- Email: [email protected]
Axial dispersion in mixed and layered bed of spheres
774
Shorter Communications
necessary to use a high-viscosity fluid. Shearing a low-viscosity fluid this way does not apparently produce adequately small bubbles. The novel idea of this procedure is to select a fluid that is miscible with the fluid in which the bubbles are desired (normally a lower-viscosity fluid such as water) and which has a much higher viscosity. In this case, the fluid selected was glycerin which is miscible with water in all proportions and has a density significantly higher than water. Small samples of glycerin were placed in a laboratory blender and sheared until they were milky with very tine air bubbles. A few minutes were allowed for the largest air bubbles to escape. Then small samples of the milky glycerin-air emulsion were withdrawn with a syringe and injected into the bottom of a column of water as shown in Fig. 2. In this situation, the glycerin slowly dissolves in the water. Those fine bubbles which were in the region near its surface are thereby liberated from the high-viscosity glycerin into the lowviscosity water and begin to rise by buoyancy. By timing the vertical rise velocity of the small bubbles (which could only be seen with very strong illumination), it was computed by Stokes Law that their diameters were of the order of 5040 pm. The rate at which such bubbles are released into the column of water is controlled by the amount of surface area of glycerin-air emulsion which is exposed to the water for dissolution. This, in turn, can be controlled by the rate at which the glyceri+air emulsion is injected through the syringe. In this way, it is possible to produce relatively dense clouds of rising air bubbles or very slow streams with only several bubbles per minute. LIMEATIONS
This shear-anddissolve method appears to be general for the production of very small bubbles of any gas in any liquid, although it has only been tested for air-water-glycerin. There must be available another thud of much hiier viscosity which is totally miscible in the fluid in which the bubbles are desired and which has a sufficiently higher density than the primary fluid so that even when a substantial number of bubbles are entrained in it, the resulting bubble-liquid emulsion will still bc denser than the primary tluid and thus will remain at the bottom of the container, releasing bubbles as it dissolves. The method does not produce bubbles of extremely reproduceable or predictable diameter. This diameter can be controlled to some extent by aging the glycerbair emulsion; duringthe aging process the smaller bubbles will disappear by dissolution in the glycerin. Thus admission of very fresh emulsion will result in the production of bubbles of a range of sizes, while emulsion which has aged for several minutes will have all the bubbles less than about 50pm diameter already dissolved. The two-fluid situation prevents the preservation of absolute purity of the fluid in which the bubbles are rising. Although molecular diffusion from the bulk of the high-viscosity fluid into the lower viscosity fluid can be shown to be’negliible, the rising bubbles will enter the less-viscous fluid carrying with them a film of the more-viscous fluid. Ordinary mass-transfer calculations indicate that this film disappears rapidly because at the scale of the bubbles, molecular diffusion is rapid. CONCLUSIONS (I) It appears to he impossible to produce bubbles smaller than about 200 pm diameter by formation at the end of capillaries or
Y
-
L
\
a 0
0-
I
5
Transparent contalnrr of less- viscous fluid
-
Small
-.
Emulsion of bubbles more -viscous fluid
bubbles
Clear layer of marsviscous fluid
Fig. 2. Schematic
of bubble release in the shear-and-dissolve method.
by any other technique which allows the bubbles to contact and attach to a solid surface. (2) Because of their rapid dissolution in the solution, bubbles smaller than about 30 pm are sufficiently unstable as to bc practically non-existent. (3) By the shear-and-dissolve method, it is possible to produce bubbles of approximately 50-60 pm in diameter in a reproduceable way. This procedure may prove useful in applications beyond that for which it was developed. Department of Chemical Engineering Universityof Utah Salt Lake City, UT 84112 U.S.A.
