, 576, 1 9 8 1 . P . M . B e r t h o u e x e t a l l . , W a t e r Res., 1 0 , 6 8 9 , 1976. J.L. Hansen, A.E. F i o k and J.C. H o v i o u s , J o u r n a l WPCF, 52, 1 9 6 6 , 1980. M. K u b f E e k , N u m e r i c k 6 a l g o r i t m y GeSeni c h e m i c k o - i n f e n f r s k f c h d l o h , SNTL P r a h a 1 9 8 3 . D.A. P i e r r e , O p t i m i z a t i o n t h e o r y w i t h a p p l i c a t i o n s , J . W i l l e y , New Y o r k 1969. R e k t o r y s a k o l . , P F e h l e d u f i t b m a k e m a t i k y SNTL P r a h a 1 9 8 8 . M. HorBkovB, P. L i s c h k e a n d A . G r u n w a l d , M e t o d y c h e m i c k b a n a l y z y vod, SNTL P r a h a , 1981. J.R. Mor a n d A. F i e c h t e r , B i o t e c h . a n d B i o e n g . , X, 7 8 7 , 1 9 6 8 . G. T c h o b a n o g l o u s , W a s t e w a t e r E n g i n e e r i n g , M c G r a w - H i l l , I n c . , New Y o r k , 1977.
and M.
KRALIK'
Department o f E n v i r o n m e n t a l Chemistry and Technology, S l o v a k Technical Univeraity, Bratislava Department o f Organic Technology, Slovak Technical U n i v e r s i t y , Bratislava SUMMARY T h i s p a p e r d e a l s w i t h e x p e r i m e n t a l i n v e s t i g a t i o n a n d m at h em at i c a l m o d e l l i n g o f a c t i v a t e d s l u d g e p r o c e s s . T h r e e m a t h e m a t i c a l mod e l s f o r p r o c e s s d e s c r i p t i o n were d e r i v e d , e x p e r i m e n t a l l y v e r i f i e d f o r a t r a n s i e n t s u b s t r a t e c o n c e n t r a t i o n l o a d a n d t h e r e s u l t s were c o m p a r e d . The f i r a t t w o m o d e l s a r e b a s e d o n s u b s t r a t e a n d b i o m a s s m a t e r i a l b a l a n c e s a r o u n d a n a e r a t e d t a n k . The t h i r d o n e i s a d i s c r e t e s t a t i s t i c a l m o d e l . The b e s t f i t b e t w e e n e x p e r i m e n t a l a n d c s l c u l a t e d v a l u e s was o b t a i n e d u s i n g t h e s t a t i s t i c a l m o d e l . PREFACE C u r r e n t l y , t h e moat economic t r e a t m e n t o f w a s t e w a t e r s c o n t a i n i n g b i o d e g r a d a b l e o r g a n i c c o m p o u n d s i s a c h i e v e d by t h e u t i l i z a t i o n o f b i o c h e m i c a l r e a c t i o n s m e d i a t e d by m i c r o o r g a n i s m s . One o f t h e moat w i d e l y u s e d b i o l o g i c a l t r e a t m e n t methods t h a t r e q u i r e s a n a e r o b i c environment f o r e f f e c t i v e o p e r a t i o n is t h e a c t i v a t e d s l u d g e pro-
cess 1 1 1 . Because o f time v a r i a t i o n a n d c h a n g e i n t h e f l o w r a t e a n d t h e composition of t h e wastewater, t h e process is usually operated under highly variable losding conditions with variability of effluent q u a n t i t y . Many d e s i g n e n g i n e e r s d o n o t a p p r e c i a t e t h e d y n a m i c c h a m r a c t e r of t h e p r o c e s s , and s t e a d y - s t a t e p r o c e d u r e s are used.
Tran-
s i e n t l o a d i n g s t u d i e s o f a c t i v a t e d s l u d g e p r o c e s s e s a r e of i n t e r e s t b o t h t o m i c r o b i o l o g i s t s and e n g i n e e r s . M i c r o b i o l o g i a t s have been i n t e r e s t e d i n t h e dynamics o f m i c r o b i a l r e s p o n s e from t h e p o i n t o f
.
view t h a t i n f o r m a t i o n o b t a i n e d c o u l d b e h e l p f u l t o u n d e r s t a n d i n g t h e mechanisms i n v o l v e d i n m i c r o b i a l growth and r e p r o d u c t i o n .
