Literalure Cited
(1) Andersen, A. E., Phillips, E. M., Hydrocarbon Process. Petrol. Refiner 43, No. 8 , 159 (1964). (2) Bainbridge, G. S., Sawistowski, H., Chem. Eng. Sci. 19, 992 (1964). (3) Berry, V. J., Koeller, R. C., A.Z.Ch.E. Journal 6, 274 (1960). (4) Colburn, A. P., Znd. Eng. Chem. 28, 526 (1936). (5) Deaton, W. M., Haynes, R. D.,- Petrol. Refiner 40, No. 3, 205 (1961). ( 6 ) Donham, W. E., Kay, W. B., Chem. Eng. Sci. 4, l(1955). (7) Durbin, L., Kobayashi, R., J . Chem. Phys. 37,1643 (1962). (8) Harriott, P., Can. J . Chem. Eng. 40, 60 (1962). (9) Harriott, P., Chem. Eng. Sci. 17, 149 (1962). (10) Harrison, S. A,, Master’s thesis in Chemical Engineering, University of Delaware, Newark, Del., 1965. (11) Hunt, C., Hanson, D. H., Wilke, C. R., A.Z.Ch.E. J. 1, 441 (1955). (12) Perry, J. H., “Chemical Engineers Handbook,” p. 18-6, McGraw-Hill, New York, 1963. 113) Prince. R. G. H.. Chan,, B.,. Trans. Znst. Chem. Eners. - (London) 43, T49 (1965). ’ (14) Schnaible, H. W., Smith, J. M., Chem. Eng. Progr. 49, Symp. Series No. 7, 159 (1953). (15) Schemilt, L. W., Espen, R., Mann, R., Can. J . Chem. Eng. ‘ 37, 142 (1959). (16) Slack, W. H., Master’s thesis in Chemical Engineering, \ - - I
University of Delaware, Newark, Del., 1964. (17) Slattery, J., Bird, R., A.Z.Ch.E. J . 4, 137 (1958). (18) Smith,. B. D., “Design of Equilibrium Stage Processes,” p. 545, McGraw-Hill, New York, 1963. (19) Zbid., p. 496. (20) Smith, J. M., Van Ness, H. C., “Introduction to Chemical Thermodynamics,” p. 359-64, McGraw-Hill, New York, 1959. (21) Smith, R. B., Dresser, T., Ohlswager, S., private communication, Feb. 23, 1966. (22) Smith, R. B., Dresser, T., Ohlswager, S., Hydrocarbon Process. Petrol. Rejiner 42, No. 5, 183 (1963). (23) Smuck, W. W., Chem. Eng. Progr. 59, No. 6, 64 (1963). (24) Thomas, W. J., Shah, A., Trans. Znst. Chem. Engrs. 42, T71 (1964). (25) “Tray Efficiencies in Distillation Columns,” Final Report of University of Delaware to A.1.Ch.E. Research Committee, American Institute of Chemical Engineers, New York, 1958. (26) “Tray Efficiencies in Distillation Columns,” Final Report of North Carolina State College to A.1.Ch.E. Research Committee, American Institute of Chemical Engineers, New York, 1959
(27) Treybal, R., “Liquid Extraction,” p. 504, McGraw-Hill, New York, 1963. (28) Zuiderweg, F. G., Harmens, A,, Chem. Eng. Sci. 9, 89 (1958). RECEIVED for review January 13, 1966 ACCEPTED July 11, 1966
LONGITUDINAL MIXING IN ORIFICE PLATE GAS-LIQUID REACTORS KENNETH 6 . BISCHOFF AND JAMES 6. PHILLIPS’ Department of Chemical Engineering, The University of Texas, Austin, Tex.
Residence time distribution data were obtained in orifice plate gas-liquid reactors for different plate designs and lengths, Both holdup and mixing information was determined from the data and correlated with that of other investigators. Short tubes had somewhat different characteristics than long ones, and plate design seemed to affect holdup mare than mixing. All of the reactors had more intense mixing than that obtained with single-phase liquid flow and thus would not give a very close approach to plug flow conditions.
