Weatherley 1984 Aquacultural-Engineering

7/28/2019 Weatherley 1984 Aquacultural-Engineering

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A q u a c u l ru r a l E n g i n e e n n g 3 (1984) 15-29

R a t e M o d e l s f o r a M a r i n e B i o l o g ic a l F i l t e r

L . R . WeatherleyAquacultural Engineering Research Gro up, D epa rtme nt of Chem ical and P rocessEngineering, Heriot-W att University, Edinburgh EH I 1HX , UK

A B S T R A C TA n e m p i r ic a l ly b a s e d m o d e l is p r o p o s e d f o r t h e k in e t i c s o f o x i d a t i o n o fa m m o n i a a n d n i t r it e i n a m a r i n e b io l og i ca l f i l t e r a t l o w c o n c e n t r a ti o n .A s s u m i n g f i r s t o r d e r k i n e t ic s , t h e r a te c o n s t a n t s f o r Nitrosomonas a n dNitrobacter r e s p e c t iv e l y a r e c o r r e la t e d as f u n c t i o n s o f p H , t e m p e r a t u r ean d d i s so l ved oxy gen . A ser ies o f exper im ent s us ing a rec i rcu la t ing ba t chb io log i ca l f i l t e r was conduc ted t o va l ida t e t he mode l over a l im i t ed rangeo f condi t i ons . Pred i c t i ons o f t h e mo de l agree sa t i sf ac tor il y w i th li t era turev a lu e s o f t h e r a te c o n s t a n t s a n d s h o w fa v o u r a b l e c o m p a r i s o n w i t h t h eo b s e r v e d e x p e r i m e n t a l d ata .

NOMENCLATUREA I , A 2c le l 0C2C2maxCO2k l , k ' lR t , R 2Tttmax~1, 5

C o n s t a n t s i n e q n s ( 5 ) a n d ( 6 )A m m o n i a c o n c e n t r a t i o n ( m g l i t r e ~ )I n i t i a l a m m o n i a c o n c e n t r a t i o n ( r a g l i t r e -~ )N i t r i t e c o n c e n t r a t i o n ( m g l it re -1 )M a x i m u m n i t r i te c o n c e n t r a t i o n ( m g l it re -x )D i ss o lv e d o x y g e n c o n c e n t r a t i o n ( m g l it re 1 )A m m o n i a o x i d a t io n r a te c o n s t a n t ( h-1 )N i t r i te o x i d a t i o n r a t e c o n s t a n t ( h -1 )M o d i f i c a t i o n f a c t o r s d e f i n e d i n e q n s ( 1 3 ) a n d ( 1 4 )T e m p e r a t u r e ( C )T i m e ( h )T i m e o f m a x i m u m n i tr i t e c o n c e n t r a t i o n ( h )F u n c t i o n s o f p H d e f i n e d in e q n s (9 ) a n d ( 1 0 )

15A q u a c u l t u r a l E n g i n e e r i n g 0 1 4 4 - 8 6 0 9 / 8 4 / 5 0 3 . 0 0 - ElsevierPublishers Ltd, England, 1984. Printed in Great Britain Applied Science


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1 6 L . R . W e a t h e r l e y

INTRODUCTIONThe difficulties of producing useful design equations for biologicalfilters in recirculating aquaculture systems have been related in a previ-ous review (Weatherley, 1982). The essence of the problem lies in themulti-variable dependence of the rate processes in the biological filterand in the lack of any systematic demonstration of correlating experi-mental data in this context involving a number of variables.

Two major areas requiring accurate analyses in order to utilise suchdata are:

(i) flow and mixing in the system; and(ii) the kinetics of ammonia and nitrite oxidation.

Weatherley demonstrated the potential of a mathematical modellingapproach to both design and control of a recirculating aquaculturesystem given a satisfactory description of liquid mixing react ion kinetics.

In this paper we seek to extend the understanding of the kinetics ofammonia and nitrite oxidation to a marine biological filter. Simple ratemodels are improved to take account of temperature, oxygen and pHdependence of oxidation kinetics. A series of experiments are describedwhich validate the proposed models over a limited range.

The significance of biological filtration as a treatment system foraquaculture waters has greatly increased with its application to inten-sive closed culture systems. The experience of a number of operatorsindicates the need for a greater understanding of the sensitivity anddynamics of biofiltration processes in the closed system context (Liaoand Mayo, 1972; Hirayama, 1974; Srna and Baggaley, 1975: Poxtone t a l . , 1981;Poxton e t a l . , 1982).

