Watten 1985 Aquacultural-Engineering

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Aqu acu l t u ra l Eng i neer ing 4 (1985) 271-2 97

Mo d e l in g G a s Tr a n s fe r in a U-Tu b e O x y g e n Ab so r p t io nS y s te m : E f f ec t s o f O f f -G a s Re c y c l in g

Barnaby J. W atten and L. T odd BeckPennsylvania Power and Light C om pany, Depar tm ent of Techn ology and E nergyAssessment, Brunn er Island A quacu lture Project, York H aven,

Pennsylvania 17370, USAA B S T R A C T

A c o m p u t e r m o d e l c h a r a c te r iz in g t h e p e r f o r m a n c e o f a u - t u b e o x y g e nabsorp t i on s y s t em was deve l op ed based on fi n i t e d i f fe r ence - m ass t rans fe rcalcula tions . Per for ma nce w as assessed in t erms o f oxyg en u t i l i za t ion ,t rans fe r e f f ic i ency and e conom y . The s y s t em eva l ua ted was un i que i n t ha toxygen no t absorbed i n i t i a l l y ( o f f - gas ) was cap t ured and r ecyc l ed . M asst rans fer coe f f i c ien t s der ived f ro m pi lo t- scale t es t data w ere used to cal i-brate the c om pu ter mo del . A separate ser ies o f tes t s served to ver i f y thee f f e c ts o f o f f- gas r ecyc l ing as p red i c t ed by t he p rogram . S i m u l a t i on da t aindicate of f -gas recycl ing can resul t in substant ial savings in variable andt o t a l cos ts o f ox ygen t rans fe r w i t h on l y a m i n or i nc rease in cap it a lexpend i t u re s , bo t h i n it ia l ly and w hen am or t i z ed . The bene f i t s ach i evedwi l l i nc rease wi t h l ower oxygen f l ow ra t e s , deeper sha f t dep t hs , and l owi n f l uen t d i s so l ved oxygen concen t ra t i ons . Per f orm ance a l gor i t hm sdeve l oped shou l d be u se f u l t o t hose e s t ab l ish i ng de s ign cond i t i ons f o r pureoxygen u - t ube s y s t em s .

N O M E N C L A T U R EA A r e a o f g a s - l i q u i d i n t e r p h a s e ( m 2)A E O x y g e n a b s o r p t i o n e f f i c i e n c y (% )B B u n s e n ' s c o e f f i c i e n t a t a g i v en t e m p e r a t u r e a n d s a l i n it y ( l it re

l i t r e - a t m - 1)C E x i s t i n g c o n c e n t r a t i o n o f a g a s i n s o l u t i o n ( m g l i tr e -1 )C * S a t u r a t i o n c o n c e n t r a t i o n o f a g as i n s o l u t i o n ( m g l it re -~ )

271Aquacu l t u ra l Eng i neer i ng 01 44 -86 09 /85 /$0 3 .3 0- Elsev ie r Applied Sc iencePublishers Lt d, England, 1985. Printed in Great Britain


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272 B. J. Watten, L. Todd BeckCFDdd CD OD O tD O oA D OD Nd teFgc/LHLA H L

iKkK LKLaNne 2oeieoPTPwQgQmQoxQwR% R% ST

M u l t ip l i e r u s e d t o c o r r e c t f o r t h e e f f e c t s o f o f f -g a s r e c y c l in g ,d i m e n s i o n l e s sU - t u b e s h a f t d e p t h ( m )D i a m e t e r o f a g as m o l e c u l e ( A )C h a n g e i n c o n c e n t r a t i o n o f a g a s in s o l u t i o n ( m g l it re -1 )D i s s 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 )I n f l u e n t D O c o n c e n t r a t i o n ( m g li tr e-1 )E f f l u e n t D O c o n c e n t r a t i o n ( m g / l it r e -~ )C h a n g e i n 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 b e t w e e n u - t u b e i n le ta n d o u t l e t ( m g l it re -~ )D i s so l v ed n i t r o g e n c o n c e n t r a t i o n ( m g l it re -~ )T i m e e l a p s e d ( h )C o m b i n e d e f fi c ie n c y o f c o m p r e s so r or p u m p a n d m o t o rP i p e f r i c t i o n l o ss f a c t o r ( P a m - 1)A c c e l e r a t i o n o f g ra v i ty ( m s 2 )O x y g e n - l i q u i d r a t i o i n u - t u b e i n f l u e n t ( % )H e a d l o ss a cr o s s u - tu b e ( c m )D i f f e r e n c e i n h y d r a u l i c h e a d l os s a c r o s s u - t u b e d u e t o o x y g e ni n j e c ti o n ( c m )G a s s p e c i e s i d e n t i f i e rI s e n t r o p i c i n d e x f o r g as m i x t u r e , d i m e n s i o n le s sR a t i o o f m o l e c u l a r w e i g h t to m o l e c u l a r v o l u m e f o r a g as ( m g m l-~ )C o e f f i c i e n t o f d i f f u s i o n f o r a g a s ( m h - a)O v e r a l l g a s t r a n s f e r c o e f f i c i e n t ( h - 1)M a s s o f t h e g a s in t h e g a s p h a s e ( m g )(K- 1)/K, d i m e n s i o n l e s sF i n i t e d i f f e r e n c e s t e p i d e n t i f i e rV a p o r p r e ss u r e o f w a t e r ( m m H g )A b s o l u t e c o m p r e s s o r i n l e t p r e s s u r e ( k P a )A b s o l u t e c o m p r e s s o r o u t l e t p r e ss u re ( k P a )T o t a l p r es s u re ( m m H g )P o w e r ( k W )V o l u m e t r i c f l o w r a te o f o f f- ga s ( m 3 h -1)M a s s f l o w o f g a s m i x t u r e ( k g s 1 )V o l u m e t r i c f lo w r a te o f o x y g e n ( m 3 h -~)V o l u m e t r i c f l o w r a te o f w a t e r ( m a h - l )G a s c o n s t a n tO f f - ga s r e c y c l e r a t e ( % )S a t u r a t i o n l ev e l o f d i s s o l v e d o x y g e n i n t h e i n f l u e n t ( % )T e m p e r a t u r e ( C )


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TETI

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XPox

Modeling gas transfer in a u-tube ox ygen absorption systemT r a n s f e r e f f i c ie n c y ( K g 0 2 k W h -~ )A b s o l u t e t e m p e r a t u r e o f g a s a t c o m p r e s s o r in l et ( K )V o l u m e o f g as a t a s p e c if ic t e m p e r a t u r e ( l i tr e )V o l u m e o f l iq u i d ( m 3)C h a n g e i n d e p t h w i t h i n t h e u - t u b e s h a f t (-+ m )KLa o f wastewater/KLa o f p u r e w a t e r , d i m e n s i o n l e ssC * o f w a s t e w a t e r / C * o f p u r e w a t e r , d im e n s i o n l e s sU n i t w e i g h t o f w a t e r , k N m -3M o l e f r a c t i o n o f t h e g a s i n t h e g a s p h a s e , d i m e n s i o n l e s sM a s s d e n s i t y o f o x y g e n , k g m -3

