Gas-Flow Patterns in Beds of Fluidized Solids

When the catalyst and car- bon dioxide ..... rent flow between the two cathodes (as ... 60% transmittance, the agreement of the calibration data with ...
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ACKNOWLEDGMENT

The authors appreciate the assistance of J. D. Nielsen and A. W. Ries in the experimental work.

(4) Kramers, H., Chem. Eng. Sci., 1, 35 (1951). (5) Leva, M., Grummer, M., Weintraub, AI., and Pollohik, M., Chem. Eng. Progr., 44, 619 (1948). (6) Matheson, G. L., Proc. Am. PetroleumInst., 27 [III],18 (1947). (7) Matheson, G. L., Herbst, W. A., and Holt, P. H., IND.ENG. CHEM.,41, 1099 (1949).

LITERATURE CITED

Fcrsythe, W. L., Jr., and Hertwig, W. R., IND.ENG.CHEM.,41, 1200 (1949). Gregory, s. J *A P p l . 2r SUPPI. Issue No* p* (1952). Gunness, R. C., Chem. Eng. Progr., 49, 113 (1953). *.I

Chern.l

( 8 ) Morse, R. D., Ibid., 41, 1117 (1949). (9) Morse, R. D., and Ballou, C. O., Chem. Eng. Progr., 47, 199

(1951). (10) Parent, J. D., Yagol, N., and Steiner, C. S., IFid., 43,429 (1947). (11) Roller, P. S., Trans. Am. SOC.Testing &futeriaZs,32, 607 (1932). ACCEPTEDApril 6, 1953 for review February 24, 1953. RECEIVED

Gas-Flow Patterns in Beds of Fluidized Solids E. R. GILLILAND, E.A. MASON,

AND

R. C. OLIVER

M A S S A C H U S E T T S INSTITUTE O F T E C H N O L O G Y , C A M B R I D G E , MASS.

T h e effect of t h e flow pattern of t h e gas is important in fluidized-solid reactors. I n previous studies on t h e residence-time history of t h e fluidizing gas, a technique was developed whereby t h e effect of nonuniformities in gas flow can be predicted for first-order homogeneous reactions. In order t o study t h e influence of gas flow patterns on chemical reactions of higher order, t h e oxidation of nitric oxide, a third-order reaction, has been carried o u t in small fluidized beds. T h e measured conversion of reactants has been compared t o t h a t predicted from known kinetics, residence-time data, and certain assumptions regarding t h e gas-flow pattern. T h e experiments were carried o u t in glass reactors using spherical glass beads (Scotchlite) as t h e fluidized solid. Preliminary work showed t h a t t h e presence of these beads had a negligible effect on t h e reaction under t h e conditions chosen. T h e progress of t h e reaction was measured photometrically. For comparison, t h e residence-time history of gas flowing through t h e same apparatus was determined. It was found t h a t knowledge of t h e residence-time distribution of t h e gases flowing through a reactor provides a good method for estimating t h e effect of gas-flow pattern on homogeneous reactions in fluidized beds.

F

1

LUIDIZED solid techniques have found widespread use in the chemical industry on both a laboratory and a plant scale. The solid mixing which takes place in fluidized beds promotes a degree of temperature control not readily obtainable in other types of chemical reactors. However, this solid motion causes mixing of the products of reaction with the entering reactants and permits some bypassing of reactants, so that the time for reaction is not uniform for all entering gas. Gas mixing and bypassing lead to a decreased reaction rate and nonuniformity of products, both of which are generally undesirable. The effect of these irregularities in gas flow becomes increasingly serious as the desired degree of conversion increases. Several experimental techniques have been employed in a n attempt to determine the nature and extent of the gas mixing in fluidized beds. Residence times of the gas flowing through small fluidized beds have been investigated by first supporting the solids with a mixture of tracer gas and air and then determining the composition of the gas leaving the bed as a function of time after the addition of tracer gas was discontinued. Studies concerning the back-mixing of the gases were made by injecting tracer gas into fluidized beds and analyzing gas samples taken from various points in the bed. The results of this work on the Table I. Size No.

Inch

;mm.

0.24 0.0178 0.0061

11 13

0.0040

15

0.00275

June 1953

Properties of Glass Beads

Diameter Microns % Deviation 6000 452 155 I 02 70

6

7

6 12

Abs. Density, G./Co.

2.24 2.78,246 2.46 2.43 2.43

gas mixing in fluidized solids have been applied t o the prediction of the chemical conversion to be expected in reactors having similar flow patterns. I n a third experiment, a chemical reaction has been carried out in laboratory scale fluidized beds in order to determine directly the effect of gas mixing on chemical reaction and t o evaluate the methods that have been proposed for predicting the effect of known gas mixing on chemical conversion. GAS-M I X I N G STUD1 ES

