Performance Analysis of a Fluidized Bed Reactor. 1. Visible Flow Behavior Claude Chavarie and John R. Grace* Department of Chemical Engmeer/ng, McGdl Un/vers/ty, Montreal. Canada H3C 3G 1
When chemical reactions are carried out in fluidized beds, the reactor performance may be strongly influenced by the hydrodynamics of the two phases. In the present study, bubble sizes, bubble frequencies, and visible bubble flow rates have been measured in a large two-dimensional fluidized bed. The operating conditions were chosen to be identical with those used in the reaction studies described in the companion papers. Coherent expressions for the bubble properties are presented and allow hydrodynamic parameters to be specified in the testing of fluidized bed chemical reactor models against measured concentration profiles and overall conversions.
Introduction The use of models to predict the performance of gas fluidized bed reactors has led to considerable controversy. A large number of models have been devised and these differ in many important aspects (Grace, 1971; Pyle, 1972; Rowe, 1972). There is lack of agreement about the relative usefulness of the whole model approach. The present study was undertaken to evaluate and discriminate between the most important fluidized bed reactor models. There are two novel aspects to the study. 1. Most chemical reactor models for fluidized beds are based explicitly or implicitly on the presence of bubbles in the bed. The number, size, and velocity of these bubbles figure prominently in many of the models, and yet the reactor models have almost invariably been tested with these hydrodynamic features unknown or subject to considerable uncertainty. A “two-dimensional” fluidized bed reactor was employed in the present study so that visible bubble properties could be measured directly. Actual bubble properties could thus be fed directly into the models as appropriate to allow a more discriminating test of the basic assumptions underlying the models and to reduce the number of fitted parameters to a minimum. 2. In the previous experimental studies, fluidized bed reactor models have been evaluated by measuring the difference in composition of the inlet and outlet gas streams. The evaluation and discrimination techniques used in the present study are much more demanding on the models. Concentrations have been measured separately in the individual phases a t various levels in the bed. Thus we are concerned not only with the ability of a given model to predict the overall chemical conversion for various operating conditions, but also with the degree of correspondence between predicted and observed reactant concentration profiles. It is apparent that a given model may fortuitously predict the correct overall conversion for a given set of conditions by predicting too high a concentration in one phase coupled with too low a concentration for the other phase, or by predicting too high a reaction rate in one region of the bed coupled with too low a reaction rate in another region. Thus even if a given model gives a good prediction of overall conversion, its failure to represent observed concentration profiles raises serious doubts about the general validity of the model. The bubble phase and dense phase concentration profiles measured in this study provide a unique method for critical evaluation and comparison of fluidized bed reactor models. An important limitation of the present study is that the reactor is a two-dimensional column and hence the quantitative information obtained could not be expected to be directly applicable to large-scale three-dimensional beds.
Moreoever, the range of operating conditions which could be studied was limited by the analysis system and by experimental problems associated with the generation and containment of ozone. Despite these limitations, the results obtained here give new insight into the behavior of fluidized bed reactors, insights which are made possible by measurement of reactant concentrations in the individual phases coupled with simultaneous bubble property measurements. Thus while the experimental results are not directly applicable to three-dimensional beds in a quantitative sense, the qualitative conclusions regarding the validity of chemical reactor models are believed to be applicable. ‘The experimental details and some preliminary conclusions of the present work were reported in an earlier paper (Chavarie and Grace, 1972). In the present papers, we present many more results regarding the physical aspects of the bed as well as an extended study of reactor models. The conclusions differ somewhat from those presented previously due to an error in a computer program used to apply the Kunii and Levenspiel (1969) model; this error has now been corrected. In Part I we present measurements of the visible bubble flow behavior which are needed to test the reaction models. Part I1 is concerned with reaction studies and with evaluation of reactor models proposed in the literature. Finally Part I11 considers the extension of reactor models to give better representation of measured concentration profiles. Measurement of Visible Bubble Properties Closely linked with the performance of a catalytic reactor is its fluid mechanic behavior. Fluidized beds give rise to two distinct flow regions, a dense phase which contains virtually all of the particles plus interstitial gas and a bubble phase which is made up of discrete rising bubbles containing few particles. Many properties of these bubbles can be measured if photographs are taken of the face of a “two-dimensional” bed. In the present study, the two-dimensional column was 245 cm high x 56 cm x 1 cm thick and it has been described in detail elsewhere (Chavarie and Grace, 1972; Chavarie. 1973). Cine films were taken of the back-lighted column at 32 and 64 frames per second using a Bolex reflex camera. Visible bubble properties were obtained from frame by frame analysis of these film. Rubble areas were measured using a Quantitative Image Analyzing Computer developed by Metals Research Limited. A grid of 2.54 cm spacing taped on the outside front wall of the column provided the scale of the photographs. The particles used, a mixture of closely sized glass beads and alumina with a minimum fluidization velocity of 5.3 cm/sec, were the Ind. Eng. Chem., Fundam., Vol. 14, No. 2, 1975
75
3
U
14-
3
u
12 7 crn / s e c = I 6 5 cm/sec
12.