THE KINETICS OF BIOLOGICAL FILTRATIONTwo approaches to the development of design equations for biologicalfilters are evident in the literature. Firstly, the ref inement of empiricalfilter perfo rmance models has been successfully achieved for municipalwater biological filtration; Pike (1978) has an excellent review. In thesecases the filter performance is defined in terms of the ratios of inlet tooutlet stream concentrations and this is correlated as a function of all


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R a t e m o d e l s f o r a m a r i n e b i o lo g i ca l f i l t e r 17

r e l e v a n t p h y s i c a l v a r i ab l e s s u c h a s f l o w r a t e , p a c k i n g s iz e , p H a n dt e m p e r a t u r e .

S e c o n d l y , a m o r e i n - d e p t h e v a l u a t i o n o f t h e c h e m i c a l k i n e t ic si n v o lv e d i n f il te r p e r f o r m a n c e h a s b e e n a t t e m p t e d a n d , w i t h s o m es u c c e s s ( S r n a a n d B a g ga le y , 1 9 7 5 ) , r a te m o d e l s f o r m e t a b o l i t e o x i d a t i o nb a s ed o n c o n v e n t i o n a l c h e m i c a l k i n e t ic s ha v e b e e n d e v e l o p e d . T h em a j o r a d v a n t a g e o f t h i s a p p r o a c h is t h a t t h e s e p a r at e e f f ec t s o f c h e m i -c a l k i n e t i c s , l i q u id m i x i n g a n d m a s s t r a n s f e r h av e t h e p o t e n t i a l o f b e i n gq u a n t i f i e d a n d c o m b i n e d t o y i e ld a n a c c u r a t e d e si g n m o d e l .

T h e c o m p l e x d e p e n d e n c e o f a m m o n i a a nd n i t r i te b i o c h e m i c a l o x id a -t i o n u p o n e n v i r o n m e n t a l c o n d i t i o n s is w e ll d o c u m e n t e d (S r na a n dB a g g al ey , 1 9 7 5 ; W h e a t o n , 1 9 7 7 ; D o n a l d s o n , 1 9 7 9 ) a n d i n c l u d e s i na d d i t i o n t o m e t a b o l i t e c o n c e n t r a t i o n , pH , t e m p e r a t u r e , d is so lv e do x y g e n , s a l i n i t y , d i s s o l v e d o r g a n i c s , l i g h t i n t e n s i t y a n d t h e p r e s e n c e o fa n t i b i o t i c s .

I t is g e n e ra l ly a c c e p t e d t h a t a t t h e l o w m e t a b o l i t e c o n c e n t r a t i o n se n c o u n t e r e d i n a q u a c u l t u r a l w a t e r s a n d f o r t h e c a s e o f s t e a d y b i o m a s sc o n d i t i o n s , t h e r a t e o f o x i d a t i o n o f t h e t w o p r i m a r y m e t a b o l i t e s ,a m m o n i a a n d t h e n i t r i t e i o n , c a n b e a p p r o x i m a t e d b y fi rs t o r d e rk i n e t i c s (S r n a a n d B a g g a le y , 1 9 7 5 ; W h e a t o n , 1 9 7 7 ) .

T h u s t h e r ate o f o x i d a t io n o f a m m o n i a b y N i t r o s o m o n a s i s g iven by :d 1

- k l C l (1 )d ta n d t h e n e t r a t e o f o x i d a t i o n f o r n i t r it e in th e p re s e n c e o f a m m o n i a ,N i t r o s o m o n a s a n d N i t r o b a c t e r is g iven by :

d c 2 = k i c k - - k~ c2 (21)d tW h e a t o n ( 1 9 7 7 ) , s u m m a r i s i n g a n u m b e r o f st u d i es , s u g ge s ts t h a t t h ef i r s t o r d e r c o n s t a n t f o r N i t r o s o m o n a s , k ~ , r e m a i n s r e l a t i v e l y c o n s t a n t ,w i t h i n g i ve n p H r an g e s. D o w n t o a p H o f a p p r o x i m a t e l y 5 .5 , th e e vi-d e n c e is t h a t a c c l i m a t i s a t i o n a c h i e v e s r e s is t a n c e t o p H c h a n g e a n d t h a tc h a n g e s i n r at es o f o x i d a t i o n m a y b e s h o r t - te r m . S u c h s h o r t - t e rmc h a n g e s a r e o f g r e a t i m p o r t a n c e i n i n t e n s iv e re c i r c u la t i n g s y s t e m s w h e r er e s id e n c e t i m e s m a y b e s h o r t a n d r e s p o n s e t i m e s lo w . S r n a a n d B ag g al ey( 1 9 7 5 ) h a v e s u c c e s s fu l ly i n c o r p o r a t e d p H v a r i a t io n s in t o t h e f i rs t o r d e r