I n the residence-time studies, a bed of finely divided solids was suspended in a mixture of tracer gas and air. After the composition in the bed had become uniform, the flow of tracer gas was abruptly halted and a series of samples was taken of the gas as it left the top of the bed, These gas samples were analyzed for tracer content. Helium and carbon dioxide were used as tracers and all samples were analyzed using a thermal conductivity apparatus. Studies were made in Lucite columns having internal diameters of 3 and 4.5 inches. The ratio of the height to the diameter of the fluidized bed, LID,was varied from 7.8 to 23:3. Various sizes of Scotchlite glass beads manufactured by the Minnesota Mining and Manufacturing Co. were used (Table I). Other data were taken using a silica-alumina cracking catalyst manufactured by the American Cyanamid Co. The method of size analysis has been reported (6). With the exception of the use of carbon dioxide as a tracer, details of the procedure and of the apparatus used have been reported (5). The data presented in Figure 1 were obtained with helium a8 a tracer, using glass beads in the 4.5-inch column a t a bed height of 35 inches, but in general respects are similar to those obtained under other operating conditions. The value of C/Co is plotted as a function of QO/Ve, where C is the tracer concentration at time 8, COis the initial tracer concentration, Q is the volumetric rate of flow, e is the time since the tracer flow was discontinued, V is the gross volume of the fluidized bed, and E is the fraction of voids in the bed. The group Q e p e represents the number of

INDUSTRIAL AND ENGINEERING CHEMISTRY

1177

I=- S - 1

s

Table I1 shows representative values for S obtained with helium under various operating conditions. I n many cases the experimental values of S are close to unity. This means that the residence-time curves are similar to those to be expected from complete mixing. Within the limits of the experimental data there was no significant trend of the residence-time curves (expressed as a function of the void volume, QS/Vt) with superficial gas velocity. As the value of LID increased, the results tended more toward the value expected from piston flow. The data obtained using carbon dioxide as a tracer agreed with the Qb helium runs when glass beads were YE used. When the catalyst and carFigure 1. Residence-Time Curves for Fluidized Bed bon dioxide were used, however, the amount of carbon dioxide void volumes of gas that have passed through the fluidized bed swept from the bed was greater than would be initially during time e. present in the void volume of the bed. This phenomenon was taken to indicate adsorption of carbon dioxide on the I n addition to the experimental data presented in Figure 1, catalyst. curves are drawn representing the residence times to be expected from two theoretical f l o patterns. ~ I n one, termed piston flow, the gas would flow through the bed with a uniform velocity profile in the absence of any back-mixing. This is the type of flow which is usually assumed in calculations for reaction rate experi1.0 ments carried out in empty tubes and fixed beds of solids. The exit gas concentration, C/Ca, remains a t unity until one void wlume of gas has floxed from the unit and then drops immediately to zero. The second theoretical case is that of complete mixing, where the degree of mixing would be so great that the concentration of gas throughout the entire bed would be uniform and equal to the exit concentration. The point a t which the experimental data first deviate from C C/Co of unity is indicative of the maximum velocity a t which gas co flowed through the fluidized beds. For example, in Figure 1, 0.1 C / C Ofirst drops below unity a t a value of approximately 0.2; this indicates that some of the gas passed through the bed at a velocity approximately five times the average velocity in the voids ( & / A €where A = cross-section area of bed). The residence-time curve also shows that some of the tracer gas remained in the bed approximately four or five times as long a s would have been expected from piston flow. I n addition to the method of presentation shown in Figure 1, the data can be represented by two straight lines on semilogarithmic coordinates with the logarithm of C / C , plotted as a function 0.01 of the number of void volumes, QS/Ve. The data of Figure 1 are given in this fashion in Figure 2. The following relationships are Q8 evident: YE

-

-

-

For QB/Ve from 0 to I : C/Co For

QB/vefrom I

=

Figure 2.

1.00

t80 m : In C/Co = -S

[E I - -I

where I is the value of QO/Ve a t which the data break away from the original concentration, and -8 is the slope of the straight line representing the region of decreasing concentration. Piston flow is characterized by S = and complete mixing by S = 1.00. The intercept and slope values are not independent variables, because the total volume of tracer must equal that originally present in the bed. From a material balance,

I178

Correlation of Residence-Time Curves

Although in many cases the residence-time data closely resemble those t o be expected from complete mixing, other experimental findings indicate t h a t the concentration is not uniform throughout the bed. I n a series of back-mixing experiments, the tracer gas was injected into a fluidized bed and samples were withdrawn through hypodermic tubing from various points both above and below the points of injection. The procedure and results of these experiments have been given (5). The sampling technique did not give truly representative samples a t a given point in the bed. The experimental data did, however, show that back-mixing of

INDUSTRIAL AND ENGINEERING CHEMISTRY

Vol. 45, No. 6

Table 11.

Gas Residence-Time Characteristics of Small Fluidized Beds Solid

P

-

Bed, Inches Diameter Height 3 37 37 3 35 4.5 3 37 37 3 4.5 35 35 4.5 37 3 37 3 3 37 70 3 70 3 35 4.5 4.5 35

Type None Glass beads Glass beads Glass beads Glass beads Glass beads Glass beads Catalyst Catalyst Catalyst Catalyst Catalyst Catalyst Catalyst

MFan size, microns

452 452 155 102 102 70 107 150 216 107 150 107 150

Air Velocity, Foot/Sec. 0.40 0.38 0.38 0 . 3 9 to 0 . 7 0 0 . 3 9 to 1 . 0 0 0.39 to 1 . 0 0 0 . 4 4 to 1 . 0 0 0 . 4 0 to 0.81 0 . 4 0 to 0.81 0.42 and 0 . 6 0 0 . 3 8 and 0 . 7 8 0 . 3 9 and 0 . 5 8 0.41 t o 1.03 0 . 4 0 t o 1.03

