I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
July 1947
lation t o rimove the 2,2,i-trimt.thylpentane first, then the charging stock for demet,hylation. The reaction product was fractionated. anti the unconvertcd material was recycled to the reaction zonr. T h r following arc the over-all yield? starting x i t h 1005 of hot-acid i.sooctane: "c by Volume
Compound
c
These data indicate that, approsimately 36 volunic~r;of ti,iptatic,, having a purity in excess of 83y0,can be ohtairicd from 100 v ~ d unies of hot acid isooctane, along with about 19 volunios oi' 2,2,~-trinic'thylperitaneand smaller vo1umc.s of 2,3-dirri~~tIi~l~i1~iitanc and 2,3-dimeth~ll~ut~aiie. LITERATURE CITED
Haensel, Y.,and Ipatieff, V. N., J . Am. Chem. Soc., 68, :N.j (1946) and Corson, B. B., IBD.ENG.CHEJI.,30, lO:{!l ( 2 ) Ipatieff, V. N., (1938). (3) Mc.Illiater, 8 . H., .Vat!. Petmlettm .'.-eu.,s, 29, S o . 4(j, l{-:{:i? (1937). (lj
3.5
2,3-Dimethylbutane Intermediate fraction Triptane, 83% pure Triptane,, approx. 90% pure Intermediate fraction 2 3-Dimethylpentane 2:2,4-Trirnethylpentane R ii t t o ms Total
a57
11.1
I
2.9 3;: 3 3 5 . 6 0.6 15.6 1s 9
2 5 __ 90.6
PAESBVTED before t h e Division of Petroleum Cheiniitry a t tlie l l l t i i i n g of the A V K R I C A X CHEWCAL SOCIETY, Atlantic City, S . .J.
A1er.i-
Heat Transfer to Gases through
Packed Tubes
U
GENERAL CORRELATION FOR SMOOTH SPHERICAL PARTICLES 3L4X LEVA Central E x p e r i m e n t Station, 1.. 3'. Btrrearr of'.Mine..*,P i t t a b u r g h , P a . dinieriaiotiallj homogeneous equation ha5 been de\eloped which permits the prediction of heat transfer coefficients to gases flowing through tubes pached with low thermal conductiiit: material. The equation giies satisfactor) results for ratios of D p D t TarJiiigfrom about 0.05 to 0.3. 1 h e equation predicts a maximum coefficient of heat transfer for a ratio of D, D t = 0.1,5, and this finding w a y \ erified by experimental midence. The equation ma) be u*ed to calriilate coefficients for gases other than air as long a5 the Prancltl group of those gases doe* not differ materially from that of air and carbon dioxide. The iticlusioti of the Prandtl group in general i.i thorouphl? disrus-ed. E\periinetital eiiidence is preietited to show that the equation holds for tube 4 7 e s \ar>ing from to 3 inches i n dianieter. ' Oter this range the agreement is good, and the application to larger tube sizes is discussed. The effect of loids in the parhinp was studied irith great care, and no coordinated relation qeein- to e\i*t between ioids arid heat tran-fer c-oefficients.
T
HE iiiveqtigation of steady state heat traiisfer to gases fiowing in turbulent motion through packed tubes was untlert:iken in connection with a broad development program on .synthetic liquid fuel proce.sies. The prohleni \vas treated in a general manner, so that fundamental result. were ohtained rather than sprcific information. For thi; reason the jireient study zliould be of interest to those engaged primarily in the dehign and operation of equipment which utilizes, in one form or another, the principles brousht forth by this researc?~. ed of deterniining t h e heat Specifically the problem con transfer film coefficients and developing from these data a general n-orking equation, which could be used to predict heat transfer coefficient- for similar systems. Rome early pioneer work in this field \ m a done by Colburn'. T h e present research is an extension in which new data are presented. rl some\yhat different method of correlation was used. ' C'olhurn, h. l',, I N D E N G .C H E X , 23, 910-13 (1931).
