1070
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 40, No. 6
NOMENCLATURE
'1 = constant in I ~ ' u r ~ i('quat ar iori ,- = heat, capacity of unit volume of nixterial of t l i t s pauticlrh, l3.t.u. p r cubic foot. F. = heat capacity of unit volunic of ga- at C C I ~ S ~ N I Ipriwilre. I I.' 13.t.u. ncr cuhic. foot, F.
J
=
fraction void9 in the b d
I , = Ir,ngth of bcd, feet ,! = a n y poaitivr nurnht~r T = temperature' in Furnah tquaticin, avc'rage ( i t cnteriiig tiuid tempcraturt' and initial hrd tenqx~raturr,A' 13. F. t C . ( , = ronstant rsntcring trmpcraturc of thc fluid, I, = the fluid ttlmperature at any point and timt., O F'. I,,,,, = initial conatant solid tempcratuw, ' F. = the solid teniperaturc at any point anti t,inir. F'. 4 = time after start of heating, hours = average volumetric fluid rate through tied, crlliii, t!,i$t pt'r hour, squaw foot total cross scction L = riistancc from cntr,ring c.nd of hPd. f w t V = h x ' c ' c = hx ~ , c ' G f,
1,
i)
o
.
= densit,. of fluid, pounds per cubic foot = viscosity of fluid. pounds per hour. foot
Heat Transfer into Cylindrical Columns of Bone Char v. R .
DElTZ
AND
H. E. R O B I N S O N . N A T I O N A L B U R E A U O F S T A N D A R D S ,
M a t h e m a t i c a l expressions have been derived f r o m t h e o r y f o r t h e temperature of g r a n u l a r materials such as bone c h a r heated in c y l i n d r i c a l r e t o r t s o f k n o w n w a l l temperatures. T h e c h a r is considered t o move t h r o u g h t h e cylinder w i t h constant velocity a n d w i t h o u t mixing. T h e t e m p e r a t u r e of t h e char a t t h e axis of t h e cylinder and t h e temperature averaged over t h e cross section o f t h e c y l i n d e r were f u n c t i o n s of t h e t h r o u g h p u t , i n i t i a l a n d w a l l temperatures, a n d l e n g t h of t h e retort. A simpleapproxim a t i o n o f a n exact s o l u t i o n of t h e problem has been f o u n d w h i c h i s v a l i d f o r t h e t e m p e r a t u r e rangeof interest in bone
B
ONE char is a graiiular adsorbent urtid chiefly i n large scale operations for the purificat,ion of sugar liquors. Efficient revivification is the key to the economic SUC('CSP of the bone char process of purification. In the revivification kiln with stationary retorts the char descends by gravit,y through the vertical retorts about 8 fert long which arr surrounded by t,he hrating medium. The developmcnt of the hone char kiln with stationary retorts reached a ronvcmtional design in the 1880's and 1890's. Little modification has bwn made sinw Thii time, though sonic changes have been proposed for the structiirc. of thP retorts uf these kiln. ( 4 ) . The proposed changes related to thP nuitcrialb 01' (*onbtrurtiiili and the geometrical shape as shown in Figure 1. Thv modt. of the transmission of heat into hone char has an important in-
WASHINGTON, D. C
c h a r revivification. T h e r e s u l t s a r e presented in t w o useful dimensionless curves of general applicability. For given i n i t i a l , axial, a n d w a l l temperatures, t h r o u g h p u t is independent of t h e diameter of t h e retort, a n d t h e average t e m p e r a t u r e o f t h e c h a r i s independent of t h e diameter of t h e retort. Experimental results observed w i t h b o n e c h a r k i l n s having 240 3 - i n c h c h r o m e steel r e t o r t s are in good agreement w i t h thecalculations. Residual m o i s t u r e in t h e entering char is shown t o decrease t h e capacity of t h e k i l n significantly. V a l u e s f o r t h e t h e r m a l diffusivity of some bone c h a r samples are reported.
