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C & m i c a / E n g i n e e t i n . g S c i e n c e . Vo l . 4 7 . N o . 1 3 f L 4 . p p . 3 5 0 1 -3 5 0 8 , 1 9 9 2 .Printed in Great Britain.

om9-2509/x ss.m+o.oo0 1992 Pergunon Press LAd

DEVELO PM ENT O F TRICKLE- BED HEA T TRANSFER CO RRELA lTO NFO R FLOW M EA SUREM ENT PRO BEDA V ID H. A ND ERSO N, FREDERIC K J. KRA M BEC K,a nd A JIT V. SA PREM o b l l Re se a rc h a n d D e v e l o p m e n t C o r p o r a t io nPaulsboro Research LaboratoryPa ulsb oro. Ne w Jersey 08066

ABSTRACTTh e h e a t t ra n s fe r c o e f fi c i e n t f ro m a h e a t e d p i p e In a t ri c k l e - b e d c a t a l y ti c re a c t o r w a sc o rre l a t e d w i th c o m b i n e d g a s a n d l iq u i d fl o w ra t e s a l o n g w i t h f lu i d a n d p a c k i n g p h y s ic a lp rop er t ies . The c or re la t i on l s rea d i l y ap p l i ca b le fo r f low ra te m ea surem ents i n c om m erc ia l -sc a le t ri ck l e -b ed rea c to rs. Da ta fo r the c or re la t i on we re ob ta ined using pe t ro l eum d i st il la tel iq u i d fe d to a l a b o r a t o r y re a c t o r o v e r a ra n g e o f t e m p e r a t u re s a l o n g w i th h y d ro g e n a n dn i trog en as ga ses . O u r an a l ys is show ed tha t the hea t t rans fe r c oe f fi c i en t da ta a re represen tedba sed on the c om bine d therma l m a ss f lux o f the f lu i ds p lus the e f fec t ive c ond uc t lv t t y o f thep a c k e d b e d . Th e l a t te r d e p e n d s o n g a s, l iq u i d . a n d so l id t h e rm a l c o n d u c t iv i tle s, b u t n o tsi gn i fi ca n t ly on f low ra tes o r f low reg ime .

KEYWORDSTri ck le -b ed ; f low m ea sureme nt ; hea t t ran sfe r c oe f fi c i en t ; e f fec t ive c ond uc t iv i ty

INTRODUCTIONTri ck le -b ed rea c to r s i nvo l ve c oc ur ren t f low o f ga s an d li qu id th roug h a p a c k e d b e d o f c a t a l y s tpa rt ic l es. These rea c to r s a re w ide l y used i n the pe t ro l eum indus try i n p roc esses suc h ashyd rod esu lfu ri za t l on . Rea c to r e f fi c i enc y i s g rea t ly red uc ed und er c ond i ti ons o f nonu n i fo rmf low ac ross the b ed . I t i s o f i n te rest , the re fo re , to m ea sure an d c on t ro l the ex ten t o f f lown o n u n i fo r m i ty i n a c o m m e rc i a l re a c t o r . A h e a t e d t h e rm o c o u p l e p r o b e w a s d e v e l o p e d In o u rl ab ora to r y to m ea sure f low d i st ri bu t i on In a t ri ck l e -b ed rea c to r ba sed on the c or re la t i on o f theprob e he a t t ran sfe r c oe f fi c i en t w i th ga s a nd l iqu id f luxes . Th i s pa pe r d i sc usses de ve lop m ent o ft h is c o r re l a t io n b a se d o n l a b o r a t o ry d a t a .m e na tu re o f th is two-p ha se f low hea t t rans fe r i n a pa c ked be d i s no t we l l de f ined . Ex i st ingresu tt s a re ge nera l l y c o r re la t i ons o f da ta o f a i r /w a te r sys tem s (e .g . , Sp ec c h la e t . ( 1979). o rWeek rna n an d My ers (196511. We de ve lop ed a c o r r e l a t i o n o f d a t a I n t h e f o rm o f a t h e o r e t i c a le x p r e s s i o n d e r i v e d f o r h e a t t r a n s f e r fr o m a n i n f in i t e c y l i n d e r t o i d e a l f l u id f l a w p e r p e n d ic u l a r t oits a xis. This c o r r e l a t i o n s u c c e s s f u l l y a c c o u n t s f o r d a t a o f h y d r o p r o c e s s i n g r e a c t o r s wi th Hz/ o i lan d N ,/ o i l two-p ha se f low a nd H , an d N , si ng le -p ha se f low w i th a si ng le se t o f pa ram eters. l tw a s su b s e q u e n t l y a p p l ie d t o c o m m e r c i a l d a t a w i th o n l y e x t ra p o l a t io n t o t h e l a rg e r p r o b ed i a m e t e r a n d h ig h e r r a n g e of va po r an d l iqu id f l uxes CSap re e t a l. 1990).