5 U
= 2 2 8 crn / s e c
=
/d-
-b e l IO
- 6
q;,/
0
4.
:
fluidized beds, the mean bubble diameter DB increases with height y . Kobayashi et al. (1965) have suggested that DB varies approximately linearly with y , and their work has been combined with that of Cooke et al. (1968) by Kat0 and Wen (1969), who suggested the following equation for three-dimensional beds with perforated plate distributors
(c)
DB = 1.4ppdD
2 /c
0
J’
+ Do (cgs units)
(2)
where Do, the initial bubble size, may be obtained from a correlation of Cooke et al.
(3) same as those used in the reaction studies. Similarily, the flow rates and bed depths were chosen to duplicate the conditions employed in the reaction studies described in Part 11. The vertical coordinate of a bubble was taken as the distance from the distributor to the mid-point between its nose and rear. The perimeter was measured with an “‘inch-counter’’(used in map-work). The fraction, cB, of the total cross-sectional bed area occupied by bubbles at a given level was obtained from the mean of the fraction of the bed width cut by bubbles for 50 to 70 frames. These measurements were relatively straightforward except in the bottom 20 cm of the bed where there were large numbers of small bubbles. The measurement of visible bubble flow rate, GB, is difficult due to coalescence and splitting accompanied by side effects such as bubble growth and leakage (Grace and Clift, 1974). The procedure adopted in the present study was to record the area of each bubble as the centroid of its visible area reached the level under consideration. GB was then calculated from the total bubble area crossing the level and the total number of frames analyzed, while the average bubble area was taken as the arithmetic mean of the areas measured. Interpretation of some events is necessarily rather subjective. For example, it is often difficult to distinguish whether a bubble has split or whether it is simply undergoing showering from the roof. Similarly the instant of completion of coalescence is often not distinct. Consequently a large number of frames (between 400 and 700 per sequence) was covered to provide a large sample of bubbles and events, and two observers collaborated in the analysis for the higher flow rates where bubble interaction was most severe. A coherent mathematical representation for observable bubble features is required to enable the reactor models to be tested. The form of all equations to be used has either been inspired by existing published work or developed from elementary interrelationships between the measured variables. The equations used have been made self-consistent and, wherever possible, based on physical reasoning. A unified global treatment of the data has been used to ensure a common coherent model for the flow rate range studied and to increase the sample size above that available for any individual run. The degree of accuracy of the data and the precision required mean that it is usually sufficient to adopt linear regression techniques. (a) Mean Bubble Size. The variation in bubble size as a function of distance from the distributor, y , and the inlet flow rate turned out to be a key factor in the overall representation of the observable fluid mechanic features of the two-dimensional bed. DHis simply defined here by
A, = nDB2/4 Since coalescence is so important for aggregatively 76
Ind. Eng. Chem., Fundam., Vol. 14, No. 2, 1975
Here no is the number of holes per unit area in the distributor. The equation employed in this work is similar in form to the above. Since neither p p nor d, nor Umf was changed in this work and since the value of the numerical parameter in eq 2 could not be expected to hold for two-dimensional systems, we write
DB = b u y
+
DO
(4) where b and D O are to be evaluated. Figure 1 shows a plot of De, obtained from the experimental measurement of AB, vs. Uy to test the form of eq 4; a linear dependence does seem appropriate. From a least-squares fit of the data the best estimates of the parameters were found to be: b = 5.3 X sec/cm f 11%a t a 95% degree of confidence and D O = 2.1 cm. For sake of comparison, this value of b corresponds to a coefficient of 0.52 (cgs units) in eq 2 where pp = 2.4 g/cc, d, = 0.0215 cm, and Umf= 5.32 cm/sec. Figure 1 also shows that uniform treatment of the data is indeed feasible for the flow range covered in this work. (b) Bed Expansion. The bed expansion, i.e., the ratio of total bed height to the bed height a t minimum fluidization, was estimated from the mean level of the top surface of the bubbling bed a t various flow rates. The bed expansion can be related to the average fraction of the bed occupied by bubbles if the dense void fraction is assumed to remain constant a t e m f . This common assumption is supported by voidage measurements of Lockett and Harrison (1967).Thus H - Hmf = H The value of (CB) determined in this way was used as a check on the equation given below describing the variation of CBwith height. The small number of data points obtained in this work does not permit a meaningful test of models suggested in the literature to describe ( t i ) . The equation (EB)
= 5.4 x lO-*(LT -
rmp
(6)
has been used only to minimize the number of input data in computer programs and to allow a certain flexibility of interpolation between the flow conditions used in this work. ( c ) Bubble Velocity. The average bubble velocity can be defined and related to the visible bubble flow rate by G, = LrBAobserved a t u =22.8 '3(e,>observed
ot
u
=I65
cm / sec crn/sec
W
Figure 5.