Huence on the design of the kiln for heating hone rhar t,o revivifiration temperatures of 750" to 950" F. This paper is coilrerned only with the problem of the transfer of heat into the slowly moving column of char under 'certain idealized conditions. -1 theoret,ical basis is presented upon which to calculate thr transfer of heat into cylindrical retorts of circular cro. D E R I V A T I O N OF H E A T T R A N S M I S S I O N FORMULAS
It is proposed to calculate the axial and the average tcmpcra.turPs of bone rhar as it slowly drscends by gravity in cylindrical caolumns through thin-walled tuhes. The walls of the tubes art' assumed to br at constant temperature by contact with rapidly circulating hot gases or some other heating medium. The kmperature of the wall, T a ,is assumed to be equal to the temperature
t,
*
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1948
1071
where J , ) and J , arc1 I j t w > I funrtions arid I I ,, is a iiunirrival (WIstant defined as thr nth root of A ( i r , , u ) = 0-- i.t,., R,, = ir,ha. The trniperaturr of the char a t t h v axis o f the' yyliii&,r, T,,?is ohtainrd hypIariiiKr = 0 : 1863
G. llulemeyer Vorying Woll Thicknen
Horseshoe
The tirst trrni of thtl m i e x gives ?'i, ivith a n wror ( ~ t I(w ' ttiail for values of at 'a2 greater than 0.18, which corresponds t o values of I - n greater than 0.4 7', 0.6 2';. The siniplificd relationship obtained by using the first term of the serics ( n = 1) is givrn h y Equation 4, The values of the numerical ?onstants, K , and J I ( R 1 ) obraintad , from the, Sniithwnian tahlrs, an' 2.405 an(1 0.5 1 9 1, Ir.pwt iv(.I y. 1';
L-Tube
Hollow
Ovol
+
..... . R. Ring
e$
J. Stroitz
1930
3-Tube Thin-Wolled
W. Bellow 1859 Topered
1931
( 5 ) . The rprcial solution presented hrrein is diff(wnt j i i tho simplification ohtained by expressing t h r result i n trrms o f t h r . axial temperature. instrad of tht, nieari temperatur? of the vliar. This is perniissiblr lor rhr ianyi, of axial trmprraturw of i n t t w s i in chai, wgc~nr.rxtion.
Hellcol
J. Gondolfo
1877
R. Bennett
Vented
Hrat c*onduc.tionfor the c of rotllikt flow \vas c.trri~itli~rc,tl I J Y(irartz in 1883 ( 1 ) and other trcatInt,rits art' rrviewt.tl by 1)rt.n
1909
lnterbcking
Figure 1. Modifications in Shape or Structure of Retorts Used i n Conventional Bone Char Kilns with Stationary Retorts of the outside arc~ad thv i*ylinticdr of char.
Longitudinal voiitluction is neglected, and it is also assumed that no mixing of the vhar particles occurs in passage through the tube. The prohlem will first be handled as if the tube were full of immobile char at wmc. initial temperaturr and a calculation made of the time rrquired for the trmperature at thr r r n t r r , T,?.to rise t o an asqigned value. The heat flox iron1 rhr walls to the individual partivlw ut h r i r I,har is complex but may he trratrd as an effectivr cwnductivity of t h i l bone c,har in bulk. T h r over-all transfer of heat into a i.j.lindrical column of hoiw c.har may tie exprr riitial equation:
c '
This equation is simply the radial part of thc. gr~iic.1~1 hwt pquation expressrd in cylindriral coordinates, Lvhrrc. T i? t h e , temperature ("F.j, tis the time (hours). r is tht>diatanwi ' r ~ n i tht. axis o f the cylinder of radius u (feet), and a is the thermal diffusivity of char (squaw frct pvr hour). T h r valutl of N i$
.I J
I
A
.S
.6
7
B
I
.9
1
1.0
How
k
t q ~ ~toa l - ,whrrc. k is tht. niran thtjrmal condric~ti PC
tic~~ir-foot-dcgree),p ir thta average hulk dtxn*ity of cLhar (pound prr cuhir foot), and c is thP nir'an spfhrific heat of vhar (l3.t.u. per pound-dpgree ) . Thf, sirnplp boundary cwiidirioris 1111 this pruhlt2ni art' that 7' = 7'. at t = 0, (0< r is pt'rtirient to an mtimate of the tlicrmal equilibriuin set up wkietl tho vhar is immersed in liquids. The values of ?"(av.j for kiliih :I anti B are about 960" and 800" F., respectively-, as calculatt~l from Equation 8. It is also desirahle to know the a tiinipcxrat,ure of the char i n a circular rt,gion in the iirighborhood of t h r wall of the retort. Thr char in this region may tw suti-
Table I I. Heat Transfer Characteristics Observed in Individual 3-Inch Retorts of Bone Char Kilns
705
7011 . ..