EXPERIM ENTA LExp er im ents we re c ond uc ted i n a 0 .10 m < ID ) p i l o t un it . Fi gure 1 show s the tes t p rob e c ons istedof a 0.05 m l o n g (0.04 m h e a t e d l e n g t h ) c a r tri d g e h e a t e r ( 0.0 1 m ID ) p l a c e d d l re c t ty I n a b e do f 0 .0016 m hyd ro t rea t ing c a ta l yst ex t ruda tes

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3502 DAVID H. A N D E R S O N e t a l . c 3in t o a g r o o v e a t t h e m i d p o i n t o f t h e h e a t e r a n d t h e p ro b e w a s p l a c e d a t t h e c e n t e r o f t h erea c to r no rma l to the f lu i d f low d i rec t ion . The rec essed thermo c oup b i s de signe d to m ea surethe hea te r su r fac e tem pe ra tu re whe n he a t is ap p l i ed . Flu ids used Inc lude d a pe t ro teumdist il la te feed stoc k fo r a hyd roproc essing reac to r a l ong w i th e i the r H, o r N , ga seo us feed s a t5.27 MPa p ressure. Tem p era tures rang ed f rom 300 K to 644 K to va ry the ga s to l iq u id rat io .

- P a c k e d - B a d

T h e r m o c o u p l e

Fig. 1. Pi lo t p lant e xp er ime nta l set -u p

Fo r a fi x e d - g a s a n d l iq u i d f lo w ra t e , a n e x p e r im e n t c o n si st e d o f m a k i n g t w o t e m p e ra t u rem ea sureme nts: one , w i th the hea te r o f f, g i ves the a m b ien t r eac to r tem pe ra tu re ; the sec ond ,w i th t h e h e a t e r sw i tc h e d o n a n d a l lo w e d t o re a c h th e r m a l e q u il ib r iu m . g i v e s a n i nd i c a t io n o fthe sk in tem p era ture of the he a ter . The he a t t ra nsfer c oe f fi c ien t i s the he a t t ra nsfer rated i v id e d b y 1 ) t h e t e m p e r a t u re ri se m e a s u re d u p o n h e a t i n g t h e p r o b e , a n d 2 ) t h e h e a t t ra n s fe ra r e a d e t e rm i n e d b y t he p r o b e d i a m e t e r a n d h e a t e d le n g t h .The he a t t ra nsfer c o e ffi c i e n t i s d e p e n d e n t u p o n g a s a n d l iq u i d m ass f luxes . a l ong w i th p hys ic a lp rop er ti es o f f lu i ds. Va po r and li qu id f luxes a nd phys ic a l p rope r ti es we re de te rm ined a f te ra c c o u n t in g fo r a n y v a p o r iza t i o n o f t h e l iq u i d fe e d . Figure 2 c om pa res the p i lo t un i t ga s an dl iq u i d fl u xe s w i th t h e ra n g e u se d c o m m e rc i a l ly . We c o u l d n o t m a t c h t h e c o m m e r c i a l ra n g e o ff luxes du e to the pum p an d c om pressor l im i ta t i ons on the p i l o t un i t.

