Table V presents heat balances on the actual kiln and the analog model. T h e over-all agreement between actual fuel consumption and corrected fuel for the analog model is quite good, differing by only 6.1Y0-i.e., 179,000,000 us. 168,100,000 B.t.u./hr. T h e actual heat required to burn one barrel of clinker (376#) is 1,180,000 B.t.u.; the analog model gives 1,115,00013.t.u. Nomenclature = heat transfer area, sq. ft./ft. = = = = = = = = = = = = = = = = = = = = =
= = =
= =
clinkerable massjunit length, lb./ft. CaO/unit clinkerable mass, lb./lb. C a O as CaCOsjunit clinkerable mass, lb lb. C o d u n i t clinkerable mass, lb./lb. specific heat of gas. B.t.u./lb. O F. specific heat of burden, B.t u./lb. F. clinkerable mass flow rate (solids only), l b . / h r . gas mass flow rate, lb./hr. nitrogen mass flow rate, lb./hr. burden mass flow rate (solids plus water), lb. /hr. heat transfer coefficient, B.t.u./hr. sq. ft. F. heat of reaction, B.t.u./lb. reaction rate coefficient, l l h r . length of kiln, ft. molecular weight gas mass/unit length, lb./ft. burden mass unit length. lb./ft. nitrogen mass’unit length, lb./ft. oxygen’unit nitrogen mass, lb./lb. rate of combustion’unit nitrogen mass, lb. fuelllb. N2 hr. rate of evaporation unit clinkerable mass, lb. HnOjlb. hr. SiOz/unit clinkerable mass, lb./lb. residence time real time ambient temprrature, R. gas temperature, O R .
T , = burden temperature. R. T , = inside wall temperature, R . T,’ = outside wall temperature, R. O
LV
W‘
= water/unit clinkerable mass, lb./lb. = waterjunit nitrogen mass, lb./lb.
x = (CaO) zSiOz/unit Y
clinkerable mass, lb./lb.
= (CaO) sSiOz/unit clinkerable mass, lb./lb.
Subscripts 1 = gas to wall 2 = gas to solid 3 = inside wall to solid 4 = inside wall to outside wall 5 = outside wall to ambient Acknowledgment
The authors gratefully acknowledge the assistance of B. E. Kester, Daniel Stocker, and R . W. Krueger of the Missouri Portland Cement Co., St. Louis, Mo., in providing data, advice, and counsel. Literature Cited
(1) Allen, J. P., Lyons, J. \V-.. Pit and Quarry 50, 135 (July 1958). (2) Callis, C. F., Van Wazer, J. R . , Cemento-Hormig6n (Barcelona) 21,122 (1955). (3) Gigy, H., Proc. Intern. Symposium on Chem. Cements. 3rd Symposium, London, 7952; Cement and Concrete dssoc., London, 1954, p. 750. (4) Lea, F. M., Desch. C. H., in “The Chemistry of Cement and Concrete” (F. M. Lea. editor), rev. ed.. Edward Arnold Ltd., London, 1956. (5) Lyons, J. W., in “Phosphorus and Its Compounds,” (J. R. Van Wazer, editor, Vol. 11. Chap. 26, Interscience, New York, 1961
(6f~Romig,J.. Kester. B., Rock Prods. 56, p. 64 (May 1953). (7) Satterfield, C. N., Feakes. F., A.I.Ch.E. Journal5, 115 (1959). ( 8 ) Weber. P., Zement-Kalk-Gips 12, 208 (1959). RECEIVED for review February 7, 1961 ACCEPTED September 1, 1961
HEAT TRANSFER AND GAS HOLDUP IN A SPARGE:D CONTACTOR J . R . F A I R , A . J .
L A M B R I G H T , AND J . W . A N D E R S E N
Monsanto Chemical Go., St. Louis, Mo.
The sporged lor bubble) contactor i s gaining importance for gas-liquid chemical reactions.
Design colculations for
the reactor require knowledge o f heat removal rates and gas residence time.
Results o f an air-water study carried out in
cornmerciol-scale equipment up t o 42” diameter are presented. Heat transfer and holdup data are correlated against gas rate and vessel geometry.
Above 18 inches, vessel diameter
does not influence Cleat transfer or holdup.
Perforated
baffles increase holdup significantly, and reciprocating movement o f the baffles increoses holdup still further.
