I
JAMES DE ACETIS and GEORGE THODOS The Technological Institute, Northwestern University, Evanston, 111.
Muss and Heut Trunsfer in
...
Flow of Gases Through Spherical Packings Contrary to usual assumptions, tempera surface is not the same as the wet-bulb entering air, unless high air flow rates C O N S I D E R A B L E INFORMATION concerning simultaneous mass and heat transfer in the flow of gases through granular packings (5, 8, 9, 72, 73) has been presented in the literature. These studies have been conducted primarily to obtain experimental data for establishing mass- and heat-transfer factors. I n 1943, Gamson, Thodos, and Hougen ( 5 ) , using psychrometric measurements and experimentally determined rates of evaporation of water into air streams from spherical and cylindrical porous pellets, developed j , and j , factor correlations for modified Reynolds numbers in the range Re, = 200 and Re, = 3750. I n their studies, surface temperature of the wet porous pellets was assumed to be the same as the wet-bulb temperature of the inlet air. Although this assumption is undoubtedly valid a t high air velocities, considerable speculation exists as to its validity a t low velocities. Because of the uncertainty involved in their experimental approach, it is desirable to measure directly the surface temperature, because this temperature has a n important effect on the values of both mass- and heattransfer factors. Therefore, in this study, the temperature of water evaporating from spherical catalyst carriers has been measured directly, and it was found that temperature of the evaporating surface was the same as the wet-bulb temperature of the inlet air only a t high air velocities.
Equipment a n d Procedure
The experimental unit consisted of two sections constructed from copper pipe, the ends of which were provided
with flanges which could be compressed tightly together to prevent air leakage. The lower part of the unit was permanently fixed, but the upper section could be disengaged so the reactor could be removed and weighed to determine the rate of water evaporation. The reactor, consisting of a cylindrical unit constructed from stainless steel inch thick, was 3.692 inches in inside diameter and 3l/4 inches high. T o support the packing, a screen was fixed to the bottom of the reactor. Another screen was placed on top of the bed to hold the packing in position. The packing consisted of porous spheres prepared from Johns-Manville Type VI11 catalyst carrier which were 0.626 f 0.005 inch in diameter. These spheres were capable of absorbing large quantities of water and exhibited a constant drying rate. To measure the temperatures of the surface of the spheres in the bed, fine-wire thermocouples were installed in several spheres by drilling through a major diameter and inserting the wire through the hole until the couple junction reached a point just below the opposite surface. The spheres were arranged into two types of packing. I n the first type, a layer of spheres was prepared in a most compact arrangement on top of the reactor screen. Additional spheres were then placed on top of this layer to produce a packed fixed bed. The spheres containing the thermocouples were randomly distributed throughout the bed. Runs were conducted using bed heights consisting of one, three, and five layers of spheres. T o minimize entrance and exit effects, the bed consisting of one layer was sandwiched
between layers of solid plastic spheres which could not absorb water. The other type of bed was prepared from packing consisting of 27 porous spheres randomly mixed with a n equal number of solid plastic spheres of the same size. The bed formed from this type of packing arrangement has been designated as an expanded fixed bed. Another bed of this type was prepared using 35 porous spheres randomly mixed with 70 solid spheres. I n a typical run, the reactor unit with included spheres and attached thermocouples was submerged in distilled water for at least 2 hours until the spheres were saturated. Air was furnished from the building supply, and the flow rates were measured using a Fischer-Porter rotameter. The air leaving the rotameter was forced through a small glass unit provided with thermometers and thermocouples for measuring the dry- and wetbulb temperatures of the air entering the unit. The air was then introduced into a calming section packed with glass spheres to ensure uniform air flow, from which it entered the reactor. After leaving the reactor, the dry- and wetbulb temperatures of the air were again measured a t the exhaust end of the unit. Pressure taps before and after the reactor unit were connected to a n inclined manometer to determine the absolute pressure at these points. The several thermocouple junctions were connected to a n indicating potentiometer through a multipoint contact connector. The socket portion of this connector was permanently positioned in a rectangular chamber located immediately below the reactor. This arrangement permitted the rapid disVOL. 52, NO. 12
DECEMBER 1960
1003
engagement of the reactor unit for the necessary periodic weighings. Removal of the reactor cartridge, its weighing. and repositioning usually consumed about 30 seconds. The operating interval beriveen weighings varied from 2 to 30 minutes depending on the air flow rate.