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18 L . R . l ' ea ther leyr a te c o n s t a n t s f o r a m m o n i a a n d n i t r it e o x i d a t i o n t h u s :

k t = 0 - 2 3 p H - - 1 -6 7 . 4 < p H < 7 . 8 ( 3 )k 2 = 0 - 0 5 3 p H + 0 . 5 3 1 6 - 6 < p H < 8 . 6 ( 4 )

T h e s e d a t a w e r e o b t a i n e d f o r a m m o n i a c o n c e n t r a t i o n s i n t h e r an g e0 . 1 -0 . 7 m g l i tr e - t a n d n i t r i t e c o n c e n t r a t i o n s i n t h e r a n g e 0 - 0 . 9 m g l it re -1.

T h e e f f e c t o f t e m p e r a t u r e o n n i t r i f i c a ti o n r a te h a s b e e n i n v e s t ig a t e di n d e p t h b y K n o w l e s e t a l . ( 1 9 6 5 ) a n d an A r r h e n i u s - ty p e d e p e n d e n c e o fr a te c o n s t a n t u p o n t e m p e r a t u r e w a s f o u n d f o r N i t r o s o m o n a s a n dN i t r o b a c t e r i n c o n t i n u o u s c u l t u r e . E x p r e s s i o n s f o r th e r a te c o n s t a n t sa s a f u n c t i o n o f t e m p e r a t u r e m a y b e i n f er r ed f r o m t h e d a t a o f K n o w l e se t a l . ( 1 9 6 5 ) t h u s :

In k t = 0 . 0 4 1 3 T + A ~ ( 5 )In k z = 0 . 0 2 5 5 T + A z ( 6 )

w h e r e T i s t h e t e m p e r a t u r e ( C ) ( 8 - 3 0 C ) a n d A t a n d A 2 a re c o n s t a n t s .I n o r d e r t o e x p r e s s t h e r a t e c o n s t a n t s , k ~ a n d k 2 , a s f u n c t i o n s o f b o t h

t e m p e r a t u r e a n d p H , w e p r o p o s e e q n s ( 7 ) a n d ( 8 ) th u s :In k~ = 0 . 0 4 1 3 T + ~ ( 7 )In k 2 = 0 . 0 2 5 5 T + ~2 ( 8 )

w h e r e ~ a n d z a re f u n c t i o n s o f p H a l o n e . U s i n g e q n s ( 3 ) a n d ( 4 ) a tc o n s t a n t t e m p e r a t u r e t o c a l c u l a te k z a n d k z a t a r a ng e o f p H v a lu e s ,e q n s ( 7 ) a n d ( 8 ) w e r e u s e d t o i n f er t a n d ~ 2 a s f u n c t i o n s o f p H o n l y .T h e r e s u lt in g e x p r e s s i o n s a r e a s f o l l o w s :

q~t = 1 0 4 - 6 5 - - 3 7 - 8 8 6 p H + 4 . 6 7 9 8 p H 2 - 0 - 1 9 4 4 p H 3 ( 9 )q~2 = 2 . 2 8 1 - - 0 . 3 9 8 3 p H - - 0 . 0 3 8 1 p H 2 ( 1 0 )

K n o w l e s e t a l . ( 1 9 6 5 ) a l so s h o w e d t h a t r a te s o f a m m o n i a o x i d a t i o nb y N i t r o s o r n ' o n a s d e c r e a s e d a t le v e ls o f d i s s o l v e d o x y g e n l e ss t h a n2 - 0 m g l i tr e -~ . R a t e s o f n i t r i t e o x i d a t i o n s im i la rl y, d e c r e a s e d b e l o wd i s s o l v e d o x y g e n l ev e ls o f 4 . 0 m g l it r e -~ .

O b s e r v a t i o n s p u b l i s h e d b y F o s t e r ( 1 9 7 4 ) s h o w e d t h a t n i t r i f i c a t i o nb y e i t h e r N i t r o s o m o n a s o r b y N i t r o b a c t e r e f f e c t i v e l y c e a s e d b e l o wd i s s o l v e d o x y g e n l ev e ls o f 0 . 7 m g l i tr e -~ . T h e s e t h r e s h o l d v a l u e s w e r el a te r c o n f i r m e d b y H a u g an d M c C a r t y (1 9 7 2 ) . T h e e x p e r i m e n t s o f


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Ra te mo dels for a marine biological f i l ter 19K n o w l e s e t a l . ( 1 9 6 5 ) s h o w e d t h a t r a t e s o f o x i d a t i o n v a r i e d l in e a rl yw i t h r e s p e c t t o d i s s o l v e d o x y g e n w i t h i n t h e t h r e s h o l d v a lu e s.

