By C. C. FURNAS
AN D
R. H. NEWTON
Department of Chemical Engineering Yale University
New Haven, Conn.
H
E A T T R A N S F E R coefficients fo r th e design of g rid -p ack ed scru b b er to w ers fo r a s a tu ra te d gas, as in oil an d w ater-g as p lants, has been given by R osebaugh ( Client. & M e t., M ar., 1928, p. 144-8). S im ilar d a ta fo r th e design o f to w ers fo r substantially dry gas a t hig h te m p eratu res, as th a t fro m p ro d u cers, have not been available and th is p ap er a ttem p ts to fill this need.T h e d a ta on w hich th is p a p e r is based w ere obtained in a 7 2 -h o u r te st a t the p ro d u c e r plant o f th e C onnecticut Coke Co., N ew H av en , C onn. G as fro m fo u r coke-fired p ro d u cers, blow n w ith steam an d air, passes th ro u g h fo u r w aste-h eat boilers, and thence to tw o scrubbing to w ers of th e com bined sp ray an d g rid -p ack ed type. T h e h u rd le p acking begins 2 ft. below th e sp ray heads, w hich are fed w ith sea w ater. T h e re a re six sp ray heads a t the to p of each tow er. T h e h u rd les are set in p airs (15 pairs to a to w e r) w ith ap p ro x im ately 2 ft. clearance betw een each set. E a c h h u rd le is m ade up o f 20 slats, £ in. x 6 in.
w ith 3-J in. clearance betw een slats. T h e hu rd les in each p a ir are set a t rig h t angles to each o th er. T h e to w ers a re 60 ft. high an d 8 ft. in d iam eter. T h e active volum e of each to w er is about 2,500 c u .ft., and th e to tal slat su rfa c e ab o u t 5,000 sq .ft. A d iag ram m atic sketch o f the p lan t lay -o u t is given in F ig . 1.
In n o rm al o p eratio n th re e o f th e fo u r p ro d u cers are used and send up to 1,000,000 c u .ft. o f gas p e r hour th ro u g h the tow ers. D u rin g th e te st th e rates of gas flow v aried fro m 0.084 lb. p e r sq .ft. of cross-sectional a re a o f to w e r p e r second to 0.231 lb ./s q .ft./s e c . T h e w a te r flow v aried fro m 0.188 lb ./s q .ft./s e c . to 0.714 lb ./s q .ft./s e c . T h e ra tio p o unds o f gas to p o u n d s of w a te r varied fro m 0.143 to 0.800. T h e tem p e ra tu re o f th e en tran ce g a s av erag ed 565 deg. F . an d th e gas leaving the to w e r averaged 74 deg. F . T h e incom ing w a te r av e r
aged 66 deg. F ., th e outgoing, 112 deg. F .
T h e gas w as essentially dry, since the coke used con
tained only 4 p e r cen t m oisture, co rresp o n d in g to only 1 p er cent w a te r v apor in the gas. T h e average gas com position in percentages w a s: CO^, 5 .0 ; Oo, 1.0; C O , 2 6 .9 ; Ho, 9 .3 ; N 2, 57 .2 ; and C H 4, 0.6 p e r cent. T h e average heat capacity o f th is gas a t the average te m p e ra tu re w as com puted to be 0.29 B .t.u ./lb ./d e g . F . T h e m easured heat capacity, as determ in ed by the heat b al
ance of th e w aste-heat boilers, w as 0.31 B .t.u ./lb ./d e g . F . T h e average figure 0.30 B .t.u ./lb ./d e g . F . w as used in m aking the design com putations w hich follow.
Coefficients in W aste-H eat B oilers
T h e m easured overall coefficients o f heat tra n s fe r b e
tw een the gases and the boiling w ater in th e w aste-h eat boilers are as follow s :
G a s V e lo c ity T h ro u g h T u b e s, L b ./S e c ./S q .F t.
0.855 0.8 52 0.730 0.719
C o e fficien t I I , B . t u . / H r . / S q . F t . / D e g . F .
6.3 «.2
5.1 5.3
T h e boiler tubes w ere 3.67 in. I.D . and 20 ft. long.
E lim in a tio n of D ust
T h e tow ers n o t only act as coolers, b u t also as d u st s c ru b b e rs .-D u s t sam ples w ere taken fro m the gas stream leaving the scrubbing tow ers. T h e average d u st content of th e gas w as 6.0 g rain s p e r 1,000 cu .ft. T h e d u st con
te n t show ed no significant v ariatio n w ith changes eith er in w ater flow o r gas flow over th e ran g e studied. T h is datu m show s th a t the d u st going into the m ains a fte r the tow ers is about 20 lb. p e r day.