PACKED FIXED BED
EXPANDED FIXED BED
Interpretation of D a t a
The experimental data obtained for the packed and expanded fixed beds (Table I) were analyzed using a n approach similar to that of Gamson, Thodos and Hougen (5) to establish the mass- and heat-transfer factors proposed by Colburn (2):
/
G
= 758
= 644
for the air entering the bed is not unexpected, because air velocity through the interstices of the bed was approximately 2.42/0.482 = 5.01 ft./sec.: which is considerably below the minimum recommended value of 15 ftJsec. (77). Thus, direct measurement of surface temperatures offers a more exact means for interpreting the experimental data, because this approach does not assume that the temperature of the drying spheres is necessarily equal to the wet-bulb temperature. Heat transfer data of the 44 runs of this study were analyzed objectively to produce the corresponding heat-transfer factors. For their calculation, Prandtl groups for average film conditions varied from 0.716 to 0.720. A comparison of the j, factors resulting from both types of beds does not show any significant differences (Figure l ) , and consequently a single relationship over the range of
Ib./hr. sq.
ft. ft./sec. F = 648 cu. ft.!hr. Inlet Temp., ' F . Thermometers t,!, = 7 6 . 8 tu] = 5 2 . 8 Thermocouple idi = 7 6 . 6 21
= 2.42
Bed Temp., F. Thermocouple Readings
In out
54.4 54.4 54.2 54.4
54.4 53.9 54.3 54.2
Av. Outlet temp. (thermocouple),
-4~. 54.4 54.15 54.25 54.3 54.28
F., t,jz
=
solid plastic spheres
The packing consisted of porous spheres which were capable of absorbing large quantities of water and which exhibited a constant drying rate
Temperature distribution obtained during a typical run (run 18) is: Re,,,
/'
imbedded fine thermocouples in porous spheres
porous celite spheres
58.6
For this run. the higher average surface temperature of 54.28' F. over the coexisting wet-bulb temperature of 52.8" F. ry and wet bulb thermometers
Reynolds numbers jnvestigated defines the variation of rhe j , factor. This relationship was not found to be linear, but could be expressed analytically as j,
=
l . l O / [ R e O ~' 0.151
(3)
over the modified Reynolds number region of 13 to 2136 covered in this study. Figure 1 indicates that the relationship between j, and Re,,, is independent of the type of packing arrangement employed and that Equation 3 produces an essentially linear relationship at high modified Reynolds numbers. Mass-transfer factors: j d , lvere calculated following an analogous approach. The Schmidt group a t average film conditions varied from 0.606 to 0.609. The j d factors, when plotted against the modified Reynolds number, produced the relationship of Figure 2 for both packed and expanded fixed beds. 'The resulting j d factor relation-
The experimental unit included a removable reactor
4
Figure 1 . Heat transfer factors resulting from the data of packed fixed beds and expanded fixed beds produced the same relationship when related to the modified Reynolds number
v 10 08 06 04 03
t o l d number cf spheres
105
02 Jh
0 10 008 006 004 0 03
002, t
-!I-
1004
INDUSTRIAL AND ENGINEERING CHEMISTRY
spheres sclid plastic spheres packed i i x e d bed 27 none 27 none 27 none expanded fixed bed
P
Re,= DPG
27 27
27 70
3
G A S FLOW T H R O U G H S P H E R I C A L P A C K I N G S I
8
IO
I I
08 06
I
1
1
1
1
I I l l i t ln,estigotors
IO 08
I Boumeister
06
04 03 02
and Bsnnetl
Film Phase Syrlem go8 oir
b DeAceIis ond Thodos m Gomran,Thodos and Hovqen
pos
water-oir
qor
voler-ow
04 03
,
In 0 2
jd
010
008 006
0 IO 008 006
004 003
004 003
oo?O
20
30 40 60 80100
200 300
Re,=
Figure 2.