Practical
i n t e r e s t o f e n g i n e e r s is focussed on d e s i g n and c o n t r o l o f t h e a c t i vated sludge process.
The i n c r e a s i n g a v a i l a b i l i t y o f c o m p u t e r s e n -
c o u r a g e s t h e uae o f m a t h e m a t i c a l models, which are a p p l i c a b l e b o t h
-
-
78
i n d e s i g n and o p e r a t i o n o f w a s t e w a t e r
treatment plants.
A l a r g e amount o f l i t e r a t u r e h a s a p p e a r e d i n t h e l a s t t w e n t y y e a r s on t h e d y n a m i c m o d e l l i n g o f a c t i v a t e d s l u d g e p r o c e s s e s . o f the transient
Many
l o a d i n g s t u d i e s have been p e r f o r m e d u s i n g t h e c o n t i -
nuous f l o w s t i r r e d t a n k r e a c t o r w i t h o u t s l u d g e r e c y c l e s t a t e o f wastewater
t r e a t m e n t system c o n t r o l ,
f2-81.
The
d y n a m i c m o d e l s a n d i-
d e n t i f i c a t i o n a p p l i c a t i o n s h a v e b e e n r e v i e w e d b y Andrews [ 9 1 a n d Olson (101.
Dynamic b e h a v i o u r o f a c t i v a t e d s l u d g e has been s t u d i e d
u s i n g c o m p u t e r s i m u l a t i o n b y B u s b y 1111. A t t i r
1 1 2 1 has d e s c r i b e d
t h e r e s u l t s o f a s i m u l a t i o n s t u d y o f t h e dynamics and c o n t r o l o f t h e a c t i v a t e d sludge process,
u s i n g a model o f dynamics o f c o n t i n u o u s
s e d i m e n t a t i o n t h a t a c c o u n t s f o r s e v e r a l d i s t i n c t models o f operation.
A dynamic model o f n i t r i f i c a t i o n i n 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 has been developed,
a n d an e x p e r i m e n t a l a n d s i m u l a t i o n s t u d y
h a s b e e n p r e s e n t e d b y P o d u s k a 1131.
T h k r i e n I 1 4 1 h a s p r e s e n t e d a mo-
d e l f o r p r e d i c t i n g t h e dynamics o f oxygen u t i l i z a t i o n i n t h e a c t i v a t e d sludge process.
M o d e l s m e n t i o n e d above u s e u s u a l l y f o r p r o c e s s
d e s c r i p t i o n Monod t y p e k i n e t i c e q u a t i o n s f o r a m i c r o b i a l g r o w t h a n d Michaelis-Menten type k i n e t i c equations f o r t h e b i o l o g i c a l o x i d a t i o n o f organic substrate.
These t y p e s o f m o d e l s c o n t a i n a l a r g e s e t o f
d i f f e r e n t i a l e q u a t i o n s i n which t h e k i n e t i c c o n s t a n t s appear.
The
v a l u e o f t h e s e k i n e t i c parameters i s sometimes d i f f i c u l t t o d e t e r m i ne w i t h p r e c i s i o n .
From t h e p r a c t i c a l p o i n t o f view t h e s t a t i s t i c a l
model c o u l d a l s o be a v a i l a b l e f o r 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 control.
Berthouex
1151 h a s d e v e l o p e d s t a t i s t i c a l t e c h n i q u e s t o s t u d y
t h e d a t a from m u n i c i p a l wastewater
treatment plants.
died the impact o f operating conditions,
Hansen I 1 6 1 s t u -
waste c o n t r i b u t i o n s ,
e n v i r o n m e n t a l f a c t o r s on t r e a t m e n t o f i n d u s t r i a l wastewater
and
evaluated
using a s t a t i s t i c a l technique. The p u r p o s e o f t h i s w o r k was t o i n v e s t i g a t e t h e r e s p o n s e t o quantitative
s h o c k l o a d i m p o s s e d u p o n t h e p r o c e s s a n d t o e x a m i n e a-
v a i l a b i l i t y o f t h r e e d e r i v e d m a t h e m a t i c a l models f o r p r o c e s s desc r i p t i o n under t r a n s i e n t
conditions.