D ata w ere taken on the am o u n t o f d u st contained in th e w ater a fte r it has passed th ro u g h th e scrubbers. T h e d a ta w ere quite erratic. T h e average d u st co n ten t w as 0.0004 lb. o f d u st p er lb. of w ater. T h is rep resen ts a d u st elim ination of ap p ro x im ately 2,000 lb. p er day in the
June, 1 9 3 3 — C h em ica l & M e ta llu rg ica l E n gin eerin g 301
tow ers. T h e scrubbing tow ers rem ove ap p ro x im ately 99 per cent of the d u st fro m the gas.
H eat Transfer in th e T ow er
T h e actu al m echanism of cooling o f th e gas in the tow er is too com plex to be ex actly tre a te d in any sim ple m an n er. A s the dry, h o t gas en ters the bottom o f the to w er its tem p e ra tu re h isto ry ten d s to follow th e ad ia
batic cooling curve, if its velocity is sufficiently high. A t som e u n know n distance up the to w er it becom es a s a tu ra te d gas a t som e tem p e ra tu re considerably below the e n tran ce tem p e ra tu re. A s it proceeds up th e to w e r fro m this p oint, it is a sa tu ra te d gas w hich is being cooled and dehum idified by the c o u n te rc u rren t stream o f w ater.
U n less te m p e ra tu res and degrees o f sa tu ra tio n are know n a t in term ed iate points it is not possible to give a com plete analysis o f the ex act conditions. T h e case fo r th e te m p e ra tu re h isto ry o f a s a tu ra te d gas w hich is being cooled and dehum idified is treated by M ason (P ro c . A .G .A ., pp. 1154-6, 1925), b u t the case u n d e r consideration is m ore com plex an d cannot be so treated .
B ecause o f the lack of a b e tte r m ethod, the d a ta w ere tre a te d as if th e y w ere those o f a d ry gas being cooled by a non-volatile liquid. T h e ex it gas w as considered as d ry gas plus a certain am o u n t o f v a p o r w hich h ad e n tered into th e gas stream .
P leat lost by th e gas w as used as th e basis fo r th e d e
te rm in atio n o f the am o u n t o f heat tra n s fe rre d . T h e h e a t-tra n s fe r coefficients w ere com puted on th e basis of the logarithm ic m ean tem p e ra tu re difference betw een gas and w a te r a t th e top and bottom of th e tow ers. I f the d ata are applied in th e sam e m an n er, i. e., u sin g the lo g arith m ic m ean te m p e ra tu re difference, th e y m ay be counted on to be fa irly accu rate in th e ran g es stu d ied and are probably reliable fo r som e ex trap o latio n .
A carefu l stu d y o f the heat tra n s fe r d a ta in the tow er show ed th a t the coefficient v aried as a lin ear fu n ctio n of the w a te r flow an d as th e 0.4 p o w er o f th e m ass ra te of gas flow. T h e v ariatio n s in te m p e ra tu re d u rin g the test w ere not sufficient to detect any effect of te m p e ra tu re change o f th e e n terin g gas.
T h e d a ta obtained are plo tted in F ig . 2 as th e heat- tra n s fe r coefficient ag ain st ra te o f w a te r flow. T h e d a ta have all been corrected to a gas flow of 0.192 lb ./s e c ./
sq .ft. (eq u iv alen t to 10,000 c u . f t . / h r . / s q . f t . ) . T h e equa
tion of this line w hich best in te rp re ts the d a ta is H v = 21 W + 14.0 G0A (1 ) w here H v = B .t.u ./h r ./c u .f t./d e g . F ., W — lb. w a te r / se c ./sq .ft., an d G = lb. g a s /s e c ./s q .ft.
T h e coefficient o f heat tra n s fe r p e r u n it o f area, H a, is equal to the value o f H c, fo r th e slat su rfa c e in the to w er is about 2 sq .ft. p er c u .ft. A plot o f equation (1 ) is given in F ig . 3, fo r several values o f G.
D esign o f Tow ers
F u n d a m en ta l R ela tio n s— A s m entioned above, the d ata fo r heat tr a n s f e r in the to w ers w ere com puted on the basis o f the logarithm ic m ean te m p e ra tu re difference w here
A T m = ~ 7~' ~E. T ~ W
T s
24
w h ere A T i is th e te m p e ra tu re difference betw een gas an d w a te r a t the bottom of the tow er and A T 2 is th e te m p e ra tu re difference betw een gas an d w a te r a t th e top o f th e tow er.
In o rd e r to design a to w er it is necessary to know the e x it an d en tran ce te m p e ra tu re o f b o th gas and w a te r. I f th e d esired en tran ce an d e x it te m p e ra tu res o f th e gas are assum ed, as well as the e n tran ce te m p e ra tu re o f the w ater, th e ex it te m p e ra tu re of th e w a te r is determ inable.
