EngKiring
Gas Mixing in Beds of
Process
Fluidized Solids
development
E. R. GlLLlLAND A N D E. A. MASON MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE, MASS.
U
NITS employing fluidized solids are finding increased applications in the chemical and petroleum industries. From the viewpoint of a chemical reaction, the degree of gas and solid mixing is of considerable importance. Reactors employing fluidized solids give more mixing of the products with the reactants than is usually encountered in packed bed types of units. Generally, this gas mixing is undesirable in t h a t it leads to lowered reaction rate, by-passing of the catalyst, and increased side reactions. The degree to which these factors apply depends on the reaction under consideration. I n the catalytic cracking of petro]cum the conversion per pass seldom exceeds 60 to 70% and a limited amount of by-passing of the feed material is not too harmful. However, in the case of chemical reactions involving high conversion per pass, a small amount of by-passing can be a1mo st prohibitive, Experimental work has been carried out in an attempt t o evaluate the magnitude of the gas mixing in fluidized beds and to determine the factors responsible for the phenomenon. The results should be useful for evaluating the suitability of a fluidized bed for a given application and for interpreting experimental results obtained in such units. The experimental program involved two techniques for studying gas mixing. I n the first, called back-mixing studies, tracer gases were introduced into the fluidized bed and gas samples taken from various positions and analyzed. I n the second, termed resLdence time studies, the solid was fluidized with a mixture of tracer gas and air and the composition of the exit gas from the bed was determined as a function of time after the tracer gas addition was discontinued. The two studiei will be comidered separately.
5-mm. glass tubing. This tubing was bent a t a right angle inside the column so as to inject the gas upwardly in the center of the column. A multipoint injection system was also employed to inject. the helium into the fluidized bed. Stainless steel hypodermic tubes projecting through the walls of the column were held in place by means of leather gaskets; these tubes were enclosed in a Lucite manifold to which helium was fed. Both of the above methods of tracer injection were used in the backmixing studies. The helium feed rate was measured by means of a capillary orifice made of glass.
emc
S
Figure 1. Gas Mixing Apparatus A.
Fluidization eolumn B . Disengaging section C . Cyclone separator D . 200-mesh screen E. Sampling ports F. Injection tube, inside diameter = 0.141 inch G . Capillary orifice H . Sharp-edged orifice J . Pressure taps every foot K. CaClp drying tube M . Gas density balance N. Pressure adjustment bottle P. Mercury-leveling bottle Q. Fine adjustment bellows R. 5:l inclined manometer S. Absolute manometer T. Thermometer 7 w . Wet-bulb thermometer U. Mercury manometer V. Water manometer
BACK-MIXIRG STUDIES
Back-mixing studies have previously been reported by Gilliland and Mason (1) and the results given here are a continuation o€ that work. The unit consisted of a Lucite FLUIDIZATION EQUIPMENT. tube having an inside diameter of 3 inches and height of 6 feet; the walls were inch thick. A schematic diagram of the apparatus is shown in Figure 1. Above the Lucite column was a disengaging section 3 feet high and having a square oross section. It was constructed of Lucite sheets, 1/8 inch thick and 6 inches wide. T o this was connected a cyclone separator, which served to remove solids from the gas stream. These solids were returned to the bottom of the unit. Pressure taps were attached to the side of the column at intervals of 1 foot from the bottom;, the manometers were equipped with stopcocks in one of the liquid legs, so t h s t the pressure fluctuations could be damped. The fluidizing gas, air in all cases, was introduced into the bottom of the column through a conical section and was distributed by II 200-mesh screen; this screen was supported by heavier wire screening having a spacing of about '/z inch. The air was metered before entering the column by means of an orifice plate. Water and mercury manometers indicated the differential and static pressures. According to the experiment that was being conducted, the tracer gas, helium, was admitted to the column in one of several ways. Runs were made in which the helium was injected a t a point 31./2feet from the bottom of the column through a piece of
i
For the back-mixing studies t,he sampling tube was a 0.075inch outside diamekr stainless steel tube soldered axially in a threaded brass rod. By means of a threaded knob on the brass rod, it was possible to position the end of the sample tube accurately to any desired radius. The sample tube projected through holes which were spaced vertically a t 1-inch intervals in the side of the column. Leather gssket,s served to make a gas-tight joint between t.he sample tube and the Lucite. Plugs were inserted in the sample holes when not in use. -MATERIALS.Gases. Air was used as fluidizing gas in all of the work reported here. The compressed air was filtered through a bed of glass wool to remove any entrained material and provision was made for humidifying the air when desired by injecting steam about 100 pipe diameters upstream from the filter. Helium was used as the tracer gas in all the runs made during the course of this work. The primary reason for its choice wa.9 to reduce, as far as possible, the part adsorption would have in the gas mixing. In addition, some of the physical properties OP helium provide for easy analysis of helium-air mixtures.