U q t d d F I I J X . Ww . m J S

Fig . 2 . Tri ck l e b ed rea c to r op era t i ng reg im e

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c 3 D e v e l op m e n t o f t r i c k le -b e d h e a t t r a n s f e r c o r r e l a t io nHEAT TRAN SFER C O RRELA TIO NS

3 5 0 3

Literature correlations of Iw o-phase f low h e a t t ra n s fe r i n p a c k e d b e d s h a v e b e e n su m m a ri ze dby Hersko w t tz a nd Sm i th ( 1983). These invo l ve be d e f fec t ive rad ia l c ond uc t iv t t y an d wa l l hea tt ran sfe r c oe f fi c i en ts i n te rms o f c a ta l yst , ga s, a nd li qu id therma l c ond uc t iv i ty va lues . an d thec on t r ibu t ions o f hyd rody na m ics . None o f these c or re la t i ons i s d i r ec t l y ap p l i ca b le to thepresen t si tua t ion be c au se o f the d i ffe ren t ge om et r y o f the p rob e i n the pa th o f the f low . Twod i fferent p ossib le m od els we re co ns id ered . The f irst re lates he a t t ran sfer c oe f fi c ien t a s afunc t i on o f l oc a l ga s an d l iqu id ma ss f luxes w i th hea t c onve c ted by the li qu id f ilm . The sec ondrelates he a t t ra nsfer C O 8 f fk i 8 n t t 0 t o t a l < g a s a n d l iquid) t h e r m a l f lUX based on th e 8ff8CtiV8c o n d u c t iv i ty o f t h e p a c k e d b e d . Th e se c o n d a p p r o a c h w a s f o u n d t o b e m o re su i ta b l e , a sexp la ined i n the fo ll ow ing sec t ions .

Liquid Fi lm Me thodThe f irst ap proa c h i s a Nusse l t num b er c or re la t i on fo rm fo r hea t t ran sfe r to the p robe ba sed onthe wa l l hea t t ran sfe r c o r re la t i on o f Spe c c h ia e t . ( 1979 . 1980) . Neg lec t ing hea t t rans fe r a tzero f lu id f low rate,

h - d P i Nu = a. bRekL

I .4 (1)

whe re the pa r ti c l e d i a m eter i s take n a s the c harac te r ist ic l eng th . Param eters a an d b a rede te rm ined f rom the da ta . A l l f lu i d phy si ca l p rop er t ies i n the d im ens ion less g roup s a re o f l iqu idwh i c h i s c ons ide red to f low as a f ilm ove r the p rob e sur fac e an d c a rr y the he a t t ran sfened .The cha rac ter ist i c l iq u id f ilm ve loc i ty . u f . Is re lated to the sup er f ic ia l ve loc i ty , us , b y

B i s the l iqu id sa tu ra t i on o f the be d vo lda ge , l 6 de pe nd s on li qu id an d ga s f luxes ; i .e . ,i nc rea sing w i th i nc rea sing l iqu id f lux a nd dec reas ing w i th i nc rea sing ga s f lux . A t c ons tan t l iqu ldf lux

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3 5 0 4 DAVID H. ANDERSON e t al. c 3

Nu SP - 0 . 8 8 F t m z , ,* P a z -= (6)

The cy l inder d iameter w as the c haracter is t ic length in th is express ion. as there was no pack ing.Larkin s et . , found Cc. d. e> = (0.774.0.525.0.109) in their f t t of l iquid satur at ion . and o u r set ofparameters (c , d , e) g ives the same qual i ta t ive dependence on l iqu id and gas f luxes. The f i t o four dat a is show n in Fig. 3.

zoo0

1500

loo0

500 0

01 500 loo0-wed Heat Transfer Coefli cient . bV.iiK

: DO

Fig. 3 . L iqu id f i lm heat t ransfer cor re la t ion

Equat ion (1) has reasonable va l id i ty as t t represents observed t rends in heat t ransfercoef l lc lent , and cor responds w i th the s ing le phase f low cor re la t ion (6) assuming B-a l w i th onfvl iqu id f lowing. However , the cor re la t ion breaks dow n for s ing le phase gas f low C&>o), w hichw ould occ ur in reg ions wi t h no l iqu id f lux e i ther by severe mald is t t ibut ion or com pletevapor izat ion a t h igh temperature: A lso, F ig. 3 shows th is cor re la t ion does not adequate lypred ic t the e f fec ts o f vary ing gas phase conduct iv i ty w hen subst i tu t ing N, for H,.