S 8.4 8.4 8.4 2.0 1.8 1.2 1.2 1.2 1.3 1.4 1.5 1.5 1.04 1.05

Comment Empty tube Fixed bed Fixed. bed Fluid!zed Fluidized Fluidized Fluidized Fluidized Fluidized Fluidized Fluidized Fluidized Fluidized Fluidized

gases does exist in fluidized beds and t h a t gas composition in fluidized solid beds can vary with both location and time. Gas samples withdrawn from the “bubbles” (regions of low solids concentration) were found to have considerably less tracer present than samples withdrawn from the dense phase of the bed. Apparently, large differences in gas composition can exist over short distances in fluidined beds. The gas-mixing studies thus indicate that the gas-flow pattern in beds of fluidized solids is neither piston nor complete mixing. Deviations from piston-type flow in fluidized beds can be thought of as falling into two different categories, mixing and bypassing. Variation in the residence time of gas molecules can be caused by both of these effects. It is theoretically possible to have bypassing without mixing, but any back-mixing of gas will of necessity lead t o some short-circuiting, or bypassing, of entering gas. Residence-time experiments of the type employed in this work show the result of any gas-flow pattern within the bed without revealing the exact nature of that flow pattern. Furthermore, conditions used were such that the change in volume of the gas flowing through the bed was negligible. I n addition to the qualitative observations which can be made from residence-time curves, it is also possible to determine the probable residence time of a gas molecule in the bed. This information can be combined with chemical rate expressions to estimate the effect of variation in residence times on the rate of reaction. The slope, -F, of the residence time curve (as in Figure 1) multiplied by d(@/Ve) represents the fraction of a n entering stream of gas that remains in a fluidized bed longer than time 8 and leaves before e de. Knowledge of the fraction of a gas stream which remains a given length of time in a reactor is essential to the prediction of the conversion rate in the reactor. The fraction conversion in a reactor can be represented by

+

*

1

- Cf/CO

of reaction. Values for F can be determined by measuring the slope of the residence-time data in the form of Figure 1 or by differentiating Equation 1. This latter method is a more convenient method for use and results in the following relationships for F: For @/Ve from 0 to I : F = 0

-

The group (1 CR/CO)must be determined for various types of reactions. The degree of conversion of a first-order homogeneous reaction is dependent only upon the specific reaction rate, IC, and the time spent in the reaction zone. The findings of the residence-time studies can thus be directly applied t o a first-order homogeneous reaction occurring without change in volume. I n this case Equation 3 reduces to 1 - C//Co

Am (1

- e-k~)Fd(&e/Ve\

(5)

In the case of higher-order homogeneous reactions occurring without change in volume, knowledge of the residence time of the molecules flowing tlirough the reactor is not sufficient t o predict the composition of the exit stream. In such reactions, the rate of conversion depends not only upon the specific reaction rate and the time of contact but also upon the concentrations of adjacent reacting molecules. However, a n estimate of the magnitude of the effect of gas-flow pattern can be obtained by considering bypassing as being distinct from mixing. Thus, if the residence-time curves are assumed to be due solely to bypassing, without mixing between increments of entering gas, it is possible to arrive a t an expression for (1 - CR/CO). Physically, residencetime curves similar to those obtained experimentally could be produced without mixing merely by a variation in the velocity profile across the reactor. Indeed, with extreme variation in gas velocities, residence-time curves are possible in which the values of C/COat low values of &e/Vedecrease more rapidly than in the case of complete mixing. Such curves could not be characterized by S values. The effect of bypassing, in the absence of mixing, upon secondand third-order homogeneous reactions occurring without change in volume is shown in Figures 4 and 5 . The effect of mixing and bypassing upon a first-order homogeneous reaction is shown in

Jm

(1- CR/CO)

F d ( c w / v s ) (3) where Co is the concentration of the reactants entering the reactor, and Cr is the concentration of reactants leaving the reactor. For piston flow, CR is the concentration of reactants in anisolatedslug of gas that has been in the reactor for time e; for completemixing, CR = Cl. This equation applies to all orders

June 1953

I - -

Figure 3.

co

Calculated Effect of Gas-Flow Pattern on First-Order Reaction

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1179

(-% co

Figure 4.

Calculated Effect of Gas-Flow Pattern on

Figure 3. The rate equations used are shown on each figure, where TZ is the mole of reactant present a t time 8, and 0 is the volume associated with TZ moles of reactant. Curves are also presented for piston flow and complete mixing. These figures present the ratio of the conversion predicted for the given gas-flow conditions, I - C,/Co, to the conver,sion predicted from piston flow in a reactor of the same size, 1 - Cf/Co, as a function of the conversion predicted for piston flow. CT is the exit concentration of reactants for piston flow. The curves thus indicate the fraction of the approach to piston-flow conversion for a given set of reaction conditions; for the simple reactions described piston flow results in a conversion which is larger than that of any other type of flow pattern. The curves arc similar in shape for all three orders of reaction. Under circumstances that lead to low or high conversion, the conversion obtained under mixing or bypassing conditions approaches that obtained with piston flow. However, the size of the reactor required to achieve a given conversion increases rapidly as the degree of mixing or bypassing increases (6), particularly if the eonversion is to be high. If some of the variation in the experimental residence times of gas molecules is due to gas mixing, then the effect on chemical reaction would be more serious for second- and third-order reactions than that shown in Figures 4 and 5 for the cases of bypassing alone. Curves for chemical conversion with some mixing would lie closer to that shown for complete mixing. The experimental work on back-mixing indicates that some mixing does occur in beds of fluidized solids.