T h e e f f e c t o f d is s o lv e d o x y g e n u p o n t h e e f f ec t iv e r a t e c o n s t a n t sc o u l d b e c o n v e n i e n t l y b u i l t i n t o t h e e x p r e s s i o n s f o r k 1 a n d k ,. u s i ngm o d i f i c a t i o n f a c t o r s w h i c h v a r y l in e a rl y w i t h d i s s o l v ed o x y g e n le ve lst h u s :

k ' = R t k t ( 1 1)k " = R 2 k 2 ( 1 2 )

! tw h e r e k I a n d k 2 a r e t h e e f f e c t i v e r a t e c o n s t a n t s f o r N i t r o s o m o n a s a n dN i t r o b a c t e r , r e s p e c t i v e l y , a n d R 1 a n d R 2 a r e t h e m o d i f i c a t i o n f a c t o r sd e f i n e d a s f o l l o w s :

R 1 = 0 . 7 6 9 2 C o - - 0 . 5 3 8 5 0 . 7 < C o < 2 - 0 m g l i t r e -1 ( 1 3)R 2 = 0 . 3 0 3 0 C o : - - 0 . 2 1 2 1 0 . 7 < C o < 4 . 0 m g l i t r e -1 ( 1 4)

E q u a t i o n s ( 1 3 ) a n d ( 1 4 ) a r e f o u n d b y l i ne a ri si ng t h e v a l u es o f R ta n d R 2 i n t h e r a n ge 0 - 1 - 0 b e t w e e n t h e t h r e s h o l d v a l u e s o f C o : a p p r o -p r i a t e t o e a c h c a s e .

P r e d i c t i o n o f d i s s o l v e d o x y g e n l ev e ls i s b e y o n d t h e s c o p e o f th isp a p e r a n d t h e re l a ti o n s h ip b e t w e e n o x y g e n c o n c e n t r a t i o n , a t m o s p h e r i cc o n d i t i o n s , f l o w d y n a m i c s , m a s s t r a n s fe r a n d b i o lo g i ca l a c t i v it y isu n d o u b t e d l y a n a r e a r e q u i r i n g i n - d e p t h s t u d y .

A p p l i c a t io n o f e q n s ( 7 ) - ( 1 0 ) f o r t h e p r e d i c t i o n o f k l a n d k 2 w a st e s t e d i n i t ia l ly u s i n g t h e e x p e r i m e n t a l d a t a o f S r n a a n d B a g g a l e y ( 1 9 7 5 ) .

T A B L E 1

p H Tem pera ture kl observe d a kt calculated, k 2 observ ed a k,. , eqn [8}(C ) (h -1) eqn (7) (h -1) (h -1) (h -1)7.3 21 0-086 0.112 0-133 0-1327.3 26 0-185 0.18 0 0-161 0.1827.6 21 0-125 0-163 0.118 0-1177.6 26 0-268 0-262 0.14 4 0.16 27-9 21 0.16 4 0-213 0-103 0-1027-9 26 0-351 0-343 0-126 0.14 2

a Srna and Baggaley (197 5).


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20 L. R. WeatherleyT a b le 1 s u m m a r i se s t h e e x p e r i m e n t a l ra t e c o n s t a n t s f o r Nitrosomonasa n d Nitrobacter a s a f u n c t i o n o f p H a n d t e m p e r a t u r e . T h e c o r r e s p o n d i n gv a l u e s o f k ~ a n d k2, c a l c u l a t e d u s i n g t h e e q u a t i o n s , a r e a s s h o w n .

E X P E R I M E N T A LT h e p r i n c i p a l o b j e c t iv e o f a c q u i r i n g f u r t h e r e x p e r i m e n t a l d a t a w as t os e e i f t h e r a t e c o n s t a n t e q n s ( 7 ) - ( 1 0 ) u s e d t o c h a r a c t e r i s e t h e d a t a o fS r n a a n d B a g ga le y ( 1 9 7 5 ) w e r e a p p li c ab l e t o a c o m p l e t e l y s e p a r a teb i o lo g i c al f i lt e r r u n n i n g u n d e r s i m i l a r c o n d i t i o n s o f p H a n d t e m p e r a t u r e .