EQUIPME.1T A \ 1) OI'EHATIOS
Figure 1 i h :i .ketch of the apparatu,- uaed for, this invc,-tig;itimi. Air \vas supplied by a hloner, and the Ho\v \vit. rn~~:i.-uI~('~i t J j - t w o rotameter6 \Titi1 overlapping ranges. The rot:unr~tc~r. \!-ere calibrated dii,ectly by a n-et teat meter and the calibt~atio~~,. corrected to stantlard conditions. -4 mercury ni:inunieter a11il tlierniometer inscrtrd into tlie upstream path u i the air iridic-ate11 the pressure and temperature of the air pas.-ing through tlrc, ters. All flon- re:idirigi \\-ere rorrrctrd for I 'iituie drriation. from the st:indard coiidi n-a> fed to either one of the te&.unit,. 9 by-p;~-h:irrangtxtiieI1t licrinitted the u\e of ritliei, t l i p 2-inch 0 1 the i,'2-iiicll pachrd tuljc,. 'The air entered the 2-inch unit througli a tec'. A 3-ir1cal1htalldarti pipe provitird a 36-inch high steam cheat around thr 2-i1ic]l ht:intlsrd pilie. The steam chert i v ~ i > properly veiited anti trapped t o prevent accumulation of ail, or ronden>atr. -4lirehi u r e gage \!-as provided at the center of the tuhe. In the annulus lietween the 3-inch :inti 2-inch standard pipe.< :t 3--in(,h long, ,j,'le-inch dialnetel. steel tube vas imtalied. Tlik tube, rveidctl *hiit at the lower end, touched the inner pipe over it. e~itirta length and served as a thermonell. At thc lover end of the 2inch pipe was a perforated plate covered hy a wire sc'reen i11:~c.ed tliirctly a t ttir lo\\-er end of the >team cheht. The 2-inrl1 p i p , extending out of the lower end of the ,team chect \vas imnwtli:ltelJ. riduced t o 1 inrli, anti a 1-inch gate valve n-as used to c o n t r o l tlic. air iioiv. Tile preisure drop acrws tlie apparatus vas measureti nit11 ;, \\-atc)i'inariometer (Figure 1). The height of t h e packing wa,~i l l all instances 36 inche3, arid the heat transfer coefficients W C ~ I ' I ~ c,:Llr*ulatedon tlie ha& of t h e inside pipe area. Thc entire apparatus W ~ Plagged froin the upper end of the steam chest to tliv throttle valre. h tliermonicter \va.s inserted into tlie t o p of til\ver enti tigations indicated that the differences in tempmitures, 3 5 determined by the thermocouple and obtained from thr, saturation hteam pressure, n-ere negligihle. For thi. wa.-oii tiit
858
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 39, No. 7
tionb could lie varied by a3 much a? j ' inch ~ without introducing an appreciable experimental errur, The height of the packing was in all r:Lses 11 inches, and here too the inqide tube diameter 11 a s u-ed t o mlculnte the effertive heat trtrn.fer area.
Figure 1 .
Apparatus for Determination of IIeat l'ramfer
wall teni,ieruture IVW determined hy simply rending the steam pres-ur~. The air; inlet :irrangement for the .-inch tube was the same :I. that d e w ~ ~ i h cfor d the 2-inch unit. The steam chest, which consi.t,d of n 1-inch standard pipe. \ ~ a q11 inches long -1 perfvr:ited plate T Y ~ Sfaitened in-itie the V2-inc1i tube (Firmre 1 ) . The entire' app:iratm \vas lagged from tlir upper ~ n ofd the steani c k t t o the air outlet. The lower end of the '?-inch tulle \v:v o p ? i , and the temperature of the
Coefficieii t s
50 0
I
1
1
1
1
1
I
I
1 ' 1
D
1
I
300
200
IO0 80
v e r e placed approximntely l/g inch helon- the perforated plate, one c o u p l ~near the center ?lid tlir other approximately i n c h an-ny from the inner tube n-rill. A careful teniperature gra.client exploration revealed t h a t the maximum devintion between t h e two temperatures amounted t o 0.05 millivolt, which for thi; range is equivalent to I .5 F. The t w o temperatures were averaged and recorded as
between the perforated plate .and the thermocouple junc-
60
40
30
20
10 40
100
Figure 2.