218 %
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
January 1952
219
other nii,cj.oupheres were bused on bhe rates of settling through w n t e ~ . 1 he particlrs are omus and a heat of adsorption was noticed while determining t i e absolute densit.y by means of water displacement. In v i w of this, the densities listed m a y not he the critical ones EO far as fluidization ia concerned. GASANALYSZS.All gas samples were drawn from the cclunins into Dreviouslv evacuated hulhs. When the em density balance ~, ~
.
oonductivity analyser, the sanipling lino led to a g& sample h o t tle, which was evacuated for sampling and served to mix the aample belore analysis. In both cases, the sampling line WBS purged several times before the final sample was taken. A small plug of knitting yarn filled the end of the sampling tube. This served BS a filter to keep solids out of the samplina and annlytiesl equipmcnt,. The p h g throttled the flow of g G from the colunin, so that the sampling time was about 30 to 40 seconds.
TABLE 11. PROPMWIES ox'A e ~ o c nMICKOSPHERES, ~ MSA Sine Rnnge, Microns
Weight %
Weight Mean Diameter, Miorons
Method of Analysis
Microwherot 1,'. tliiough IC0 mesh
0 25 26-50 51--75 76-105
>lo5
0-10 11-20 21.-30 31~~40
Figure 2.
2.0 20.6 $1.1 46 1 0.2
70
Screening and miCroBDOPe
Mierosc>hcier U. Fines OnlyL R6 17 65.4 21~4 4.6
Rate of nrttiing in water
Photomicrographs of Glass Beads and Miemspheres No. 11 .lass
A. B.
bends
Micmsphsm, M3 MicrwDpheras M 2 . 150-200 Meah
Solids. Two ciifiercot solib were em loyed-sphericrri p1a.s beads and w petrolrum craeljngcstalyiit rejbrred to BS mioroSphWeS. The shapes of both type8 of solids may he seen in Figure 2. The ~IHSS beads w r c H oroduct of the Minuesota Minine and Manuficturing Co. mid -have the trade name of ScoGhlite Glass Heads. roperties are listed in Table I. The avcragr d i a m e t t ~ t e ~closely ~ sized fractions were determined hy Trilline (8). He used Dhotonraohs taken throueh a miorosoope fittea witti a calibrated eyepiice micrometer; ;his method w m checked by micrometer. The average diamcter is tho arittimetie average of R group of about 50 particles. The absolute densit,ies were determined hy water displacement. The microspheres were 9r silics-alumina crackina catalyst
were fluidized for ahout an hour rtt an air &?locity of 1.5 f&t er second; the fines removed in the cyclone were discarded. #he solids remaining in the column were then scrcened into the various size fractions shown. The fractions all contain considerxble quantities of particles larger than the largest openina
Filar miErometer eyepiece and con&ted to weikht per cent by usuming the particles to be spherienl. The size analyses of the
Diameter -...______ 6iM
KO. 7 9 11
13
Ineh Microns 0.017~ 452 0.OloP' 0.0061 0.0040
262 155 102
tion. %
Siae A n a h i s
Abs. Density. .as.. Lb. DBI . Ft.8
6
Mierophotogrnphs
173
Devi*-
7 7 6
MiCiOlnetW
Micrometer Micrometar Micrometer
169 151 151
74 74-104 104-124 124-141 117-208 >208
Y.8 19.9
Mioruaghaiea I1 130
S0ree"ilW
16.6 18.4 a4.7 1.6
In some of the early experiments, the gas a m les were analyzed for helium using an Edwards-type gas density !almce. The a p plaIatUS WBS found to he trouhlesoine and 8 1 0 ~and wu? abandoned xu favor of a thermal conductivity system. A pair of thermal conductivity cells, Leds and Korthrup Model No. 3284-F; were conneoted BS t N 0 of the legs of B Wheatstone bridge circuit,. The oells were suspended in a constant, tempfrature bath. One cell was used BS a standard and was always filled with air; the other cell WBS used for analyzing the unknown air-helium Tmixtures. The bridge circuit was o erated in unbalance under a constant impressed electromotive Ibrce;. the unbalance potential, which was B measure of the helium concentration, wzu determined hy a potentiometer. Drying tubes filled with indicating Drierite (calcium sulfate) served to dry the gas before analysis. A calihrlttion of helium concentration against unbalanced elrctromotive force WBS made by repeated subdivision and dilut,ion of a known volume of helium. The analyzer gave trouble-free operation and proved to he much faster in use than the gas density balance. Each day, before using the thermal conductivity gas analyzer, the zero-point was checked by drawing fresh air from the column into both cells to determine m y drift. This was to prevent any dsmage to the circuit from going unnoticed: in the 7-m0nt.h period in which calibration NM used, the zero-point drift,ed about