Holdup
and heat transfer dattr for bubble-agitated vessels are found t o be similar to those for vessels agitated by stirrers operoting a t moderate speeds.
THE
SPARGED COXTACTOR, in which a gas is bubbled through a liquid, is frequently used in chemical processing. T h e contactor is usually a simple affair-a vessel of liquid with a gas disperser a t the bottom. Because of this simplicity, overdesign has not been expensive and there has been little incentive to develop procedures for precise sizing of the equipment components. Increased interest in gas-liquid reactions has brought about a need for more precise design methods. Many of these reactions, such as liquid-phase oxidations and hydrogenations, are highly exothermic and rates of heat removal are therefore critical. Recognition of the interphase mass transfer limitations of such rapid reactions has also suggested a need for predicting dynamic gas holdup. This article is concerned with these two considerations in the over-all sparged contactor design process-Le., heat transfer and gas holdup. Other considerations, such as mass transfer and liquid mixing, are outside the scope of the work.
VOL.
1
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JANUARY
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33
Table 1.
Perforated Baffles for Vessel A Hole Diameter, Inch 0.125 0.187 0.246 0.250 0.312
BajYe Xo. 1-4 5-8 9-1 2 13-1 6 17-20
Open Area.
% 9.5 21.4 21 . o 21.6 33.0
Experiments were carried out in commercial scale (18-inch and 42-inch diameter) contactors, using the air-water system. Data were collected on gas holdup and on heat transfer from jacket and vertical tube wall surfaces to the gas-liquid mixture. Internal perforated-plate baffles were used in some of the experiments, and tests were made with and without movement of the baffles. The data were compared with bench-scale information to determine empirical scaleup factors. Experimental Work
Equipment. Two vessels were used (Figure 1). Vessel A , 18-inch diameter, was constructed of Plexiglas and provided a 10-foot 0-inch height between base and liquid overflow. For some experiments, an assembly of 20 perforated-plate baffles with 5.5 inches of spacing was suspended in the vessel Hole size and total area varied among the baffles; details are given in Table I. In some of the tests. the baffles were given a rapid (1050 cycles per minute) reciprocating motion; amplitude was inch, and motion was imparted by a horizontal rocker arm actuated by a motor-driven eccentric. Vessel B, 42-inch diameter. was constructed of sheet metal and equipped with large Lucite inspection windows. A 10foot 0-inch height was provided betiveen base and liquid overflow. The vessel contained 42, 1.5-inch O.D. aluminum tubes arranged in two concentric circles of 38.5- and 34.5-inch diameters. For heat transfer studies in A , a copper section. 18-inch I.D. X 6 inches high X l / 2 inch thick. was inserted a t the center of the vessel. This section formed a part of the inside wall of the vessel and was heated by Chromalox strip heaters. The temperature of the copper section was measured by eight thermocouples imbedded at various points.
Air, Out
Air Out
For heat transfer studies in B , one of the vertical tubes was replaced by a copper tube, 1.5-inch O.D. by 9.08 feet long containing a 3.7 kw. Chromalox heating cartridge immersed in oil. Koroseal pipe fittings were used to insulate the ends of the tube. Nine thermocouples were imbedded in the tube wall at three levels. Thermocouple probes were attached to 26 guide wires and could be moved vertically to cover the aerated liquid from 5 inches to within inch of the tube wall. Experimental Method. Water flow (10 to 13 g.p.m.) was metered and distributed to the base of the vessels: in A through radial slots in a ’/?X 4 inch pipe nipple, and in B through a sparge ring 18 inches in diameter having perforations facing downward. Air flow was metered and distributed to both vessels through a sparge ring 9 inches in diameter. (For A , the sparge ring contained 47 X 0.020-inch upward orifices; for B. the orifices were enlarged to 0.030 inch.) Gas holdup was determined by actuating quick-closing valves on the inlet water and air lines. Such determinations were made only after equilibrium was established, and gas holdup was taken as the “shrinkage” in volume after residua! air bubbles had escaped. Thus, for all runs the “aerated” height was 10.0 feet (10.5 feet for heat transfer runs in the 18inch diameter unit). Heat transfer rate was determined conventionally. Heat input was calculated from voltage-amperage readings and checked against temperature rise of the flowing air-water mixture. Temperature distribution in the vessels was determined by thermocouple probes: in B. these probes were mounted on guide wires to obtain vertical profiles as well as horizontal profiles based on measurements at 1.O-inch increments from the tube surface. The driving force was taken as the temperature difference between the heating surface and the outlet liquid temperature. (For all runs with gas flow temperature was found to be uniform throughout the vessel.) Results