400
1,000
Heat Transfer through Two-Inch Tube
4 000
INDUSTRIAL AND ENGINEERING CHEMISTRY
July 1947 I
4001
I
1
I
I
I
I
I
I
I
I
659
such measurement had been omitted, much uncertainty \vould have per&ted, and it would have been extremely difficult t o recognize clearly the effect of other variables on tlie heat transfer coefficients. It is difficult to pregare beds composed of diffe~,entpal ticle diameters but the ,Game percentage voids. The 2-inch tuhe was charged by setting a 1-iiicli pipe on t o p of tlie perforated plate. The packing material U Y L ~ cni efully introduc'ed into the I-inch pipe, and a t the same time it \r:ia .lo~rly antl uniformly lifted up~vard,>-o that the ninterinl could cli-tribute itself freely in the 2-inch pipe. T!ii- niethod IYR? quite .:itiCfactory. Tlie height of the packing \vas adjusted to exactly 36 inches, and the lieat transfer coefficients ivpre d e t ( ~ r n i i n ~ l . -kt the end of tlie run the height of the packing i r a rec.lir~ckrtl ~ :111(1 i,ecorded. Then tlie materid n-as cli.vhnrged from tlie pi1ie ani1 carefully ilitroducrd into R graduated cylincler p u t l y filled \\.it11 \\-:itei~. The ri-e of the \rater level indicated tlie the piickiiig, This volume and the tlinicn,.ions o Tvcre -ufficient for calcul:ition of the percerirage vo ing in t h e tuhe. Tlie effect of vvida i\-a+ -tudiecl for three 1):~ckingni:itr~ial-. Tlie datci :ire recorded in Tnhle I and Figure 2 , ~ l i c r eSusselt n u n i b e r ~are plotted againqt modified R e p o l d ; numliei,;, usine logarit!iniir ciiortliiiates. Thi; plot indic:rtt~that 110 coordiii:iteti relation esi.qts betn-een tlie voids and the heat t r a n ~ f c coc,ffic>ients i~ for the r m g e ,studied. Figure 3 4 o n . s the pressure d r o p n.; :L velocity for tlie rarious case, in qucztion. .1 heries of straight and more or le>s p a r a l l ~ llines rrsultetl; tho effect of roitlq on tlie pre'iure drop is apparent antl run.istc~nt, R S one n.oultl oidinari1~-e s p w t , CORREL.iTION OF RESLTLTS
of porcelain halls, arid a tJ-pe of clay h l l z . Table I gives the diameters of the various materials. The '.-inch apparatus 1 ~ 3 s .chargeid iritti pl:is. be:idb of various dianietera. REPRODUCIBILITY A S D EFFECT O F VOIDS
Before any sy.teniatic ~ o r could k he started, it i r a z necessary to check tlie rei~roclucihilit~of results. The accompanying data indicxte that the espe~inient:d wror invol~etl~ a ' :-mall, in the neigliborliood of =3.5Yc. The fii.-t varialile to ))E htutlietl WRS the effect of voids in the bed 011 1ie:it trari.fcr cwfficients. The percentage of voids in a packed l m l esei.th :Lpronounrcd effect 011 the preqhure drop. If
Dp
200
Figures 2 and 4 lion. that the average .lopr v i the h i e s for the vnriou. packing material.; i i approximately 0.90, cxcrpt :it tlic l o ~ r e range3 r n-here tlie ma+ 1-elocitiesare such that viscous tiow
\vould result through the empty tuhe. by the follo~vingequation:
This may be exprcr:ed
~
1)
J\-here 0, tlie ~i~~oportioriality comtant, is a function uf Il,,/Dj. Hence,
Figure 5 i.- a iilot of log I t against Dl,/D:; for the greater p a r t of tlie tlat:i a 5tr:iight line relation exists. At loiv vslues of
0 . 1302" 0 . 1417"
11, ' I ) , !lon.ever, tlie line seems to curve slightly and tends to a i m tri\\-ai,d t!ie o+n. Tlie equntioii of the htraiglit line is found to be:
which simplifies to: -6
40" 4"
300
R =e
1
-
500 MODIFIED
1,000 2,000 R E Y N O L D S NUMBER
3,000
Figure 4. Heat Transfer through Half-Inch Packed Tube
(%)- 0.207
Equation 3-4 finally hecomes:
INDUSTRIAL AND ENGINEERING CHEMISTRY
860
1-n
b c d e f
2-a b r
d
e
f
p
44 :i
36 29 22 19 6
3 8 0 5.5 53
256 172 120 63 24
1900 1564
6
280
12ii
94i ,582
433 h 254 1 191 6 133 I) 82
38 31 25 20 12
54
8 4 5:i
59 22.5 5 0
18;
,524 45;
1357 1117 897 549 194 3
.A,
.\IT;
3-8 b c
d e f g
h 4-8
b c
-.9
-
Figure 5 .