273

I N T R O D U C T I O NA l i m i t i n g s u p p l y o f d i s s o lv e d o x y g e n ( D O ) is a c o n d i t i o n t h a t o f t e nr e s tr i c ts t h e p r o d u c t i o n c a p a c i t y o f i n te n s i v e a q u a t i c c u l t u r e s y s t e m s( W e st er s a n d P r a t t, 1 9 7 7) . A l t h o u g h n u m e r o u s m e t h o d s f o r s u p p le -m e n t i n g D O h a v e b e e n d e s c r i b e d ( C h e s n e s s et al., 1 9 7 2 ; C o l t a n dT c h o b a n o g l o u s , 1 9 8 1) p u r e o x y g e n a b s o r p t i o n s y s t e m s a p p e a r p a r t ic u -l ar ly a t t r a c t iv e . T h e s e s y s t e m s h a v e t h e u n i q u e c a p a b i l it y o f p r o v i d i n gs a t u r a te d o r s u p e r s a t u r a t e d D O c o n c e n t r a t i o n s e c o n o m i c a l l y w h i le av o id -i ng t e m p e r a t u r e c h a n g e , n o is e , a n d n i tr o g e n s u p e r s a tu r a t i o n p r o b l e m sa s s o c i a te d w i t h d i f f u s e d a ir a n d / o r s u r f a c e a e r a t io n e q u i p m e n t . S p e e c e( 1 9 8 1 ) d e s c r i b e s f i v e t y p e s o f p u r e o x y g e n c o n t a c t s y s t e m s , e a c h o fw h i c h p r o v i d e s a h ig h o x y g e n u t i li z a t i o n e f f i c i e n c y w i t h r e a s o n a b l ec a p i ta l c o s t s a n d e n e r g y c o n s u m p t i o n r a ti o s. T h e f iv e s y s t e m s a r e:( 1 ) e n c lo s e d p a c k e d c o l u m n , ( 2 ) u -t u b e , ( 3) d o w n f l o w b u b b l e c o n t a c ta e r a t i o n , ( 4 ) r e c y c l e d d i f f u s e d o x y g e n a t i o n a n d ( 5 ) ro t a t i n g p a c k e dc o l u m n . O f t h e a b o v e , t h e u - t u b e w a s s e l e c t e d f o r e v a l u a t i o n a t t h eB r u n n e r I sl a nd w a s te h e a t a q u a c u l t u r e p r o j e c t , Y o r k H a v e n , P e n n s y l-v a n i a . A p r e l i m i n a r y d e s i g n a n a l y s i s i n d i c a t e d t h e p r e s s u r e d r o p a c r o s st h e u - t u b e w o u l d b e w i t h i n t h e r a n g e o f t h e h y d r a u l i c h e a d t h a t i s a v ail-a b le a t t h e p r o p o s e d s i te . T h i s c h a r a c t e r is t i c n o t o n l y p r o v i d e s a s a vi ngi n e n e r g y c o s ts b u t m o r e i m p o r t a n t l y r e d u c e s t h e r is k o f s y s t e m f a il ur et h r o u g h t h e e l i m i n a t i o n o f e le c tr ic a ll y o p e r a t e d m e c h a n i c a l e q u i p m e n t .F u r t h e r m o r e , t h e u - t u b e r e q u i r e s l it tl e s p a c e , is s i m p l e t o c o n s t r u c t a n dc o n t r o l .A s o r i g i n a l l y d e s c r i b e d b y B r u i j n a n d H e n d r i k ( 1 9 5 8 ) , a u - t u b es y s t e m i n c o r p o r a t e s t w o b a s ic c o m p o n e n t s , ( 1 ) a g a s d i f f u s e r a n d ( 2 ) a


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274 B . J . W a t t e n , L . T o d d B e c kvertical u-shaped conduit which provides a contact loop of aboveatmospheric pressure. In use, air or oxygen is dispersed at a fixed rate inwater entering the system. The gas-liquid mixture is then directeddown one side of the u-shaped conduit and up through the other. Watervelocity in the clown-leg portion is maintained above the buoyantvelocity of the entrained gas bubbles. As the gas-liquid mixture movesthrough the contact loop a temporary increase in hydrostatic pressureserves to increase the dissolved oxygen deficit which in turn acceleratesthe rate of oxygen transfer.

Previous research (Speece e t a l . , 1969; Speece and Orasco, 1970;Mitchell, 1973; Speece e t a l . , 1980) has shown that oxygen transfer in au-tube system is influenced primarily by shaft depth, inlet gas flow andcomposition, water velocity, diffuser depth, and inlet DO concentra-tion. In this report, a mass transfer model is developed for purposes ofcharacterizing the performance of a u-tube system in which commercial,or pure, oxygen is dispersed. The system studied is unique in thatoxygen not absorbed in the first pass is collected and immediate lyrecycled. Speece e t a l . (1983) suggested the use of the recycle step as ameans of improving oxygen utilization and thereby reducing transfercosts. The algorithms we develop should be of value to those establish-ing design conditions for pure oxygen u-tube systems.

BACKGROUNDG a s t r a n s f e r r a t e

The primary resistance to oxygen and nitrogen transfer in a gas-liquidmixture is usually provided by a stagnant liquid film present at theinterphase between the gas and the liquid (Lewis and Whitman, 1924).The rate at which transfer occurs is then proportional to the differencebetween the existing and saturation concentration of the gas in solution.In differential form the relationship is expressed as

dC KL Ad t = (C*-C)

Because of the difficulty in measuring the area of the gas-liquidinterphase (A), the diffusion coefficient (KL) is often combined with


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M odel ing gas trans fer in a u- tube oxyg en a bsorpt ion s ys tem 275the ratio A / V L to establish an overall transfer coefficient K L a , i.e.

dC- - = K L a ( C * - - C ) (2)dtThe overall transfer coefficient will reflect the conditions present in

a specific gas-liquid contact system. Conditions of importance includeturbulence, waste characteristics of the liquid, the extent of the gas-liquid interphase and temperature. Values of K L a can be co rrected forthe effec ts of temperature using the following expression (APHA, 1975):

( K L a ) T = ( K L a ) 2 o (1-024) T-2 (3)Although each gas species in a contact system will have a unique

value of K L a , it has been established that relative values for a specificgas pair are inversely proportional to their molecular diameters (Tsivo-glou e t a l . , 1965), i.e.

( K L a ) J ( K L a ) 2 = ( d )2 / ( d ~) (4)The relationship above, based on Einstein's law of diffusion, provides aconvenient means of establishing mul tic ompone nt gas transfer models(Speece and Orasco, 1970; Mitchel, 1973).Gas solubilityThe saturation concentration of a gas in solution (C*) will influencethe direction as well as the rate of gas transfer (eqn (2)). The C* of agas is a function of its partial pressure in the gas phase, liquid tempera-ture, and liquid composition as related by Henry's law. In equationform (Colt, 1984),

( x ( P ~ - - P r ~ o ) ~C * = B k 1000\ 760--0 / (5)The C* of oxygen in a u-tube system is increased temporarily by

hydrostatic pressure. Those systems in which pure oxygen is dispersedfur ther increase C* by increasing the mole fraction of oxygen in thegas phase. The increase in C* serves to (1) accelerate the rate of gastransfer (eqn (2)), and (2) provide the capability of achieving an effluentdissolved gas level in excess of the air saturation concentration at localbarometric pressure.


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276 B. J. Watten, L. Todd BeckM O D E L D E V E L O P M E N T

A c o m p u t e r m o d e l o f t h e g a s t r a n sf e r p r o c e s s w a s d e v e l o p e d b a se d o ne q n s ( 2 )- -( 5) . T h e p r o g r a m s i m u l a t e s t h e p e r f o r m a n c e o f a n e x p e r i-m e n t a l u - t u b e s y s t e m i n w h i c h p u r e o x y g e n i s d i s p e r s e d a n d o f f- g as isr e c y c l e d . A s s u m i n g c a r b o n d i o x i d e c o n c e n t r a t i o n s a r e n e g li g ib l e , t w op r i m a r y g a s t r a n s f e r o p e r a t i o n s w i l l o c c u r i n s u c h s y s t e m s . T h e s e ar e( 1 ) o x y g e n t r a n s f e r f r o m t h e g a s p h a s e t o t h e l iq u i d p h a s e a n d ( 2 )n i t r o g e n t r a n s f e r f r o m t h e l i q u id p h a s e to t h e g a s p h a s e ( S p e e c e , 1 9 8 1 ).T h e p r o g r a m d e v e l o p e d h e r e a c c o u n t s f o r t h e s e c h a n g e s a s i t p e r f o r m sf in i te d i f f e re n c e c a l cu l a ti o n s. T h e l og ic a n d m a j o r c o m p o n e n t s o f th ec o m p u t e r p r o g r a m a re p r e s e n t e d i n F ig . 1 .

F i g . 1 .

III

READ NPU T /

CALCULATE ACKGROUND ARAMETERS IiI

ESTIMATENITIALVALUESOF KL.aoxyg, and KL'aoitrogen //t

MAKEFINITEDIFFERENCE ALCULATIONSTHROUGH OTH EGSOF THEU.TUBE

IS OFF.GASRECYCLED? )YES

I S C e x itSUFFICIENTLY LOSE O PREVIOUS e x i t ? >t NO

BASEDON OFF.GASCHARACTERISTICSNDOFF.GASRECYCLE ATECALCULATE EW NLETGASCOMPOSITION ND N LETGAS.LIQUID ATIO

CALCULATE XITCONDITIONSANDSUMMARIZE ERFORMANCE

PRINTOUTPUT /

Computation sequence used in the computer model of the experimentalu-tube system.