I f the gas c a rrie d the sam e a m o u n t of m o istu re w hen it le ft th e tow er as w hen it en tered , all the sensible h eat o f th e gas w ould be tra n sm itte d directly as sensible h eat to th e w ater, th e heat tra n s fe r being re p resen ted by the equation
A T 0 G Cg = A T w W C w
Fig. 3—R elatio n betw een h eat tran sfer coefficient, w ater flow and gas flow
Fig. 2—R elatio n betw een h eat tran sfer coefficient and w ater flow
0.4 0.6 OS
W a te r Rate, Lb. p er Sec. p e r Sq. F t.
0.2 W a te r
302 C h em ic a l & M e ta llu rg ic a l E n g in eerin g — V ol.40,N o.6
Fig. 4—D iagram fo r D e
term ining R elations of T em perature Changes and
Flow Rates In th e exam ple, w here the w ater tem p eratu re increases 85 deg., and the gas tem p eratu re decreases 520 deg. to 80 deg. F., the ratio of w ater rate to gas rate is found to be
1.55
Fig. 5—L ogarithm ic m ean tem p eratu re difference in
cooling tow ers
w here V t is th e pounds o f w a te r v a p o r in sa tu ra te d gas a t th e ex it tem p eratu re of th e gas, an d Qt is the latent heat o f vaporization o f the w a te r a t the given tem p eratu re.
Qt and Vt are both functions o f th e ex it tem p e ra tu re o f the gas, T 2, and so should be expressible in term s of T 2. H ence, fo r a gas o f a given heat capacity, th e ratio o f A T g to A T w is determ ined by the ex it te m p e ra tu re o f the gas, T 2, and by th e ratio, W /G .
F o r convenience in com putation, th e relatio n betw een A T g and A T w fo r various values o f T z and W / G is given in the double g rap h o f F ig. 4, fo r a gas w ith a heat capacity o f 0.30 B .t.u ./lb ./d e g . F . A s a fu rth e r convenience, th e logarithm ic m ean te m p e ra tu re d iffer
ences fo r various values o f A T i and A T2 are plotted in F ig. 5.
In tow er design, the values obtained fro m these figures a re to be used in the equation
A T g GCg = hv L A T m ( 4 ) w here h v = B .t.u ./c u .ft./d e g . F ./s e c ., L is the tow er height in feet and A T m is th e logarithm ic m ean tem p er
a tu re drop.
T ow er D esign E xam ples
E x a m p le — A ssum e th a t 200,000 c u .ft. o f gas per h o u r of specific g rav ity 0.07 and specific heat 0.30 is to be cooled from 600 deg. F . to 80 deg. F . in a to w er of the type described above, w ith w a te r e n terin g at 65 deg. F . W h a t is the m inim um d iam eter and heig h t o f to w er and th e m inim um w a te r ra te w hich will handle th is am o u n t of cooling?
So lu tio n , L im itin g C onditions-—T he o peration of the tow ers described above indicated th a t it is n o t feasible to op erate w ith e x it w a te r te m p eratu res g re a te r th a n 150 deg. F ., fo r above this tem p eratu re, th e fo rm atio n of steam in the bottom o f the to w er seriously in te rfe re s w ith the cooling function. T h is e x it-w a te r tem p e ra tu re fixes the m inim um w ater rate. In th e problem A T g — 520 deg. F . and gas flow = (2 0 0 ,0 0 0 /3 ,6 0 0 ) X 0.07 = 3.89 lb. p er sec. F u rth e rm o re , the m axim um perm issible A 7',r = 150 — 65 = 85 deg. F . T h e ratio of w a te r flow T h is equation m ay be re w ritte n in th e fo rm
A T g = A T , lVC u
w here A T g an d A T w a re respectively the change in tem p e ra tu re of the gas and the w a te r; G — ra te of flow o f gas, l b ./ s q .f t ./ s e c ; W = ra te o f flow o f w ater, lb ./sq . f t ./ s e c .; Cg — heat capacity o f th e gas, B .t.u ./lb ./d e g . F . ; and C w = h eat capacity o f th e w ater, B .t.u ./lb ./
deg. F .
H eat for V ap orization
H o w ev er, this condition does n o t hold, fo r, in th e case being considered, the gas en ters practically d ry an d leaves th e to w e r s a tu ra te d a t som e te m p e ra tu re above th a t o f th e en tran ce w ater. T h en , in stead o f all o f th e sensible heat o f the gas g o ing in to sensible h eat in th e w ater, p a rt o f it goes into heat o f v ap o rizatio n o f sufficient w a te r to sa tu ra te the gas leaving the tow er. T h is con
dition is re p resen ted by th e equation
A Tg GCg — QtVtG = A T k W C ,o ( 3 )
0 100 200 300 400 500 600
A T ,, Deg. F.