MATHEMATICAL MODEL DESCRIPTION
F o r t h e m a t h e m a t i c a l p r o c e s s d e s c r i p t i o n we d e r i v e d t h r e e models.
The f i r s t two a r e k i n e t i c models,
t h e t h i r d one i s a s t a t i s t i -
c a l model. The s u b s t r a t e a n d b i o m a s s m a t e r i a l b a l a n c e f o r a c o m p l e t e l y m i x e d b i o r e a c t o r i n k i n e t i c m o d e l s may be d e s c r i b e d i n e q u a t i o n s (1, 2 ) .
-
79
-
Substrate balance
(Symbols a r e e x p l a i n e d a t t h e end o f t h i s p a p e r ) . Biomass b a l a n c e dX R9
-
= dt
qx
Michaelis-Menten
(2)
'a
t y p e r e l a t i o n s h i p was u s e d f o r d e s c r i p t i o n
o f s u b s t r a t e u t i l i z a t i o n r a t e rs
r
x.5
= - - pmax
8
K~
'obs
+
Monod r e l a t i o n s h i p was u s e d f o r d e s c r i p t i o n o f maximum m i c r o o r g a n i s m s g r o w t h r a t e pmax
5 "max Model No.
KS
(4)
+
2 i s b a s e d on t h e same p r i n c i p l e s ,
l a t i o n s h i p i s extended,
b u t t h e Monod r e -
and s l s o t a k e s i n t o a c c o u n t t h e decay o f
which can be d e s c r i b e d as
microorganisms,
S
p
=
%ax
Ks
+
The e x p l i c i t f o u r t h - o r d e r
S
-
(5)
kd.X
Runge-Kutta-Merson
m e t h o d [ 1 7 1 was
used f o r s o l v i n g t h e s e t o f d i f f e r e n t i a l equations.
The s i m p l e x o p -
t i m i z a t i o n t e c h n i q u e 1 1 8 1 waa u s e d t o d e t e r m i n e t h e v a l u e o f b i o k i n e t i c p a r a m e t e r s by m i n i m i z a t i o n o f t h e f u n c t i o n
To r e d u c e t h e c o m p u t a t i o n a l t i m e , r i z a t i o n u s i n g t h e T a y l o r s e r i e s 1191.
we u s e d t h e m e t h o d o f l i n e a -
-
80
-
The t h i r d m o d e l i s a d i s c r e t e s t a t i s t i c a l m o d e l w i t h one i n p u t a n d one o u t p u t ,
and c a n b e d e s c r i b e d a s
... an,
The p a r a m e t e r s al
...
bo
bm w e r e e s t i m a t e d u s i n g l i n e a r
[ 19 1 .
regression
EXPERIMENTAL The e x p e r i m e n t s w e r e c a r r i e d o u t i n l a b o r a t o r y a p p a r a t u s c o n s i s t i n g o f a c o m p l e t e l y m i x e d b i o r e a c t o r and s e t t l e r . had a volume o f a p p r o x i m a t e l y f e e d f l o w r a t e o f 3.06
4.4
ml.min-l.
The b i o r e a c t o r
1 and was s u p p l i e d w i t h a c o n s t a n t T h r e e a i r d i f f u s e r s a t r i g h t an-
g l e s a t the bottom o f the bioreactor provided aeration o f the biomass.
S l u d g e was c o n d i t i o n e d t o a f e e d c o n t a i n i n g c y c l o h e x a n o l e
( c = 0.56 (c
=
0.33
dehyde ( c
k ~ j . m - ~ ) c, y c l o h e x a n o n e ( c
= 0.56
k g . n ~ - ~ ) ,p e n t a e r y t r i t o l
k g . ~ n - ~ ) ,h e x a m e t y l e n e t e t r a a m i n e ( c
=
0.0375
0.48
k g . ~ n - ~ ) ,as s o u r c e s o f c a r b o n ,
a m o u n t s o f m i n e r a l s a l t s a c c o r d i n g t o t h e r a t i o C:N:'P The a v e r a g e COD v a l u e was 3.894
k g . n ~ - ~ ) ,f o r m a l -
besides the proper o f 100:5:1.
k g . ~ n - ~ .The b i o d e g r a d a b l e p o r t i o n
o f s u b s t r a t e corresponds t o 0.5.