known, the effect of gas-flow pattern on the reaction was determined by comparing the conversion obtained in the reactors with that predicted from piston flow and from residencetime data. Reaction Equipment. A schematic diagram of the apparatus employed in the chemical reaction studies is given in Figure 6. Information concerning the reactors used is given in Table 111. All equipment that came in contact with gases other than air or nitrogen was constructed of borosilicate glass; groundglass joints and silicone stopSecond-Order Reaction cock grease were used throughout the annaratus. The fluidized react'& were all encased in water jackets. Pressure taps were attached a t the base and top of the columns; these were connected to manometers filled with nonvolatile liquids. Temperatures a t various points in the bed were observed by raising and lowering an iron-constantan thermocouple which entered through a gas seal in a groundglass joint a t the top of the column. One of the reactors used was a round 500-ml. flask, to which was fitted an electrically driven stirrer. This reactor was connected into the experimental apparatus a t points 1-1 and 2-2 shown on Figure 6 and replaced the fluidized-solid reactors. N o solids were added to the round flask, and it was suspended in a constant temperature bath during operation. Gas distribution plates were fixed a t the base of each column. The air and nitric oxide were metered by means of glass capillary orifices; liquid-filled manometers indicated the static and differential pressures. These capillaries were connected to a common header a t each end, so that variations in the relative flow rates of the two streams due to fluctuations in the static pressure a t either end were reduced. The upstream header was connected to a bubbler and the flow rates of air and nitric oxide were adjusted so that some of each flowed to the bubbler. When this Table II I .

Reactor Characteristics

Reactor Zone, Inches solid I.D. Height Glass Bead Size

Bed Action

CH E M I CA L R EACTl ON

STUDIES

Residence-time studies provide an approximate method for predicting the effectof gasflow pattern on chemical reaction. An experimental program attempting to determine directly the effect of gas-flow pattern upon chemical reaction and to evaluate theeffectiveness of residence-time studies in predicting chemical reaction was undertaken. The oxidation of nitric oxide, a homogeneous third-order reaction, has been carried out in small fluidized beds. As the kinetics for this reaction are well 1180

0

0. I

0.2

0.3

0.4

0.5

I -

Figure 5.

cf" co

0.6

0.7

0.8

0.9

Calculated Effect of Gas-Flow Pattern on Third-Order Reaction

INDUSTRIAL AND ENGINEERING CHEMISTRY

Vol. 45, No. 6

PHOTOMETER

w

lar to one given by Hill (7), and the principle of operation was to balance the voltage developed by the phototube current with a voltage from the potentiometer.

w

The circuit variables were adjusted to give: (1) zero current flow between the two cathodes (as indicated by the milliammeter and galvanometer) with no phototube current (shutter closed) and the grid grounded or the potentiometer a t zero volts, and (2) zero current flow between the cathodes with the shutter open, the cell filled with nitrogen, the potentiometer set a t 1,0000 volt, and the lampcurrentcausing a 1.0000-volt drop across the 0.23-ohm resistor. The fkst case represents zero light transmittance and the second 100% transmittance. With a colored gas in the cell, the phototube current was decreased c and the required balancing A/R voltage (measured by the po-€i NO tentiometer) was also decreased in exactly the same proportion ; percentage transmittance was thus read directly. A warm-up periodof about2 hours was used GAS SUPPLY sysrm to minimize changes in light Figure 6. Apparatus for Chemical Reaction output a t constant voltage drop across the 0.23-ohm resistor. N. Green filter A. CaCll drying tube E. Mg(C1Oa)z or PZOKdrying tube P. Pressure tap Reproducibility of reading Q. Cell C. Sulfuric acid scrubber was checked daily by use of a D. Tube containing NaOH pellets and Mg(C10d)z R. Reactor “standard” glass filter and was S. Screen E. Air ftowmeter T. Thermometer F. Nitric oxide flowmeter found to be approximately 1 U. Shutter G. Pressure dropping bubbler part in 500. Changes in the V. Vent H. Bromine bubbler relative transmission of about W . Ciroulatlng water 1. Water jacket X . Stlrrer K. Cooler 0.02% were detectable, but not Y. 500-ml. flask L. Lamp reproducible. This sensitivity TC. Thermocouple M . Lens was achieved through use of a sensitive (0.23 pa. per mm.) galvanometer to detect unbalance. The milliammeter was used when bringing the circuit happened, a brown color, due to nitrogen dioxide, was evident to balance; final adjustment was made with the galvanometer in i n the line to the bubbler. The gases leaving the fluidized reacthe circuit. tors passed through a filter of fritted glass to remove solid parThe photometer was calibrated by passing metered streams ticles. of nitric oxide and air through the cell. After this mixture had Materials. SOLIDS. The properties of the spherical glass displaced the gas initially in the cell, the cell outlet was closed and the nitric oxide-air mixture allowed to bypass the photombeads used are given in Table I. eter, The oxidation in the cell thus proceeded toward completion under conditions of constant pressure. The concentration GASES. The nitric oxide used was a product of the Matheson of nitrogen dioxide in the cell was then calculated from the initial Co., Inc., and, when scrubbed by sulfuric acid, was found to conconcentration and known kinetic data and correlated with the tain 94.6% NO. The remainder was inert; no detectable relative transmittance. I n the normal operating range of 20 to amount of nitrogen dioxide was present. The’gas was bubbled 60% transmittance, the agreement of the calibration data with through a sulfuric acid scrubber followed by a column packed with sodium hydroxide pellets and magnesium perchlorate before a smooth curve was better than =klyoof the nitrogen dioxide concentration. flowing to the reactor. Compressed air was used as the oxidizing agent and was passed over calcium chloride and magnesium perchlorate before Operating Procedure. Chemical reaction studies were made metering. in all the units listed in Table 111. Gas Analysis. After leaving the reactor and before analysis, t h e gases were taken through a small heat exchanger t o bring Some runs were made a t low velocities under fixed-bed condithem near the temperature used during calibration to minimize tions. All fluidized runs were made with batch beds-Le., no t h e effect of uncertainties in the dioxide-tetroxide equilibrium. solid removal from the bed. Sufficient solids were placed in the ‘The gases then flowed through a water-jacketed glass cell which reactor so that the upper level of the fluidized bed just came to the formed part of a photoelectric colorimeter. This photometer fritted-glass filter. was used to measure the blue-green light absorption, and thus I n all runs, metered amounts of nitric oxide and air flowed into the concentration, of nitrogen dioxide which was the only colored the reactor until the composition of the gases leaving had reached gas present. The photometer is outlined in Figure 6 and cona steady value as indicated by the photometer reading. This :sisted of a 6-volt, 32-candle power, auto headlight as light source, reading was the measure of the conversion achieved in the bed. a condensing lens, a green filter, a gas cell either 5 or 10 em. I n general, the exit from the photocell was then closed, and the long and 2 em. in diameter, a shutter, and a RCA-929 phototube. gases from the reactor were allowed to bypass the cell, as during ‘The pressure of the gas entering the cell and the temperature in calibration. The composition as calculated from the photometer the cell were measured. readings on the trapped gases was then checked against the composition as determined by the gas flow rates. This technique A schematic drawing of the measuring circuit used in conjuncwas used in all except a few high velocity runs, where the compotion with the phototube is given in Figure 7 . The circuit is simisition as determined by the flow rates was used. Y

