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
October 1949
(1 = total volume of comporients i n the liquid phase of evaporating solvents in case 111,cu. cm. q = denominator in Equation 33 K = observed indicator or chart readings of combmstibli.
*ith it combustible vapor-measuring instrument. The relation,hip between the actual and observed per cent of the lower e\plozive limit is given in Figure 6. Since there is a pronounced deatio ion from linearity in the upper portion of the plotted range, Equation 44 will give a value of 1.39 for the factor as compared tci i valiir of 1.30 based on the linear portion.
vapor measuring instruments slope of the line representing chc nietlxr readings m. p.p.m. 7 = absolute temperature,, K. 1 = time of evaporation t1 = denominator in Equation 32 1. = molecular volume used for calculating iliffusion coc,t. ficients i t 7 = evaporation rate, !veight/unit area:'unit time S,Y,Z = mole fractions of components J:, y , : = molar concentration of components, gram molt unit volume: in Equations 16 to 26, gram moll volume of liquid phase 8
NOM E3-CLATI-RE
- rota1 pressure, atmospheres = . denominator of Equation 34 B = gas constant, 82.07 cc.-atm. i u
'i
i
conrtarit representing
(3' (3%
-'
;v
C -- integration constant for Equation 14
D
diffusion coefficient or diffusivitv, area 'unit time
1
-. constant representing
b
i
9
.=
*
:
P ' P,
2209
:1
per cent by volunie that a component comprises of the total vapor volume in air proportionality constant in Maxwell-Stefan equation factor by which the observed reading is multiplied to 01)tain the true reading
=
I'o\rard, H . F.. and Jones. G . W., U . 3.'. B u r . Mines, / i d / 279, 46 (1939).
- constant representing ,q)wific gravity of a component
*;
==
.I
= vapor phase ratio betffeen the hrst and second com-
ponents of a three-component mixture vapor phase ratio between the first and third components of a three-component misture 5 .; exponent for diffusion ratio between coni onents I = vapor phase ratio between the second a n t t h i r d components of a three-component misture K = constant represented by Equation 8 i = the kth component L.E.1,. = lower explosive limit (lower flammability limit) If = molecular weight vi -:distance in direction of dift'usioii through stagnant film cm. \ =- ratr of diffusion for 2 gxs, molt+ u i i i ~area,'unit time i
:.
2 p l in Equation 40
-1 +' q-1 +' -a
"
A!
vapor pressure of pure Iquid, mrn. Hg -= partial vapor pressure of liquid component, nim. [I :! o.p.m. = parts per million. v o l i i r n ~ti> volume =:
?'
,cj
Heat Transfer Characteristics of Fattv Acids J
DO3 ILD Q . KERN' A ~ WILLIAM D V-41NOSTRAND? Pol.ytechnic Institute of Brooklyn, Brooklyn, S. Y .
!'tie ordinar) equations describing heat transfer to liquids tiow-ing in tubes give coefficients for fatty acids which .ire unsafe. The ph?-sical properties and heat transfer coefficients of four commercial fatty acids have been imvestigated. .in equation correlating the heat transfer data is reported.
T
HF: t ~ c w i v use e of stainless stwl in the fabrication of equip-
ment for fatty acid processes has focused attention upon the :acI’.~R.IT[--, The apparatus consistcti of n double pipe ste:rm 1ic:iter of 10-foot rtTective length, a douljle p i p cooler, storage t:ink, pump, weighing tank, and suitable piping equipment in contact with t h e fat o. 316 stainless steel. Th(. douhle pi TrXraI aims of inner tubi’s :in11for this
I-rsccisrn-. T’iscosities viere tieterniiiird in an O*t\\-ald tylw viscometer, allowing one-half hour for t h c attainnirnt of tIici,mal equi1iI)rium. D a t a ir-ere reproducihle \\-it11an error of 2.0%. T h e Lauric Oleic Palmjtic Stearic
Fatty .icid Lauric
Oleic
374.0 311.0 287.6 ”66.0 389.3 384.8 357.8 343.4 324.5 308.3
2i3.2 255.2 384.8 381.2 339.8 332.6 303.8 289.4 285.8 262.4 388.4 Stearic 370.4 331.4 311.0 266.0 Computed from obseri-cd values in O C. Palmitic
5
1n.i 10.0 0.2
10,5
0.74 1.12 1
.xs
Ternpevature,
1.67
Acid
i.nn
188.0 208.4 2Y4.8 325.4 357.8 388.4 148.1 Oleic 295.5 332. n 362.3 303.6 178.2 Palmitic 291.2 324,3 367.6 389.6 242.2 Stearic 264.0 337.9 387.8 Computed from otrserred valiies i n C. Lauric
1.02 1.25 1.38 1 so 1.81 2 41
2.Gi 1.02 1,05 1.41 1.62 1.93 2.08 2.14 2.67 1.14
1.32 1.70
2.01 3.55 ‘I
F.G
Specific €Imperaturcand the mean temperature of the fluid in the tubes. Since the inside tulle surface was known in each casc, the heat transfer coefficient could then lie calculated. T h e ohserved data and values of the calculated heat transfer coefficients arc givc~li l l Tnl)le 1.111.