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M o de l i ng gas trans fe r i n a u - t ube oxy gen absorp t i on s y s t em 2 7 7Finite difference calculationsFinite difference calculations are similar to those employed by Speeceand Orasco (1970). The following variables are recalculated at eachdistance step in the program: ( 1)mas s of oxygen and nitrogen in thegas phase; (2) total pressure; (3) overall transfer coeffic ients ; (4) dis-solved gas deficits; and (5) changes in dissolved gas concentrations. Atthe start of each calculation series, the Ideal Gas law is used to relatevolume, temperature, pressure and molar composition of the gas phase.Pressure at each step, n, neglecting pressure drop due to two-phaseflow, is defined as follows:

( P T ) n + I = ( e T ) n - - ( A Z P g ) n - - ( I A Z I)n f f (6)The change in hydrostatic pressure that occurs in a u-tube system

affects the number, not the size, of the gas bubbles present (Speeceand Orasco, 1970; Mitchell, 1973). Therefore , given the volume of gasat any two program steps n, a relative interfacial area to volume ratiocan be determined, i.e.

( A / V L ) n l / ( A / V L ) n 2 = ( V g ) n l / ( V g ) n 2 ( 7 )Since K L a is the product of A / V L and the constant KL (eqn (1)),relative values of K L a may be established in a similar manner (Speeceand Orasco, 1970):

(KL at )nJ (K L ai),,: = ( Vg),n/ Vg)n: (8)The expression above is used to calculate relative values of K L a at

each step n with respect to u-tube inlet conditions. Based on eqn (4),values of K L a for nitrogen are assumed to be 0.9 times that estimatedfor oxygen. Gas saturation concentrations required to establish dis-solved gas deficits are calculated using Henry's law (eqn (5)). Bunsencoefficients (Bi) and vapor pressures (PH20)used in this determinationare obtained from equations presented by Weiss (1970) and ASHRAE(1972), respectively. Given the gas deficits and K L a values, the changesin dissolved gas concent rat ions are established using rate express ion,eqn (2), i.e.

( C i )n + l = ( C i) n + ( K L a i ( C ~ - - C i ) ) n d t (9)The change in gas phase mass is determined in a similar manner byperforming a mass balance on the volume segment represented by


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278 B . J . W a t t e n , L . T o d d B e c ks t e p n .

( ~ ' l i ) n+ l = ( ~ t ) n - - ( K L a i ( C * - - C i ) ) V L d t ( 1 0 )U p o n c o m p l e t i n g f i n it e d i f f e r e n c e c a l c u l a ti o n s , e x i t c o n d i t i o n s a r ei d e n t if i e d a n d p e r f o r m a n c e i n d i c a to r s c a l c u l at e d .P e r f o r m a n c e i n d i c a to r s

U - t u b e p e r f o r m a n c e i s e v a l u a t e d i n t e r m s o f tr a n s f e r c o st s, t r a n s f e re f f i c i e n c y a n d o x y g e n a b s o r p t i o n e f f ic i e n c y . T h e l a t t e r r e p r e s e n t s th er a ti o o f m a s s o x y g e n a b s o r b e d t o m a s s o x y g e n a p p l ie d , a s d e f i n e d i nt h e f o l l o w i n g e x p r e s s io n :

A E = (Q w (D~-~0ox~DO01-3)0 0 _ ( 1 1 )T r a n s f e r e f f ic i e n c y re p r e s e n t s t h e m a s s o f o x y g e n a b s o r b e d p e r u n it

o f e n e r g y i n p u t . I n t h e e x p e r i m e n t a l u -t u b e , to t a l e n e r g y i n p u t is t h es u m o f t h e e n e r g y u s e d i n p u m p i n g w a t e r ( P w , p u m p ) a n d r e c y c li n go f f - g a s ( P w , c o m p r e s s o r ) , e . g .

Q w ( D O o - - D O 0 1 0 - ,T E = ( 1 2 )P w , p u m p + P w , c o m p r e s s o rE n e r g y u s e d i n p u m p i n g w a t e r i s c a l c u l a te d a s f o ll o w s :

P w , p u m p = ( ( Q w / 3 6 0 0 ) (H E s in g le p h a s e + A H L ) q ,) /e ( 1 3 )A n e s t i m a t e o f t h e e n e r g y r e q u i r e d t o r e c y c l e o f f -g a s is o b t a i n e d f r o mt h e a d i a b a ti c c o m p r e s s i o n f o r m u l a ( Y u n t , 1 9 7 9 ):

Q m R T I [ ( P o ~ N _ _ I ]P w , c o m p r e s s o r - N ~ L \- ~- i / ( 1 4 )

M O D E L C A L I B R A T I O NP r i o r t o m o d e l u s e , t w o s e ri es o f t e s ts w e r e u n d e r t a k e n t o e s t a b li s ha p r e d i c t i v e e q u a t i o n f o r h e a d l os s d u e t o tw o - p h a s e f l o w , a n d f o rK L aox yg en a t t h e u - t u b e en t r a n c e ( s t ep n = 1 ). K L aox yg en v a l u es a t o t h e rp o i n t s a r e c a l c u l a t e d u s i n g e q n ( 8 ). I n a ll t e s t s w a t e r f l o w w a s h e l dc o n s t a n t a t 1 9 7 l i t r e m i n -~ .


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Fig. 2.

Modeling gas transfer in a u-tube oxyg en abs orption s ystem 279HIGHPRESSUREJl] ~ WATER UPPLY

OFF.GASRECYCLE ~ ,S - WATER ETEXHAUSTERI . . 1[~ '1" WATER ROMCONSTANT" HEADRESERVOIRMETERED 2 FLOW--* " ~ WATER AMPLE ORTOFF.GAS OLLECTORD I S ~ , ~ , _ _ . " - - ~ / ~ , . ~ DISCHARGE

5 0 LITERVOLUME ~' ~ WATER AMPLE ORT

--~ 6.35cm IPE~

,S 10.16cm ASING

Diagram o f the p i lot scale u-tube oxy gen absorp t ion system incorporat ingoff-gas recycling.

T e s t a p p a r a t u sT h e e x p e r i m e n t a l u - t u b e is i l l u s tr a t e d i n F ig . 2. A s s h o w n , t h e s y s t e mc o n s i st s o f f o u r m a j o r c o m p o n e n t s . T h e s e a re (1 ) a c o n c e n t r i c p i p eu - t u b e , ( 2 ) a n o x y g e n s p a r g e r , ( 3 ) a n o f f- g a s c o l l e c t o r , a n d ( 4 ) a w a t e rj e t e x h a u s t e r . T h e u - t u b e w a s f a b r i c a t e d w i t h P V C p ip e a n d s t a n d a r dt h r e a d e d f it ti n gs . U - t u b e t y p e f l o w w a s a c h i e v e d b y p o s i t io n i n g a 6 . 3 5c m o u t s i d e d i a m e t e r p i p e s e c t io n ( d o w n - l e g s h a f t) in th e c e n t e r a n ds li g ht ly o f f t h e b o t t o m o f a c a p p e d s e c t i o n o f 1 0 . 1 6 c m o u t s i d e dia -m e t e r p i p e . T h e c r o s s s e c t i o n a l a r e a o f t h e d o w n - l e g a n d a n n u l a r s p a c ei n t h e u p - le g s h a f t s w e r e 3 0 . 3 c m 2 a n d 3 9 -1 c m 2, r e s p e c t i v e ly .

P u r e o x y g e n w a s d is p e r s e d t h r o u g h a 6 m m d i a m e t e r o r i f ic e p o si -t i o n e d n e a r t h e d i s c h a r g e o f t h e w a t e r j e t e x h a u s t e r ( F i g . 2 ) . A p r e s su r er e g u l a to r , t h r o t t l e v a l v e a n d r o t a m e t e r ( B r o o k s M o d e l 1 1 1 0 ) w e r e u se dt o m e t e r t h e o x y g e n f l o w . A c a p p e d s e c t i o n o f p i p e 2 0 . 2 c m in d ia -m e t e r a n d 1 3 3 c m i n l e n g t h s e r v e d a s t h e o f f - g a s c o l l e c t o r . T h e e f f e c t i v ev o l u m e o f th e c h a m b e r w a s 5 0 li te r s w h i c h , w h e n u s e d , p r o v i d e d s u ff i-c i e n t d e t e c t i o n t i m e f o r s e p a r a t i o n o f u n d i s s o l v e d g a se s . T h e d i sc h a r g ee n d o f t h e c o l l e c t o r w a s e l e v a t e d s li g ht ly ( 8 - 8% s l o p e ) t o c o n c e n t r a t eg a s n e a r t h e v a c u u m l in e in l e t ( F ig . 2 ) . T h e w a t e r j e t e x h a u s t e r p r o -


10/27

280 B . 3 " . W a t t e n , L . T o d d B e c kvided the vacuum necessary to recycle collected off-gas. The exhausterwas operated at a water pressure of 241 kPa resulting in a water con-sumpt ion rate of about 15 liter min-1. Water at this pressure wassupplied by a jet pump coupled with a pressure tank and regulator.