Ottmers and Rase (9) proposed the use of multiple orifice plate contactors as a n alternative to stirred tanks for gas-liquid chemical reactions. They discussed several practical advantages such as the lack of moving parts in the reactor. Another important point was the possibility that the flow patterns in the orifice reactor could be made to approach plug flow rather than perfect mixing, as is the case in stirred tanks. Plug flow is definitely preferred for certain types of reactions, particularly those with side reactions making unwanted products (6). From motion picture studies, Ottmers and Rase found that a single large hole in the center of a n orifice plate produced a long jet of highly dispersed mixture in the center of the column along with considerable backmixing along the walls. With 16 small holes with the same fractional free area, a more uniform flow was observed with a finer scale of turbulent motion. O n the basis of these qualitative observations, they concluded that plate designs with one or 16 holes would tend to perfectly mixed or plug flow conditions, respectively. Mass transfer data from Ottmers and Rase (9),however, showed little difference among the various types of plates. Since a relatively small amount of mass transfer occurred in a pass through the column, this could not be used to indicate clearly any quantitative differences between the flow patterns ECENTLY,
1
416
Present address, Humble Oil and Refining Co., Baytown, Tex. I h E C PROCESS D E S I G N A N D DEVELOPMENT
for the plates. The motion picture studies used a very much smaller gas velocity than that found useful for mass transfer, which also makes comparative interpretations difficult. The purpose of this investigation was to delineate the types of flow patterns existing by means of residence time distribution (RTD) studies using tracers. Previous Work
There has been very little previous work on RTD in cocurrent gas sparged tubular reactors of any type. Siemes and Weiss (74) presented data for a 1.65-inch tube. More recently, Argo and Cova (7) considered backmixing in 1.8-, 4,and 176/s-inch vessels under various conditions. The above works (and this one) were concerned with the “bubble flow” regime (72). Tracer data for “annular” flow (72) in helical coiled tubes have been given by Rippel, Eidt, and Jordan ( 7 7 ) but are not directly applicable. Countercurrent bubble flow RTD information has been presented by Tadaki and Maeda (75). Information on longitudinal mixing for two-phase flow in packed beds is available and some work has been done in other geometries such as distillation column plates. These studies c a n serve as guides to experimental procedures and give orders of magnitude of the mixing effects. Some of the work is summarized by Levenspiel and Bischoff (7).
Theory
AIR OUT
Previous investigators interpreted their mixing data in terms of the axial dispersed plug flow model with a n effective diffusion coefficient, DL. With gross flow patterns such as those visually observed by Ottmers and Rase (9) a t low gas velocities, this model would probably not be appropriate. At higher practical flow rates, however, there is intense local turbulence and the diffusion model type basis is probably closer to the actual physical behavior. One complication is the "decay" of the turbulence downstream from the plate, which means that the dispersion coefficient should properly vary with the length. This enormously complicates the model if taken into account and usually a constant D L is used, even though it may be a function of the length-diameter ratio of the vessel. This procedure is followed here for simplicity in applications. The liquid phase mass balance, then, is
AIR WIRE MESH WATER
A L L WATER SIPHON BREAKER
u
WATER
[ ,-8RASS
AIR a u a a L E s
1I
NIPPLE
PROBE
SAMPLE
DRAIN
a
RU0BER STOPPER
PLASTIC
---
TO DRAIN
ELECTRIC LEADS
2 nd SECTION ( 6 INCH)
TO RECORDER
P L A T E POSSIBLY h E R E
12 " COLUMN
AIR
R A T E POSSIBLY HERE
NEEDLE VALVE
I st SECTION
JwATER
T
TRACER INJECTION POINT
ROTAMETER
BLEED
ROTAMETER ilR+@
NEEDLE VALVE WAJER
where c l is the observed liquid-phase tracer concentration. T h e over-all properties of R T D functions are well known (7). A convenient way to obtain the axial dispersion coefficient from the R T D is by comparing the measured variance and the model variance found from solving Equation 1. Depending on the exact end conditions assumed, a variety of formulas for the variance from the axial dispersion model (Equation 1) may be found, but all of them approximately reduce to g2
D UL
= 2 L-
The method of using variances was particularly useful here, since the gas-liquid disengaging section had a fairly large effect (-20%) on the total mixing observed and corrections for this had to be made. This can be done by measuring the R T D of just the injection, disengaging, and probe sections alone and subtracting its variance from the total (7), UZc,renetor
=
U2t,total
- QZt,ends
(3)
Equation 3 assumes statistical independence between the various sections, which usually is satisfied reasonably well in practice. The subtraction must be done in dimensional units in order to have all variances on the same basis. T h e liquid holdup can be found from the mean of the R T D curve, f from el
U,i
= -
L
"
WATER CONTROL VALVE
Figure 1.