c

e

lune 1953

I N D U S T R I A L A.ND E N G I N E E R I N G C H E M I S T R Y

1181

dioxide ( 9 0 ~ )the ; relative amounts of the two forms is strongly dependent on temperature [20% dissociation of nitrogen tetroxide a t 0 ", 89% a t 100 C. (10)1. The rates in both directions for the nitrogen tetroxide-nitrogen dioxide reaction have been reported as extremely rapid (10). It has therefore been assumed that the two forms are always present in their equilibrium ratio. The oxidation kinetics have been investigated over a wide range of initial concentrations j(0.5 atm. nitric oxide (8) t o 0.02 mm. nitric oxide ( S ) ] . The classic investigation was made by Bodenstein (1). If pistontype flow of the gases in the reactor is assumed, using Equation 7 the following relationship results:

70 UEfLAND

O

330 K

27K

330 K

I\

POTENTIOMETCR 0-f.0f VOLTS

z' [l

+ (;

(yo

- 1) z J 3 dz

- z)2(zo,-

z/2)

(8)

/

Figure 7.

Light-Measuring Circuit

If complete mixing in the reactor-& assumed, the expression becomes: Residence-Time Studies. Residence-time data were taken on gases flowing through the 16/a- and 3-inch columns and the stirred reactors. Bromine and nitrogen dioxide were chosen as tracer gases, so that analysis could be made with the photometer. When nitrogen dioxide was used, the tracer was vaporized from a cylinder containing liquid nitrogen dioxide. When bromine was used, a stream of air was passed through orifice F of Figure 6 and then through a bubbler containing liquid bromine. This bubbler was mounted in a constant temperature bath. Before entering the reactor, the tracer stream was mixed with air which flowed through E on Figure 6. When the composition of the gases leaving the reactor had become uniform, the photometer readings were transmitted t o a Heiland continuous recording oscillograph (Heiland Research Corp. Type A500-R12), and the flow of tracer was abruptly stopped. The photometer then made a continuous record of the composition of the exit stream as the tracer was swept out of the bed. The photometer was calibrated for bromine by bubbling the bromine-air stream through a solution of potassium iodide; the liberated iodine was titrated with sodium thiosulfate. Allowance for External Volume. I n determining the conversion of reactants occurring in the reactor proper, it was necessary to allow for reaction that took place in the lines after the reactor. The conversion indicated by the photometer was corrected for reaction in the lines using Bodenstein's kinetic data (9) and the assumption of piston flow in the lines. To reduce the extent of this correction, the volume of the external circuit was kept to a minimum. The uncertainty in the results due to the correction for the external circuit was small.

(9)

where

(CC.)Z reaction rate constant, (mole)2(sec.) = !2.06, cc. atm./' K. R T = K. T = total pressure, atm. ( V E ) = reactor void volume, cc. ( V t l ~= volume of reactor swept out when z moles have reacted = feed rate, moles entering mixture per second F a = fraction dissociation of N204 moles of NO present ! I = mole of original mixture = original mole fraction of nitric oxide yo = original mole fraction of oxygen $0 moles of nitric oxide reacted z =y o - u = original mole mixture entering k,

=

Since the fraction dissociation varies with y, a: and y can be related as follows:

The reaction 2NO

+

0 2

=

N*0* = 2N02

+

(6)

with A H O ~ ~ = ~ , ,- 40,817 13,693 a: cal. ( h ) , where = fraction of nitrogen tetroxide dissociated, proceeds as a thirdorder reaction ( 1 ) in accordance with the following equation O(

Near room temperature, the oxidation is practically complete at equilibrium. The oxidation product exists as an equilibrium mixture of the colorless tetroxide ( N s 0 4 ) and the deep brown

1182

P&2 where K = __ a t the reaction temperature PN%Oa

P

=

partial pressure, atm.