June, 1933 — C h em ica l & M eta llu rg ica l E n g in eerin g 303
to gas flow can be determ in ed fro m F ig . 4, w h ere the solution is show n in d otted lines. F ollow line ab from A T g = 520 to th e intersection w ith th e line T2 = 80, follow line be h o rizontally to the rig h t to in tersect line cd, w hich rises vertically fro m the value o f A T w = 85.
T h ese tw o lines intersect a t point c, w hich, by in terp o la
tion, is fo u n d to be on th e diagonal fo r W / G — 1.55.
T h e re fo re , w a te r flow = 1.55 X 3.89 = 6.03 lb. p e r sec.
N o te th a t F ig. 4 can be used fo r e ith er to tal gas and w a te r flow, o r fo r flow p e r u n it o f area.
I t is generally considered in tow er design th a t w a te r flows g re a te r th a n 0.8 lb ./s q .ft./s e c . cause flooding o f the tow er an d blocking of th e gas flow. H o w ev er, w ith the spaced-grid co n stru ctio n o f the type of to w er u n d e r co n sid eratio n th is figure can safely be increased to 1 lb ./
sq .ft./se c .
T h e n the cross-sectional area o f the to w er = 6 .0 3 /1 = 6.03 sq .ft. and D = 2.77 ft. G as flow = 3 .8 9 /6 .0 3 = 0.645 lb ./s q .ft./s e c . T h is ra te is la rg e r th a n an y show n in F ig . 3 so th e value o f H v will be com puted fro m eq u a
tion ( 1 ) . I n this equ atio n H v — 21 X 1 + 14.0 X (0 .6 4 5 )0-4 = 32.7 B .t.u ./h r ./s q .f t./d e g . F . A t th e b o t
tom of th e to w er A 7 \ = 600 — 150 = 450 deg. F . ; at th e to p o f th e to w e r A To — 80 — 65 = 15 deg. F . F ro m F ig . 5, A T m — 128 deg. F . F ro m equation (4 )
L = 520 X 0-645 X 0-3 X 3,600 _ g 6 5 ft 32.7 X 128
T h is gives as th e solution a d iam eter o f 2.77 ft. an d a height o f 86.5 ft.
Practical S o lu tio n — Such a tow er, 2.77 ft. in d iam eter and 86.5 ft. high, w hich re p resen ts th e m inim um d iam eter, is decidedly out o f p ro p o rtio n fo r co n stru ctio n p u r
poses. I t is m uch m ore feasible to use a to w e r o f g re a te r diam eter. H ence, assum e a to w er 5 ft. in d iam eter w ith the sam e to tal w a te r an d gas flows, a n d sam e ex it tem p era tu re s. T h e n G = 0.21 lb ./s q .ft./s e c . an d W — 0.325 lb ./s q .ft./s e c . F ro m F ig . 3, H v — 14.3. F ro m equation (4 )
520 X 0.21 X 0.325 X 3,600
L = 70 ft.
14.3 X 128
In th is case th e to w er called fo r has a d iam eter o f 5 ft.
an d a h eig h t of 70 ft.
Increa sin g W a te r F lo w — I f w a te r flow w ere increased to 0.5 lb ./s q .ft./s e c ., leaving th e gas e x it te m p e ra tu re a t 80 deg. F ., a sh o rte r to w e r w ould suffice. F o r this case W / G = 2.4. F ro m F ig . 4, w ith A T a — 520 deg.
F ., 7 ', = 80 a n d W / G — 2.4, A T w — 55. T h e re fo re , ex it w a te r te m p e ra tu re = 65 + 55 = 120 deg. F ., A T \
— 480 deg. F ., and A T 2 = 15. F ro m F ig . 5, A T m = 134 deg. F . F ro m F ig . 3, H v — 18. F ro m equation ( 4 )
520 X 0.21 X 0.325 X 3,600
18 X 134 ~ 5,5
H ence, in th is case a d iam eter o f 5 ft. an d a heig h t of 53 ft. suffice.
A c k n o w le d g m e n t— T h e a u th o rs w ish to acknow ledge the g en ero u s aid an d cooperation of W . C. W a rd n e r and B. R . H asselm an an d o th e r officials of th e C onnecticut Coke Co., w ho m ade it possible to ob tain th e d a ta p re sented above. W e also w ish to acknow ledge th e services o f P ro fs . B. F . D odge an d M . C. M o lstad an d o f the follow ing stu d e n ts o f Y ale U n iv e rs ity : H . H . B assfo rd , C. C. D onovan, W . L . E lw ood, J . R . E rick so n , R . B.
K o rsem ey er, J . L. M a rsh , PI. W . P e y se r, A . Sinnickson, J . F . T h o rn to n and W . H . W eth erill.