Flow diagram of experimental equipment
in a vertical position, such that the air and water passed upward cocurrently. The actual mixing part of the columnthe part which contained the plate(s)-sat on a 1-inch i.d. glass tee. Water was admitted through the side leg of the tee and air through the bottom of the tee. A 3-mm. diameter tap was located 1.5 inches from the end of the tee that joined to the actual mixing column, and was used for injection of the tracer. The glass tee was joined to the mixing column by a neoprene gasket and aluminum flanges. The orifice plates had the extremes of either one hole (I/dinch diameter), or 16 equally spaced holes ('/lC-inch diameter), as shown in Figure 2. These plates were '/a .inch thick and made of brass. TRACER FLOWSYSTEM.T h e tracer flow system consisted of an injection device, an injection point, and a sampling point. Potassium chloride was chosen for the tracer, mainly because it had a linear relationship of conductivity and concentration over a much wider range of concentrations than was needed in I CENTERED 114" DIA HOLE
(3)
since the actual flow velocity appears in i. These values were checked by the classical flow stopping methods, with good agreement. Experimental Details. The apparatus used in this research may be broken down into three important parts: the orificeplate column, the tracer flow system, and the measuring system. These components and their relationship with one another are shown in the over-all diagram of Figure 1.
ORIFICE-PLATE COLUMN.T h e orifice-plate column was the same as that of Ottmers and Rase ( Q ) , but modified for this work. T h e sections which made up the column were 1-inch i.d. borosilicate glass pipe which could be joined by aluminum flanges. Neoprene gaskets, ' / 8 inch thick, separated glass from glass. T h e lengths of glass pipe available were 6 and 12 inches. Thus a column which was 6, 12, or 18 inches long with either one or two plates was possible. T h e glass column was mounted
NEEDLE VALVE
WATER DRAIN FOR COLUMN WATER AFTER SHUTDOWN
-2
318"
-
/"\ I 6 E Q U A L L Y - SPACED I /16" D I A H O L E S
Figure 2.