An elevated head tank was used to maintain gravity flow through theu-tube. The tank received unaltered wa ter from the Susquehanna Riverpumped from a point near the Brunner Island Aquaculture Project.The head tank also provided water for the jet pump system. Water flowwas measured with a stopwatch and barrel of known capacity. U-tubeinfluent and effluent samples were obtained from sample ports locatedupstream of the exhauster and just below the discharge (Fig. 2). DOconcentrations in samples were determined using the azide modificationof the Winkler method (APHA, 1975). During head loss tests, mano-meter tubes connected to the water sample ports described aboveprovided influent and effluent static pressure readings. Barometricpressure, water and gas temperature were measured with a standardmercury barometer and thermome ter.M e t h o d s - T e s t Series IThe ef fect o f influent oxygen-liqu id ratio and shaft depth on head lossdue to two-phase flow was determined. Oxygen-liquid ratio here isdefined as the volumetric flow rate of oxygen under standard condi-tions (21 .IC and 760 mm Hg pressure) divided by the volumetric flowrate of water . Oxygen was metered into u-tubes 6.10, 12.19 and 18.29 mdeep. During tests, oxygen-liquid ratios were varied from 0 to 28%.Water flow was regulated by adjusting a valve positioned upstream ofthe influent sample port. Following data collection, head loss due totwo-phase flow (AHL) was computed using recorded pressure dropsacross the system (HL) under single-phase (water) and two-phase(oxygen and water) flow conditions, i.e.

AHL = HE two phase -- HL singlephase (15)M e t h o d s - T e s t S e r i e s I I

In this second test series, the effect of influent oxygen-liquid ratio andshaft depth on oxygen transfer was evaluated. Oxygen was metered intou-tubes 6.10, 12.19 and 18 .29m deep. Oxygen-l iquid ratios were


11/27

M o d e l i n g g as t ra n s f e r in a u - t u b e o x y g e n a b s o r p t i o n s y s t e m 281varied from 2.3 to 11.7%. Water flow was regulated by adjusting theu-tube discharge valve. Because off-gas was not recyc led, the water jetexhauster was operated with its vacuum line closed. At each establishedcombination of depth and oxygen-liquid ratio, samples were taken forDO analysis once steady-state conditions had been maintained for aminimum of 10 min. Reagents used in the DO analyses were addedimmediately after sample collection:R e s u l t s - T e s t S e r i e s I

Data illustrating the effect of u-tube depth and influent oxygen-liquidratio on head loss (AHL, eqn (15)) are presented in Fig. 3. Note thatas the depth and/or oxygen-liquid ratios increased so did AHL. As aconsequence, and due also to a limiting available hydraulic head, therange of oxygen-liquid ratios evaluated at a shaft depth of 6.10 m

1.78.

U-TUBE DEPTH /1 .52. D 6 .10m J ~~, 1 2 . 1 9 m:, 18.29rn /

1.27. /, ~ 1 . 0 2 .

0.76_

0.51_

0.25_

0.00 0 I ; 2 lh ~ 4 3 ~INFLUENT OXYGEN.LIQUIDRATIO, PERCENT

Fig . 3 . Ef fec t s o f u -tube dep th and in f lu en t oxyge n- l iqu id ra t io on head lo ss dueto two-phase f low (ZM-/L, eqn (1 5)) . W ater tem pera ture and inf luen t DO during

tes ts were 23 .4-23-9 C and 7-4-7-8 m g l i te r z , respec tive ly .


12/27

282 B. J. Watten, L. To dd Beckexceeds the range evaluated at greater depths (12.19 and 18-29 m).Multiple linear regression was used to establish a model of the inter-action observed between AHL, oxygen-liquid ratio, and depth:

In AHL = 0.888 + 0-0758(D) + 1.021 (In G / L ) (16)R 2 = 0-98

R e s u R s - T e s t S e r i e s I I

The effec t of u-tube depth and influent oxygen-liquid ratio on oxygentransfer is illustrated in Fig. 4. As shown, increasing the oxygen flowrate increased effluent DO concentrations at a diminishing rate whilereducing absorption efficiency. It can also be seen that both exit DOand absorp tion efficiency increased with greater shaft depths. The gastransfer program was used to establish values of KLaoxygen for each setof observations by determining the K L a value at the u-tube entrancethat resulted in the observed effluent DO concentration. During thisiteration procedure, influent dissolved nitrogen was assumed to be atthe saturation concentration estimated using eqn (5). EstablishedKLaoxygen values were adjusted to 20C using eqn (3). Multiple linearregression was then used to define KLaoxygen in terms of influentoxygen-liquid ratio and shaft depth:

(KLaoxygen)2oOc = 62-1161 --4-3331(D) + 6 7 . 7 5 7 7 ( l n G / L ) (17)R 2 = 0.90

The above expression, and that defining AHL established in TestSeries I, were incorporated into the computer model of the u-tubesystem.

MODEL VERIFICATIONUsing the apparatus evaluated in Test Series I and II, the effect ofoff-gas recycling on oxygen transfer was determined for purposes of(1) demonstrating the feasibility of the recycle step and (2) verifyingthe effects of off-gas recycling as predicted by the calibrated computermodel.


13/27

Modeling gas transfer in a u-tube oxygen absorption system 2 8 36 0 -

48 -

z 36+

~ 24 .= = =

12

3510

~ 2 8E

0~ 14.

Fig. 4. Effects of u-tube

i * I I i i

/ / 8 . 1 0

OXYGEN. IQUIDRATIO,PERCENTdepth and influent oxygen-liquid ratio on oxygen

transfer. Original data had variations in influent DO (8.6-9.4 mg liter-l), tempera-ture (26.7-27-2C) and barometric pressure (757-760 mm Hg). Data presented herehave been adjusted to a standard set of conditions (temperature, 27C; influent DO,7.95 mg liter-l; barometric pressure, 760 mm Hg) using the computer program andKLa values established for each observation.

Meth ods - Test Series IIIOff-gas recycle rates of 25, 50 and 60% were established at a shaftdep th of 12.19 m. Initial influe nt oxygen--liquid ratios were varied from2.3 to 6.2%. As in Test Series II, water flow was regulated by adjustingdischarge valves. When recycling off-gas at a specific rate (e.g. 50%),


14/27

2 8 4 B. J . Wa t t e n , L . To d d Be c kt h a t s a m e f r a c t i o n o f u - tu b e f l o w w a s d i v e r te d t h r o u g h th e o f f- g a sc o l l e c t o r . U n d i s s o l v e d g a s e n t e r i n g t h is d e v i c e w a s c o l l e c t e d a n di m m e d i a t e l y r e c y c l e d . W a t e r f l o w i n t h e r e c y c l e l i n e ( c le a r t u b i n g ) w a sk e p t t o a m i n i m u m b y a d j u s t i n g a v a c u u m r e g u l a t o r v a lv e ( F ig . 2 ) .C o l l e c t o r e f f l u e n t w a s d i r e c t e d t h r o u g h a c le a r c a r b o y o f 1 9 - li te rc a p a c i t y t o v i s u a l ly t e s t f o r c o m p l e t e s e p a r a t i o n a n d u s e o f a v a il a b leo f f- g as . S a m p l e s w e r e o b t a i n e d f o r D O a n a l y s is a f t e r s t e a d y - s t a t ec o n d i t i o n s h a d b e e n m a i n t a i n e d f o r a m i n i m u m o f 1 0 m i n .R e s u l t s - T e s t S e r i e s I II