Flow Behavior. In both vessels, stable bubbles were formed within 1 to 2 feet of the disperser. Most of the bubbles were in the l 1 1 6 - to 1,!4-inch size range. Bubble travel was essentially vertical, but temperature measurements indicated a high degree of back-mixing in the liquid phase, even with baffles in place. At superficial air velocities above 0.20 foot per second, ”particulate” bubbling tended to give way to a turbulent contacting action wherein definition of bubble action was difficult. (In this article, “superficial velocity” is based on volumetric gas flow divided by total cross section of the vessel.) Gas Holdup. Holdup of gas in a sparged contactor is important in determining residence time and interfacial area for mass transfer. Accordingly. holdup was measured for most of the experiments covered by this report. If Z L is the clear liquid height and Z , the expanded “aerated” liquid height. gas holdup is
z,=
8, -
ZL
Average fractional gas holdup is e=-
2, - ZL Zf
Water in
Air in
Figure 1. The experimental equipment was large enough to simulate commercial operation Vessel A, 1 8-inch diameter Vessel E , 42-inch diameter
34
X 10 feet 6 X 10 feet 0
inches inches
l & E C PROCESS D E S I G N A N D D E V E L O P M E N T
Local values of 6 can vary somewhat Lvith height, depending upon disperser design and upon opportunities for bubble contact and coalescence. In the present work, there was little height-dependence of holdup. Figure 2 shows results of holdup measurements made on the 18- and 42-inch vessels. .Also shown on this figure are the
!i-
Bi
Columns /4"
Column (Ref. 6 )
l'//12'o
/
/42"
Columns
(Flg. 2 1 I-
o
- 42" Vessel
--I
0
V
2U
18" Vessel Foust a1 (Stirred 9? Vessel)
a I
0.10 SUPERFICIAL GAS VELOCITY, fVsec
0
1
0.20
~
I
0
0.20 SUPERFICIAL
GAS
VELOCITY, ft/sec
Figure 2. Holdup varies directly with gas rate and compares well with that obtained in stirred vessels
Figure 3. U p to 18 inches, vessel diameter significantly affects holdup
limits of holdup values obtained by Foust. Mack. and Rushton ( 7 ) for the air-!rater system in a stirred 8-foot 0-inch diameter tank. These authors used a clear liquid height of 6.35 feet and a 20-inch diamei:er, 10-blade disperser rotating in the 150- to 200-r.p.m. range. For this particular comparison, representative of commercial practice. holdup in the sparged vessels coxpares \vith that for the stirred vessel. I t ivould be possible. of course. to increase gas holdup in the latter by increasing energy input to the stirrers. The holdup values i n Figure 2 appear to be independent of vessel diameter. Figure 3 shoivs comparative air-water data of Shulman and 5lolsiad (6) for 2- and 4-inch vessels. Also sho\vn are data obtained by the authors in glass laboratory columns using fritted-qlass dispersers. \Val1 effects in small vessels increase holdup: this has been confirmed by the present authors in numerous laboratory tests using conventional fritted-;lass dispersers. So long as gas is adequately dispersed. and for systems resembling air-water, the holdup data
for the 18- and 42-inch vessels should be applicable for plant design. Figure 4 shows the effect of baffles on holdup in the 18-inch vessel. The baffles increased holdup by some 40 to 507, in the gas flow range covered. Movement of the baffles (';'*-inch stroke. 1050 cycles per minute) further increased the holdupby some 23 to 307, over the stationary case. as sho\vn in Figure
5. Heat Transfer. Exothermic gas-liquid reactions carried out in sparged contactors necessitate means for heat removal. Other operations, such as gas absorption, may also create heat dissipation problems. Commonly. this heat is transferred either to tubes within the sparged zone. or to the walls of the vessel. Studies were made of heat transfer from the wall to the contents of the 18-inch vessel and from tubes to the contents of the 43-inch vessel. The direction of heat flow was purely for convenience: since electrical heating \vas used.