Designs of orifice plates
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417
this work. A 5-cc. Vim metal tip interchangeable syringe with an 18-gage needle was used to inject the tracer solution into the column. The syringe had sufficient friction on the plunger to prevent the plunger from being forced back by the pressure in the column. In order to inject the tracer by means of the syringe, a 3-mm. tap was placed in the side of the glass tee, located 1.5 inches from the top of the tee; this small distance was needed to provide time for radial gradients to disappear as visually checked by injection of potassium permanganate. An approximate material balance indicated that any sample withdrawn from the column would be representative. A circular piece of rubber septum was placed over the opening of the 3-mm. tap and was held to the opening by wrapping plastic tape around both the rubber and the glass tee. A piece of ordinary rubber was then stretched over the plastic tape and around the glass tee and wired into place. I n this manner, an injection could be made into the column and then the needle withdrawn without water leaking out through the puncture. Approximately 40 injections could be made before the rubber septum had to be replaced. T o withdraw a continuous sample a piece of ‘/l-inch copper tubing was inserted concentrically with a 5/8-inch brass nipple located a t the beginning of the column discharge. The tubing was flared on the end to ensure a more representative sample. Before the conductivity of the liquid could be measured, all air had to be removed. Therefore, a disengaging system was employed (Figure 1). Using more copper tubing and rubber tubing, the sample line was placed in the disengager, a 6-inch section of 1-inch i.d. glass pipe, by means of a rubber stopper. Copper wire mesh placed 11/4 inches from the rubber stopper helped disengage the air from the liquid. Another short piece of copper tubing in the rubber stopper served as a drain from the disengager. A liquid level of about inch was maintained above this drain line. This disengaging system was the best result of many designs tried and was believed to have as little effect on the mixing as was possible. MEASURING SYSTEM.The measuring system consisted of a flow-through conductivity cell. a continuous-reading conductivity meter, and a recorder. The conductivity cell was provided with three electrodes; the middle one was electrically shielded from the interconnected outer ones. The conductivity meter was a Radiometer, Type CDM2, which used a highly stable a x . test voltage. A frequency of 3000 cycles per second a.c. was applied a t specific conductivities above 150 micromhos per cm. to minimize errors caused by polarization, whereas below 150 micromhos per cm. a frequency of 70 cycles per second was used to prevent errors due to the capacitance of the cell leads. Even though the meter deflection was essentially instantaneous and easily read, the rapidity of the pulse required continuous recording of conductivity. The recorder was an Offner Type RS 2-channel Dynograph with a curvilinear inkrecording medium. Operating Procedure. The operating procedure consisted of two parts: the setting of the flow conditions and the injection of tracer and subsequent measurement. The flowthrough conductivity cell, or probe, was kept in distilled water when not in use. Just before a set of runs was started, the probe was attached to the outlet of the disengaging system and to the drain line and the conductivity meter was warmed up. Next, the water and air flows were started and the pinchclamp on the discharge side of the probe adjusted so as to set the height of liquid in the disengager a t a constant value. The conductivity meter was then grounded and the probe attached. Approximately 0.2 cc. of tracer was injected in each run. At the instant of injection, a stop watch was started. After the curve had been tested, the watch was stopped and the point of the stylus on the recorder graph paper was also marked. In this manner the time scale for the tracer curve was established.
equipment and were in the so-called “turbulent” or bubble coalescence region. Both air and water rates were varied, to check the effect of these variables. Other types of information besides mixing data resulted from the study. The gas and/or liquid holdup was calculated for the different plates to see the effect of the design. I t could also be found as a function of length-diameter ratio by using sections of different lengths. This permitted comparison of the region close to the plate with the free motion further downsueam. Holdup. The holdup values were calculated as discussed above. Values for successive 6-inch sections could then be found by difference between 12- and 6- and also 18- and 12inch tubes (Figwe 3). Lines were drawn through the data points for clarity, although the precision of the data actually does not warrant this. The holdup increases along the tube for both the one- and 16-hole design plates. Some data a t the same gas flow rate in nonmoving liquid from Braulick, Fair, and Lerner (2) are also shown and follow a similar trend. The two plate designs seem to produce different levels of holdup. There are few detailed data for similar situations in the literature. A study of foams and froths on sieve plates with about 6-inch liquid levels a t relatively high gas velocities by Calderbank and Rennie (4) gave values of the same order but with a larger spread between different plate designs. A more extensive comparison of the present data with those of previous investigators is shown in Figure 4. The closest similar type of cocurrent systems was studied by Argo and Cova ( 7 ) ; the long tube data tend to coincide with theirs. They found little effect of liquid flow rates in the ranges of interest, as was true in the present investigation. Some recent data of Yokota (77) for horizontal cocurrent conditions showed some variation with liquid flow rate and the range of values is plotted on the figure. Also shown on Figure 4 are the stagnant liquid data of Braulick, Fair, and Lerner ( Z ) ,
0.6
Ug = 0.40 ft./sec.
U, = 0.94 ft./sec.
z
0.5
I
I I
I
I
0.4 w!