NOEL DE NEVERS
NOTATION
bubble diameter, pm oritice diameter, wrn acceleration of gravity, m/se? fluid density, kdm3 gas density, kg/m3 interfacial (surface) tension, kg/m
REFERENCES
Blanchard D. C. and Syzdek L. D., Chem. Engng Sci. 1977 32 1109. [21 Macintyre Ferren, Rev. Sci. Inst. 1968 38 969. [3] Epstein P. S. and Plesset hf. S., J. Chem. Phys. 195018 1505. [4] Yang W.-J., Echigo R., Wotton D. R. and Hwang J. B., L Biomech. 1971 4 275. [5] Gram H. I. and Belliier J. C.. Ind. Engng Chem. Fun& 1968 1516.
Chmical En.ginacrin#Science Vol. 36, pp. 774-776 Q Pcrpmon PressLid.. 1981. Printed in GrealB&in
Axial dllpersion
In mlxed and layerred bed of spheres
(Receiued 29 .hanuory 1980; occepred I7 July 1980) Axial dispersion in packed beds has been treated in chemical engineering literature extensively. investigations of both a theoretical and an experimental nature have been numerous, and, with a few recent exceptions, were concerned with beds of
uniformpackings.
However, in some applications such as for example the metallurgical blast furnace-a high temperature chemical reactor of great economic importance-the packings (ore and coke) consist of mixtures of different size particles deliberatelyarranged as layers in the furnace.
715
Shorter Communications
The structural non-uniformity of such a packed bed, called the stock column, results in a flow maldiatribution of the reducing gases which ultimately affects furnace efficiency and productivity. Flaw maldistribution in packed columns with non-uniform porosities has been studied theoretically in recent years&41 and also applied to structural bed non-uniformities of the type occurring in the blast furnace to show how these affect the resultant gas flow paths[S, 61. Additionally, of course, these bed non-uniformities also affect the energy losses (pressure drop) and dispersion. Tbe former has been investigated by a number of workers recently [7- IO] but fluid dispersion has not. The purpose of this communication is therefore to present the results of fluid dispersion in mixed and layered beds of spheres under flow regimes of interest to blast furnace and see how they compare with the entensive data for beds of uniform packings. It is considered that the results of this investigation could be useful in examining chemical engineering-type packed beds apart from blast furnaces and possibly also to reservoir engineering should the conditions there approach those of this investigation. EXPERIMENTAL The apparatus used consisted of a packed column (150+X lOSO),two conductivity probes each consisting of two Nichrome wires 1 mm dia., I4 mm apart, wired to an AC bridge, rectifier and a two-pen recorder. The conductivity probes extended the full diameter of the column. U-tube manometers were provided for measuring the pressure drop in the column as a check of previous data[9]. The water flow rate was metered by an orifice meter in the usual way. Packings employed were 2 mm and 6 mm dia. glass spheres. Investigations were carried out on beds of these two sizes separately, and also when mixed in various proportions and when layered alternately. The beds were prepared by hand charging the packings from a height of about 10 cm through water on the bed surface. A typical run was started by setting and maintaining the water flow rate at the desired value. The measuring and recording equipment was standard&d. When steady state was reached a I ml of concentrated KCI was injected with a hypodermic needle through the rubber tube at the inlet of water to the base of the column. KCI and the quantity used was chosen because preliminary work showed that at the resulting concentrations conductivity was directly proportional to concentration. As the KCI pulse passed the conductivity probes the consecutive responses were recorded on the chart recorder. In all instances short-tail, symmetrical response curves were obtained. All curves were compared for tracer batance and mean residence time and only those results which did not exceed + 5% error were used.