Ef fec t ive Conduct iv i t y MethodAn al temat fve heat t ransfer cor re la t ion w hich inc ludes thermal propet t les f rom a l l three phasesder ives f rom the so lu t ion o f pseudcrhomogeneous conduct ion and convect ion about acy l inder in a s t ream f low ing perpendicu lar to the ax is . Th is method w as i l lus t ra ted by DrewC1931). At s teady s ta te w i th constant f lu id proper t ies , the equat ion descr ib ing the bedtem perature, T , is

a l a f r a * t c a * T-1cp~By K + ay y = k _- + - )a=* au*(7 1

The bu lk f lu id f low is paml le l to the y-ax is outs ide the reg ion around the c y l inder (probe) . me x-ax is is perpendicu lar to the ax is o f the cy l inder and the y-ax is . The system supposes an in f in i tecy l inder length. F , and F are the c ombined gas and l iqu id mass f luxes in the x and yd i rec t ions. respect ive ly : 8pt is the heat capac i t y o f th is com bined s t ream. and k , is he three-phase ef fec t ive bed conduct iv i ty . Upst ream f rom the probe, the so lu t ion should reduce to thef ree-s t ream tem perature; i .e ., that measured by the probe w i thout heat input , T , . The probe isassumed Isothermal and t he f lu id in contact w ith the probe is a t the probe temperat ure. TP.On approx imat ing the f lu id f low as kro ta t iona l . the system can be tm nsformed to f la t p la tegeometry w i th the d i rec t ion o f f lu id f low para l leE to the heat t ransfer sur face. Conduct ion is

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c3 D e v e l op m e n t o f t r i ck l e -b e d h e a t t r a n s f e r c o r r e l a t io nneg lec ted In the m a in f low d i rec t ion . The so lu t ion und er these c ond i ti ons c om es f romBoussinesq < 1903) . a nd whe n t ran sfo rm ed ba c k to c y l ind ri ca l p rob e g eo m et r y I s:

3 5 0 5

WC P T -r = 1 . 0 1 6 ( k - / C - p - D P ) l/2P T (8 )

Th is exp ression wa s used to de te rm ine the e f fec t ive b ed c ond uc t iv i ty wh i c h p rod uc es them ea sured hea t t ran sfe r c oe f fi c i en t a t the g i ven co m b ined therma l m ass f lux , CPTF,

= p T * = G-C + L-CP Q PL (9)Th e e ffe c t iv e b e d c o n d u c t iv i ty h a s b e e n f o u n d t o b e a su m o f st a t ic a n d d y n a m i cc on t r ibu t i ons b y Spe c c h ia e t . ( 1979).

ke = (Q, + (k-ID Q + (kJD L (10)I IThe f irst te rm i s ba si ca l ly a vo lum e av erag e o f the c ond uc t iv i ti es o f the so l i d , l iqu id , andga seo us ph ases. We assum e the c a ta l yst po res a re l iqu id - f il led i n the two- pha se f low runs an dn e g l e c t th e i n te r p a r ti c l e l iq u i d h o l d u p c o n t r ib u t io n t o b e d c o n d u c t iv i ty . C o m p l e t e l iq u i dsa tu ra t i on i s assum ed i n c ases o f si ng le -p ha se l iqu id f low , how eve r. Conv ec t ive m ix ing o f thef lu i ds in the d i rec t ion norm a l to the b u l k f low i s i nc l ude d i n the dy na m ic te rms.

Sta t ic c ond uc t iv i ty , ( k& The sta t i c c ond uc t iv i ty wa s c or re la ted b y Spe c c h ia e t . ( 1979) i nthe fo l l ow ing fo rm w here k , i s the in te rpa rt ic l e ( ga s ph ase) c ond uc t iv i ty .

(kJ,, = kg cc + (l-c)/49 + 7k P

Q ,w a s a fu n c t i o n o f v o i d a g e , w h i c h w o s c o n st a n t fo r o u r ru n s. 7 =2 / 3 w a s e x p e c t e d b a se d o ng e o m e t ry a n d w a s o b se r v e d i n t h e ir d a t a .The e f fec t ive pa rt ic l e c ond uc t iv i ty , kP, i s a func t i on o f so l i d an d l iqu id ph ase va lues u nd er ourassum pt i on . Seve ra l p ropo sed exp ressions fo r k , ha ve be en eva lua ted by Lin an d Ford (1984).w i th the rec om m end ed fo rm be ing ba sed o n Ma xwe l l s d er iva t ion (1954) fo r pa rt ic l es w i thinternal poros i ty . 8 .

k P kL- = (1 - ( l - f - _) e ) / ( 1 + ( f -1 ) 8 ) ( 1 2 )k 1 k d

a n df = 3 k S /( 2 k S + k L ) ( 1 3 )