The reaction was reported by Bodenstein to be homogeneous and unaffected by sulfur dioxide, water vapor, or excess nitrogen dioxide. Some workers (g, 6 , 1I ) , however, questioned the homogeneity and reported conflicting results of the effect of increasing the glass surface. Because the reaction was to be carried out in a fluidized bed of very small glass beads, with greatly extended surface, it was necessary to study the effect, if any, of the extended

INDUSTRIAL AND ENGINEERING CHEMISTRY

Vol. 45, No. 6

packed tube. At high flow rates and concentrations, this heat generation led to an uncertainty in the average temperature and thus became a factor limiting accuracy of the results. At the lowest concentration for both open tube and packed bed, a tendency toward increased conversion is noted. Because of experimental difficulty in this region, the data were not very reproducible, but it is difficult t o ascribe all of the difference in the experimental 2$! S T and predicted values t o error. 1.1 0 Smith (11)has also reported a sim5 2 ilar rise a t low partial pressures of ‘3 nitric oxide under certain condi0 5: 1.00 tions. As operation in this range 3 of concentration was avoided in the fluidized-bed e x p e r i m e n t s , 0.90 further investigation of this point 0 0.M 0.04 0.06 0.06 0.10 0.12 0.14 0.1s 0. was not made. In the range of Yo, INITIAL M O L E fRACTiON NITRiC OXIOC operation no trends were noted in the data when the surface area was Figure 8. Effect of Glass Surface on Conversion varied by 30-fold, and the experimental conversion agreed very well glass surface. If any surface effect (heterogeneity) is involved with those predicted from Bodenstein’s values. The rein this reaction, different apparent reaction rates should be obaction was therefore assumed t o be truly homogeneous and the tained when the total surface area in the reactor is varied. rate constants of Bodenstein were assumed to hold a t concenExperiments were therefore conducted in which nitric oxide trations greater than about 6% nitric oxide. The agreement of was oxidized in a tubular reactor 1 inch in inside diameter, under the experimental conversions with those predicted from Bodenempty-tube and packed-bed conditions. The tube was packed stein’s values and the assumption of piston flow also confirms the with glass beads of various sizes to give different surface-to-volprediction, based on the residence-time experiments, that rate ume ratios. The initial concentration of nitric oxide was also studies in packed beds can be calculate& using the assumption varied and the measured conversions were compared to those of piston flow. To test the ability of the analytical apparatus to detect the predicted using the rate constant data obtained manometrically in a constant volume apparatus by Bodenstein and Lindner ( I ) , presence of mixing, nitric oxide and air were fed to the stirred as recalculated by Kassel (9). The summary of data on the reactor shown in Figure 6. As the purpose of the reaction studies nitrogen tetroxide-nitrogen dioxide equilibria by Giauque and was to determine the effect of gas-flow pattern on conversion and Kemp ( 4 ) was used. As the data in Table I1 indicate that the to evaluate methods for predicting conversion, several methods flow in empty tubes and fixed beds is similar to that of pistonfor presenting the results were available. Comparison of the type flow, piston flow was assumed in making the calculation for experimental conversion achieved under each set of operating these oomparisons. A11 of the small glass beads contained black conditions with that expected from piston flow and from complete particles when purchased. Runs were therefore made with mixing shows the effect of gas mixing, while comparison with these beads in the shipped condition and after they had been the conversion calculated using residence-time data and curves scrubbed by boiling with concentrated sulfuric acid and potassium of the type presented in Figures 3, 4,and 5 permits evaluation of sulfate solution for 4 hours. the effectiveness of residence-time data in the prediction of chemiThe results of these experiments are shown in Figure 8. For cal conversion in a reactor. the packed beds, conversions were in the 80 to 90% range except The results of the reaction studies in the stirred vessel are given a t the lowest nitric oxide concentration. The data appeared in Figure 9, which provides for the comparisons mentioned. B e to group along two lines-one for the packed bed and one for the coordinates are the same as in Figures 3, 4, and 5 and present open tube. I n the packed-bed experiments, no separation is conversion, as the fractional approach to piston-flow conversion, evident between the runs made with different surface areas or plotted against the piston-flow conversion. The experimental with the scrubbed and unscrubbed beads. Except at the very results are given in this fashion as one set of points, while the low concentrations, the agreement between the experimental corresponding conversions calculated from the actual operating and predicted conversion is within the experimental error. Beconditions on the basis of complete mixing are given as another cause experimental errors are more serious a t both extremes of set of points. I n these two sets of points, the conversion resultconcentration, the slight trend of the data for the 10-em. cell ing from piston flow was obtained from Equation 8, while the away from the predicted conversion at higher concentrations conversion for complete mixing was obtained from Equation 9. may not be significant and is not evident in the data from the For the points, the actual concentrations of oxygen and nitric 5-cm. cell taken with unscrubbed beads. oxide (which were not necessarily equal) were employed, and At values of yo greater than 3%, the open-tube data lie below allowance was made for any change in volume due t o reaction. the predicted conversion. I n most of the open-tube runs, the The curves on Figure 9 are for two of the simplified reactions Reynolds number was approximately 50 and conversion was from ‘ shown in Figures 4 and 5 for the case of no change in volume 80 t o 90%. Most of the difference between the experimental and permit easy comparison of the plotted points with conversion and predicted conversion can be explained if a parabolic velocity predicted from residence times. profile in the tube is assumed. The effect of heat generation upon I n all but two runs, the experimental conversion was subthe flow pattern was more serious in the open tube than in the stantially less than expected from piston flow and agreed closely -.)

r

*s

..