The porosity of beds of 2 mm, 6 mm and their mixtures were determined using the bed weights, volumes and densities in the USI@ way. The mean particle size of mixtures was calculated as d_l,o. i.e. the harmonic mean, it being the mean size expression that best corresponds to the mixing cell model of a packed bedIll The porosity of interfacest was measured separately by a counting technique[T]. which also gives the interface height. The value of I5 mm compares well with the detailed results of Propster and SzekeIy[l2] for the same size ratio of 3.0 (= (6 mm/2 mm)). For this ratio Propster and Szekely found the interface height to equal 2.213 larger particles, which for the present system gives 2.213 x 6 = 13 mm. The mean particle size of the interfaces was taken as gta. i.e. the arithmetic mean, it being reasoned that this mean value best reflects the directional nature of interfacesI7.9, 121. For the single packings and also for mixtures of these Le, was obtained in the normal way from the variances measured. For the interfaces, I+ was obtained by subtracting the variances of the 2 and 6mm packings which would result if no interface was present from the measured total variance of the layered bed. In other words, using the resulting obtained for 2nu-n and 6mm packings individually variances due to these packings if they merely adjoined in the layered bed were calculated and the sum subtracted from the total measured variance. RESULTS All results of this investigation are plotted in Fig. 1which also includes the solid curves given by Levenspiel[ll] which bracket a large number of experimental findings reported in the literature. By inspection of Fig. I it is seen that the results of this investigation for 6 and 2 mm spheres are well within the band of the literature data and that the results for mixtures and interfaces lie near, or just below, the lower limit of the band. Although Le, values for packed beds below the general trend, as well as above it, have been reported for small diameter beds[l3], this is obviousty not the reason here. Since the results included in Fig. I have been obtained with great care and with measuring technique free of complex boundary conditions, it is unlikely that the results give a distorted picture. Of course, tbe method used for calculating the mean particle size in mixtures and interfaces can always be criticized, but onlyon the grounds that using some other mean particle size expression would displace the results into the accepted range (or move them away further). However, we do not believe that in the absence of functional relationships for the pore size distribution involved forcing the results in this way to achieve conformity is
IO
CALCULATIONS Each pair_ of response curves was used to obtain graphically Au: and At values and hence A&, i.e. the one-shot dimensionless variance change. For this particular boundary conditions we may write without error [ 1I) A&=2
I
.
I
.
,
.
,
.
,
I
.
I
“,‘I’
(2).
4 Noting that (LXUL). i.e. the vessel Leveospiel number, Lz, is the product of the particle Levenspiel number, Le, ( = (c&d,)), and the geometric fac!or ($,/Lr), Le, was readily obtained for each run. The correspondmg particle Reynolds’ number was calculated in the usual way from the definition of Re, [Ill.
tInterfaces in layered beds are defined as the regions of small particle penetration into the underlying layer of large particles. Therefore, interfaces occur only when small particles are placed on top of larger particles. They do not occur when large particles are placed on top of small particles: in this case large particles do not penetrate into the layer of small particles and the two layers merely adjoin. Furthermore, interfaces are not uniform mixtures but are directional assemblage of particlesr],9,12].
1.0
0.1 IO
I
.
,...1*1
I
100
.
I.,...
IO00
REP Fig. 1. Particle Levenspiel number as a function of particle Reynolds number.
776
Shorter Communications
valid. Unfortunately, we have no quantitative means at this stage to assign the pore distribution functions to oure beds and so enable us to apply the generalized equations of dispersion in porous media such as for example those given recently by Carbonell[14]. Nevertheless, we believe that our results in Fig. 1 are useful as they show that for layered beds and those consisting of uniform mixtures of particles of different size, axial dispersion can be accounted for by the correlations in the literature if one properly accounts for the geometric factors. No doubt further investigation to supplement this work on dispersion data would be of great help and avoid uncertainties by Prop&r and Szekely[l2] would materially assist our understanding of the way the various structural and fluid parameters intluence the particle Levenspiel number Le,,, especially in the turbulent flow case, i.e. Re, 3 IO. In the meantime we believe that some standardization of dispersion data would be of great height and avoid incertainties that exist in literature. In this connection a most recent example that can be mentioned involves the presentation by Trasi and Khang[lS] of their RTD results in a packed column with intermittent voids using an experimental setup practically identical to the one used here. These authors show that their packed column with intermittent voids gives lower dispersion than the same column packed conventionally. This is clearly a useful result when comparing the behaviour of the two columns with respect to their performance, i.e. comparing their vessel Levenspiel numbers (Le,). However, to then present a Lc,-Ru, plot without accuunting for the new geometry due to intermittent voids and conclude that the particle Levenspiel numbers for the packed beds with voids are l-l.5 times those for the conventional packed beds, cannot be considered helpful. CONCLUSIONS The results of this investigation have shown that for layered beds-so important for blast furnaces-the axial dispersion can *Author to whom correspondence
should be addressed.