D y n a m i c c o n d u c t i v it y , < k & _ D y n a m i c c o n d u c t iv it y w a s c o rre l a t e d b y Sp e c c h i a m , ( 19 79 )by l inea r va ri a t ion w i th therma l m ass f lux o f ea c h ph ase , i .e . ,( k e ) , 9 = A - Cps - G - d p, (14=)

(kelp L = B - CpL - L - dp (1-1I

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3506 DAVID H. ANDERSON et a l . 0w i th c o n st a n t c o e f fic ie n t s A a n d B. d is t h e p a rt ic l e d i a m e t e r. G a s p h a se d e p e n d e n c e i n t h isf o rm h a s b e e n o b se r v e d f o r a i r i n b o t R si ng l e - p h a s e a n d tw o - p h a s e fl o w s b y 5 p e c c h ia m a r.Li q u id p h a s e d y n a m i c c o n d u c t io n h a s a l so b e e n o b s e rv e d t o d e p e n d o n g a s v e l o c i t y t h ro u g ht h e i m p a c t o n h o l d u p , w h i c h w o u l d i nt ro d u c e so m e a d d i ti o n a l c o m p l e x i ty a s w e l l a sc or re la t i ng pa ram eters. Since our exp er im enta l da ta show s the dy na m ic c on t r ibu t i on i s sm a l l ,the fo rm i n eq ua t ions (14) wa s used .Figure 4 is a log - log p lot o f the he a t t ra nsfer c oe f fi c ien t vs . a ve rag e therm a l m a ss f lux , Cp t F. inthe p i l o t un i t test r uns. C + wa s assum ed to inc l ude hea t e f fec ts o f va po ri za t i on . and it asc a l c u la ted fo r ea c h run & y the s lop e o f the to ta l f lu i d spe c i fi c en tha lpy vs. tem pe ra tu re .

Fig . 4. Exp er ime nta l d a ta Fig. 5 . Cor re la t i on w i thou td y n a m i c t e r m s

0

The le a st -squ a res f tt o f the d a ta is ne a r iy h = QFI 112,wh i c h i s i tse l f a rea sona b le c or re la t i onan d fo l l ows eq uu t i on (8 ) assum ing c ons tan t k , fo r a i l runs . k , va lues wh i ch a re re la t i ve l yi nsens it ive to va ri a t ion i n f lu i d c ond uc t iv i ty by e i ther tem pe ra tu re o r c om po si ti on c ha ng es i sa c c o u n t e d fo r b y a l a rg e c o n t ri b u t io n o f t h e so l id - p h a s e c o n d u c t iv it y , & . O u r d a t a w e r ere p re se n t e d b y a c o n st a n t v a l u e o f b a s a c o rre i ~ io n p a ra m e t e r .Con stan t pa ram eters to be de te rm ined we re & , a i ong w i th # i n eq ua t ion (11) . an d A . B i neq ua t ions (14) . 8 wa s take n as 0 .6 an d c wa s f ixed a t 0 .4 . For the dyna m ic c on t r ibu t ions i neq ua t ions (14) . CPL wa s a ssum ed to be 3 .14 J /g m / K.Wi th N2-oi l . i t wa s tak en a s 3.14. With HS-o i l system s, C,, wa s set to 6.28.

The bes t f it o f the da ta wa s ob ta ined w i th the fo ll ow ing pa ram eter va lues b ased on m in im izi ngthe d i f fe renc e be twee n k , b y eq ua t ion < 10) an d k , wh i c h sa t isf ies equa t ion (8 ) ba sed on them ea sured hea t t ran sfe r coe f fi c i en t .q , = 0.0138 A = 0.033k , = 7 .75 W/ m / s/ K B=O