220
INDUSTRIAL AND ENGINEERING CHEMISTRY
0.1 millivolt, which corresponds to about o.0370 helium, and is well within the accuracy desired. Once the zero-point had been checked, the standard cell was sealed from the rest of the sampling and analysis t T i n , while the unknown cell was evacuated in preparation for use. All of the studies conducted in the course of this PROCEDURE. work were made using a batch fluidized bed. Any small amount of solid that was carried into the cyclone and there separated from the gas stream was returned through a tube leading to the bottom of the bed. This tube was tightly clamped during the course of any run, so that no gas flowed up the tube, by-passing the fluidized bed; the solids were returned between runs. I n the case of the glass beads, there was no solid carryover, and in the case of the microspheres the carryover during a run was less than 0.570of the total solids present, even in the case of the smallest size fractions. The back-mixing runs were made with the fluidized bed just filling the column. The beds fluctuated in height, because of the passage of bubbles and slugging, and the weight of solid in the bed for any given air velocity was adjusted so that, a t the maximum height of the bed, just a little solid entered the bottom of the disengaging section. This gave a length to diameter ( L / D ) ratio of roughly 24. Once the weight of the solid and the superficial air velocity had been adjusted to the desired conditions, the helium feed to the column was adjusted so that the helium concentration in the exit stream was about 10%.
Typical data for glass be& and petroleum microspheres are given in Figures 3 and 5 . The glass bead data of Figure 3 were obtained with a single point injection system and the multipoint injector was used for the results shown in Figure 5. Considering the glass beads data first, it is noted that helium gas is present for over a foot below the injection point. These data definitely indicate that back mixing of the gas does occur. Above the injection point the concentrations in the center of the tube are very 1
I
I
I
I
I
1
RAb/US ./UVfES
Figure 4. Sample Traverses with Single Tube Injector Using No. 13 Glass Beads
RESULTS
Some of the experimental results obtained in the back-mixing studies are shown in Figure 3. The complete results are available elsewhere (9). In these figures, C is the analysis of 3 SO the gas from the point being studied and Co is based on the analysis of a sample of 3.00 gas drawn from the cyclone separator. This latter value was checked by the stoi250 chiometric values based on the orifice readings. With 2 00 the thermal conductivity system it was possible to 2 c, determine the composition I50 of the gas sample t o within approximately 0.05% helium. This error would lead to IO0 an error in C/Co of about 0.5%. When traverses were made, 0 50 symmetry of mixing about the axis of the column 0 was assumed and in most 0.5' 1.0 RADrus /NCHES cases the samples were withdrawn only along one radius. Figure 3. Sample Traverses with Single Tube Injector Figure 4 shows the values Using No. 11 Glass Beads along four radii a t a given Distances given are above and level, indicating that the below injection level gas distribution is fairly symmetrical. With the small diameter tubing used for the injection of the tracer gas, the superficial velocity of the gas leaving the tube was considerably higher than the superficial velocity of the air in the column. I n a part of the work a 12-point injection system was employed in order to distribute the tracer gas over the whole cross section more uniformly a t the injection level. The results shown in Figure 5 were obtained with the multipoint injection system. Because of the plug of wool in the end of the sample tube, the time of sampling in most cases was about 30 seconds. No attempt was made to keep the time constant from sample to sample. Instead, the sample was drawn until the pressure in the sampling tube was essentially atmospheric. Repeat samples gave values of C/C, checking within 10 t o 15y0.