d e
4b 0 4.' i 38.2 33 0 2i 1 19 1 11 8 .3.K
2533
200 160 I23 84 42 16 3
50 4 43 4 32!1 26 19
242
2
76 48 2b
48 1 42 6
200
52.6
1416
401 :329 231 143 461
1412 1128 845
296 299 :301, 3 :301 :301 296
90 90 !I0 87 90 94 2
320.5 320 5 320.5 :i17 8 :320 5 :324
92 87 5 82 0 78 0 i8 7 83 8
114 115 I18 120 5 124 13 5 166
:329 i328 :32s 5 .3.'30
137 3 1;16 5 135.5 I35 1x5 5 134.5
351 8 1351.1 350.3 ,350 :i 3.50 5 3350 :348.8
91 8 2 2 2 5 9 1 . 7 1923 6 9 . 0 1578 6 6 . 2 1231 85 , 1021 a91 82.7 169 60 3
:i30 329.5 :i2 3
G!ns,c J3e:idi: /I= 511 164
2152 1772 1436 1039 600 251
90 94 98 101 T7 114 5 134
04 !I6 90 3
102 104 108 7 118 7 150
13e:ici+; 11, 87 966 690 !I,? 530 !i!l 416 102 316 105
=
132.5
14 8
13!l
0
120
9
4 41
101 1 82 (I ti8 4 40 7
130
11.h
13 10 8 7
84 ;36
0 172 In : Void< = 4070
316
3316 :ilh
:il7 :ili 317.7 i116.7 :ill = 0
228
312 :i2.3 :iIfl.5
:{IS :320
123 122 5 116 113 .5 114 J 116 8 I90 2 1238
343 342.6 338.6 :137 :Xi7 7 :338 !4 :141 2 ;34:3,6
2.530 2240 1977 168% 1369 948 554 70 S9.t 149
100 96 9
8'3.0 67 0 b7 8 87 6
2
\ = 41.9c; 100 116 :X38 122 89 :349 111.5 :338 8.57 87 4 115 ;1.38 11!i :140 67.9
15 ti
148
14
I:iR 1:30
,
13 11 !I5 9 64 6 88 :3 80 10:3
1l:I !J1 H:i 0 :lr? h !I51J
!ri.:
3;iO
2.365 1724 1391 1003
19.7 16 5 1248 9 58 7.06
1x0 156
19 5 5 17.6 15.65 12.22 9 24 4 bi
18; li0 150 Ili 88 t i 48 t i
21
202 184 16!l
Ilk.? '30 1 66 4
Graph of D p , D t
b DISCbSSI0.1 01:EOUATIO>S
Equation 4 is diiiieii~ionally hnniogeneou,~and expe-ses h iii relation t o the phyi-ical propertiea of t h e gaa cvaluatcd at the average hulk t c i n p i ~ r a t u i and ~ ~ phj-sical dimensions of the apparat'ua. It contains two parameters which exert an opposing iriflueiice upon the magnitude of h . Thr:,~ two factor. arc
r
d e
f
7-a
b c
d e f
h"i 8-a b c d e f g
h
One noultl therefore expect that for certain c o n d i t i o n s a niaximuni heat trnii.frr coefficient ~voulcl re-
.ult
9-a
b
c
d e K
h
10-a
b c
d e i g
h 1.6)
0
309 248 150
,586
2548 1862
against Log R
'
-7
2060 1832 1639 1163 8151 ,506 167
129
. ,
Vol. 39, No. 7
.I
9
I
I
.2
.3
Dt
Figure 6. Graph of DplDc against 100h/G0.90 for
Two-Inch Tube
11-a b c d e f
3 2 9 24 i 1;3 s 56 ti 50 2 45 :i 35 6
30 i 2;32 16 0 9 77 7 1;
18
24110 2158 160
100 7'3 4.5 22 i 8 25 4
IW3 152i 1.317 99.5
b2
84 :3 112
1151
8.5 5
2 ,'Dt the coefficient i i le;.. than 30. For still larger pipes tliis ccit=fhcierit would be even lair-er.