D u e t o a l i m i t in g h y d r a u l i c h e a d , o b s e r v a t i o n s a t t h e 6 0 % o f f- g a sr e c y c l e ra t e w e r e r e s t r i c t e d t o a n i n f l u e n t o x y g e n - l i q u i d ra t i o o f 2 .3 % .T a b l e 1 p r e s e n t s a c o m p a r i s o n b e t w e e n T e s t S e r i es I I I d a t a a n d g ast r a n s fe r m o d e l p r e d i c t i o n s . A s s h o w n , m o d e l p r e d i c t io n s a r e in v e r yc lo s e a g r e e m e n t w i t h t h e p i l o t s t u d y d a t a . T h e r e l a t i v e e r r o r o f t h ee s t i m a t e s a v e r a g e j u s t 2 - 9 % w i t h a r a n g e o f 0 -9 t o 6 . 3 % . D a t a in T a b l e 1

T A B L E 1Com par i s on Be t ween Obs e r ved ( Tes t Se r i e s I I I ) and Mode l P r ed i c t ed Ef f l uen t DOCo ncen t r a t i ons a t Seve r a l Ra t e s o f Of f -Gas Recyc l i ng . U- t ube Sha f t D ep t h , 12 -19 m ,

T e m p e r a t u r e , 2 5 - 6 -2 7 . 8 C ; B a r o m e t r ic P r e ss u re , 7 5 7 - 7 6 2 m m H gO x y g e n - O f f -g a s I n f l u e n t M e a n M e a n P r e d i c t e d R e s i d u a l

l iq u i d r e c yc l e D O A E e f f l u e n t e f f l u e n t a sr a ti o r a t e ( m g l i te r - 1) ( % ) D O D O p e r c e n t( % ) ( % ) ( m g l i t e r -1 ) ( m g l i t e r - 1)2 . 3 0 9 . 4 41 - 7 , N = 2 21 . 8 22 . 3 + 2 . 32 .3 25 9 .0 48-0 , N = 3 23 .3 23-7 + 1 .72 .3 50 8 .3 54 .3 , N = 3 2 4 .4 25 .1 + 2 .92 . 3 60 9 . 4 60 . 5 , N = 3 27 - 3 26 - 7 - - 2 . 24 .1 0 9 . 4 34 . 6 , N = 2 27 . 9 28 . 9 + 3 . 64-1 25 8 .8 40-7 , N = 3 30 .5 30 .2 - - 1 .04 .1 5 0 8 -3 4 3 - 1 , N = 2 3 1-1 3 2 -2 + 3 . 56 - 2 0 9 - 4 26 . 9 , N = 2 31 . 4 33 . 4 + 6 . 36 .2 25 8-5 31 .6 , N = 2 34 .4 34 .7 + 0-96 .2 50 8-3 33 .3 , N = 2 35 . 6 36-9 + 3 .7


15/27

M o d e l i n g g a s t r a n s fe r in a u - t u b e o x y g e n a b s o r p t i o n s y s t e m 285also demonstrate the substantial increase in oxygen utilization that canbe achieved by off-gas recycling; e.g. with an influent oxygen- liquidratio of 2.3%, recycling 60% of the available off-gas resulted in a 45%increase in absorption efficiency.

MODEL APPLICATIONEffects o f off-gas recyclingA b s o r p t i o n e f f i c i e n c yFollowing Test Series III, the computer program was used to simulatethe response of u-tube effluent DO to changes in design and operatingconditions. Results of a simulation run used to establish the ef fects ofthe off-gas recycle rate are illustrated in Fig. 5. Note t hat as the recyclerate approached 100%, effluent DO rose steadily from 15.0 to 28.5 mgliter-1. The improvement in oxygen utilization occurs in response tothe increase in the effective gas-liquid ratio despite the concurrentreduction in the oxygen pur ity level of the influent gas mixture (Fig. 5).Additional simulation runs indicate the improvement in oxygen utiliza-tion, resulting from a fixed rate of off-gas recycling, will increase with(1) greater shaft depths (Fig. 6), (2) lower pure oxygen flow rates(Fig. 6), and (3) lower levels of DO in the influent (Fig. 7). Tempera-ture has a relatively minor effect at a given saturation level of DO inthe inf luent (Fig. 7).

The rise tha t occurs in the gas-liquid ratio with off-gas recycling willbe more dramatic than indicated in Fig. 5 at higher pure oxygen flowrates. This effect may limit the off-gas recycle rate, i.e. the two-phaseflow that occurs in a u-tube is, under normal conditions, representedby the bubble flow regime, a continuous liquid phase in which a gas ishomogenously dispersed as bubbles (Mitchell, 1973). If the gas-liquidratio becomes excessive, bubbles coalesce forming large bullet-shapedslugs of gas. The transition to slug flow should be avoided as it resultsin discharge surging and a rapid increase in AH L. The max imum accept-able gas-liquid ratio is influenced primarily by velocity (Speece e t a l . ,1969), although shaft depth and diameter may also have an effect(Mitchell, 1973). Speece e t a l . (1969) suggest a 20% air-liquid ratio isabout the limit at a veloci ty of 1.22 m s 1 while at velocities of 1.83-2.44 m S 1 a 25% air-liquid ratio was sat isfactory. In Test Series I,


16/27

286 B. J. Watten, L. Todd Beck

8-o~ - 6 -_d= ~

o 4 -o- -- 2 -

0~ 95-

~ 80-

z 65-

35

25-E

20 -

15-

Fig . 5 . Eff ec t of off-gas

COMPUTERSIMULATION

. . . . O X Y G E N " " 6 0, ' ,- , ISO3.0

--"" 2 .5

2.0 ~

" t5 ~/ ABSORPTIONFFICIENC'~

, , , , 1 . 013.0

" -11.25~9.50z--E

. . . . D IS SO LV EDITROGEN 7.75DISSOLVED XYGEN

6.002 0 4 0 6 0 8 0 1 0 0RECYCLE ATE, ERCENTrecyc l ing on e f f luen t DO and DN, oxygen abso rp t ion

eff ic iency, t ransfer e ff ic iency, e ffec t ive gas - l iquid ra t io and off-gas compos i t ion .Te m pera ture , 22 .5C; inf l uen t D O, 4 .32 mg l i te r 1 , inf luen t D N, 1 4-23 mg l iter-Z;

shaf t d epth , 18 .29 m ; ve loc i ty in down-leg 1-08 m s - l ; ve loc i ty in up- leg , 0 .8 4m s z .


17/27

M o d e l i n g g a s tr a n s f e r i n a u - t u b e o x y g e n a b s o r p t i o n s y s t e m 287

oo

1 . 4 0 1

1 '3211 . 2 4 -

1 . 1 6 -

1 . 0 8 -

1.O04.0 20 .0

COMPUTER S IMULATION

. . . . . . . . . . . . . . . . . . . . . . ~ - - ~

2 .0 % G I L. . . . . 3 . 0 % GIL- - - 5 . 0 % G /L

8 1 0 1 2 ' 0 l i 0S H A F T D E P T H ,M E T E R S

Fi g . 6 . E f f e c t o f i n it ia l oxy gen - l i qu i d r a t i o (G/L) and u - t ube sha f t dep t h on t hei nc rea se i n D O r e su l ti ng f r om an o f f- ga s r ecyc l e r a t e o f 60% . Tem per a t u r e , 30 C;i n f l uen t D O , 7 . 54 m g l i t e r -l ; ve l oc i t y i n dow n- leg , 1 -08 m s - l; ve l oc i t y i n up - leg ,

0-84 m s 1 .

= = _o .

= E

o

1.7 COMPUTERSIMULATION

1 .8

1 . 5 -

1 .4 1 5 . 0 C- - - 2 2 .5 C1 . 3 - . . . . . 3 0 .0 C

-I1 2 2 ' 5 s b ; 5 1 0 0I N F L U E N TD O P E R C E N TO F S A T U R A T IO N )

F ig . 7 . E f f e c t o f i n f l u e n t D O (% o f s a t u r a ti o n ) a n d w a t e r t e m p e r a t u r e o n t h ei nc rea se i n D O r e su l ti ng f r o m an o f f - ga s r ecyc l e r a t e o f 60% . U - t ube sha f t dep t h ,

1 8 . 2 9 m ; i n i t i a l o x y g e n - l i q u i d r a t io , 2 % .