Vol. 44, No. 1
11 inches above
high owing to the injection of helium in this region. The variation in the concentration across the tube decreases with the distance above the injection point as a result of the cross mixing. The traverses made above the injection point appear to indicate a minimum concentration between the center and the wall. This is due t o the definite circulation pattern within the fluidized bed. The gas has a high upward velocity in the center but is dragged downward along the wall by the circulating solids. Figure 3 shows that a t 12 inches above the injection point all of the samples show a higher gas composition than the analysis of the gas leaving the system. This is more clearly seen in Figure 4. It is obvious that these results cannot be consistent with the
I t
O b
C
G 0.4
0
#
1.2
08
C CO
04
0 0
0 5
10
150
4 5
IO
(5
RADIUS, INCHES
Figure 5. Microspheres Less Fines, D Sample Traverses Number on curve is inohes above injection level
exit gas analysis. The results obtained with the multipoint injection system shown in Figure 5 do not show as large a discrepancy, but, even in this case, all of the samples taken a t 11 inches above the injection level show values of C/Co greater than one. The cause of this discrepancy was investigated. Helium had been chosen as the tracer gas because of its low adsorption, particularly on the glass beads, and it does not appear likely that an
.
INDUSTRIAL AND ENGINEERING CHEMISTRY
January 1952
22?
TABLE111. BUBBLEAND DENSEPHASESAMPLING (No 13 lass beads 12- oint injection system stlmljle numbers 313-15 273L90, 3 % M . All 4ampfes from center of bed ’ 10 inches below inject0r.j Air Velocity, Feet per Second 0.6
Normal sample 0.44 0.38
1.2 1.6
Values of C/Co Lean phase
Dense phase sample 0.61,O 53 0 56,0.75 0 78, 0 . 7 3 0 4 0 , O 39 Av. 0 . 5 9
sample 0.19,O.16 0 . 2 2 , o . 18 0 18
Av. 0 . 4 1
Av. 0 . 1 8
0.89 0.95 0.69 Av. 0 . 8 2
0.6.5 0.67 0.22 Av. 0 . 4 5
0.95 0.96 Av. 0 . 9 6
below the injection point. This semilogarithmic type of plot usually gave reasonably good straight lines and a typical curve is shown in Figure 6. The slope of the line was taken as the superficial velocity divided by the eddy diffusivity and these eddy diffusivities were correlated by plotting them as a function of the product of the superficial gas velocities and the fluidized bed density. The correlation is shown in Figure 7. Figure 6.
Back-Mixing Results with No. 11 Glass Beads
RESIDENCE TIME S T U D I E S
internal circulation of helium due t o selective absorption could have been set up. It was found t h a t the samples were not representative because the gas passes through the fluidized bed both in the form of bubbles and by flowing through the voids between the solid particles. The bubbles pass through the bed with a much higher velocity than the gas passes through the voids, t p d thus relatively the bubbles cover the injection tube less of the time than the dense phase, and proportionately more helium is 6 4
t
1.0 8 6
I n view of the fact t h a t the back-mixing studies were unsatisfactory owing t o nonrepresentative gas samples, residence time studies were made in a n attempt t o obtain a more accurate pirture of the gas mixing in the fluidized bed. The apparatus employed was similar in construction t o t h a t used for the back-mixing studies. The same 3-inch column was employed for part of the experimental work and in addition a unit 4l/2 inches in diameter and 50 inches high was used. Helium gas was used as a tracer and all of the samples were analyzed by the thermal conductivity method. The solids used were t h e same glass beads and microspheres already described. I n these experiments the fluidizing gas introduced at the bottom of the column was a mixture of helium and air and this flow was continued until the composition was uniform throughout t h e fluidized bed. The helium introduction was then discontinued and a series of samples were rapidly taken of the gas leaving the top of the dense fluidized bed. I n this manner the composition of the exit gas from the unit was obtained as a function of time. Typical results are shown in Figures 8, 9, and 10. I n these figures the value of C/Co is plotted as a function of
4
&e -, Ve
where Q
10
2 Od
0./ I
I
6
uOp8,
810
t
4
6
LB/(SEC)(FTY
8/00
Figure 7. Correlation of Eddy Diffusivities
06
C
-G 04
injected into the voids. Likewise the sampling tube tends t o remove gas predominantly from the dense phase. The gas in the voids contains a higher percentage of helium than the average and the sampling technique tends t o sample this high concentration region selectively. This effect was shown by experiments in which samples were primarily withdrawn either from the bubbles or from the gas in the dense phase. The results are shown in Table 111. These results show a large difference in composition and all the data obtained in this investigstion by removing samples from the bed are in error. However, they do conclusively show t h a t back mixing occurs and t h a t the bubbles and the gas in the dense phase can have different compositions. The data were correlated on a n eddy diffusivity type of basis by plotting the logarithm of C/C, as a function of the distance
02
0
0
OS
IO
IS
20
t 3
1.0
85
4.0
4.5
oe/vc Figure 8. Residence Time Curve
is the volumetric rate of flow, 0 is the time since the helium flow was discontinued, V is the gross volume of the dense fluidized bed, and c is the fraction voids in the bed. This last group represents the number of void volumes of gas that has passed through the fluidized bed since the helium injection was discontinued. The results shown in Figure 9 were obtained in the
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INDUSTRIAL AND ENGINEERING CHEMISTRY
222
3-inch column and those for Figures 8 and 10 are from the 4'/2inch column. Although there is some scattering of the experimental data, there does not appear to be any significant variation with the superficial gas velocity, uo, and all of the experimental data obtained with the glass beads and microspheres did not give any significant trend of the residence time curves with superficial gas velocity.