he accounted for by the correlations in the literature if one properly accounts for small particle region, large particle region, mixed particle region aad the interface region. lkpartment
of Metallurgy The University oj HroNongong Australia. 2500
N. STANDISH* G. D. BULL
RErEaENcFs
[I] Stanek V. and Szekely J., A.LCh.E.J. 1974 20 974. [2] Stanek V. and Szekely J., Can, J. Chem. Engng 1972 58 9. [3] Choudhary M.. Szekely J. and Weller S. W., A.6Ch.E.J. 1976 22 1021. [4] Szekely J. and Poveromo J. J., A.LCh.E.L 1975 21769. [5] Poveromo J. J., Szekely J. and Pmpster hi., Pmt. Symp, Blast Furnace Aerodynamics, p. I. Woollongong 1975. [6] Kuwabara M. and Muchi I., Pmt. Symp. fllus? Furnace Aerodynamics, p. 61. WoUongong 1975. [7] Standish N. and Williams I. P., Pmt. Symp. Blast Furnace Aerodynamics, p. 9. Wollongong 1975. [81 .%e$ylf and Propster M., Imnmaking and See/making [91 Standish i. and Wiltshire B. D., Ironmaking and Steelmaking 1978 5 253. [lo] Sparrow E. hf., Beavers 0. S.. Goldstein L. and Bahrami P., A.1.Ch.E.J. 1916 22 194. [ll] Lcvenspiel 0.. Chcmicai Reaction Engfncering, (2nd Edn). Wiley, New York 1972. [12] Propster M. and Szekely J., Powder Techno/. 1977 17 123. [l3]. Haiang T. Chu-Shao and Haynes H. W., Chem. Engng Sci. 1977 32 618. [l41 Carbonell R. G., Chem. Engng Sci. 1979 34 1031. [I51Tcasi P. and Khan8 S. J., ind. Engng Chem. Fundls 1979 18 256.
Experimental observations of complex dynamic behavior in the catalytic oxidation of CO on Pt/alumfna catalyst (Received 9 April 1980: accepted 17 July 1980) Chemical reaction occurring on a solid catalyst is represented by a dynamic system of a complicated nature. The systemequations written as a mathematical model corresponding to a real system, are in fact a vary rough approximation. In the past there have been numerous attempts to formulate heterogeneous catalytic reactions in terms of differential equations. References to most of the work on this subject may be found in the book by Aris[ll. The singular and oscillatory solutions of these equations are of great sigai&nce for understanding the fundamental laws governing the behavior of a reaction occuring on a catalyst. The appearance of bifurcation phenomena in heterogeneous catalytic systemshas been a subject of theoretical[l] and experimental studies[2,3]. Recent experimentally oriented publications have demonstrated a need for physicists and engineers to be aware of the fundamental nature of complicated bifurcations in modelling catalytic processes[rl-61. The purpose of this paper is to show experimentally the complex behavior of a catalytic reaction, as, e.g. complicated hysteresis loops and pathological dynamic which indicate the importance of bifurcation behavior, phenomena in the analysis of catalytic systems. This paper reports on an experimental study of the complex dynamics of the platinum catalyzed oxidation of CO.
EXPERIMENTAL.
A detailed description of the experimental portion of this research is published elsewhere[l]. Here only a brief summary of the facts associated with the experimental system is presented. A mixture of CO and O2 was fed continuously to a laboratory differential reactor provided with a recirculation pump. The necessity of using a differential reactor is given by the fact of large heat liberation effects of the CO oxidation. The cecirculation arrangements guarantee a finite degree of conversion along with an intensive axial mixing and elimination of any temperature and concentrationgradients.The experimentalconditions ace reported in Table 1. Calculations for experimental conditions indicated that the heat and mass gas-to-solid transfer is completely eliminated. The axial temperature difference was measured by two thermocouples located in the fore and aft sections of the differential reactor. The maximum axial temperature difference even for large oscillations was 2’C. As a result the experiments can be considered isothermal.