.

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signed using the second-order curve for S = 1.0 with no mixing would be one half t o one third as large as that actually used to achieve the experimental conversions ( 5 ) . 1.0 The results obtained for the air oxidation of nitric oxide in fluidized beds of glass beads are 0.0 given in Table I V and on FigY ‘US ure 11. The coordinates of Figure 11 are the same as in q.-y; Figure 9 ; all points in Figure 0.8 11 represent conversions obtained experimentally. ExMIXING amination of the results in 0.7 -----.? ND ORDER Table IV shows that thp repro-3 RD ORDER ducibility of conversion under similar experimental conditions 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 was approximately 1 to 2% in the 1 j/8-inch reactor, and 5% /Yo in thr 3-inch reactor. In all fluidized-solid runs, the outlet Figure 9. Effect of Gas-Flow Pattern in Stirred Reactor gas composition, as measurcd by the photometer, fluctuated with that calculated for complete mixing. During the two runs over short intervals of time(0.5to 1second); averagereadings~~.ere used in the calculations for Table IT. These variations in outlet which correspond to an abscissa value of about 0.8 on Figure 9, the concentration of nitric oxide was so low that accurate analysis nitrogen dioxide concentration were probably caused by the was difficult and was in the range where the ratio of the measured bubbles in the fluidized bed and by variations in the inlet comto calculated conversion had begun t o rise in both the open tube position caused by pressure (and thus flow rate) fluctuations a t the base of the bed. As the change in oxygen concentration and packed bed (see Figure 8). The general agreement between the calculated and experimental points indicates that the effect was small in all the fluidized runs, the oxidation of nitric oxide of mixing on chemical reaction can be detected by the experibehaved essentially as a second-order reaction occurring with only minor changes in volume. Several curves representing the mental technique used, The calculated points for complete mixing on Figure 9 agree more closely with the simplified comeffect of various gas flow patterns on a second-order reaction of plete mixing curve for a second-order reaction than for a thirdthe type shown in Figure 4 have therefore been included in Figure 11 for the sake of comparison. A few calculations using order reaction. Because the relative change in the concentration of oxygen was less than that for nitric oxide, this tendency Equations 3 and 7 and S values showed that variations in the for the oxidation reaction to follow the characteristics of a secondintial oxide concentration had a very minor effect on the predicted conversion ratios, and hence the simplified curves are used. order reaction is to be expected. Because of the nitrogen diluent in the gases, the assumption of a constant volume reaction in the Residence-time data were collected in the 16/8- and 3-inch columns using bromine and nitrogen dioxide as tracers. The calculation of the curves is reasonable; the maximum shrinkage amount of tracer swept from the bed after tracer addition was experienced was 11% of the initial volume, and in most runs the stopped was found t o be greater than that contained in the void shrinkage was only 3 to 6%. volume of the bed. This phenomenon was discovered using the The results of residence-time runs made a t both low and high gas flow rates through the stirred reactor are presented in Figure 10. They are characterized by X = 1.0. AI1.0 t ough both curves on Figure 9 for the si plified second-order reaction were derived from gas-flow patterns having 0.8 S = 1.0, the results of the reaction studies agree more closely with the conversion predicted from the assumption 0.6 of complete mixing than from the assumption of no mixing and S = 1.0. ‘O As an example, if the eecond-order curve 0.4 for S = 1.0 with no mixing had been used to predict the conversion obtained, an error of 7 to 8% in the conversion would have resulted in the range of 0.2 conversions covered by the experimental work. Although this error in conversion is relatively small, it might 0 have serious effects on certain other 0 0.5 1.0 f.5 2.0 z.5 3.0 9.5 4.0 4.5 factors, such as the size of a reactor Qe YE required to achieve a given conversion. In the above example, a reactor deFigure I O . Residence-Time Curve for Stirred Reactor

-

G

h

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effect of the solid and gas phases needs to be studied before any such statement can be made concerning heterogeneous reactions, because such reactions would be affected by the gas-solid contact time. In the two largest reactors, the ratio of the experimental to

1.0

0.9

Yf Yo-

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0.8

piston flow conversion, ‘ H

Yo - Y?’