T h e s y s t e m u s e d w a s a b a t c h r e c i r c u l a t in g m a r i n e b i o lo g i c al rf l te r( F ig . 1) c o n s i s t i n g o f a c y l i n d r i c a l p a c k e d b e d f i lt e r t h r o u g h w h i c h

Air l i f t

i i

Samplepoints

Fig. 1. Ex pe rim en tal marine biological filter.


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R a t e m o d e l s f o r a m a r i n e b i o lo g i ca l f i l t e r 2 1

w a t e r w a s r e c i r c u l a te d b y a ir li ft . T h e m a i n b o d y o f t h e f il te r c o m p r i s e do f a 0 - 2 5 m d i a m e t e r s e c t i o n , t o t a l h e i g h t 0 . 7 m f a b r i c a t e d f r o mo p a q u e P V C . T h e b a s e o f t h e f i l te r w a s f i t te d w i t h a 0 - 0 1 2 5 m d i a m e t e ro u t l e t p i p e a b o v e w h i c h a p a c k i n g s u p p o r t p l a te , o f 5 X 1 0 - 4 m m e s hs iz e, w a s l o c a te d . T h e f il te r p a c k i n g c o n s i s t e d o f a l a y e r o f 0 - 0 1 5 ms i ev e d g ra n i te c h i p s b e l o w t h e p a c k i n g s u p p o r t p l a te , t w o l a y er s o f0 - 0 1 5 m c h i p s a b o v e t h e s u p p o r t p l a t e a n d a b o v e t h e se t h e m a i n b o d yo f p a c k i n g c o m p r i s i n g 0 . 0 0 5 m g r a n i t e ch i p s u p t o t h e t o p o f t h e f il te r.T h e t o t a l p a c k i n g i n v e n t o r y w a s 3 3 k g .

A s e ri e s o f s a m p l e p o i n t s w a s l o c a t e d a l o n g t h e a x i s o f t h e f i l t e r t oe n a b l e l i q u i d s a m p l i n g a n d t e m p e r a t u r e m e a s u r e m e n t .

T h e a ir li ft s y s t e m w a s m a d e u p o f a n o u t e r s l ee v e o f 0 - 0 5 m d ia -m e t e r a n d a n i n n e r s l e ev e o f 0 . 0 1 2 5 m d i a m e t e r . T h e r el a ti v e v e r t ic a lp o s i t i o n s o f a i rl if t a n d f i l te r w e r e a d j u s t e d t o g i v e t h e n e c e s s a r y s u b -m e r g e n c e f o r e f f i c ie n t a n d s t e a d y w a t e r fl o w . A d e t a il e d d e s c r i p t i o n o ft h e e x p e r i m e n t a l a r r a n g e m e n t is g i ve n b y D o n a l d s o n ( 1 9 7 9 ) .

T h e w a t e r f l o w a r o u n d t h e s y s t e m w a s m a i n t a i n e d a t a s t e a d y v a lu eo f 0 . 0 8 4 m 3 h -~ a n d t h e f il t er c o n d i t i o n e d o v e r a p e r i o d o f e ig h t w e e k sb y d a i ly s p i k e a d d i t i o n o f 1 0 6 m 3 1M a m m o n i u m c h l o r i d e s o l u t io n .T h e f il te r w a s c o n s i d e r e d t o b e c o n d i t i o n e d w h e n a s t e a d y re s p o n s e t oa m m o n i a a d d i t i o n w a s o b s e r v e d .

F o l l o w i n g c o n d i t i o n i n g a s e ri es o f f o u r t r i al s w e r e c o n d u c t e d w h i c hi n v o l v e d d e t a i l e d m o n i t o r i n g o f th e f i l te r fo r s e v e r al h o u r s a f t e r t h ed a i ly s p i k e a d d i t i o n o f a m m o n i a . A t h o u r l y i n te rv a ls f o l l o w i n g a dd i -t i o n , s a m p l e s o f w a t e r w e r e t ak e n f r o m e a c h o f t h r e e s a m p l in g p o i n t sa l o n g t h e v e r t i c a l a x is o f t h e f i lt e r l o c a t e d a t t h e t o p , m i d d l e a n db o t t o m o f t h e f i lt e r b e d , a s s h o w n i n F ig . 1. T h e w a t e r s a m p l e s w e r ea n a l y s e d f o r a m m o n i a , n i t r i te , o x y g e n , p H , s a li n it y a n d p H .