The sm a l l va lues o f A an d B i nd i ca te tha t the da ta a re bas ic a l l y rep resen ted by the sta t icc ond uc t iv i ty on l y . Neg l ig i b l e dy na m ic c on t r ibu t i ons o f ( k&n were a i so found w i th pu re NP orH,. We t h e n d e t e r m i n e d t h e M o f t h e e n t ire d a t a w i t h o u t a c c o u n t in g fo r t h e d y n a m i c t e rm s .The resul ts a re sho wn in Fig. 5 . The re 9 = 0.0094 a nd k , = 7.69 W/ m / s/ K. A i tho ug h thesep a ra m e t e r s a r e d t ffe r e n t n o w , i n d ic a t i n g so m e d y n a m i c a l c o n t ri b u t io n , n o si g n if ic a n tde te r io ra t i on i n the p rec i si on o f the c or re la t i on oc c ur red .Th e d a t a w e r e t a k e n o n l y o v e r a lo w ra n g e o f g a s fl ux e s re l a t iv e t o c o m m e r c i a l t ri c k l e - b e drea c to r c ond i ti ons. Re ta in ing the ga s ph ase d yna m ic te rm wo u ld resu l t i n si gn i fi ca n te x t ra p o l a t io n o f d e p e n d e n c e o n g a s f iu x fo r a c o m m e r c i a l a p p l ic a t io n . i n o u r u se . w en e g l e c t e d t h e d y n a m i c c o n t ri b u t io n . a n d d o n o t n e e d to k n o w th e g a s t o l iq u i d ra t i o t o

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c3 D e v e l o p m e n t o f t r i c k l e -b e d h e a t t r a n s f e r c o r r e l a t i o n 3 5 0 7determine thermal f tux f rom the measured heat t ransfer Co8f f ic i8nt . As shown i n t he nex tsect ion, th is form of cor re la t ion w as va l idated in h igh f lux tes t ing.

APPLICATIONThisef fec t ive conduct iv t t y cor re la t ion w as used a long w i th equat ion (8) in a com merc ia lt r ic k le-bed reac tor appl icat ion (Sapre et . . 1990). Much h igher f lu id f luxes w ere invo lved. sothere w as some concern about the impact o f the dynamic terms t o e f fec t i ve conduc t i v i t y .And f low reg ime t rans i t ion on increas ing f luxes ( i .e . , t r ic k l ing to pu ls ing f low) w as found toincrease rad ia l heat t ransfer ro tes by Weekm an and Myers (19651. Bu t w e neg lec ted theseef fec ts in i t ia l ly , and appl ied equat ion (81 to the comm erc ia l data in a h igh tem perature Hro i lsys tem. Probe d iameter w as about 0 .025 m. Neglect o f the dynamic terms to e f fec t iveconduct iv i ty a l lows ca lcu la t ion o f com bined thermal mass f lux , CP+F, w i thout needing to knowthe gas/l iqu id ra t io . F igure 6 shows the compar ison betw een thermal m ass f lux mR va luesdetermined w i th th is probe cor re la t ion and t he average va lues ca lcu la t ed f rom to t a l gas andl iqu id f low ra tes in the react or . The cor respondence is good. w i th no ind icat ion o f s ign i f icantb ias a t t r ibutab le to dynamic e f fec t ive conduct iv i ty or change in f low reg ime.

0

r0 C o m m e r d a l P r o b e D a t a 0 _.-.. O

- .. Ptbt Unit C o m 3 l a t t o n ,_/ ._- 0.e 2omo- ,,, .$I.-. 0 _... 0__... .~~

,. /0

Fig. 6 . Comm erc ia l reactor /p ilo t p lant com par ison

CONCLUSIONSHeat t ransfer data f rom a heater probe in the laboratory p i lo t exper iments arecorre la ted based on three-phase s ta t ic bed conduct iv i ty . The cor re la t ion representspacked bed heat t ransfer to f lowing H, and N, . and f lowing tw o-phase mix t ures o f thesegases w i th pet ro leum d is t i l la tes a t react ion tem peratures.Based on th is heat t ransfer cor re la t ion. the ca lc u la ted thermal mass f luxes f rom a heaterprobe agreed w el l w i th observat ions in a comm erc ia l reactor a t s ign i f icant ly h igher gasand l iqu id f luxes than in the laboratory exper iments .Our data suggest hat the cont r ibut ion o f dynamic terms for the gas and l iqu id phase isnegl ig ib le t o the e f fec t ive bed conduct iv i ty even at h igh gas and l i qu id fluxes in Mck le-bed reactors .F low reg ime t rans i t ion has no apporent impact on the heat t ransfer ra te .

ACKNOWLEDGEMEMWe are grate fu l for the suppor t and ass is tance of Mobi l Research and DevelopmentCorporat ion and t he Paulsboro Research Laboratory in th is w ork .