I O
0.0
O b
L =0 04
Or 0
3 ,NUMBER OF VO/D VOLUMES "€
Figure 9.
Comparison of Residence Time Curve with Limiting Conditions
If the gas flowed through the bed at a uniform velocity without a n y back mixing, then the helium-air mixture in the bed would be displaced as if by a piston. This idealized case is termed piston flow and with such a system the exit gas concentration expressed as C/C, would remain a t unity until one void volume of gas had flowed through the unit and i t would then drop sharply t o zero. Another limiting case would be a degree of back mixing so great that a uniform composition was maintained throughout the bed equal to the exit composition. This condition is termed complete mixing. The theoretical curves for piston flow and complete mixing are shown on Figure 9. I O
Ob
for runs made with three different L I D ratios are shown in Figure 11. As the L/D value is increased the curves tend more toward the piston flow condition, although a t the highest L I D values employed the results still indicate considerable mixing and bypassing. Although the LID'S employed here correspond to those normally used in laboratory units, they are much higher than those encountered in commercial reactors, and the latter units probably would have more by-passing than indicated by these data. Larger particle diameters also gave rcsidence time curves more nearly like those obtained with piston flow. Typical results are shown in Figure 12 for four sizes of glass beads. These runs were made at a given superficial gas velocity and for that reason are not truly comparable. T o obtain a n equivalent fluidization, the larger size beads should have had a higher gas velocity. I n fact, the largest size beads used were not fluidized a t the vclocity employed and this change in the character of the fluidization may be the chief factor. I n general, the microspheres gave experimental curves that came closer t o the complete mixing curves than did the glass beads. Visually the microspheres appeared to give very smooth fluidization and i t may be that the greater mixing indicated is due to their porous nature, which results in considerable quantities of gas being carried in the voids of the solids. The breakaway of the experimental data from an ordinate value of unity in Figures 8, 9, and 10 indicates that some of the air which has entered since the helium flow was discontinued has penetrated to the top of the column. The fact that this breakaway occurred long before a volume of gas equal to the void volume of the bed has passed through the unit indicates t h a t some of the air is passing through i t at a rate much greater than the superficial velocity. For example, in Figure 9 the breakaway occurs a t a value of the abscissa equal to about 0.15, which would indicate that some of the gas passed through a t a velocity a t least six times the superficial velocity. In the case of Figure 10 the breakaway occurs even earlier, indicating a maximum velocity a t leaat fourteen times the superficial velocity. For the various runs made this maximum velocity varied between five and twenty times the superficial velocity showing that the bubbles rise through the fluidized bed rapidly. The curve shown on Figure 14 for the fixed bed condition would indicate a maximum penetration equal to 1.5 times the superficial velocity.