TABLE VII. RASGE OF VARI.~BI.ES F a t t y acids: Lauric, oleic, palmitic, i r e a r ~ < ' L e n g t h t o diameter ratios 9 5 . 5 , 194 ,O, 304, Viscosities 0 . 9 7 t o 8 , ' centipokrs Reynolds numbers 2,260 t o 39,700 Prandtl nunihers 2 6 . 9 to I l g . 2
-
experiments err carried out on inner tubes of 0.375-heh outsiile diameter x 20 Birmingham wire gage, 0.75-inch outside diameter X 16 Birmingham wire gage, and 1.5-inch outside tiianieter x 11 Birmingham \\.ire gage. These had inside diameters of 0.305. 0.62, and 1.26 inches, respectively. Table VI1 gives the i'ange of the variables investigated. The temperatures of heating steam and tube n-all temperatures were measured ivith calibrated iron-constantan thermocouplr~. The latter were silver-solclered to the outside of the wall :it four equallj- sp:rceti points along the tube length. The method and arrangement of parts \\-as similar to those eniplo?-ccl . , 1 Kern anci Othnier (9). T o establish a uniform steam temperatui,e on the outside of the tubes it n-as found necessary first to pull :t vacuum exceeding 25 inches because a continuous vent did not adequately purge the system. F a t t y acid was brought to circulating temperature by means of a steam coil in a storage tank and was then recirculated through the heater-cooler system until a steady state was reached. The steam pressure in the heater was adjusted for the desired saturation temperature. I t required about 30 minutes to arrive a t the steady state a t which time readings
" I 1-
2-
*. .-I
3I
Re
Figure 2.
Correlation of Data
2212
INDUSTRIAL AND ENGINEERING CHEMISTRY G h
TABLL 1-111. CiLci7r,a.rro\Run
kcid
17
J
0 10
Oleic
I1 12 13 14 15 7
Palmitic Stear;?
1,auri.c
12
23 24 25 253 26 27 28 20 30 31 32 33 34 35 16 17 18 19 '20
Oleic,
Palmitir
Btearlr
21
Oleic
Palmitic Stearic
Q
/,
1.5-Inch Outside Diameter Tube 20,420 1 0 5 , ? 17,640 83.9 8,380 32.3 54,300 2 2 2 . 5 20,250 65.9 23,850 121.ki 17,160 96.0 14,320 64.3 52,000 365,O 26,720 1 2 2 . 4 21,050 88.4 72.G 19,300 71.i 18,450 21,320 78. < 22,180 80.1
Laurlc
1
Ttc
t.