500
1000
4000
2000
0 02
DPG P
Re,=
Mass transfer factors resulting from the data
o f p a c k e d fixed beds and expanded fixed beds produced the same relationship when related to the modified Reynolds number
pressed analytically as
jd
0.725/[Re:41 - 0.151
(4)
Equation 4 indicates that the j d factors vary with Re,*.d1 at high modified Reynolds numbers. A similar variation has been reported (5) in this region. The j , factor values produced in the low Reynolds number region,
Table 1.
T. Nin.
tdl
Temp., tw1
O
F. td2
The j , and j , factor relationships of Figures 1 and 2 have resulted directly from experimental measurements. The ratio of j h / j d = 1.10/0.725 = 1.51 does not agree with the reported value of 1.08 ( 5 ) , obtained on the assumption that temperature of the evaporating surface was at the wet-bulb temperature of the air entering the bed. Ratios of j h / j d were calculated for each of the 44 runs of this study and produced an aver-
Basic Experimental Data for Fixed Beds ( D p = 0.0522 f t . ;
Run No.
P
Figure 3. Heat transfer factors obtained in this study are compared with the results of previous investigations
Re,,, < 25, have been found to be consistently lower than the corresponding values calculated wih Equation 4. This behavior can be explained by increased back-mixing effects at these low air velocities. The analysis of these effects becomes a separate problem requiring more extensive experimental information, such as the determination of concentration gradients within the bed.
ship is analogous to the corresponding
j , factor relationship and can be ex-
D.G
(tdev.
B
=
0.482)
Mm. Hg PO
331
r, Lb.Moles/Hr.
G, Lb./Hr. Sq. Ft.
j d
jh
Re,
0.164 0.0668 0.0552 0.0414
0.192 0.124 0.0874 0.0504
89.6 291 758 2136
0.162 0.101 0.0621
0.364 0.236 0.170 0.0973
31.9 90.6 154 562
0.289 0.271 0.213 0.0753
0.730 0.541 0.378 0.105
13 .O 27.0 56.6 409
0.257 0.198 0.125 0 .OS75 0.0599 0.0361
0.786 0.386 0.255 0.134 0 .OS69 0.0536
16.02 57.73 103.7 329.8 755.2 1773
0.226 0.148 0.0871 0.0675 0.0365
0.464 0.242 0.149 0.0948 0.0588
21.65 82.0 170.8 564 1676
Packed Fixed Beds Five Layer Bed: No Porous Spheres, 135; a V , 1.154 sq. ft. 8 11 18 15
743.8 742.2 747.1 748.1
82.6 80.5 76.7 77.0
56.9 55.2 52.8 54.0
24 26 25 27
745.0 747.5 746.2 745.4
80.9 80.9 80.8 80.0
56.8 56.0 56.0 56.2
32 30 28 33
747.6 742.3 741.9 746.5
85.4 89.0 87.0 82.4
56.6 58.4 58.4 56.2
62.15 59.0 58.6 62.0
59.9 56.4 54.4 55.7
4.67 4.32 3.75 4.44
13.17 10.32 8.67 8.08
0.00228 0.00521 0.01101 0.02268
76.91 248.4 643.6 1812
Three Layer Bed; No. Porous Spheres, 81 ; a V , 0.6924 sq. f t . 64.0 61.3 62.2 63.0
61.0 58.5 58.1 57.0
5.32 4.81 4.81 4.98
0.00088 0.00186 0.00259 0.00642
14.53 11.66 10.39 8.80
aV,0.2308 sq. f t .