18/27

288 B. J. Watten, L. Todd Beckpressure oscillations were observed when the oxygen-l iquid ratioexceeded 28% (shaft depth, 6-10 m; system flow rate, 197 liter min-1).Transfer efficien cySimulation runs indicate transfer efficiency will vary widely withoperating conditions. At low influent oxygen-liquid ratios, there is anoff-gas recycle rate that will maximize transfer effic iency (Fig. 5). Athigher oxyge n flow rates, off-gas recycling will result in reduced transferefficiency. When off-gas is not recycled, there is an oxygen flow ratethat will provide maximum transfer efficiency at a given u-tube depth.It is also clear that u-tubes of shallow construction will favor transferefficiency, e.g. with an influent oxygen-liquid ratio of 5%, transfereffic iency at shaft depths of 18.29 and 6.10 m would be 4.02 and13.87 kg 02 kW h -1, respectively (tempera ture , 30C, percent saturationof DO in the influent, 100%).Transfer e cono myAmortized capital and bulk oxygen are the expenditures of primaryimportance in the operating budget of a pure oxygen u-tube system.Unlike conventional aeration systems (e.g. surface aerators) energycosts are minimal. Figure 8 provides a comparison of oxygen transfercosts established for a u-tube of 18.29 m depth with and withoutoff-gas recycling. In the analysis, unit oxygen and elec tricity costs wereassumed to be $ 0-146 kg- IO2 and $0-055 kWh -1, respectively. Theinitial capital costs used are summarized in Table 2. From this com-parison the following observations were made:

1. Inco rporation of the recycle step results in a minimal (8.4%)increase in the total annualized equipment cost (Table 2).

2. Off-gas recycling reduced variable costs by 49-55%. Tota l transfercosts were reduced by 25-41%. The savings achieved increase withgreater effluent concentrations of DO (Fig. 8).

3. When off-gas is not recyc led, there is an effluent DO at which totaltransfer costs are minimized (Fig. 8).4. Variable costs for both systems evaluated increase with greaterconcentrati ons of effl uent DO (Fig. 8).

P e r f o r m a n c e a l g o ri th m sU-tube simulation data were modeled to establish performancealgorithms for those who do not have access to computer equipment.


19/27

Modeling gas transfer in a u-tube oxygen absorption sys tem 2890 . 6 6 0 - ~

0 . 5 9 4

0 . 5 2 8 -

0 . 4 6 2 -

~ 0 . 3 9 6 -

0 . 3 3 00 . 5 5

0 . 4 4 - -

t' a

~ 0 . 3 3 -

o 0 . 2 2 -

~ 0.11

C O M P U T E R S IM U L A T I O N

I I I l I I

. . . . . NO OFF.GASRECYCLINGWITH 90% OFF.GASRECYCLERATE

0,00 2 0 2 ' 3 2 ' 6 3 ' 2E F F L U E N T O ,m g l L I T E RFig. 8 . Effec t o f off-gas recycl ing on t ransfer econom y. Tem perature, 22-5C;influe nt DO , 4-32 m g liter-Z; shaft d ep th, 18-29 m ; velocity in down-leg, 1.08 m s-l;

velocity in up-leg, 0-84 m s z.

T h e a l g o r i t h m i c f u n c t i o n s e s t a b l is h e d d e s c r i b e d a t a g e n e r a t e d i n a s er ie so f 4 3 2 c o m p u t e r r u n s in w h i c h a t e a ch o f th r e e u - t u b e d e p t h s ( 6 -1 0 ,1 2 -1 9 , a n d 1 8 .2 9 m ) a l l c o m b i n a t i o n s o f t h e f o ll o w i n g i n d e p e n d e n tv a r i a b le s w e r e t e s t e d : i n f l u e n t o x y g e n - l i q u i d r a t io , 2 , 5 , 8 a n d 1 2% ;w a t e r t e m p e r a t u r e , 1 5, 2 2- 5 a n d 3 0 C ; p e r c e n t s a t u r a t i o n o f D O int h e i n f l u e n t , 0 , 5 0 a n d 1 0 0 % ; a n d o f f - g a s r e c y c l e r a t e , 0 , 3 0 , 6 0 a n d9 0 % . T h e c o n f i g u r a t i o n o f t h e s y s t e m e v a l u a t e d is t h e s a m e a s t h a tu s e d i n T e s t S e r i e s I - I I I . B a r o m e t r i c p r e s s u r e a n d l i q u i d f l o w w e r e h e l dc o n s t a n t a t 7 6 0 m m H g a n d 1 9 7 l i te r m i n -~ , r e s p e c t iv e l y .


20/27

290 B . J . W a t t e n , L . T o d d B e c kT A B L E 2

S u m m a r y o f C o s t sa for a Concentr ic Pipe U-tube 18 .29 mDeep. In ner Pipe D iame ter , 0-203 m ;Ou ter Casing Diam eter ,0 .305 m . I t i s Assum ed Th a t A dequa te Hyd rau l i c Head is

Available fo r U-tube O pera t ionP a r a m e t e r U S d o ll a r, 1 9 8 3

U-tube (PVC)Sh af t dr i l ling @ $171 m -1 3 129Casings insta l led @ $122-6 m -1 2 242Flow con t ro l valve 245Miscellaneous fi t t ing s 463L i q u i d f l o w m e t e r 9 7 6Assembly 240

R e c y c l e e q u i p m e n tOff-gas colle ctor 2 100Off-gas b low er 473Assembly 120

Oxy gen de l ive ry sys t emLiqu id oxyg en t ank ( ren ta l) 3 300O x y g e n m e t e r i n g s y s t e m 1 6 0 0Ox ygen sparger 320Assembly 270

Ann ua l i zed equ ipm en t cos t bW ithout off-gas recyc l ing 4 693W ith off-gas recy cling 5 088

yea r 1

a Equ ipmen t cos t e s t ima te s a re ba sed on b ids r ece ived fo rcons t ruc t ion a t Brunne r I s l and .b Capi ta l recovery fa c tor used is based on a 12% in te restra te and a 15-year am ort iza t ion per iod .

F o l l o w i n g d a t a c o l l e c t i o n , m u l t i p l e l in e a r r e g re s s io n w a s u s e d in c o n -j u n c t i o n w i t h c o m p u t e d c o r r e l a t i o n o f c o e f f i c i e n t v a lu e s t o e s t a b l is ht h e m o s t a p p r o p r i a t e m o d e l f o r m f o r a g iv e n d a t a s e t. A re g r es s io ne q u a t i o n p r e d ic t in g e f f l u e n t D O a s a f u n c t i o n o f th e i n d e p e n d e n tv a r i a b le s t e s t e d , e x c l u d i n g % R , i s l i s te d b e l o w :


21/27

Modeling gas transfer in a u-tube ox yge n abso rption sy stem 29 1D O o = - - 3 . 7 7 + 1 2 - 1 9 8 ( 1 n G / L ) + 0 - 9 0 6 9 ( D ) - - 0 . 14 0 5 ( T )

+ 0 - 0 5 7 5 ( % S ) ( 1 8 )R 2 = 0 . 9 2 ; S E = 2 . 9 7

T o c o r r e c t t h e a b o v e f o r t h e e f f e c t s o f o f f -g a s r e c y c l i n g , a d i s so l v e dg a s m u l t ip l i e r o f t h e f o l l o w i n g f o r m w a s e s t a b l i s h e d :

D O C F = ( D O o ) r e c y c l i n g / ( D O o ) n o recycl ing ( 1 9 )T h e r e g re s s io n e q u a t i o n d e f i n in g t h e D O o m u l t ip l i e r i s

In D O C F = 0 - 1 6 3 4 7 - - 0 - 0 9 2 2 ( l n G / L ) + 0 . 0 0 2 7 9 ( D )- - 0 - 0 0 1 4 3 ( T ) - - 0 - 0 0 0 7 8 ( % S ) + 0 . 0 0 3 9 3 ( % R ) ( 2 0 )

R 2 = 0 . 8 6 ; S E = 0 . 0 4 9A m u l t i p l i e r s u c h a s t h a t d e f i n e d i n e q n ( 1 9 ) w a s e s t a b l i s h e d t o

s i m i la r ly c o r r e c t t h e i n f l u e n t g a s - l i q u i d r a t i o f o r t h e e f f e c t o f o f f -g a sr e c y c li n g . T h e m u l t ip l i e r w a s p o s t u l a t e d t o b e o f t h e f o l l o w i n g q u a d -r a t i c f o r m :