Results of experiments
REsuLh employing the apparatus
described
Shorter Communications
necessary to use a high-viscosity fluid. Shearing a low-viscosity fluid this way does not apparently produce adequately small bubbles. The novel idea of this procedure is to select a fluid that is miscible with the fluid in which the bubbles are desired (normally a lower-viscosity fluid such as water) and which has a much higher viscosity. In this case, the fluid selected was glycerin which is miscible with water in all proportions and has a density significantly higher than water. Small samples of glycerin were placed in a laboratory blender and sheared until they were milky with very tine air bubbles. A few minutes were allowed for the largest air bubbles to escape. Then small samples of the milky glycerin-air emulsion were withdrawn with a syringe and injected into the bottom of a column of water as shown in Fig. 2. In this situation, the glycerin slowly dissolves in the water. Those fine bubbles which were in the region near its surface are thereby liberated from the high-viscosity glycerin into the lowviscosity water and begin to rise by buoyancy. By timing the vertical rise velocity of the small bubbles (which could only be seen with very strong illumination), it was computed by Stokes Law that their diameters were of the order of 5040 pm. The rate at which such bubbles are released into the column of water is controlled by the amount of surface area of glycerin-air emulsion which is exposed to the water for dissolution. This, in turn, can be controlled by the rate at which the glyceri+air emulsion is injected through the syringe. In this way, it is possible to produce relatively dense clouds of rising air bubbles or very slow streams with only several bubbles per minute. LIMEATIONS
This shear-anddissolve method appears to be general for the production of very small bubbles of any gas in any liquid, although it has only been tested for air-water-glycerin. There must be available another thud of much hiier viscosity which is totally miscible in the fluid in which the bubbles are desired and which has a sufficiently higher density than the primary fluid so that even when a substantial number of bubbles are entrained in it, the resulting bubble-liquid emulsion will still bc denser than the primary tluid and thus will remain at the bottom of the container, releasing bubbles as it dissolves. The method does not produce bubbles of extremely reproduceable or predictable diameter. This diameter can be controlled to some extent by aging the glycerbair emulsion; duringthe aging process the smaller bubbles will disappear by dissolution in the glycerin. Thus admission of very fresh emulsion will result in the production of bubbles of a range of sizes, while emulsion which has aged for several minutes will have all the bubbles less than about 50pm diameter already dissolved. The two-fluid situation prevents the preservation of absolute purity of the fluid in which the bubbles are rising. Although molecular diffusion from the bulk of the high-viscosity fluid into the lower viscosity fluid can be shown to be’negliible, the rising bubbles will enter the less-viscous fluid carrying with them a film of the more-viscous fluid. Ordinary mass-transfer calculations indicate that this film disappears rapidly because at the scale of the bubbles, molecular diffusion is rapid. CONCLUSIONS (I) It appears to he impossible to produce bubbles smaller than about 200 pm diameter by formation at the end of capillaries or
Y
-
L
\
a 0
0-
I
5
Transparent contalnrr of less- viscous fluid
-
Small
-.
Emulsion of bubbles more -viscous fluid
bubbles
Clear layer of marsviscous fluid
Fig. 2. Schematic
of bubble release in the shear-and-dissolve method.
by any other technique which allows the bubbles to contact and attach to a solid surface. (2) Because of their rapid dissolution in the solution, bubbles smaller than about 30 pm are sufficiently unstable as to bc practically non-existent. (3) By the shear-and-dissolve method, it is possible to produce bubbles of approximately 50-60 pm in diameter in a reproduceable way. This procedure may prove useful in applications beyond that for which it was developed. Department of Chemical Engineering Universityof Utah Salt Lake City, UT 84112 U.S.A.
NOEL DE NEVERS
NOTATION
bubble diameter, pm oritice diameter, wrn acceleration of gravity, m/se? fluid density, kdm3 gas density, kg/m3 interfacial (surface) tension, kg/m
REFERENCES
Blanchard D. C. and Syzdek L. D., Chem. Engng Sci. 1977 32 1109. [21 Macintyre Ferren, Rev. Sci. Inst. 1968 38 969. [3] Epstein P. S. and Plesset hf. S., J. Chem. Phys. 195018 1505. [4] Yang W.-J., Echigo R., Wotton D. R. and Hwang J. B., L Biomech. 1971 4 275. [5] Gram H. I. and Belliier J. C.. Ind. Engng Chem. Fun& 1968 1516.