One Layer Bed; No. Porous Spheres, 27; 75.6 75.0 74.5 74.2
66.85 66.0 64.0 58.2
4.03 4.34 4.77 4.63
13.14 12.69 11.11 6.82
27.36 77.44 131.9 480.1
0.00036 0.00068 0.00109 0.00256
11.17 23.21 48.89 350.5
Expanded Fixed Beds No. Porous Spheres, 27; No. Solid Plastic Spheras, 27; aV,0.2308 sq. ft. 38 39 37 36 35 34
749.5 749.5 750.1 752.2 747.4 744.5
81.2 83.1 80.4 78.7 75.0 79.8
56.5 57.0 55.2 55.0 54.0 56.8
44 43 42 41 40
749.2 745.4 747.8 750.4 751.4
84.7 90.0 86.0 79.8 79.5
56.1 59.4 57.0 56.2 56.2
70.4 69.1 68.0 70.2 69.0 74.9
63.5 61.7 59.8 57.6 55.3 58.7
4.79 4.97 4.63 4.87 4.54 5.53
11.69 10.25 8.22 7.19 6.00 6.57
0.000331 0.000906 0.00110 0.00224 0.00327 0.00545
13.7 49.3 88.2 280.6 642.4 1516
No. Porous Spheres, 35; No. Solid Plastic Spheres, 70; a V , 0.2992 sq. f t . 73.8 72.6 70.7 69.0 72.0
64.6 64.1 61.7 57.7 58.0
3.84 4.85 5.06 6.57 4.89
12.44 9.91 8.55 7.39 6.28
0.000555 0.00126 0.00177 0.00345 0.00691
18.54 70.6 146.0 481.2 1432
VOL. 52, NO. 12
DECEMBER 1960
1005
10
0.8 06
04
inveitigators Film Phose POI
Syrtem
De Acetis and Thedas v Gaffney and Drew
l01el-01,
liquid benzene-rolicyhc ocid m Gomsm,Thodoa and Hougen gar (10181-011 Hobron and Thodor liquid methyl ethyl ketone-voter Hobron ond Thodor gas loluane-carbon dioxide A M C C u n l ond Wllheim ilquld ~-nophihol-wO1ei 4 Wlike and Hougen wmer-oii
*+
u, Superficial Air Velocity, ftlsec R e , =DpG
P Figure 4. Mass transfer factors obtained in this study are compared with values of previous investigations
age value of 1.65. This difference in ratios results from the deviations of the individual points, particularly those in the low Reynolds number region. The ratio j J j d = 1.51 resulting from Equations 3 and 4 is recommended. Comparison of Results
Experimental j , factors are limited to those previously reported (7, 5, 6)i.e., for modified Reynolds numbers above Re,, = 6 0 . I n each of these investigations, a different experimental technique was utilized. In Figure 3, the j, factors produced from these studies are compared with the results of the present study. The direct surface temperature measurements of this investigation indicate that the surface temperature of the spheres approached the wet-bulb temperature only at high air velocities. This explains the small disparity between the j , factors produced in this study and those previously reported (5). A higher surface temperature would produce smaller temperature differences in the previous work (5). The new heattransfer coefficients would give rise to higher j, factors, which would agree more closely with the results of this study. I n Figure 4, the j, factors resulting from this study have been compared with those of several other investigations (3-5, 7, 8, 70, 73) for systems involving both gas and liquid films. As opposed to the case of the j, factors, the j, factors previously reported (5) are consistently higher than the values obtained in this study. This is because a higher surface temperature would produce a larger driving force and consequently both lower mass-transfer coefficients and j d factors. To determine more exactly the conditions under which the surface tem-
1006
Figure 5. In the evaporation of water from spherical particles, the surface temperature is not necessarily the same as the wet-bulb temperature of the inlet air, unless high air-flow rates are used
perature of the spheres is the same as the wet-bulb temperature of the air, air was passed through a packed fixed bed containing wet spheres, several of which contained imbedded thermocouples. The results indicate that the temperature of the surface steadily decreases with increasing air velocity and approaches the actual wet-bulb temperature of the air at high air velocities. The wet-bulb temperature was measured on the upstream section of the equipment with a thermocouple covered with a wetted wick. From Figure 5, it becomes apparent that the temperature of the wet surface may be considerably different from the wet-bulb temperature of the inlet air unless the velocity of the air through the particles is maintained sufficiently high. For a superficial air velocity, u = 2 . 5 ft. 'sec., or an interstitial velocity of u' = 2,510,482 = 5.1 ft./sec. (corresponding to Re, = 7 0 0 ) , a net difference of 1.5" F. exists between the surface temperature of the wet spheres and the wet-bulb temperature of the air entering the bed. This temperature difference increases with decreasing air velocity. Nomenclature a
= effective surface area of spheres
cp
= heat capacity of air at constant
D,
= sphere diameter, ft. = diffusivity of transferable
per unit volume, sq. ft. 'cu. ft.