G / L C F = ( 1 / 2 X 2 ) + 1 ( 2 1 )T h e t e r m X is d e f i n e d b e l o w a s a f u n c t i o n o f t h e i n d e p e n d e n t v a r ia b l esi n c l u d e d i n e q n ( 2 0 ) :

l n X = - - 1 . 0 2 1 6 + 0 . 1 3 6 3 ( l n G / L ) ~ 0 . 0 1 (D ) + 0 . 0 0 0 9 9 ( T )+ 0 . 0 0 0 4 3 ( % S ) + 0 . 0 2 0 5 6 ( % R ) ( 2 2)

R 2 = 0 - 9 9 ; S E = 0 . 0 5 5T h e a l g o r it h m s p r e s e n t e d h e r e , w h e n u s e d in c o n j u n c t i o n w i t h

m o d e l s d e s c r i b e d in p r e v i o u s s e c t i o n s , p r o v i d e a r e la t iv e l y s im p l e m e a n so f p r e d i c t i n g u - t u b e p e r f o r m a n c e w i t h in t h e r a n ge o f o p e r a t i n g c o n d i -t io n s e v a l u a t e d . F o r e x a m p l e , g i v en s h a f t d e p t h , w a t e r te m p e r a t u r e ,i n f l u e n t D O s a t u r a t i o n a n d g a s - l iq u i d r a t i o , t h e r e s p o n s e o f e f f l u e n tD O t o v a r i o u s r a t e s o f o ff - g a s r e c y c l i n g c a n b e c h a r a c t e r i z e d ( e q n s( 1 8 ) - ( 2 0 ) ) . O x y g e n a b s o r p t i o n e f f ic i e n c y c a n b e o b t a i n e d f r o m e q n( 1 1 ) . T o e s t a b li s h t r a n s fe r e f f ic i e n c y , t h e p o w e r re q u i r e d t o r e c y c l eo ff -g a s ( P w , c o m p r e s s o r ) a n d p u m p w a t e r ( P w , p u m p ) m u s t b e k n o w n( e q n ( 1 2 ) ) . P w , p u m p c a n b e d e t e r m i n e d b y a d d in g th e e s t i m a t e d h e a dl os s r e s u lt i n g f r o m p i p e f r i c t i o n , v e l o c i t y a n d e l e v a t i o n c h a n g e s to t h eh e a d l os s d u e t o t w o - p h a s e f l o w ( e q n ( 1 3 )) . T h e l a tt e r , A H L , is o b t a i n e d


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292 B. J. Watten, L. Todd Be ckfro m eqn (16) using a corrected influent gas-liquid ratio (eqns (21) and(22)). Pw, compressor is calculated using the expression for adiabaticcompression (eqn (14)). The absolute pressure differential required,neglecting gas condui t friction losses, is taken as the total pressure dropacross the u-tube. The volumetric flow of off-gas being compressed canbe derived by subtracting the pure oxygen flow rate from the effectivegas--liquid ratio, i.e.

a g = ( ( ( G / L C F " G / L ) - - G / L ) / 1 0 0 ) Qw (23)To obtain the mass flow rate from the above, an estimate of the molarcomposition of the off-gas is required. An expression describing theoff-gas mixture (primarily O~ + N2) has not been provided. However,if one assumes the gas is pure oxygen or air, a reasonable approxima-tion of the mass flow and hence Pw, compressor, can be obtained.Disperser dep th, system flow rate, and water quality are design variablesthat have not been incorporated in the computa tion sequence justdescribed. Their potential effects are addressed briefly in the followingparagraphs.

D i s p e r s e r d e p t hIncreasing disperser depth will result in reduced oxygen transfer andAHL (Speece e t a l . , 1969). Implicit in the performance algorithmspresented above is that commercial oxygen and recycled off-gas isintroduced in water at the top of the down-leg shaft. The dispersionof gas at this point will maximize oxygen utilization while also mini-mizing compressor power requirements.S y s t e m f l o w r a t eThe algorithmic functions derived assume a velocity o f 1.08 m s 1 inthe down-leg and 0.84 m s 1 in the up-leg shafts. Higher velocities mayresult in a moderate reduction of both effluent DO and AHL (Speecee t a l . , 1969; Mitchell, 1973; Speece e t a l . , 1980). Figure 9 gives a com-parison of oxygen transfer data obtained at two flow rates in theexperimental u-tube system (Fig. 2). Note that oxygen transfer at 274liter min -x is nearly the same as tha t obtained at 197 liter min-~ despitea 39% reduction in residence time. A comparison of corresponding K L avalues derived as in Test Series II, and plotted below the transfer data,indicate the reduction in residence time was off-set in this case byincreases in the overall transfer coefficient. The increases in K L a are


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M o d e l i n g g a s t r a n s fe r in a u - t u b e o x y g e n a b s o r p t i o n s y s t e m 29325.0

20 .0 -

t5.0-

= d l o o -

5.0-

0. 0360-

288-

210-

~ 144-

72 "

|&|

It :

FLOW :274 L ITERIMIN . FLOW : 197 L ITERIMIN .

i I i

0 o o 3 1 o 6 1 o m lo 1 2 ' oOXYGEN.LIQUIDRATIO,PERCENT

Fig. 9. Effect of system flow rate on oxygen transfer (ADO) and overall oxygentransfer coefficient (KLa). Shaft depth, 6-10 m. Data have been adjusted to astandard set of conditions (temperature, 27C; influent DO, 7.95 mg liter-l; baro-metric pressure, 760 mm Hg) using the computer program as in Fig. 4.

attribute d to the greater levels of turbulence associated with the higherflow rate (Mauvinic and Bewtra, 1976).W ater qualityThe performance algorithms were established with the assumption thatpure water is being treated. Wastewater characteristics such as BOD,COD and suspended solids will, if present, affect both the rate andext ent of gas transfer. The alpha fac tor (a) is used to represent th e ratioof KLa in wastewater to KLa in pure water unde r a co mmo n set ofoperating condit ions (Gilbert, 1979), i.e.

ot = (K La ) w a s t e w a t e r / ( g L a )pua -e w a t e r (24 )


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294 B . J . W a t t e n , L . T o d d B e c kSimilarly, the beta fac tor (13) represents the ra tio o f C* in wastewater

to C* in pure water (Gilbert, 1979):13 -'~ ( C * ) w a s t e w a t e r / ( C * )p u r e w a t e r (25)

o~ and (3 values were inc orpora ted into eqns (9) and (10) o f thecomp uter model. A series of c ompu ter runs were then used to simulatethe effects of various combinations of the waste correction factors.The effe ct of two combina tions on ox ygen transfer are given in Table 3.Note that the percent reduction in the change in DO (ADO)remainedrelatively co ns tant for a given combina tion o f ot and 13 despite changesin influent oxygen-liquid ratio. Additional runs indicated the percentreduction in ADO was also independent of shaft depth, water tempera-ture and influent DO. Thus the effect o f a given combina tion of wastecorrec tion values can be appr oxi mat ed using a continge ncy table ofADO multipliers established for a single set of operating conditions.Multipliers established for a u-tube of 18.29 m d ept h are plotte d inFig. 10. It is appa rent tha t t he response of ADO to changes in bothot and 13 is linear. Under the wors t case co ndi tio n repr esented (i.e.

T A B L E 3Effect of Wastewater Quality on Oxygen Transfer in aU-tube Oxygen Absorption System. Data are EffluentDO in mg liter 1 Followed by the Percent Reduction inADOa due to a and /3 Values of < 1. Temperature,22.5C; DO Saturation in Influent, 50%; U-tube Depth,18.29 m; Velocity in Down-leg Shaft, 1-08 m s-1;Velocity

in Up-leg Shaft, 0-84 m s a] n f l u e n t

o x y g e n - l i q u i dr a t i o ( % )

W a s t e w a t e r q u a l i ty~ a n d /3 = 0 . 9 a a n d /3 = 0 . 8

258

12

13-4 (15.0%) 11.8 (30.0%)27.5 (14.1%) 23-7 (28.2%)34-1 (14-4%) 29-1 (28.8%)39-2 (14.5%) 33.4 (28.7%)

a ADO = (DO)emuen -- (DO)influen .