Chmical En.ginacrin#Science Vol. 36, pp. 774-776 Q Pcrpmon PressLid.. 1981. Printed in GrealB&in
Axial dllpersion
In mlxed and layerred bed of spheres
(Receiued 29 .hanuory 1980; occepred I7 July 1980) Axial dispersion in packed beds has been treated in chemical engineering literature extensively. investigations of both a theoretical and an experimental nature have been numerous, and, with a few recent exceptions, were concerned with beds of
uniformpackings.
However, in some applications such as for example the metallurgical blast furnace-a high temperature chemical reactor of great economic importance-the packings (ore and coke) consist of mixtures of different size particles deliberatelyarranged as layers in the furnace.
715
Shorter Communications
The structural non-uniformity of such a packed bed, called the stock column, results in a flow maldiatribution of the reducing gases which ultimately affects furnace efficiency and productivity. Flaw maldistribution in packed columns with non-uniform porosities has been studied theoretically in recent years&41 and also applied to structural bed non-uniformities of the type occurring in the blast furnace to show how these affect the resultant gas flow paths[S, 61. Additionally, of course, these bed non-uniformities also affect the energy losses (pressure drop) and dispersion. Tbe former has been investigated by a number of workers recently [7- IO] but fluid dispersion has not. The purpose of this communication is therefore to present the results of fluid dispersion in mixed and layered beds of spheres under flow regimes of interest to blast furnace and see how they compare with the entensive data for beds of uniform packings. It is considered that the results of this investigation could be useful in examining chemical engineering-type packed beds apart from blast furnaces and possibly also to reservoir engineering should the conditions there approach those of this investigation. EXPERIMENTAL The apparatus used consisted of a packed column (150+X lOSO),two conductivity probes each consisting of two Nichrome wires 1 mm dia., I4 mm apart, wired to an AC bridge, rectifier and a two-pen recorder. The conductivity probes extended the full diameter of the column. U-tube manometers were provided for measuring the pressure drop in the column as a check of previous data[9]. The water flow rate was metered by an orifice meter in the usual way. Packings employed were 2 mm and 6 mm dia. glass spheres. Investigations were carried out on beds of these two sizes separately, and also when mixed in various proportions and when layered alternately. The beds were prepared by hand charging the packings from a height of about 10 cm through water on the bed surface. A typical run was started by setting and maintaining the water flow rate at the desired value. The measuring and recording equipment was standard&d. When steady state was reached a I ml of concentrated KCI was injected with a hypodermic needle through the rubber tube at the inlet of water to the base of the column. KCI and the quantity used was chosen because preliminary work showed that at the resulting concentrations conductivity was directly proportional to concentration. As the KCI pulse passed the conductivity probes the consecutive responses were recorded on the chart recorder. In all instances short-tail, symmetrical response curves were obtained. All curves were compared for tracer batance and mean residence time and only those results which did not exceed + 5% error were used.