The s e t t l e d s l u d g e was r e c y c l e d t o
t h e b i o r e a c t o r u s i n g a p e r i s t a l t i c pump a n d t h e s l u d g e was w a s t e d f r o m t h e a e r a t i o n t a n k i n o r d e r t o m a i n t a i n t h e mean s l u d g e age Qx
= 10
days.COD,
suspended s o l i d s ,
NH;
and f o r m a l d e h y d e c o n c e n t r a -
t i o n a n a l y s i s were p e r f o r m e d f o l l o w i n g s t a n d a r d m e t h o d s b y 1201. pH and d i s s o l v e d o x y g e n m e a s u r e m e n t s w e r e p e r f o r m e d u s i n g a R a d e l k i s Aquacheck. R E S U L T S AND D I S C U S S I O N
Before s t a r t i n g t h e s t e p shock l o a d , under steady-state
conditions.
t h e s y s t e m was o p e r a t e d
A f t e r reaching the steady-state,
( o u t p u t C O O and M L S S v a l u e s were o s c i l a t i n g a r r o u n d s t a t i o n a r y
va-
l u e s ) t h e s t e p t w o f o l d d e c r e a s e i n s u b s t r a t e c o n c e n t r a t i o n was i m possed t o t h e system.
The d i s s o l v e d o x y g e n c o n c e n t r a t i o n
r e a c t o r was a l w a y s m a i n t a i n e d a b o v e t h e g r o w t h - l i m i t i n g i.e. the
above 2 m g . 1 - l .
i n the bio-
conditions,
The a v e r a g e C O D s u b s t r a t e c o n c e n t r a t i o n a f t e r
s t e p c h a n g e was 1 8 0 0 m g . 1 - l .
The C O O c o n c e n t r a t i o n r e s p o n s e o f
t h e a c t i v a t e d s l u d g e r e a c t o r i s shown i n F i g .
1. One c a n o b s e r v e
oscillations
COO v a l u e s .
-
r a n g i n g a b o v e a n d b e l o w new s t e a d y - s t a t e
possed change. steady-state
81
after
an i m -
R e l a t i v e l y s m o o t h t r a n s m i t i o n s w e r e made t o t h e new
i n t h e case o f biomass c o n c e n t r a t i o n i n comparison w i t h
I n l e s s t h a n 1 0 d a y s a f t e r s h o c k was i m p o s e d , c h a n g e s o f
biomass c o l o u r and f l o c s m a c r o s c o p i c appearance were observed. new s t e a d y - s t a t e ved,
was r e a c h e d ,
b u t no changes i n m a g n i t u d e o f
o f the transient
After
t h e i n i t i a l b i o m a s s c o l o u r was o b s e r s l u d g e f l o c s had occured.
Some
r e s p o n s e d a t a were u s e d t o o b t a i n t h e b i o k i n e t i c
parameters f a r t h e m a t h e m a t i c a l models.
The c a l c u l a t e d COD v a l u e s
d u r i n g t h e s t e p s h o c k t e s t u s i n g t h e Monod and m o d i f i e d Monod equat i o n are a l s o p l o t t e d i n F i g .
l. F r o m t h i s F i g . l one c a n s e e t h a t
a b e t t e r f i t b e t w e e n e x p e r i m e n t a l a n d c a l c u l a t e d d a t a was o b t a i n e d
n 0 u
T
O
5
1;
1;
2b
215
o;
3;j
Lb
L; t IDAYSl
F i g . 1. C O O c o n c e n t r a t i o n r e s p o n s e o f a c t i v a t e d s l u d g e p r o c e s s t o twofold decreasing o f feed concentration experimental - - - - - - c a l c u l a t e d u s i n g Monod e q u a t i o n . . . . . . . . . . . c a l c u l a t e d u s i n g m o d i f i e d Monod e q u a t i o n .
-
u s i n g t h e m o d i f i e d Monod e q u a t i o n .
The g r e a t e s t d i f f e r e n c e s between
e x p e r i m e n t a l a n d c a l c u l a t e d v a l u e s w e r e o b s e r v e d i n t h e c a s e o f COD d u r i n g t h e f i r s t stage o f t h e experimental run.