0.3 0.2
0.1
0 I
2
3
SIX INCH SECTION Results
Scope. The major purpose of this work was to compare the mixing with the different plate designs described above. The flow rates were chosen to be close to those for optimum mass transfer as found by Ottmers and Rase (9) in the same 418
I h E C PROCESS D E S I G N A N D DEVELOPMENT
Figure 3.
Gas holdup in local sections 0 1 hole -0-
-&
16 holes l/d = 4 (2)
l/d
= 7 (2)
0.5I
1
0
1.0
HUGHMARK CORRELATION
Y
‘/ 0
/
I
0 0.2
0.6
0.4
0.8
1.0
1.2
@’
Up ,ft/sec. @’
Figure 4.
Gas holdup
Curve
0
A
1 2
X
3 4
5 6
7 8 9
Short ( 6 inches), 1 hole Long (1 2, 1 8 inches) 1 hole Short ( 6 inches), 1 6 holes long (1 2, 1 8 inches), 1 6 holes Cocurrent ( I ) Stagnant liquid (2) Countercurrent ( 1 5) Countercurrent ( I 8) Cocurrent [horizontal (1711
and some countercurrent data of Tadaki and Maeda ( 7 5 ) and Yoshida and Akita (78) for several liquid flow rates. T h e fact that all of these are similar indicates that liquid flow rate is not a very important variable. Most of the standard correlations consider long tube data in order to avoid end effects. T h e present data along with those of Argo and Cova (7) were recalculated on the basis of the correlation of Hughmark ( 5 ) , who used the Armand type equation (72),
where K is theoretically a constant with the value, K = 0.83. Many data give different values (as does the present work) and Hughmark correlated K with a Reynolds number, a Froude number, and the volume fraction of liquid fed, but in Figure 5 it is seen that there is not very good agreement. Scott (72) argues that the very small exponents used in Hughmark’s correlation make it not very meaningful and the value of K = 0.83 = constant is preferable, but this does not fit the existing data. Argo and Cova’s values also show a n effect of vessel diameter not accounted for by the correlation. The data used by Hughmark, are mostly for values of the abscissa greater than 10.0 and in the present range of interest have considerable scatter. Thus the Hughmark correlation is not entirely reliable for the types of reactors investigated but the holdups for long tubes can be estimated from Figure 4, putting more emphasis on the vertical cocurrent lines. Further work is needed to define the situation completely, especially for short vessels. Mixing. The conductivity readings for the impulse response were processed by well known methods (7) to yield the dimensionless R T D curves and their means and variances. All calculations were performed on T h e University of Texas
0.I
Figure 5.
Hughmark (5) data
Present dat(’J A 1-hole plate X 16-hole p l ~ i t e Argo and Cova ( 1 ) data 0 1.835-inch diameter -04.0-inch diameter I -017.63-inch diameter, 750 p.r.i.g. I 17.63-inch diameter, 1 5 0 0 p.s.i.g.
‘4 \/
Computation Center digital computer. An example of an R T D curve is shown in Figure 6 along with the internal age distribution, I(B), and the intensity function, h(B), recently proposed by Naor and Shinnar (8). The latter gives a measure of “stagnancy” (bypassing on dead space), in that if the h(0) curve has any maxima or minima, stagnancy exists. This is not the case for the present system (Figure 6). T h e RTD curve does not have exactly the right shape to be fitted by the axial dispersion model, which would have been expected from the earlier discussion. However, the comparison is not too bad and, for simplicity, we retain the model. T h e dimensionless variances, corrected for probe effects, were determined for all runs by numerical integration (70) and from these the length Peclet numbers, v L L / D L were , calculated. T h e end effects were determined for each set of flow rates, but they did not vary greatly. To check the accuracy of the system, three runs were made with only water flowing and with no plates in the column. Existing data and theory for this case (7) could then be compared with the present experimental results. A problem in this is that the mixing is very small and the corrected variance results from the difference between two large numbers and is thus not very precise. Within this limitation, the comparison with other investigators was satisfactory. Because of the much larger mixing effects with two-phase flow, this precision problem was not as severe for the other runs. Figure 7 shows the detailed mixing coefficients in the orifice plate apparatus for the different sections. Lines were drawn VOL. 5
NO. 4
OCTOBER
1966
419
again through the points for clarity. The points for the second and third sections were calculated by using data from columns of different length. I n other words, the variance in the second section was found by difference between the variances of 12- and 6-inch lengths, and similarly for the third section. As expected from visual observation, the mixing is most intense close to the plate and decreases downstream in the column. Thus, the mathematical model should properly use a length variable DL,but this would complicate things enormously and for practical applications a n over-all length average value will probably have to be used. This is probably satisfactory, since a simple one-plate column would usually be
T
- I PLATE I HOLE 18 INCH HEIGHT.