The porosity of beds of 2 mm, 6 mm and their mixtures were determined using the bed weights, volumes and densities in the USI@ way. The mean particle size of mixtures was calculated as d_l,o. i.e. the harmonic mean, it being the mean size expression that best corresponds to the mixing cell model of a packed bedIll The porosity of interfacest was measured separately by a counting technique[T]. which also gives the interface height. The value of I5 mm compares well with the detailed results of Propster and SzekeIy[l2] for the same size ratio of 3.0 (= (6 mm/2 mm)). For this ratio Propster and Szekely found the interface height to equal 2.213 larger particles, which for the present system gives 2.213 x 6 = 13 mm. The mean particle size of the interfaces was taken as gta. i.e. the arithmetic mean, it being reasoned that this mean value best reflects the directional nature of interfacesI7.9, 121. For the single packings and also for mixtures of these Le, was obtained in the normal way from the variances measured. For the interfaces, I+ was obtained by subtracting the variances of the 2 and 6mm packings which would result if no interface was present from the measured total variance of the layered bed. In other words, using the resulting obtained for 2nu-n and 6mm packings individually variances due to these packings if they merely adjoined in the layered bed were calculated and the sum subtracted from the total measured variance. RESULTS All results of this investigation are plotted in Fig. 1which also includes the solid curves given by Levenspiel[ll] which bracket a large number of experimental findings reported in the literature. By inspection of Fig. I it is seen that the results of this investigation for 6 and 2 mm spheres are well within the band of the literature data and that the results for mixtures and interfaces lie near, or just below, the lower limit of the band. Although Le, values for packed beds below the general trend, as well as above it, have been reported for small diameter beds[l3], this is obviousty not the reason here. Since the results included in Fig. I have been obtained with great care and with measuring technique free of complex boundary conditions, it is unlikely that the results give a distorted picture. Of course, tbe method used for calculating the mean particle size in mixtures and interfaces can always be criticized, but onlyon the grounds that using some other mean particle size expression would displace the results into the accepted range (or move them away further). However, we do not believe that in the absence of functional relationships for the pore size distribution involved forcing the results in this way to achieve conformity is
IO
CALCULATIONS Each pair_ of response curves was used to obtain graphically Au: and At values and hence A&, i.e. the one-shot dimensionless variance change. For this particular boundary conditions we may write without error [ 1I) A&=2
I
.
I
.
,
.
,
.
,
I
.
I
“,‘I’
(2).
4 Noting that (LXUL). i.e. the vessel Leveospiel number, Lz, is the product of the particle Levenspiel number, Le, ( = (c&d,)), and the geometric fac!or ($,/Lr), Le, was readily obtained for each run. The correspondmg particle Reynolds’ number was calculated in the usual way from the definition of Re, [Ill.
tInterfaces in layered beds are defined as the regions of small particle penetration into the underlying layer of large particles. Therefore, interfaces occur only when small particles are placed on top of larger particles. They do not occur when large particles are placed on top of small particles: in this case large particles do not penetrate into the layer of small particles and the two layers merely adjoin. Furthermore, interfaces are not uniform mixtures but are directional assemblage of particlesr],9,12].
1.0
0.1 IO
I
.
,...1*1
I
100
.
I.,...
IO00
REP Fig. 1. Particle Levenspiel number as a function of particle Reynolds number.
776
Shorter Communications
valid. Unfortunately, we have no quantitative means at this stage to assign the pore distribution functions to oure beds and so enable us to apply the generalized equations of dispersion in porous media such as for example those given recently by Carbonell[14]. Nevertheless, we believe that our results in Fig. 1 are useful as they show that for layered beds and those consisting of uniform mixtures of particles of different size, axial dispersion can be accounted for by the correlations in the literature if one properly accounts for the geometric factors. No doubt further investigation to supplement this work on dispersion data would be of great help and avoid uncertainties by Prop&r and Szekely[l2] would materially assist our understanding of the way the various structural and fluid parameters intluence the particle Levenspiel number Le,,, especially in the turbulent flow case, i.e. Re, 3 IO. In the meantime we believe that some standardization of dispersion data would be of great height and avoid incertainties that exist in literature. In this connection a most recent example that can be mentioned involves the presentation by Trasi and Khang[lS] of their RTD results in a packed column with intermittent voids using an experimental setup practically identical to the one used here. These authors show that their packed column with intermittent voids gives lower dispersion than the same column packed conventionally. This is clearly a useful result when comparing the behaviour of the two columns with respect to their performance, i.e. comparing their vessel Levenspiel numbers (Le,). However, to then present a Lc,-Ru, plot without accuunting for the new geometry due to intermittent voids and conclude that the particle Levenspiel numbers for the packed beds with voids are l-l.5 times those for the conventional packed beds, cannot be considered helpful. CONCLUSIONS The results of this investigation have shown that for layered beds-so important for blast furnaces-the axial dispersion can *Author to whom correspondence
should be addressed.