8/7/2019 Anderson Et Al,1992

8/8

3508 DAVID H. ANDEIUON et l. c3SYMBOLS

A.B,a.b,c .d,ec,&a&,dPDPfF.F,.FyZG,hk,.k,.k,kpk&k&+k&ILNuPrLZ8ReLT,TrTPATWJS

c ons tan t pa ram eters i n hea t t ran sfe r co ne la t i onsspe c i fi c he a t c ap ac i ti es: ga s, Ii qu id .m ix tu rep a r t i c l e d i a m e t e rp r o b e d i a m e t e rg r o u p d e f in e d b y e q u a t io n 1 3m a ss flu x o f m b c t u re a n d it s c o m p o n e n t s i n x a n d y d i re c t io n sgrav i t y c onve rsion fac to rgas mass f lux , mass f lux of phase ihea t t ran sfe r coe f fi c i en t , q / rD&tga s, l iqu id , and so l i d pha se c ond uc t iv i ti esp a r t i c l e c o n d u c t i v i t ye f fe c t iv e b e d c o n d u c t iv i ty , st a t ic a n d d y n a m i c c o n t ri b u t io n sp r o b e h e a t e d le n g t hl iqu id mass f luxNusse i t num b er , hd , / k ,Prandt l number , CpLYL/kLhea t t ran sfe r r a te pe r p rob e l eng thRey no lds num b er , Ldp / pLcBRey no lds num b er for sing leb e d t e m p e r a t u r e p h a s e f l o w . L d p / p Lp r o b e t e m p e r a t u r eTp - Tol iq u id in terst it ia l a nd sup er f ic ia l ve loc i t iespressure g rad ien ts: ga s, l iqu id . two-p ha se f lowb e d i n te r p a r tic l e v o i d a g et e rm d e f in e d b y e q u a t i o n 4te rms i n eq ua t ion 11int rapar t i c ie poros i tyde nsi ty o f ph ase Iv isc os i ty of p ha se i

REFERENC ESBou ssinesq (1903) . The or ie An a iy t ique d e la Cha ieur , I I , Ga uth ier -Vi l la rs, Pa r is.Cha ng . M. W., B. A. Fin iayson, a nd C . A. Sle ic he r (1983) . Num er ica l Prope r ties a ndMe thod olog ies in Hea t Transfer , Ed . b y T. M. Shlh, Hem isp he re Pub . Co rp. , Wa shing ton, 349.D rew , T. B. ( 193 1 ) . Ma them at i ca l A t tac ks o n Force d Con vec t ion Prob lems : A Rev iew : A iChETrans., 26.26.Hersko wifz, M., a nd J. M. Sm ith (1983). Tr ic kle Bed Re a c tors: A R8Vi8W. A lChE J.. 29.1.La rkin s, R, P., R. R. Wh ite , D. W. Je ffrey (196 1). A iC hE J.,& 231.Lln, F., a nd J. P. Ford 9184). Ca n. J. Ch e m . Eng ., 62, 125.Ma xw el l . J . C . (1954) . ATreat ise on Elec t ri c i ty a nd Ma q ne t ism . Dove r Pub . Inc . , 2 ,435.Sa pre. A. V. . D . H. An d erson , a nd F. J . Kra m b ec k (1990 ) . Hea ter Probe Tec hniq ue to Me a sureFlow Ma id ist ribut ion in La rge Sc a le Tr ic k le Bed Rea c tors, Che m . Ena . Sc i .. 3 .2263.Spe c c hia, V. , A. Ba id i , a nd S. Sica rd i (1979) . Che m . Ena . Co m m un. , 3 ,483.Sp ec c hia. V. . A. Ba td i , a nd S. Sica rd i (1980) . Che m . Ens. Co m m un. . 4 .361.Wee km a n, V. W., J r. , a nd J . E. My ers (1965) . Hea t Transfer Cha rac ter ist i cs of Co nc ur ren tGa s-Liquid Flow in Pa c ke d Bed s, A lChE J ., 11, 13.Wefers, K., a nd G . M. Bel l (1972) . Ox ide s a nd Hyd rox ide s of A lum ina, Tec h. Pa p er X19,A lc o a R. E. Se a rie s La b s, E. St. Lo uis, iii., 17.