,
for a 6-inch column. For reactions requiring plug flow for optimum conditions, this is a n improvement over a stirred tank but still not close to ideal plug flow. The present data are compared with those of other investigators in Figure 8. The simple liquid-phase inverse Peclet number of Figure 7 , DL/uLdt, could not be used in general, since Siemes and Weiss (74) had no liquid flow. Since the intense mixing over single-phase flow obviously is caused by the presence of the gas flow, a Peclet number based on the
I
I
0.94 FT/SEC WATER RATE 0.40 FT/SEC AIR RATE
2 .o I.0 Q
1.6
v
1.4
2
1.2
-4
- .o w
A ‘
m
E.
rather long and most of the reactor would have the asymptotic “long tube” mixing level. If the multiple orifice plant concept of Ottmers and Rase (9) were used, a more detailed study as a function of length would be required. T o check the application of the “short tube” values in a multiple plate reactor, 12-inch sections with two plates, or thus two 6-inch sections in series, were tested. The mixing in each section was identical to that of the 6-inch reactor for both one- and 16-hole plates. The degree of mixing with either type of plate is relatively intense, about 2 to 3 times that for single-phase liquid flow, and gives length Peclet numbers of the order of (at ug = 0.4 foot per second)
IO
I
.a
/
.6 .4
.2
0
.2 e
Figure
6. Example of a g e distribution curves
9 t
ug =
P-I
0
a
0.40ft/sec.
U I = 0.94 ft/sec.
=
2.0
.-0
. I -
u
I . %
0
I
++ 0.I
I
2
Figure 8.
Mixing in local sections
0 1 hole 16 holes
_-_
Only liquid flow, Rei = 7300
Ug ’Vt
3
SIX INCH SECTION Figure 7.
0
0. I
I
6
(7)
l&EC PROCESS D E S I G N A N D DEVELOPMENT
-+-
A X \ /
,0\
Mixing correlations 1 hole 1 6 holes Argo and Cova
(I)
-e Siemes and Weiss ( 1 4 )
liquid dispersion coefficient and the gas velocity was tried, with the reasonable correlation of Figure 8 resulting. Only the “long tube” data were used for comparison with the other investigators. The abscissa was made dimensionless by arbitrarily dividing the superficial gas velocity by the rise velocity for 0.2-to 0.5-cm. diameter bubbles, ut = 0.87 foot per second. This range of bubble sizes was found by Siemes and Borchers (73) to be remarkably prevalent for gas superficial velocities over about 0.5 foot per second and was also the order of magnitude visually observed by Ottmers and Rase. Of course, a t the high end of this range, coalescence begins to occur with eventual slugging of the flow and it is not as clear what to do in this region. Also, the presence of electrolytes has a n effect. T h e numerical value was taken from Calderbank (3), who found that a similar rather arbitrary insertion of u I into a correlation for stirred tanks had some basis, and from Tadaki and Maeda (75). If the fully dimensionless plot of Figure 8 is not desired, gas velocities may be obtained by multiplying the abscissa by 0.87 foot per second. Another feature of the correlation of Figure 8 not completely defined by all the available data is the rather involved behavior a t higher gas velocities. If the individual data points from each of the vessels from Argo and Cova (7) and from the present studies are examined, the indicated type of curve with a minimum is found. The three are not coincident, but since the data of Argo and Cova were taken not only in a large vessel but also