he accounted for by the correlations in the literature if one properly accounts for small particle region, large particle region, mixed particle region aad the interface region. lkpartment
of Metallurgy The University oj HroNongong Australia. 2500
N. STANDISH* G. D. BULL
RErEaENcFs
[I] Stanek V. and Szekely J., A.LCh.E.J. 1974 20 974. [2] Stanek V. and Szekely J., Can, J. Chem. Engng 1972 58 9. [3] Choudhary M.. Szekely J. and Weller S. W., A.6Ch.E.J. 1976 22 1021. [4] Szekely J. and Poveromo J. J., A.LCh.E.L 1975 21769. [5] Poveromo J. J., Szekely J. and Pmpster hi., Pmt. Symp, Blast Furnace Aerodynamics, p. I. Woollongong 1975. [6] Kuwabara M. and Muchi I., Pmt. Symp. fllus? Furnace Aerodynamics, p. 61. WoUongong 1975. [7] Standish N. and Williams I. P., Pmt. Symp. Blast Furnace Aerodynamics, p. 9. Wollongong 1975. [81 .%e$ylf and Propster M., Imnmaking and See/making [91 Standish i. and Wiltshire B. D., Ironmaking and Steelmaking 1978 5 253. [lo] Sparrow E. hf., Beavers 0. S.. Goldstein L. and Bahrami P., A.1.Ch.E.J. 1916 22 194. [ll] Lcvenspiel 0.. Chcmicai Reaction Engfncering, (2nd Edn). Wiley, New York 1972. [12] Propster M. and Szekely J., Powder Techno/. 1977 17 123. [l3]. Haiang T. Chu-Shao and Haynes H. W., Chem. Engng Sci. 1977 32 618. [l41 Carbonell R. G., Chem. Engng Sci. 1979 34 1031. [I51Tcasi P. and Khan8 S. J., ind. Engng Chem. Fundls 1979 18 256.
Experimental observations of complex dynamic behavior in the catalytic oxidation of CO on Pt/alumfna catalyst (Received 9 April 1980: accepted 17 July 1980) Chemical reaction occurring on a solid catalyst is represented by a dynamic system of a complicated nature. The systemequations written as a mathematical model corresponding to a real system, are in fact a vary rough approximation. In the past there have been numerous attempts to formulate heterogeneous catalytic reactions in terms of differential equations. References to most of the work on this subject may be found in the book by Aris[ll. The singular and oscillatory solutions of these equations are of great sigai&nce for understanding the fundamental laws governing the behavior of a reaction occuring on a catalyst. The appearance of bifurcation phenomena in heterogeneous catalytic systemshas been a subject of theoretical[l] and experimental studies[2,3]. Recent experimentally oriented publications have demonstrated a need for physicists and engineers to be aware of the fundamental nature of complicated bifurcations in modelling catalytic processes[rl-61. The purpose of this paper is to show experimentally the complex behavior of a catalytic reaction, as, e.g. complicated hysteresis loops and pathological dynamic which indicate the importance of bifurcation behavior, phenomena in the analysis of catalytic systems. This paper reports on an experimental study of the complex dynamics of the platinum catalyzed oxidation of CO.
EXPERIMENTAL.
A detailed description of the experimental portion of this research is published elsewhere[l]. Here only a brief summary of the facts associated with the experimental system is presented. A mixture of CO and O2 was fed continuously to a laboratory differential reactor provided with a recirculation pump. The necessity of using a differential reactor is given by the fact of large heat liberation effects of the CO oxidation. The cecirculation arrangements guarantee a finite degree of conversion along with an intensive axial mixing and elimination of any temperature and concentrationgradients.The experimentalconditions ace reported in Table 1. Calculations for experimental conditions indicated that the heat and mass gas-to-solid transfer is completely eliminated. The axial temperature difference was measured by two thermocouples located in the fore and aft sections of the differential reactor. The maximum axial temperature difference even for large oscillations was 2’C. As a result the experiments can be considered isothermal.
Results of experiments
REsuLh employing the apparatus
described