(1
Re
11,320 7,085 3,310 16,650 4,075 11,220 8,850 3,220 2,300 12,650 8,330 6,130 3,728 3,476
z,,m
111.2 87.5 32.3 311.5 84.1 157.6 111.2 70.7 43.4 200.5 141.4 112.5 97.4 101.2 m , 8
30
8.54 3.10 23.6 6.40 13.3 8.50 60.4 4.83 53.4 3.56 47.4 16.5 47.3 11.7 49.0 8 65 4.45 104.2 3.81 117.3 119.2 3.98
4920 $440 3960 3300 1380 ,4560 3060 2460 1440 2856 480 4800 3840 3360
0.75-Inch Outside Diameter Tube 2 4 0 . 8 2 5 0 . 7 289.4 25,700 4 0 6 . 0 237.2 246.2 2 8 8 . 0 20,600 297.0 235.4 244.4 2 8 8 . 5 18,180 2 4 6 . 5 2 3 4 . 4 244.3 2 9 3 . 0 16,640 2 0 5 . 0 9,320 89.8 220.1 233.9 293.5 3 1 7 . 3 321.8 3 4 5 . 0 16,520 4 5 5 . 5 3 1 2 . 8 3 1 8 . 2 3 4 9 . 0 10,900 2 1 2 . 0 8,760 1 5 1 . 6 309.2 314.0 3 4 9 . 0 6.730 95.5 296.6 3 0 3 . 8 345.2 3 0 6 . 5 3 1 4 . 5 357.3 15,030 208.0 3.760 36.9 3 5 4 . 2 281.3 295.7 325.4 3 3 0 . 8 3 5 2 . 5 15,680 4 4 6 . 0 14.600 3 40.2 327.2 3 5 4 . 2 320.9 2,660 4 0 7 . 0 318.2 324.5 353.0
25,350 22,000 19,300 15,900 5,860 28.850 18,920 14,950 (,go0 16,760 2,260 25,800 20,300 19.750
27.2 27.5 27.6 1 9 . 7 27.2 16.2 27.3 13.2 29.6 5.08 43.5 38.7 43.0 17.5 42.3 12.2 44.0 6.97 40.5 1 9 . 5 46.8 2 69 57.4 3 8 . 9 28.8 JJ.2 34.0
U b 0 \ 1'1
3OMENCL4TLRE
F.
inside diameter of inner tube, ft.
Vfi
P7 (J
Rc 11
ti
72n 600
= specific heat, R.t.u./lb./"
.-1 1 3
k
12.J 14.0 12.5 44.2 6.51 13.6 30.7 40.5 16.2 37.5 30.7 29.1 20.7 12.2 6.78 17.0 13.8 15.6 14.1 7.11 4.73
T, !J' u tiy
xr
hD(cpr-n . ,
, dimensionless
- theimal conductivity, R , t . u , . (hr.)(sq. ft.)( O F./ft.) = Yusselt number, h D / k . ciinrrr' sionlefis - Prandtl number, cpLjli, J i n i ~ r i sionless =: heat flow, B.t.u./hr. Reynolds number, DG'/p, Sirrri~ri sionless -= fatty acid inlet tcmDernture. 1 - fattk acid outlet 'tempcratiiv F. = tube wall temperature, F = vieight flow, lb./hr. viscosity a t the avwage tlui( temperature, lb./(ft.)(hr.) -. viwosity at the average pipe ir R I temperature, lb./(ft.)(hr. 7
LCKNOW LEDGhl ENT
r h e authors are indebted t u i,!lr Colgate-Palmolive-Peet C o m p a n y io. ?upplying the equipment and material. for this investigation and to the Patterson Foundry & Machine Corn pany for the recalculation of snmP 07 t h c (lata a n d thr. drawings. LITERATCRE CITED ( 1 1
'21
;e.?
.? C olhurn, A. P.
NO,
mb5s velocity, lb./(hr.) (sq. ft. coefficient of h e a t t r a n s f e r R.t.u./(hr.)(sq. i t . ) ( ' F.) hrattransferfactor,-k k '
(i)
2:;
2G.9 27.4 29.3 20.4 30.2 30.5 43.5 40.2 43.4 44.2 43.9 43.8 39.9 45.6 45.7 62.6 63.3 63.1 63.8 63.9 70.0
225.0 162.5 134.2 111.4 47.4 392 5 177.5 123.5 74.2 297.5 32.4 476.5 354.2 414 8
7
n 11.7
33.3 32.6 45.8 49.4
13,940 101 . O 11,550 1 1 6 . 2 8,820 93.5 39,700 289.0 7,090 59.7 8,070 1 2 8 . 2 22,720 328.4 27,520 4 0 5 . 6 20,610 1 7 1 . 8 29,120 3 8 9 . 0 23,050 3 2 2 . 2 28,820 3 0 2 . 0 17,050 2 0 3 . 0 9,710 1 3 7 . 2 5,860 (9.5 74,300 239.7 10,920 1 9 7 . 0 9,740 2 1 7 . 5 8,910 201.2 6,230 1 0 7 . 1 3,.550 79.6
1380 1200 960 1860 660 780 1800 2016 1620 2280 1860 1680 1440 900 600 1740 1416 1320 1140
The equation is applicable for heating and in the range %I\ t I I '1, Table VII. It would appear from the correlation of Sicd(sr aiid Tate t h a t the inclusion of the ratio p / p w should also peiniir the, use of the equation for cooling except near the melting T m n t - nl the respective Itrids
=
3H F
The data were tested by means of the equations ot Co1t)iilI I Sheder and Tate (I.5), Kern and Othmer (9), and Sorris ani1 Sim. ( I S ) all of which indicated coefficients higher than those actual15 obtained. T h e deviations mere not calrulated in detail because the majority of test points in each case fell belo\!- the theoretical prediction. The suggested correlation, giving an avr1rag:c (lrrol oi 17.89/,, is plotted in Figure 2. The equation 1s
r)
P.