705 705 680 750 760 790
Kiln B a t Tu 0.80 0.75 0.80 0.80
3.0 3.0 3 0 3 0 2 .3
3.5 3 ,2 4 0
0,7fi
0.87 0.8Y 0.Y4
=
X 3 0 O F. a n d Tt = 212O
0.37 0.37 0.37 0,3i
0.31 0 . 43 n, 4.3 0.49
0.36 0.35 n 36 0.36 0.33 0 43 0.4G n ;18
F. 8.3
8.5 8 , .?I 8.5
10.2 7.3 7 3 6.4
8.7 8 , !A 8 7 8.7 9.6 7.0 6.8 ;7 , 7
June 1948
INDUSTRIAL AND ENGINEERING CHEMISTRY
j w t t d t o temperatures that may h r ah d e operating conditions. The average temperature of the located, for example, betwen thv cylinders drfined 1)y I' = u and r = 0 . 9 ~is the same for rt,torts of any diamrtw. .I3 i t has been shown that the throughput is the samr for retorts of any diameter, it follons that, the amount of char that is h w i t d w a r the walls to an exceseivc tcmipiarci1urt' i. thf, sanir in rtitorty of any tiia1iirtc.r.
Cotter (3)has directed attention t o the iniportance of thr time factor in thr above considerations. Thr, aniourit of char heated to !Val1 temperatures is the same i n rrtortq of any diameter, but, hei'ausc the time of passage of char is i 1)- proportional t o the linear rate o f flow, the char in conta the n.all is heated to 'l', for a longer time in the retort' of larger diameter. There are .some reactions which takr place in bone char which depend oil both temperature and time, an example of which is the so-called "overburning" of bone char. Thr time of heating, which 8houlr-l bel kept at a minimum, i9 an additional important factor t o con.sidwin t h r r h i g n o f arrtort. DISCUSSION
.I n u n i h r of factors niust be considt,red in the clhoicc of the optimum dianieter of stationary rylindrical retorts for the transfi,r of h r a t into hone char. It has been shown in this paper that the quantity of mattJrial passing through the retort and ht,atrd to a drsignatrd axial temperature is independent of thts tiianirtc>r of thr retort, providing that the wall temperature is actually maintained constant for* retorts of various diameters. The average rixmperature of thc erit char is liktvise independent of the dianirtrr of the retort. For a given throughput and axial trwiprraturt: retorts of larger iliameters have a .snialler trmperature difference hetn-eeri the hot gases and the tube wall hecause in the larger retorts a greater surfarc, is al-ailablr for abstrarting thr heat froni the surrounding medium. In thr preceding calculations on heat transfer the tvmperature of the wall hap heen employed and not that of the 1i1,atrcwrvair. Heating of retorts hy condensing vapors instead (IF hot gases should promote uniformity in wall temperatures and [nay he of poe4blc application in laboratory units. The conitnwcial applicability of such a 3ysteni of heating for hone char iristallations would have to be demonstrated. From on(' point of view, rodlike flow of bone char througli rctorts should be realized more closely with tubes of large diameters. The f o x of char through the 210 retorts of kiln A \vas 60 cuhic feet per hour. This would correspond to the rrplacement of t h c contents in I-, 2-, 3-, or +inch diameter rotorts of 5.1, 1.3, 0.6, and 0.3 times prr hour, respectively; or to linear speeds of 45.9, 11.5, 5.1, and 2.9 fcet pc~rhour, respectively. The more rapid linear flow for the smaller retorts should result in greater mixing, inasmuch as any lateral movement iri the rc.tort is a greater percentage of the dianirter than in retorts of 1:irger diameter. Evolved gases are wilted better in tubes of large diameter. For a given nioisture content of the char the amount of steam tu he cqx4led is the same for retorts of any diameter, as it has been hhoivn that the throughput is independent of the diameter. For ii given throughput the cost of the material for the manufacture of thin-walled (20-gage) chrome-strd retorts is ~iiorefor large tubes, since the area of the cylinder walls increases in proportion to rlic diameter. Less char is contained at any moment i n the retcirts of smaller diameter and, thus, theri. i- l e h s char to be damaged hy uncontrollahle fluctuations in the hourre of heat. The retorts of larger diametrr, 011 the other halid, hal-1, a greater and mechanical .strength. rious disadvantagr of retort!, of sinall dianirter ir t h piissiblt~bridging-ovw of thta damp char at thr t o p of t,he reto1'ts. This is a IiktJly owurwnct' i n the existing inrtallatioiis whrrt. vliaI enters the retort6 with 7 ti) 15(-; moisture. Furthermore., if char containing an apprec'iabli. amount of uriivashid sugar errtcrrd a retort of too sriiall N tliametrr, i t i s likely that thll red t i n g mixture of ~ ~ I ~ ~ ~ ~ I I ~ rei.idnih ~ I Y ~ I Iw nI 1I1 S tixwss moisturf~