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M o d e l i n g g a s t r a n s fe r in a u - t u b e o x y g e n a b s o r p t i o n s y s t e m 2 9 5

1.00- COMPUTER I M U L A T I O N ~

0.~-

g 0.82- ~ ~ = o . ~

0,76-

0,700 . 8 0 o . ~ s o . ~ o o . ~ s ~ . ~ oALPHAFig. 10. Effe ct of a and 13 wa ste correct ion values on oxy gen transfer. Tem pera-ture, 22-5C; influen t DO , 4.32 mg l i ter-l ; veloc i ty in down-leg, 1.08 m s-l ; veloc i ty

in up-leg, 0.8 4 m s 1. ADO mu ltiplier = (mD O)w ~ewa ter/(,~DO)pur water.

t~ = 0 . 8 ; (~ = 0 - 8 ) , o x y g e n t r a n s f e r i s r e d u c e d t o a l e v e l o f a b o u t 7 2 %o f th a t e x p e c t e d w i t h p u r e w a t e r .

I n a d d i t i o n t o ~ a n d ~ f a c t o r s , u - t u b e p e r f o r m a n c e w i l l a l s o b ea f f e c t e d b y i n f l u e n t d i s s o lv e d n i t r o g e n ( D N ) a n d c a r b o n d i o x id e (D C O 2 )c o n c e n t r a t i o n s . T h e a l g o r i th m s e s t a b l i s h e d a s s u m e D N a n d D C O 2 a rea t n o r m a l s a t u r a t io n c o n c e n t r a t io n s . T r e a t m e n t o f w a t e r w i t h D N a n dD C O z a b o v e C * w il l r e d u c e f u r t h e r t h e m o l e f r a c t i o n o f 0 2 in th e g a sp h a s e w i th i n t h e u - t u b e w h i c h , in t u r n , w il l d e c r e a s e o x y g e n tr a n s f e r( e q n s ( 2 ) a n d ( 5 )) . T h e e x t e n t o f t h e e f f e c t w i ll i n c re a s e w i t h ( 1 ) t h es u p e r s a t u r a t i o n l ev e l o f D N a n d D C O 2 , a n d ( 2 ) th e o f f -g a s r e c y c l e ra t e .

I n s u m m a r y , d a t a p r e s e n t e d in th i s r e p o r t i n d i c a t e o f f- g a s r e c y c l in gc a n r e s u l t i n a s u b s t a n t i a l s a v i n gs i n b o t h v a r i a b l e a n d t o t a l c o s t s o fo x y g e n t r a n s f e r w i t h o n l y a m i n o r i n c re a s e in c a p it a l e x p e n d i t u r e s . T h eg r e a t f l e x i b i l i t y in e f f l u e n t D O c o n c e n t r a t i o n p r o v i d e d b y u - t u b eo x y g e n a b s o r p t i o n s y s t e m s ha s a ls o b e e n d e m o n s t r a t e d . T h is p e r f o rm -a n c e c h a r a c t e r is t ic , c o m b i n e d w i t h s i m p l e c o n s t r u c t i o n a n d lo w e n e r g yr e q u i r e m e n t s , m a k e s a q u a c u l t u r a l a p p l i c a t i o n s o f s u c h s y s t e m s h i gh l ya t t r a c t i v e .


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296 B. J. Watten, L. Todd BeckA C K N O W L E D G E M E N T S

W e t h a n k T . F r i d i ri c i , B . N g u y e n a n d M . S r n y s e r f o r a s s i s ta n c e i n d a t ac o l l e c ti o n a n d J . C o l t, V . M u d r a k , R . S o d e r b e r g a n d R . S p e e c e f o rr e v i e w i n g t h i s a r t i c l e .

R E F E R E N C E SAPHA (1975) . Standard M ethod s for the Exam inat ion o f W ater and tCastewater ,

14th edn, American Water Works Associat ion, and Water Pollut ion ControlFed erat ion , Am erican Pub lic He alth Association, W ashington, DC.A S H R A E H a n d b o o k o f F u n da m e n ta ls (1972) . American Society of Heat ing,

Refrigeration and Air Condit ioning Engineers, New Yo rk.Bruijn, J . & Hen dr ick , H . (1958) . T he relationship betw een depth of u- tubes and

the a erat ion process. J . A m . Water Works Assoc . , 50 , 879-83 .Chesness, J. L., Step hens, J. L. & Hil l, T. K. (1972). G ravity f low aerators for race-

w ay fish cul ture system s. Coll . Agric. Exp . Sta., Univ. Georgia, Athens . Res.Rep. 137.Col t , J . (1 984) . Com putat ion of d issolved gas concent rat ions in water as funct ions

o f tem pera ture, sal ini ty, and pressure. American Fisheries Socie ty SpecialPublicat ion 14, Bethesda, Maryland.Colt , J . E. & Tc hob ano glous , G. (19 81). Design of aeration system s for aquaculture.

In : Proceeding of the Bio-engineering Symposium for Fish Cul ture, eds L. J.Allen and E. C. Kin ney , Fish C ulture Sect ion of the American Fisheries Soc ietyand the No rtheast So ciety of Conservation Engineers, Bethesda, Maryland,pp . 138-48 .

Gilbert , R. G . (197 9). Measurement of alpha and beta factors. In: Proceedings:Workshop Toward an Oxygen Transfer S tandard, EPA-600/9-78-021, ed. W. C.Bo yle, U S Environmental Pro tect ion A gency, Cincinnat i, Ohio, pp. 1 47-6 2.

Lewis, W. K. & Whitman, W. C. (1924). Principles of gas adsorpt ion. J. Ind. Eng.Chem. , 16 , 1215-20 .

Mavinic, D. S. & Bewtra, J. K. (1976). E fficiency of diffused aeration system s inwastewater t reatment . J . l~at. Po ll . Contr. Fe d., 4 8 , 2 2 7 3 - 8 3 .Mitchell , R . C. (197 3). U-tube aerat ion. EPA 670/2-73-031, US EnvironmentalProtec t ion Ag ency, Cincinnati , Ohio .Spe ece, R. E. (1981). M anagement of dissolved oxygen and ni trogen in f ish hatche rywaters. In: Proceedings o f the Bio-engineering Sym pos ium for Fish Cul ture, edsL. J. Allen and E. C. Kinney, Fish Culture Sec t ion of the American FisheriesSo ciety and the N orthe ast Soc iety of Conservation Engineers, Bethesda, Mary-l and , pp . 53 -62 .


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M o de l i ng gas trans fe r i n a u - t ube oxyg en absorp t i on s y s t em 297Speece , R . E. & O rosco, R . (1 970) . Des ign of u- tube aera t ion sys tems . A m . S o c .

Civi l Eng. , 9 6 ( S A 4 ) , 7 1 5 - 2 5 .Speece , R . E. , Adams, J . L. & Wooldr idge , C . B. (1969) . U-tube aera t ion opera t ing

characteris t ics . A m . Soc . C i v i l Engr . , 95 (SA3) , 563-74 .Speece, R . E . , Ga l laghe r , D . , Kr ick , C . & Th om son , R . (1980) . P i lo t pe r fo rmance o f

deep u - tubes .Prog . Water Technol . , 1 2 , 3 9 5 - 4 0 7 .Speece , R . E. , Ehear t , J . W. & Givler , C . A. (1983) . U-tube aera t ion sens i t iv i ty to

design parameters . J . Wat . Pol l . Contr . F ed. , 55 , 1065-9 .Ts ivoglou, E. C . , O 'Conn el l , R . L. , W al te r, C . M. , Gods i l , P . J . & Lo gsdon , G. S .

(1965) . Trace r measu rem en t s o f a tmosphe r i c reae ra tion - 1. Lab ora to ry s tud ie s.J. IVat. Pol l . Co ntr . Fe d. , 37 , 1343-62 .

Weiss , R . F . (1970) . The so lub i li ty o f n i t rogen , oxygen , and a rgon in wa te r and s eawa te r . D eep- Sea Res . , 17 , 721-35 .Westers , H. & Pra t t , K. M. (1977) . Rat iona l des ign of ha tcher ies for in tens ive

sa lmon id cul ture , based on metab ol ic charac te r is t ics .Prog. Fi sh - Cu l t . , 39 , 157-65 .Yu n t , F . W. (1979) . Gas f lows and pow er measu rem en t . In: Proceedings: Workshop

Tow ard an O xygen Transf e r S t andard , EPA-600/9-78-021, ed. W. C. Bo yle.US E nv i ronm en ta l P ro tec t ion Agency , C inc inna t i , Oh io , pp . 105-27 .

Watten 1985 Aquacultural-Engineering

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