-

0.7

0.6

0

Tav.,

Atm. 1 08 1 06 1 1 08 10 1.09 1.15 1 11 1 11 1.05

1.31 1 35 1 36 (1 * refers

was less than unity. This ratio decreabed in going from the smallest of the three fluidized reactors to the largest, The con0. 1 0.2 0.3 0.4 0.5 0.5 0.7 0.8 0.9 1.0 version in the 3-inch column was Yf” appreciably lower than t h a t cal1-iz culated assuming piston flow. Figure 11. Effect of Gas-Flow Pattern in Small Fluidized Beds Although the degree of conversion of nitric oxide obtained in the two largest reactors under varying conditions agreed reaTable IV. Results of Reaction Studies sonably well with that predicted from the experimental residence-time data and the curves drawn on $01; “0 Figure 4, the three values for the 3-inch column all lie uo Super- go, Mole Reacted ,-!e &cia1 Fraction per Initial + , Velocity), NO Mole cas yo - u Fracd& below that predicted using experimental residence C. Foot/Seo. Entering Entering uo - ? J * ~ Conversion times. These differences can be explained by lack I-Inch Reactor, L / D = 27, No. 11 Glass Beads of precision in the experimental determinations, but 32 0 35 0 0715 0 0465 1 00 0 57 31 0 13 0 0720 0 0590 0.99 0 71 may reflect on the assumption of no mixing. It apls/s-Inch Reactor, L / D = 10.4, No. 15 Glass Beads pears that a reasonable estimate of the effect of gas31 0 22 0.0702 0 0399 0 93 0 57 flow pattern on chemical conversion in small fluidized 0 0431 0 94 0 57 31 0 24 0 0758 0 0539 32 0 24 0 0907 0 94 0 60 beds can be made by employing residence-time results 0 0441 0 92 0 50 0 45 0 0914 32 0 98 0 59 and assuming bypassing with no mixing. 0 26 0 0926 0 0556 32

0 26 0.0926 0 0549 0 97 0.11 0.1183 0.0915 0.94 3-Inch Reactor, L / D = 6, No. 15 Glass Beads 33 0 28 0.0805 0 0428 0 85 33 0 27 0 0840 0 0492 0 88 33 0 30 0 0845 0 0480 0 89 to piston flow.

32 33

photometer readings and checked for bromine by bubbling the exit streamthrough a solution of potassium iodide. The excess from adsorption On the glass beads. tracer probably The effect of adsorption on residence-time data is to cause the concentration of tracer to be maintained at a higher level during the period of falling concentration than would be the case without adsorption. This effect is particularly noticeable at high values of @/ve and causes the data to give a Curve which is concave upward on semilogarithmic coordinates. It seems likely that adsorbed gas would affectthe concentration of tracerleast in the region where the tracer concentration is high. The characterizing slope, -8, was therefore obtained from composition readings made on the first void volume of gas to leave the bed. The residence-time data for fluidized beds of No. 15 glass beads in the 16/s-inch reactor, which had an LID of 10.4, are characterized by an S value of approximately 1.8. With the same beads in the 3-inch reactor ( L I D = 6), and of approximately 1.3 to 1.4 was obtained. The reaction experiments in the l-inch column show conversions near that of piston flow. The fluidizing qualities of the the NO. 11 glass beads in this tube were poor, however, tending either to slug 01-channel. The higher velocity run (see Table IV) slugged; the lower velocity run channeled somewhat near the bottom of the reactor, No residence-time data were collected in the 1-inch column, but an extrapolation of the results of the gas-mixing studies would predict reasonably high values of S for this reactor with its small diameter and high L/D ratio. The conversion in this column would consequently be expected t o approximate that resulting from piston flow. The combined

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SUMMARY

The gas-flow pattern in small fluidized-solid reactors has a n important effect on chemicalconversionin 0 64 these reactors. Residence-time data can be used to predict the magnitude of the effect for all orders of homogeneous reactions. However, in the application of this method, i t is theoretically possible for extreme cases of gas flow to arise in which the conversion may be less than that expected of complete mixing. The @;as-flowpattern and hence chemical conversion in small fluidized beds depart from that corresponding to piston flow as the L I D ratio decreases. Accurate prediction of the effectof gas-flow pattern in large units awaits gas-mixing studies in such equipment. In heterogeneous reactions carried out in fluidized-solid beds, the gas-solid contact time as well as the gas-flow pattern will be important in affecting chemical conversion. The results of the gas mixing and homogeneous reaction experiments carried out to date should be useful in separating these two effects when heterogeneous reactions are studied. On the basis of both gas mixing and chemical reaction studies, chemical reactions in packed, or fixed beds can be handled by assuming piston flow. 0 63 0 66

LITERATURE CITED

(1) Bodenstein, M., and Lindner, 2.p h y s i l . Chem , 100, 68 (1922). (2) Briner, E., PfeiRer, and Malet, G,, J . chzm. phys., 21, 25

w.,

(1924). (3) Brown, F. B., and Grist, R. H., J. Chem. Phys., 9, 840 (1941). (4) Giauque, W. F., and Kemp, J. D., Ibid.,6, 41 (1938).

ENG.CHEM.,44, 218 (5) Gilliland, E. R., and Mason, E. A., IND. (1952). (6) Hasche, R. L., and Patrick, W. A,, J. Am. Chem. me., 47, 1207 (1925). (7) Hill, W. R.,“Electronics in Engineering,” 1st ed., pp., 257-61, New York McGraw-Hill Book Co., 1949. (8) Johnston, H! s,,and Slenta, H, s,,j,Am. Chem, sot+, 73, 2948 (1951). (9) Kassel, L. S., “Kinetics of Homogeneous Gas Reactions,” A.C.S. Monograph, New York, Chemical Catalog Co., 1932. (10) Mellor, J. W., “Comprehensive Treatise on Inorganic and Theoretical Chemistry,” Vol. VIII, p. 532, New York, Longmans, Green and Co., 1940. (11) Smith, J. H., J . Am. Chem. SOC., 65, 74 (1943). R E ~ ~ Z for ~ E review D

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