1075
w.ould plug the retort. The 3-iIlCh retort now in use in almost all char kilns niay b e a happy compromisci of t,he conflicting factors .1 retort designed and operated for heating bone char to elnvated temperatures should not also be burclened with the task of drying the char. The drying of the char may be Inore erononiically done at lon.er temperatures hy other equipnient. The capacity of a kiln operated as in Figure 5 is ahout half that, which could he ohtained with dry char. There arr several precautions to takr, horvwer, beforc "bone-dry" bone chat is revivified iri the prewnt type of installation. Cooler capacity, draw niecharrianis, n i m n s for venting incwased volatile deconiposition Ilroducts, and control of the amount of air taken in must he considered and investigated experimentally. The mechanical details in the ronstruction of equipnient in lvhich the hot char is brought, into contact with the oxygen of the air are very important,. "Hot spots" in the char, readily apparent by the iiicantiescencc, of individual particles, can cause the destruction of the adsorhrnt propertirs. The treatment given in this paper, with its simplifying assumptions, yields results that are reasonably concordant a.ith r~xperiniental observations. The assumption that the ~vallof the retort is uniform in temperature along its length differs from the probable fact that the wall temperature increases ivith L, because the rate of hcat transfer to t'he char decreases as it? temperature increases. That this assumption is a good first approsiniation is borne out by the agreement with observations. An estimate of the temperature difference btwwm the rcltort wall and th(3 surrounding gas is difficult. The factors to be considerd are the decrease in the rate of heat transfer to the char as its temperature increases, and the pffect of longitudinal conduction in the metal wall of the retort. An approximate solution ran probably be developed, but cxperiniental data on the retort iwll t emperat ure in actual are at present unavailablp for conipariiorr. NOMENCLATURE
t
r .
1
= time =
tempcwture
Ya = \Tall temperature 7't) = axial temperature 1', = initial temperaturt) j" = ( T o - Ti),/(T! 7 ~r = thermal diffusivity t = tliermal conductivity a = temperature coefficient of thermal conductivity c = specific heat P = density I' = radius a = radius oi cylinder L = length of cylindrr 6 = width of rectangles d = r/a (4 = throughput J,,, J , = Bessel func~tion,* II', = nth root, of .lu(U,a) = 0 T I b )
LITERATURE CITED
Te.-titig Material,. "Tentative Method of Test ior Thermal Condurtil-ity of Insulating Materials by h l r a n - of the Guarded Hot Plate," Designation C177-45. 121 Hroivii, J. 51.. and Bemk, IT. .4.. I s u . Es(;. ('HEM.. 32, 1112-4 (1) . h i . Sur.
(195oJ. ('otter, 9. IC,. Peiiti>ylvairia Sugar Divi4on. Saticiiial Sugar Hefiriiiig Po., ycrsoiral rommuniration. ( 4I 1)eite. v, H.. "PI,elirninary Surrey of Bone Char llerirification a ~ i dF ' i l t r n t i m " (1947, arailshie from Publications Section, Sationai Huieau of 9tandardi. Kashington 25, D. (3.1. ( 5 , Drew, T . R..Trona. Am. I m t . ( ' h i m . Engrr.. 26, 26-79 !1931). f f i i C,jnniiigs, D. C . . a n d ('oi.ruccitii. It. J., .I. Resrarch .Vat/. Bur. .Ytn,cdnrds. 38, 583-600 ( 1 9 4 7 ) : K t w a r c h P a p e r s 1796 and 1797. 7 , ( ; r a p t z . J... .I,!,(, Phj/,sik.. 254, 79-SI1 (15831: 261, 337-57 (18S5). atiuri has r r u l t a d f r o u n joint t(>:(;>.Ij 5.1) J d m i n r y 2 , lY48. This i n States Cane Sugar Refirieri a n d rereari.l~~ , r n j r r . tundertaken by t h e LriiifacEorers, a greater part of the refinirin industry of the r l ~ e n l t h n. n r i t l l c . S R t i n n n l H l l w a u of .ranriard-.