One c a n c o n c l u d e t h a t
an i n s t a n t a n e o u s c h a n g e i n e p e c i f i c g r o w t h r a t e d i d n o t o c c u r a s p r e d i c t e d b y t h e Monod e q u a t i o n . w o r k o f Mor 1 2 1 1 .
These r e s u l t s a r e c o n s i s t e n t w i t h t h e
I t was o b s e r v e d t h a t t h e t i m e d e l a y f o r t h e s y s t e m
t o r e s p o n d t o t h e s h o c k was d e p e n d e n t o n t h e m a g n i t u d e o f t h e s p e c i f i c growth rate.
I t s h o u l d be n o t e d t h a t s a t u r a t i o n c o n s t a n t s c a l c u -
l a t e d ( f o r t h e Monod m o d e l
-
82
K s = 0 . 7 8 4 kg.m-3
a n d f o r m o d i f i e d Monod
K s = 0.786 k g . ~ n - ~ )a r e s i g n i f i c a n t l y h i g h e r t h a n t h o s e p u b l i s h e d e l s e w h e r e 1 2 2 1 . We assume t h a t t h i s i s b e c a u s e o f a r e l a t i v e l y h i g h p o r t i o n o f b i o l o g i c a l l y r e s i s t e n t HMT compound i n t h e f e e d 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 o p e r a t e d u n d e r pH v a l u e s a b o u t 7 .
Comparing
c a l c u l a t e d a n d e x p e r i m e n t a l v a l u e s one c a n s e e t h a t t h e M o n o d - t y p e k i n e t i c e q u a t i o n i s n o t adequate f o r t h e p r e d i c t i o n o f t r a n s i e n t b e h a v i o u r o f an a c t i v a t e d s l u d g e p r o c e s s . S i m i l a r r e s u l t s w e r e o b t a i n e d a l s o u s i n g l i n e a r i z e d Monod a n d m o d i f i e d Monod e q u a t i o n s . E x p e r i m e n t a l a n d c a l c u l a t e d v a l u e s o f COD c o n c e n t r a t i o n u s i n g s t a t i s t i c a l m o d e l s a r e shown i n F i g .
2.
2 one c a n c o n f i r m
From F i g .
t h a t t h e d i s c r e t e s t a t i s t i c a l m o d e l i s more s u i t a b l e f o r d e s c r i b i n g a c t i v a t e d sludge process dynamics.
The c o m p u t a t i o n s 1 t i m e f o r t h e
m o d e l p a r a m e t e r s e s t i m a t i o n was s i g n i f i c a n t l y s h o r t e r i n c o m p a r i s o n t o b o t h n o n l i n e a r and l i n e a r i z e d k i n e t i c models.
mL
l5
0.6
Y
I
0
0
0.5
OA
0.3
0.2
(
5
10
15
20
25
30
35
40
45 t [ OAYSl
F i g . 2. C O D c o n c e n t r a t i o n r e s p o n s e o f a c t i v a t e d s l u d g e p r o c e s s t o twofold decreasing o f feed concentration experimental ------ c a l c u l a t e d u s i n g d e s c r e t e s t a t i s t i c a l model. CONCL US I ON5 The m a j o r o b j e c t i v e o f t h i s w o r k was t o e x a m i n e t h e e x p e r i m e n t a l l y dynamic b e h a v i o u r o f a c t i v a t e d s l u d g e process.
Previously the
-
83
-
o b t a i n e d e x p e r i m e n t a l d a t a was u s e d f o r v e r i f i c a t i o n o f t h r e e d e r i ved m a t h e m a t i c a l models.