(y)o,4 (y)?)~
(Y)
Gas or ~ a p o r
Air, CO,Hz, SZ, 0 2 SHa CO?. 802 C2R; HnS CH4 Steam,low pressure
ASU
Vol. 39, No. 7
0.699 0 905 0.914 0.928 0,900 0 909 0.905
0.818 0 848 0 862 0 863 0 840 0 855 0 848
ACKNOWLEDG3lEST
The autlior \\-islies t o esprehs gratitiide tu lf.11-eiiitraub and If. Grunimer for :is-i.+tance in collectirlg the data and also for considerable effort spent in correlating the results. Run So.
?c
G
Re
tz
tl
pst.
kt.
A.O>lENCLATURE
At
A i r ; D p = 0.126 In.: D3>Dt = 0 202
100-a b c
d e
8.73 1.34 5.94 4.39 3 23
4150 3480 2820 2080 1535
131 136 569 142.5 150 416 306.5 156 848 706
338 341 341 340 338
b c
d
8.00 3800 7.27 3456 4.84 2300 3.46 1642
777 706
471 331
125 127 126 142
341 342 339 340
141 141 140,5 140,5
353.5 353.5 353 353
74 3 23.4 16 6 71 0
34 9 28.7
410 371 244 162
37.1 34.0 21.4 15.3
78 79
508 4i4
80 72.5
4.3 6 40 1
424 317
36.4 59.2
Air; D p = 0.1302In.;D p ; D l = 0.209
102-a 10.43 b 9.93 c 8.94 d 6.95 103-a
b c
d e
9.61 8.19 7.17 5.76 3.60
4940 1020 4700 971 4230 875 3290 676
c d e
2
337 335 334.5 337
139.5 138 138.5 138
353 352 352.5 352
Air; D p = 0.142I n . ; D p / D t = 0.228 339 141 353 5 79 4550 1038 116 5 124 339 140 353 3880 876 77 127.5 339 139.5 353 3400 768 76 135 340 138 5 352 2730 614 72 143.5 341 136 5 351 1706 382 65 S ? :D
104-a b
131.5 133.5 135 145
92 2340 500 I 82 3720 798 12 0 5700 1218 7700 1643 16 2 20 8 9900 2110
p
=
137 131 122 118 112
5
0 0 5
0
40 8 34 i 32.5 280 24.7 168 6 16 6 507 417 385
0.1302 In.:D p / D t = 0 209 331 126.5 346 71.0 2 2 i 333 130 347 5 74 0 875 331 125 344 7 5 0 591 330 131 348 64 5 813 327 133 349 BO 3 1060
For carbon dioxide the group CP,,/X: = 0.80 and differs only slightly from the value for air. T h e good agreement betn-eeii t h e calculated and. observed values for carbon dioxide heat transfer coefficients indicates that the Prandtl group should probably appear as a small fractional power in Equation 4, and its effert on h n-ould be insignificant. This small effect could hardly tje determined with any reliable degree of precision, and it \\-oultl be necessary t o extend t,liis work to liquids for irliich the Prandtl group changes more profoundly for different cases. The good correlation presented indicates that lieat tr:m.fer data may be estimated by means of Equation 4 for gaie. other than air as long as the Prandtl group of the gas in que4tioii doe3 not differ materially from a value of 0.744.80. It must he understood, however, t h a t some gases, and especially tures of hydrogen and nitrogen have Prandtl groups considerably from those of the gases listed in Table 11. In such cases it is buggested that E:quation 4 lie used v i t h caution. Equation 4 incorporates, finally, another vnri:il)le--liamel?, tlie diameter of the tuhe. To prove the correctnew of Ut in the de1iomin:itor of the equation, a series of experiments n-as made with a 1 '?