0 4
c -
10
CO
0 4
Ob 02 06 0
o
os
io
15
PO
cs
IO
3a
40
4s
0e/vc
C
c7; 04
Figure 10. Residence Time Curve or
The experimental results are very close to the complete mixing curve but the back-mixing experiments.demonstrate conclusively that complete mixing does not prevail in these fluidized units. A combination of mixing and gas by-passing can give curves equal t o or even lower than the complete mixing chrves. It is concluded that the results obtained are the result of mixing with considerable gas by-passing in the form of rapidly rising bubbles. Figure 9 also shows a curve that is labeled fixed bed. These d a t a were obtained in both the 3-inch and the 41/~inchunits with No. 7 glass beads operating a t velocities low enough t o avoid fluidization. They indicate that the small beads in a fixed bed aystem give residence times that come fairly close to the piston flow condition. The effect of the length t o diameter ratio, LID, of the fluidized bed on the reRidence time curves was investigated and the results
0 0.5
1.0
1.5
1.0
2.5
a.0
J.S
4.0
4.6
0e/vt
Figure 11. Effect of Bed Dimensions on Residence Time Curve
The residence time curves can be used to calculate a number of other factors, such as the probable residence time of a molecule or the effect of the residence time on the rate of reaction. The slope, --F, of the residence time curves multiplied by d(&@/VE) represents the fraction of a n entering stream of gas that remains in the fluidized bed for a time, 8, and leaves before 8 de. The fraction of the reactants that have reacted in time, 8, is 1 CR/CB,where C, is the concentration of the reactants in the feed
+
January 1952
INDUSTRIAL AND ENGINEERING CHEMISTRY
and CRis the concentration unreacted at time, 8. Multiplication of these two terms results in an expression for the fraction of the gas leaving a fluidized bed that has reacted
223
experimental data are plotted as the logarithm of C/CO as a function of the number of void volumes,
&e -, they V€
can be repre-
sented by two straight lines-one, a horizontal line a t a value of C / C o equal to unity and the other, a straight line of negative slope for the decreasing portion of the curve. The results given in Figure 9 are plotted in this manner on Figure 13. All of the data obtained correlated satisfactorily in this manner. Figure 14 is a similar plot for the fixed bed runs. These plots can be
io
IO
08
aa 0.6
06
04
c co
04
C co
02
01
01
0 08 0.06
0 0
0.5
io
1.9
2.0
CJ
0 04
3.0
O@/Vc
Figure 12. Effect of Particle Size on Residence Time Curve
0 02
0011 0
where Cy is the concentration of reactants leaving reactor and Co is the concentration of reactants entering reactor. Equation 1 is general for reactions of all orders, and the problem is that of evaluating the term 1 - C R / C ~ . For a first-order reaction, the basic rate equation is
1.0
' I I5
I
I
20
2 5
I
30
0 @/Vc
Figure 14. Residence Time Curve for Fixed Bed and Empty Tube
characterized by an intercept, I,indicating the value a t which the data break away from the original concentration and the slope, -S, of the straight line for the falling concentration region on the curve. The relationships then are
For &B/Vfrom I to
0.4
a:
In C / C , = -S
[E &e - I ]
(5)
The intercept and slope values are not independent of each other because the total volume of helium must equal that originally present in the bed, and t o satisfy this condition it can be shown t h a t
O.?
CO
O/ Ood 0
I 10
For & 8 / V from 0 to I: C/Co = 1
0.8 0.6
c -
I 0.5
os
I=- 8 - 1
0.04
S
o=020 '0
0)
O@/Vr
Figure 13.
Correlation of Residence Time Curves
where n equals moles of reactant present a t time, e, and k equals the rate constant. If the reaction occurs without change in volume, then (3) and combining Equation 3 and Equation 1 gives
1 - Cf/C, =
som
1
- e-ke
Fd(Q8lVe)
(4)
The value of F can be obtained by taking the slopes of the residence time curves and the integration of Equation 4 performed graphically. This procedure is time consuming, and it has been found that the experimental data can be correlated empirically in a form that makes reaction rate calculation simpler. If the
A bed with piston flow would have a value of I equal t o one and the slope equal t o infinity. The complete mixing curve would have a value of I equal to zero and S equal to one. The values of the intercept and the slope were determined for the various runs and these constants were then employed to calculate the effect of gas mixing on a first-order uncatalyzed homogeneous gas reaction occurring isothermally without change in volume. For such a reaction the effect of the gas mixing is only important in determining the residence time-Le., the residence time history is adequate to calculate the effect on the reaction. This effect can be expressed in a number of ways and one useful form is shown in Figure 15, in which the volume of the reactor required to obtain a given conversion for a given feed rate is expressed as a ratio to the volume required to obtain the same conversion if piston flow prevailed. These volumes are the void volumes in both cases. This ratio is shown as a function of the fraction conversion. If piston flow were obtained the ratio would have a value of one for any fraction converted. The fixed bed data of Figure 14 are shown on this plot and they approach the piston flow condition very closely, indicating that the amount of mixing encountered in this case was not very serious from the point of view of reaction rate. The curve for complete mixing is also shown and, while the volume ratio is not large a t low conversion,
INDUSTRIAL AND ENGINEERING CHEMISTRY
224
i t does not become very high if complete conversion is approached. At low conversion the gas leaving the unit has essentially the same composition as the gas entering and mixing is not very detrimental, while a t high conversions the product gas contains very little of the reactant and i t therefore dilutes the feed upon mixing with it. Curves for three of t h e fluidized bed operations are shown. With the lower L I D ratio and the small microspheres, the result is almost equal t o t h a t for complete mixing. The larger L/D and the larger particles result in curves that approach the piston flow condition more closely. IO 0
so 80
Vol. 44, No. 1
similar t o those found for homogeneous reactions.