From c a l c u l a t i o n s we c a n assume,
that the
Monod-type k i n e t i c models a r e n o t a c c u r a t e i n t h e p r e d i c t i o n o f t r a n s i e n t behaviour o f t h e a c t i v a t e d sludge process. r i f i e d model
-
d i s c r e t e s t a t i s t i c a l model
-
The t h i r d ve-
provides a better f i t
between e x p e r i m e n t a l and c a l c u l a t e d v a l u e s . The n e x t s t e p o f o u r work i s t o v e r i f y a s t a t i s t i c a l m o d e l u s i n g more i n p u t s . SYMBOLS ai, COD kd KS
bi
J
parameters o f d i s c r e t e s t a t i s t i c a l model c h e m i c a l o x y g e n demand endogenous decay c o e f f i c i e n t substrate saturation constant
M
number o f m e a s u r e m e n t s
m
number o f p a r a m e t e r s b .
n
number o f p a r a m e t e r s a
9
feed flow r a t e
qX
rs
R
9
RS
S
=o t
J
i
biomass wastage r a t e substrate u t i l i z a t i o n rate microbial growth r a t e substrate removal r a t e e f f l u e n t substrate concentration feed substrate concentration time
A t
time
U
i n p u t i n s t a t i s t i c a l model
Ut "a
X
'obs Y
yY
L1
Pmax
interval
value o f u i n time t a e r a t i o n t a n k volume mixed l i q u o r suspended s o l i d s ( M L S S ) observed y i e l d c o e f f i c i e n t o u t p u t i n s t a t i s t i c a l model value o f y i n time t s p e c i f i c growth r a t e maximum s p e c i f i c g r o w t h r a t e
w
minimization
e
s l u d g e age
function
-
84
-
REFERENCES
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21 22
M e t c a l f Eddy, W a s t e w a t e r E n g i n e e r i n g , T r e a t m e n t , d i s p o s a l , r e u s e , M c G r a w - H i l l I n c . , New Y o r k , 1972. K . K o m o l r i t a n d A.F. Gaudy, J o u r n a l WPCF, 3 8 , 85, 1 9 6 6 . K. K o m o l r i t a n d A.F. Gaudy, J o u r n a l WPCF, 3 8 , 1 2 5 9 , 1 9 6 6 . J.R. M o r a n d A. F i e c h t e r , B i o t e c h . a n d B i o e n g . , X , 7 8 7 , 1968. J.W. G i l l e y a n d H.R. Bungay, B i o t e c h . a n d B i o e n g . , I X , 6 1 7 , 1967. J.W. G i l l e y a n d H.R. Bungay, B i o t e c h . a n d B i o e n g . , X, 99, 1968. T.B. Young e t a l , B i o t e c h . a n d B i o e n g . , X I I , 747, 1970. S. Koga a n d A.F. Humprey, B i o t e c h . a n d B i o e n g . , I X , 3 7 5 , 1 9 6 7 . J.F. Andrews, W a t e r Res., 8, 261, 1974. G. O l s o n , A I C h E Symp. S e r . N. 1 5 9 , 72, 52, 1976. J.B. B u s b y a n d J.F. Andrews, J o u r n a l WPCF, 47, 1055, 1 9 7 5 . V . A t t i r a n d M.M. Denn, A I C h E J . 24,, 6 9 3 , 1978. R.A. P o d u s k a , J.F. Andrews, J o u r n a l WPCF, 4 7 , 2599, 1 9 7 5 . N. T h 6 r i e n a n d S. P e r d i e u x , J o u r n a l WPCF, 53, 576, 1 9 8 1 . P . M . B e r t h o u e x e t a l l . , W a t e r Res., 1 0 , 6 8 9 , 1976. J.L. Hansen, A.E. F i o k and J.C. H o v i o u s , J o u r n a l WPCF, 52, 1 9 6 6 , 1980. M. K u b f E e k , N u m e r i c k 6 a l g o r i t m y GeSeni c h e m i c k o - i n f e n f r s k f c h d l o h , SNTL P r a h a 1 9 8 3 . D.A. P i e r r e , O p t i m i z a t i o n t h e o r y w i t h a p p l i c a t i o n s , J . W i l l e y , New Y o r k 1969. R e k t o r y s a k o l . , P F e h l e d u f i t b m a k e m a t i k y SNTL P r a h a 1 9 8 8 . M. HorBkovB, P. L i s c h k e a n d A . G r u n w a l d , M e t o d y c h e m i c k b a n a l y z y vod, SNTL P r a h a , 1981. J.R. Mor a n d A. F i e c h t e r , B i o t e c h . a n d B i o e n g . , X, 7 8 7 , 1 9 6 8 . G. T c h o b a n o g l o u s , W a s t e w a t e r E n g i n e e r i n g , M c G r a w - H i l l , I n c . , New Y o r k , 1977.