W a t e r lo s s es d u e t o s a m p l i n g w e r e r e s t o r e d p e r i o d i c a ll y w i t h w a t e rc l o se in q u a l i t y a n d c o m p o s i t i o n t o t h a t i n t h e s y s t e m a t th e t i m e o fs a m p l i n g .

C A L C U L A T E D R E S U L T SA n e a r l ie r p e r f o r m a n c e a p p r a i s a l o f th e b i o l o g i c a l f i l te r u s e d h e r e( W e a t h e r l e y , 1 9 8 2 ) s h o w e d t h e l i q u i d p h a s e i n t h e f i l te r b e d t o b e w e l lm i x e d u n d e r t h e s e f l o w c o n d i t io n s . T h i s w a s c o n f i r m e d b y t h e l a ck o fa n y s i g n if ic a n t c o n c e n t r a t i o n - p o s i t i o n p r o f i le a lo n g th e ax is o f t h e


8/15

2 2 L. R. ~earherley

F i g . 2 .

Cl

0 - 5 -

O-

+ + +

A A A

0 0 0

I I ITop M i d d l e B o t t o m( a )

+ + +A

t~ Z~

Cl

O /

Cl

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4 -

_ + +

tXD 13 O

I I [T o l 0 M i d d le B o t t o m(b )

+t

O 13131 3 0 1 3

I I I I 1T op M i d d l e B o t t o m T o p M i d d l e( c ) ( d )

IB o t t o m

A m m o n i a c o n c e n t r a t i o n p r o f i l e s i n f il te r . ( a ) T r ia l 1 ; ( b ) t ri a l 2 ; ( c ) t ri a l 3 ;( d ) t r ia l 4 . ( + ) I h ; ( 4 ) 2 h ; ( o ) 3 h ; ( ~ ) 4 h .

filter (see Fig. 2 showing the results for ammonia concentration). Thefilter was thus assumed to be well mixed and the mean values ofammo nia and nitrite conc entr atio n were calculated at each time interval.These experimental rate data are plotted in Figs 3 and 4 for ammoniaand nitrite respectively.

The conc entra tion -time data for ammonia in the filter were fittedto the integrated form o f the first order rate eqn (1) thus:

In c~ = k~t + constant (15)


9/15

04 03 02 O

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(d)

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10/15

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ntrteconnraonvutmeexpmenaanpdcedda(aTa1"(btra2

(ctra3(dtra4(+Epmena;(

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t~ .$


11/15

Ra te mod e ls for a mar ine b io log ica l f i l t e r 25The value of k t for each trial was ob tai ned by a least squares fit of theexperiment al data to eqn (15). The values of kl are shown in Table 2toge ther with a summary o f pH, tempera ture and oxyg en concentra-tion for each particular trial.

The values of kl, predicted using eqn (7) using the appropriate valuesof pH and temperature, are also shown in Table 2.

The experimental data for nitrite concentration-time were used tocalculate the rate constant for N i t r o b a c t e r .

The integrated form of eqn (1) may also be expressed in the form:cl = cl0 ex p( -- kt t) (16)

where ct0 is the initial ammonia concentration. Substitution in eqn (2)yields for nitritedc2 = kt Clo exp( -- k I t) -- k2c 2 (17)dt

The nitrite concentration in the filter will vary according to therelative rate of production, by ammonia oxidation, and the rate ofnitrite oxidation by N i t r o b a c t e r . If, therefore, k 2 < k t , the nitriteconcentration-time profile will display a maximum value during thecourse of batch reaction as we have in this case. At the maximum valueof c 2, d c 2 / d t = 0, c 2 = c2rmx and t = trr~. Therefore, eqn (17) becomes

andkl CLo exp( -- kl t~oax) - k 2 c 2 m a x = 0

k2 = k I Clo exp(- - k I trrax) (18)C2max

In order to ext rac t the values of c2,mx and t,mx from the experimentaldata, the nitrite concentration-time data for each trial were fitted to apolynomial function and these are shown in Table 3. Each polynomialwas diff erent iated with respect to time and t he value of t,~x extractedat d c 2 / d t = O .

The cor responding value of C2max was calculated using the originalfunc tion . Values of c2~ax and tmax, calcula ted using each set o f data, areshown also in Table 3.