a t nonstandard conditions, there may be other complicating effects not well defined as yet. T h e curves also have a shape similar to those for single-phase flow a t the laminarturbulent transition [see (7), for example]. Another feature of the hydrodynamics in bubble reactors observed by Siemes and Borchers (7 3 ) was that the point a t which bubble coalescence began was approximately ‘/3 foot per second, which is the indicated transition point in Figure 8. If this basis is correct, the minimum could be explained by a “hindered” mixing when the bubbles touch each other, which is eventually overshadowed by the large amount of gas. Further work will be required to define this completely. Again, the liquid rate does not seem to have a large effect, since data ranging from zero to velocities larger than the gas velocity coincide. T h e countercurrent data of Tadaki and Maeda (75) and Yagi and Kat0 (76) appear to differ in the coalescing range, although they also found no liquid flow effect. Thus, the mixing seems to be primarily caused by the gas flow in the range of interest, which is the major variable, and the correlation of Figure 8 should permit a n estimation of axial dispersion in bubble reactors: although more data are definitely needed.
Nomenclature = concentration of tracer dl = tube diameter D L = axial dispersion coefficient E(@) . . = exit age distribution or residence time distribution function g = acceleration of gravity, used in Figure 5 I(0) = internal ape distribution function K ’ = empiricalvconstant L = tube length t = time = mean residence time = v / L t u = superficial velocity u = actual velocity = rise velocity of bubbles ut t = axial coordinate position B = void fraction A(0) = intensity function p = density uz = variance = dimensionless time = vt/L 0 c
-
SUBSCRIPTS g 1 t
= = =
gas liquid dimensional time basis
Acknowledgment T h e support of the National Science Foundation through grants NSF GP 865 for part of the work is gratefully acknowledged. Literature Cited (1) Argo, W. B., Cova, D. R., IND.ENG.CHEM.PROCESS DESIGN DEVELOP. 4,352 (1965). ( 2 ) Braulick, W. J., Fair, J. R., Lerner, B. J., A.Z.Ch.E. J . 11, 73 (1965). (3) Calderbank, P. H., Trans. Znst. Chem. Eng. 36, 443 (1958). (4) Calderbank, P. H., Rennie, J., Zbid., 40, 3 (1962). (5) Huahmark, G. A., Chem. Ene. Proer. 58, No. 4, 62 (1962). (6) Leienspiel, O., “Chemical Reaction Engineering,” Wiley, New York, 1962. (7) Levenspiel, O., Bischoff, K. B., Advan. Chem. Eng. 4, 95-198 (1963). (8) Naor, P., Shinnar, R., Znd. Eng. Chem. Fundamentals 2, 278 (1963). (9) Ottmers, D., Rase, H. F., Zbid., 3,106 (1964). (10) Phillips, J. B., M.S. thesis, Department of Chemical Engineering, University of Texas, 1965. (11) Rippel, G. R., Eidt, C. M., Jordan, H. B., IND.ENC.CHEM. PROCESS DESIGN DEVELOP. 5 , 32 (1966). (12) Scott, D. S., Advan. Chem. Eng. 4, 200-73 (1963). (13) Siemes, W.,Borchers, E., Chem. Eng. Sci. 12, 77 (1960). (14) Siemes, LV., Weiss, W., Chem. Zng. Tech 129, 727 (1957). (15) Tadaki, T., Maeda, S.,Kagaku Kogaku (Eng. Ed.) 2, 195 ( 1 9641. \ - -
I -
(16) Yagi, S., Kato, S., from (15). (17) Yokota, T., Kagaku Kogaku 29, 687 (1965). (18) Yoshida, F., Akita, K., A.Z.Ch.E. J . 11, 9 (1965). RECEIVED for review January 14, 1966 ACCEPTED June 8, 1966
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