0.375-Inch Outside Diameter T.ib8 233.6 2 5 1 . 6 287.6 13,000 3 8 3 . 0 2 2 7 . 3 2 5 0 . 7 283.6 14,600 436. (1 2 2 2 . 8 248.0 284.2 12,540 338. j 323.6 3 4 1 . 6 3 6 8 . 6 20,760 812. (1 2 1 2 . 0 242.6 285.3 10,260 229 5 2 6 8 . 7 3 1 2 . 5 3 7 6 . 0 21,900 3 4 2 . 0 3 0 4 . 2 3 3 8 . 3 3 7 3 . 1 31,350 7 8 8 . 0 3 2 5 . 2 3 4 2 . 3 369.9 23,150 907.0 3 0 7 . 4 3 3 0 . 3 3 6 9 . 7 15,650 4 0 9 . 0 3 1 4 . 6 3 2 7 . 2 3 5 0 . 6 17,060 8 0 8 . 0 3 0 7 . 4 323.6 3 5 1 . 3 17,780 688 0 3 0 5 . 6 3 2 3 . 6 3 6 1 . 7 17,850 6 4 4 . 0 3 0 2 . 0 3 2 0 . 0 3 5 2 . 2 15,080 4 2 9 . 5 2 8 6 . 7 3 1 1 . 9 3 5 3 . 5 12,950 313..7 2 7 4 . 1 3 0 5 . 6 3 5 8 . 7 10,580 1 9 7 . 0 2 8 5 . 8 3 0 5 . 7 3 4 6 . 1 19,660 5 2 5 . 0 287.6 311.0 3 4 8 . 3 18,040 4 4 1 . 0 2 8 1 . 3 3 0 8 . 3 3 4 6 . 8 18,500 4 7 6 . 5 2 7 6 . 8 3 0 5 . 6 3 4 6 . 1 18,560 4 5 0 . 5 269.6 3 0 2 . 0 3 5 2 . 4 13,060 225, (1 214.T 286.7 3 4 9 . 9 13,140 201. n
OKKhL4 I L O \
'i
VU
=
voi. 41,
Bates, 0 . K., IND.END. CHml., 25 431 (1933); 28, 494 (1936): 33 375 (1941); 37, 195 (1945).
Holland, J. L., and Melville, IT. & ' Traqs. Faraday Soc.,
33.
(1937). 3 [bid.,pp. 1316-29 i 4 Rridgman, P. IT., Proc. Ani l r t s Sci , 59, 149 (1923). 7rofis
4~
131f
* 4 a(, ~
Inst. Chem. Engrs., 29, i 7 1 21(
(1933). ti) (;oldsctimidt, Physik Z . , 12, 417 i.1911). '7) Hutchinson, E . . T i a n s . Faraday S o c . ~41, 87-9 (1948). 8 ) "Iiiternstionnl ('ritiral TRhlPs..' S e w York, McGraw-Hill t+s(oh Co., 1929. ~ .T - u n s . Am.. I n s t . Chetn F:,,u-', 9 1 Kern. D. 0.. aii(-10 t h ~ I )~. k-., 39, 517--51 I 19-13) I
101 Lee>. Phil. Trans.. 191, X W IlWJh,. : J 1 J Long, J. S.,8: nl.. Isn. Ex