Thus the expe rimental values o f rate cons tan t k 2 were calculatedusing eqn (18) and are tabulated in Tables 2 and 3. The predicted values


12/15

t~

TABLE2

nmlb

Co

(rare~)

(mea

pH

Sby

(mea (%0

Tmpaue

(C)

kl

epemenaI

(h-)

kl

eq(7

(h-)

k2

epmena

(h-~

k2

eq(8

(h-~)

.e

7.70

7-85

7-67

7-62

7-56

7.50

7-59

7.74

31.0

29-1

30.5

33.5

22-1

21-7

21-8

21-8

0.4624

0-3435

0-4845

0.4278

0.4539

0-4339

0.4544

0.4832

0-1195

0-1210

0-08270

0.07635

0-09593

0.10065

0-09245

0-07978

"e


13/15

R a r e m o d e l s f o r a m a r i n e b i o l o g ic a l f i l te rT A B L E 3

N i t r i t e C o n c e n t r a t i o n - T i m e D a t a

2 7

T r ia l E x p e r i m e n t a l c u r v e f i r e q u a t i o n 2max t m ax k 2n u m b e r f m g l it re - 1 ) { h ) e x p e r i m e n t a le q n ( 1 7 )(h-')

1 c , = 0 - 0 7 2 8 + 0 . 5 1 8 6 t 1 . 3 0 85 3 . 6 8 6 5 0 . 1 1 9 5- - 0 - 0 0 8 5 7 1 t 2 - 0 . 0 1 1 1 7 t 3

2 c : = 0 . 2 0 9 9 + 0 . 9 1 4 9 t 1 .3 5 4 6 3 . 9 1 8 6 0 - 1 2 1 0- - 0 . 1 5 2 7 t 2 + 0 . 0 0 6 1 1 7 t 3

3 c 2 = 0 . 5 7 3 7 + 0 - t 2 4 2 t 1 .3 7 5 9 4 . 2 4 1 7 0 - 0 8 2 7 0+ 0 . 0 7 5 2 0 t 2 - - 0 . 0 1 4 1 2 t 3

4 c 2 = 0 - 1 9 3 2 + 0 - 4 1 5 1 t 1 - 2 2 5 0 4 . 9 7 1 3 0 . 0 7 6 3 5- - 0 . 0 4 1 7 5 t 2

o f k 2, o b t a i n e d u s in g e q n s ( 8 ) a n d ( 1 0 ) , a r e a l s o s h o w n i n T a b l e 3 f o rc o m p a r i s o n .

I n o r d e r t o d e m o n s t r a t e t h e a p p l i c a t i o n o f t h e p r e d i c t e d r a t e c o n -s t a n t s k ~ a n d k s f o r N i t r o s o m o n a s a n d N i t r o b a c t e r , r e s p e c t i v e l y , t h ei n t e g r a t e d f o r m s o f e q n s ( t ) a n d ( 2 ) w e r e u s e d t o p r e d i c t t h e p e r f o r m -a n c e o f th e f il te r u n d e r t h e c o n d i t i o n s o f t h e e x p e r i m e n t a l tr ia ls .

E q u a t i o n ( 1 5 ) w a s u s e d to p r e d i c t t h e ra t e c u r v e f o r a m m o n i a . F o rn i t ri te e q n ( 2 ) w a s i n t e g r a t e d a n d , c o m b i n e d w i t h e q n ( 1 6 ) , y i e l d e d c2a s a f u n c t i o n o f t im e :

c l k t { e x p ( - - k l t ) - - e x p ( - - k 2 t ) } ( 1 9 )C2 - - k 2 ~ - 1

T h u s a p r e d i c t e d v a r i a t i o n o f c2 w i t h t i m e w a s o b t a i n e d . C o m p a r i s o n so f p r e d i c t e d a n d o b s e r v e d r a t e c u r v e s f o r t h e f i l te r a r e s h o w n i n F i g s 3a n d 4 f o r a m m o n i a a n d n i t r it e , r e s p e c t iv e l y .

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

T h e e x p e r i m e n t a l r e s u l t s r e c o r d e d in F i g s 3 a n d 4 c o n f i r m t h a t u n d e rc e r t a i n c o n d i t i o n s t h e o x i d a t i o n o f a m m o n i a a n d n i t r i t e m a y b e


14/15

28 L. R. IVeatherleydescribed using first order kinetics. In this case a state approaching idealmixing was confirmed within the biological f-flter and thus made therepresentation of filter perfo rmance very straightforward.Under different conditions of filter geometry and flow rate theeffects of non-ideal mixing would require careful consideration in orderto utilise the simple kinetic models as a means of predicting filterperformance. Observations by others indicate that plug flow conditionsmay be encountered in working biological filters.