0.40
cn 0.20
1
I
1
1
0 S U P E R F I C I A L GAS VELOCITY, ft/sec
Figure 4. Close-fitting perforated baffles increase gas holdup
I
0.40
0.20 SUPERFICIAL GAS V E L O C I T Y , ft/sec.
Figure 5. Imparting a reciprocating motion to the baffles further increases h o l d w VOL. 1
NO. 1
JANUARY
1962
35
-This work, 42" This work, 18" + Kolbel &pI, I 7.6" 0
I
,
O1
I
0.10 SUPERFICIAL GAS VELOCITY, fWsec.
I
-
IO0
0.005
0.20
0.05 0.10 SUPERFICIAL GAS VELOCITY, ftdsec.
0.01
0.50
Figure 6. The moving baffles also increase heat transfer r a t e
Figure 7. For the air-water system, heat transfer rate a p pears to b e a simple function of gas velocity
Film heat transfer coefficients for the 18-inch vessel are shown in Figure 6. Results are shown for both stationary and moving baffles; movement increases the transfer rate by some 10 to 15%. Even a t low gas rates, liquid mixing was quite good, and liquid temperature was uniform in the vicinity of the heater. (In a typical case, aerated liquid temperature over a distance of 0.5 to 5.0 inches from the tube surface showed a uniform radial temperature of 6.0 + 0.1' F. below the tubeall temperature.) At zero gas flow, however, there \vas both nonuniformity of liquid temperature and absence of turbulence at the boundary layer. The low coefficients under this condition, while in the expected range, are not based on a reliable temperature driving force and must be considered approximate. Coefficients for the 42-inch vessel are shown in Figure 7. Measured temperatures of the gas-liquid mixture showed complete uniformity both vertically and radially to within 1 inch of the heating surface. This was indicative of the very large degree of liquid backmixing that is typical of sparged contactors. Data for the 18-inch vessel are included in Figure 7. The data of Kolbel and others ( 4 ) published after the present work was completed, have also been added to Figure 7 to show further the effect of vessel diameter. The equation of the line representing all the data is
agitation does not greatly increase heat transfer rates in sparged vessels. Bubble action itself is sufficient to agitate the liquid film at the heating surface.
Gas holdup in sparged contactors baaries direcrl\ \\ith superficial gas rate, is less in large equipment than in small. but in vessel sizes of 18 inches and larger is not influenced by vessel diamete1. Perforated baffles in the contactor increase holdup significantly, and movement of the baffles provides some additional holdup. I n general, holdup appears to be about the same as for stirrer-agitated vessels at moderate stirrer speeds. Heat transfer coefficients between the gas and heating surface are high and vary directl) with superficial gas rate. Baffles in the vessel do not appear to influence heat transfer. except \\hen they are in motion; then they increase the transfer rate. As in the case of gas holdup, heat transfer rates for bubbleagitated vessels are comparable with those for stirrer-agitated vessels. Acknowledgment
The authors wish to acknowledge the assistance of H. B. Jankowsky in the experimental phases of the work.
1200 UsQ.22
h
=
h
= film coefficient, B.t.u./hr.-ft.20 F.
where
Us = superficial gas velocity, ft./sec. Neither vessel diameter (over 8 inches) nor type of heating surface appears to influence heat transfer rates. The results in Figure 7 are intended to elucidate effects of flow and geometry variables. For systems other than air-water, reference should be made to recent publications by Kolbel and coworkers (2, 3 ) . The work of Rushton, Lichtmann, and Mahony (5),carried out in equipment of comparable size, shows that mechanical
36
Conclusions
I&EC PROCESS DESIGN AND DEVELOPMENT
literature Cited (1) Foust, H. C., Mack, D. E., Rushton, J. H.. IKD.ENG.CHEM. 36, 517 (1944). (21 Kolbel. H.. Borchers., E.,, Martins,. J.,. Chern. Iiw. Tech. 32, 84 I
,
'(1960). (3) Kijlbel. H.. Borchers, E., Muller, K., Ibid., 30, 729 (1958). (4) Kijlbel: H., Siemes, \V., Mass, R., Muller. K., Ibid., 30, 400 '
(1958). (5) Rushton, J. H., Lichtmann, R. S., Mahony, L. H., IND.ENG. CHEM. 40, 1082 (1948). (6) Shulman, H. L.. Molstad, M. C., Ibid.: 42, 1058 (1950).
RECEIVED for review hiay 10, 1961 ACCEPTED September 11, 1961