-i:ich tube. The data are recorded in Table I11 and plotted in Figure 4 :I, hDtik against UDG,',u: they are also used i r i Figure 5. This graph indicates that the data are in line ir-ith those ohtiii:led \ritil larger tube sizes. In fact, Equation 4 ma:- be used t o predict heat transfer coefficieiitf for the '?-inch tuhe, and the mea.ured and predicted data are in good agreement. Figure 7 s h o w how h varies with Dl for an air m of 3600 pounds per hour per square foot and three xitios of
=
110 8 94 3 77 9 21.4 5i.8 15.4 41.8
40 4
A i r ; D p = 0.126 I n . ; D p D t = 0 202
101-a
.specific heat a t constant pressure, 13.t.u.: lb./' F. d = tiiffermtial = base of natural l o g a r i t h i s e j" = fuiictiori !I = g:i+filni licat transfer coefficient, I3.t.u.i 102 111.. ' c I.'.!aq. ft. 93 5 59 1 /I, = out4cie-film heat transfer coefficient, 41.i H.t.u.,hi,. '"F.:sq.ft. ii = average thermal conductivity of gas, 120 I3.t.u. lir./ F.,/ft. 111 97 7 /;u = thermal conductivity of tube materid, iD.8 1 3 . t , u . , ~ h r .F.!ft. /o pSL,= ateam ;nesaure, lb./sq. i n . a h . 113 2 q = lieat transferred to air, H . t . u . / h . 95 'J 80 , r O = i.r-i>tance to heat flow through gas 68 0 45 7 film ra = i,esistance to lieat flow through outside film 60 5 95 6 rl, = resi.taricc to heat floir- tlirougli t u b e 150 \Val1 ___ 5 ti = inlet ail, temperature, F. i, = outlet aii temperature, F. = n-eight rate of ga.4 through tube, lb., hr. i(' -1, = g:ier area, sq. ft. = partic,le diamrtei~,I t . = tube diameter, i t . = ma.-- velocity, I t ) . sq. ft./lir. = ir-all t!iickiie>s ~f t u k , f t .
C,
135 350 71 3 428 138 352 68 8 356 137 5 351.5 65 3 279 134 349.5 62 2 198 130 5 347.5 60.5 139
21 5 34 0 53 0
:tj
$4 16 5
7
.L .1
IL
:l [I,,
Di G L,
. . .
IT
,
ovrr-:ill 1ie:it trniiifer coefficient, B.t.u.l'lir.~' F./sq. it. N = ii functioii of D,, Ut, proportionality constant = Io:.:ii~ithniic tei1iper:iture difference, F. tsr. = er:iture, F . iin, cni. H.0,,36-iiich tipigfit =
D,C
'p =
Ikyntjl(1- iiumt)er ( l i e ) , dimeri.ioiiles5
Su..\:,lt iiunitjer (Su),dinienGionless Cp@,'/i = Prttndtl group, dinieri.~ionle~z
hDt 'i:
=
1 ' n ~ s ~ s before . i ~ ~ the I l i v
o f Indubtrial ;%ridEngineering Chenii-try at Chicago, 111. PubD i r e c t o r , U.8 . Bureau of l l i n e s . C I S C H E M I C n L SoClETl-,
*
Fluorine Xomenclature-Correction
The editors n-i,+hto correct an error ir-hich appeared in the list of nomenclature of fluorine-rontaining compound5 011 page 242: of the RIarch 1917 issue. The formula for the fourth compound,> pentadecafluoroheptane, should lie CiHF1;.