In addition to gross liquid mixing within the filter bed a secondcomplicating feature o f performance predictions may be the effects ofliquid film resistance to the mass transfer of metabolites from the bulkliquid phase to the biologically active gravel surface. Observationsrecorded in freshwater systems (Goldsworthy, 1983; Pooley, 1983)suggested that the overall rate of metabolite oxidation in packed bedfilters can be strongly dependent on liquid velocity. In these cases thefilm mass transfer resistance appears to be significant with the overallrate of oxidation increasing with flow velocity. Atkinson (1974)provides extensive treatment of these cases and demonstrates the needto model separately mass transfer resistance and biochemical kineticsin order to provide an overall.rate prediction.

The levels of oxygen concentration recorded during the experimentswere well in excess of the range of oxygen limited kinetics (see eqns(11)-(14)) and therefore the modification factors k~ and k2 are takenas unity. Thus it was not possible to test the validity of this approach.

The values of first order rate constants, k~ and k z , measured experi-mentally agree well with those predicted using eqns (7)-(10) (seeTable 2). The validity of the suggested correlations for k~ and k2 is alsosupported by the earlier comparisons with other published experimentaldata (see Table 1).Figures 3 and 4 show how the predicted values of rate constants canbe used to calculate the performance of the batch f'flter for bothammonia and nitrite oxidation. This is possible in this case since thefilter is well mixed and the overall rate of oxidation controlled bykinetics alone. In order to use similar kinetic data in the design of acommercial system would require appraisal of the likely mixing regimeand of the importance of film mass transfer. Future work proposes toanalyse the importance of these ef fects in aquacultural filters.


15/15

Rare mo dels fo r a marine biological filter 29R E F E R E N C E S

Atkinson, B. (1974) . Bl"ochemicalReactors, Pion Pres s, Lon don .Don a ldson , D . (1979) . Co ns t ruc t ion of a m ar ine exper imen ta l b io log ica l fi lt e r and

i ts ni t r i f ica t ion kinet ics . Heriot-Watt University Ho nou rs Research Re po rt,Edinburgh , UK.

Foster, J . R. M. (1974). Studies on nitrification in marine biological fi l ters . Aqua-culture, 4 , 387 - 97 .Go ldswo r thy , G . (1983) . P r iva te co m mu nica t ion .Haug, R. T. & M cCarty, P . L. (1972) . Ni t r i f ica t ion wi th subm erged f i l ters . J. WaterPollu t. C ontro l Fed ., 44 , 2986- 3102 .Hirayama, K. (1974) . Water control by f i l t ra t ion in c losed cul t ive sys tems. Aqua-

culture , 4 , 3 6 9 - 8 5 .Knowles , G. , Downing, A. L. & Barre t t , M. J . (1965) . Determinat ion of kinet iccons tan t s for n i t r i fy ing bac te r i a in mixed cu l tu re , w i th the a id o f an e l ec t ron icc om pu t e r . J. Ge n. Microbiol. , 3 8 , 2 6 3 - 7 8 .

l . . iao, P . B. , Mayo, R. D. (1972) . Salmonid hatchery water reuse sys tems. Aqua-culture, 1 , 3 1 7 - 3 5 .

Pike , E. B. ( I 978) . The design o f percola t ing f i lters and rota ry biological c ontac torsincluding deta i l s of internat ional pract ice . WaterResearch Centre Re po rt TR9 3,Stevenage, UK.

Po oley, A. B. W. (1983) . Pr ivate co m m un icat io n.Po xto n, M. G. , M urray, K. R., L info ot , B. T. & Poo ley, A. B. W. (1 98 l) . The des ignand perfo rm ance of biological f i lters in an experim enta l maricul ture fac i l i ty .In : Proceedings World Syrup. o n Aq uaculture in Hea ted Eff luents and Recircula-t ion Sys tems, vol. I , ed. K. Tiews, World Mariculture Society, Berl in, pp. 370-82.

Po xton , M . G ., M urray , K . R. & Linfoot , B. T . (1982) . The growth of tu rbot(Sc oph tha lmus m ax imus (L. )) in rec i rcula t ing sys tems. Aqu acultural Engineering,1, 23-34.

Srna, R. F . & Baggatey, A. (1975) . Kine t ic response of per tu rbed marine nit r if ica-t ion sys tems . J . WaterPollut. Co ntrol Fed ., 4 7 , 4 7 2 - 8 6 .

Weather ley, L. R. (1982) . Appl ica t ion of s imple dynamic response analys is to areci rcula t ing aqu acul tu re sys tem - a review. Aqu acultural Engineering, 1, 93-11 3.

Whea ton , F . W. (1977) . Aqu aculture Engineering, John Wi ley , New York , chapte r13.

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Weatherley 1984 Aquacultural-Engineering

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