D,
pressure, B.t.u./lb.
F G
=
h
=
H
=
j,
=
j,
=
INDUSTRIAL AND ENGINEERING CHEMISTRY
=
" F.
component, sq. ft./hr. volumetric flow of air, cu. ft./hr. superficial mass velocity, 1 b . d hr. sq. ft. heat-transfer coefficient for gas film, B.t.u./hr. sq. ft. ' F. absolute humidity, lb. of water/ lb. of dry air mass-transfer factor, dimensionless heat-transfer factor, dimensionless
k
= thermal
k,
=
M
=
p
=
fib/
=
q r
= =
Re, =
t
=
td
= =
ti t, V
=
u u'
=
p
=
= =
7
=
p
=
conductivity of film, B.t.u./hr. sq. ft. 'F. mass-transfer coefficient for gas film, 1b.-moles/hr. sq. ft. atrn. molecular weight of flowing gas partial pressure of transferable componeni, mm. of mercury partial pressure of nontransferable component, atm. rate of heat transfer, B.t.u.,'hr. rate of mass transfer, 1b.-moles/ hr. modified Remolds number. D,G, /P temperature, ' F. drv-bulb temperature. O F surface temperature of spheres. " F. wet-bulb temperature, F. volume of fixed bed, cu. f t . superficial velocity, ft./'sec. interstitial velocity, ft./sec. absolute viscosity, lb./hr. ft. total pressure, mm. of mercury density, Ib./cu. ft.
literature Cited (1) Baumeister, E. B., Bennett, C. O., A.I.Ch.E. Journal 4, 69 (1958). (2) Colburn, A. P., Trans, Am. h t . Chem. Engrs. 29, 174 (1933). (3) Gaffney, B. J., Drew, T. B., IND. EKG.CHEM.42, 1120 (1950). (4) Gamson, B. W., Ph.D. thesis, University of Wisconsin, Madison, 1943. (5) Gamson, B. W., Thodos, George, Hougen, 0. A , , Trans. A m . h t . Chem. Engrs. 39, 1 (1943). (6) Glaser, Marvin, Thodos, George, A.?. CI1.E. Journal 4, 63 (1958). (7) Hobson, Merk, Thodos, George, Chem. Eng. Progr. 45, 517 (1949). (8) Zbid.,47, 370 (1951). (9) Hurt. D. M., IND. END. CHEM.35, 522 (1943). (10) McCune, L. K., Wilhelm, R. H., Ibid., 41, 1124 (1949). (11) Perry, John H.. Chemical Engineers' Handbook, p. 776, McGraw-Hill, New York, 1950. (12) Resnick, William, White. R. R., Chem. Eng. Progr, 45, 377 (1949). (13) Wilke, C. R., Hougen, 0 . A., Trans. A m . Inst. Chem. Engrs. 41,445 (1945). RECEIVED for review April 5, 1960 ACCEPTED September 16, 1960