I n the case
of strong adsorption it is possible that the effect of the solid circulation can be either beneficial or harmful.
The by-passing and mixing encountered in a fluidized bed can be an important factor in interpreting the result obtained in such units or in the design of a large unit. It would be expected that the by-passing would be more wrious. in the commercial units than in the laboratory equipment and difficulty may be encountered in going from a small t o a large reactor. On the basis of the data so far available, it would appear that the assumption of complete mixing in the large units having low values of L / D would be the most logical assumption, although i t should be borne in mind that i t is at least theoretically possible for the large unit t o require larger volume than for complete mixing. The
TO
10 0
60
eo
no 70 6 0
SO
40
($1 80
8 0
0
02
04
06
08
I O
FRACT/ON CONVERTLO
Figure 15. Comparison of Reactor Volumes in First-Order Homogeneous Reaction V . Reactor volume required V*. Reactor volume required for piston flow
In the case of a second-order homogeneous uncatalyzed gas phase reaction occurring isothermally without change of volume, t h e residence time data are not sufficient t o predict the effect on reaction rate. I n this case, the residence time of the molecule in the reactor alone is not sufficient, but its position relative to other molecules with which i t can react must also be known. The experimental data obtained in this investigation do not give adequate information on this latter factor. However, certain limiting cases can be evaluated. For example, it can be assumed t h a t the residence time curves obtained are the result solely of by-passing and that no mixing of the gas in successive increments occurs. Thus the only effect on the reaction would be the fact that different portions of a n increment of entering gas had different residence times in t h e unit. The results of such a n assumptio? are shown in Figure 16 together with the curves calculated for complete mixing and piston flow. In general, the curves are similar t o those of Figure 15. The effect of complete mixing is more serious for the second-order reaction than for the first-order. The curves for the fluidized operation are essentially the same. The actual effect for the fluidized bed would be somewhere between the curves shown and the complete mixing curveLe., the effect would be more serious for the higher order reaction. I n the case of reactions involving the fluidized solid and t h e gas, the problem is more complex. From the viewpoint of maintaining isothermal conditions, the circulation of the solid is very beneficial. However, in addition t o the mixing and bypassing of the gas, there is the possibility of the reactants and products being adsorbed and carried by the solid. If the amount of adsorption by the solid is low, the reaction rate results should be
10
0
OP
04
Ob
08
10
FRACVON C?’fVERTEO
Figure 16. Comparison of Reactor Volumes in Second-Order Homogeneous Reaction V . Reactor volume required V*. Reactor volume required for piston flow
results indicate t h a t the effect is largely by-passing and not back mixing and, although the volume required for a given conversion may be the same as for complete mixing, the reaction results may be different particularly if side reactions are involved. Most laboratory units probably operate somewhere intermediate between piston flow and complete mixing and results probably cannot be adequately analyzed on either basis. The same difficulties would also apply to investigations of mass transfer in fluidized powder units. LITERATURE CITED
(1) Gilliland a n d Mason, IND. EXG.CHEM.,41, 1191 (1949). ( 2 ) Mason, E. A., Sc.D. thesis i n chemical engineering, Massachusetts I n s t i t u t e of Technology, 1950. (3) Trilling, C. A., Sc.D. thesis i n chemical engineering, Massachusetts I n s t i t u t e of Technology, 1949. RECEIVED April 16, 1951. Presented as part of a Symposiiim on Chemical Engineering a t the dedication of the East Chemistry Building, University of Illinok, Urbana, Ill., March 31, 1951.