Experimental b u b b l e v o i d fractions compared w i t h curves p r e d i c t e d by t h e o v e r a l l b u b b l e flow s i m u l a t i o n .
in order to minimize the error in predicting CB. Equation 19 is plotted in Figure 2 and it is obvious that the new equation fits the velocity data very nearly we well as eq 12. As a further test of the validity of the C B representation, the predicted average bubble void fraction was obtained by numerical integration of each of the profiles and compared to the observed (CB)values. Agreement was within 4% for each case.
Discussion The equations for bubble properties to be used in testing chemical reactor models are summarized in Table I. The hydrodynamic measurements reported here were taken only for conditions corresponding to the chemical conversion studies discussed in Part 11. Thus the range of variables covered is severely limited, and it is important not to seek to generalize these results beyond the scope of this work. Nevertheless, it is of interest to point out that the mea.surements of Ge show that the visible bubble flow rate appeared to increase with distance, y , and that while the simple two-phase postulate of Toomey and Johnstone (1952) did not apply, it may provide a limiting value of Gg well above the distributor (see Figure 4). It is also im78
Ind. Eng. Chem., Fundam., Vol. 14, No. 2, 1975
Nomenclature AB = frontal area of two-dimensional bubble b = constantineq4 dp = mean particle diameter U B = bubble diameter defined by eq 1 D O = bubble size at the distributor f = bubble frequency f o = bubble frequency a t the distributor g = acceleration due to gravity GB = visible bubble flow rate H = mean expanded bed height H,r = bed height at minimum fluidization K , K' = constants in eq 10 and 11 no = number of distributor holes per unit area m, m' = exponents in eq 10 and 11 R, S = constants in eq 17 U = superficial gas velocity UB = bubble rise velocity U g m = bubble rise velocity in isolation Umf = superficial gas velocity at minimum fluidization w = thickness of two-dimensional bed y = distance above the distributor
Greek Letters /3 = constantineq4 tg = fraction of bed occupied by bubbles a t some partic-
ular height = overall fraction of bed occupied by bubbles pp = density of solid particles (Cg)
Literature Cited Angelino, H., D.Sc. Thesis, Toulouse, 1964. Calderbank, P. H., Toor, F. D . . in "Fluidization." p 652, J. F. Davidson and D. Harrison, Ed.. Academic Press, New York, N.Y., 1971 Calderbank, P. H., Toor, F. D., Lancaster. F. H., "Proceedings of International Symposium on Fluidization," A. A. H. Drinkenburg, Ed., Netherlands University Press, 1967. Chavarie, C., Ph.D. Thesis, McGill University, 1973. Chavarie. C., Grace, J. R., "Proceedings of 5th European/2nd International Svmoosium on Chemical Reaction Enaineerinq, - . D 69-37, Amsterdam', 1972. Cooke, M J., Harris, W., Highiey. J., Williams, D. F.. /.Ch.E. Symp. Ser., No. 30, 14 (1968). Davidson, J. F., Harrison, D., "Fluidized Particles," Cambridge University Press, 1963. Grace.J. R.,A./.Ch.E. Symp. Ser.. 67, No. 116. 159 (1971). Grace, J. R . , Clift, R.. Chem. E n g . Sci., 29, 327 (1974) Grace, J. R . , Harrison, D., Chem. Eng. Sci., 24, 497 (1969). Kato. K..Wen, C. Y., Chem. E n g . Sci., 24, 1351 (1969).
Kobayashi, H.. Arai. F.. Chiba, T., Chem. Eng. Tokyo, 29, 858 (1965). Kobayashi. H.. Arai. F.. Chiba. T., Chem. Eng. Jpn.. 4, 147 (1966). Kunii. D . , Levenspiel, O.,"Fluidization Engineering," Wiley, New York, N.Y., 1969. Lockett, M. J . , Harrison, D., "Proceedings of International Symposium on Fluidization," A. A. H. Drinkenburg. Ed., Netherlands University Press, 1967. Pyle, D. L.,Adv. Chem. Ser., 109, 106 (1972). Pyle, D. L., Harrison, D., Chem. Eng. Sci., 22. 531 (1967). Rowe, P. M . , "Proceedings of 5th European/2nd International Symposium on Chemical Reaction Engineering," p A9-1, Amsterdam, 1972.
Toomey, R. D., Johnstone, H. P., Chem. Eng. Progr., 48. No. 5 , 220 (1952). Turner, J. C. R., Chem. Eng. Sci., 21, 971 (1966).
Received for review J u n e 14, 1974 Accepted F e b r u a r y 7,1975 A c k n o w l e d g m e n t i s m a d e t o t h e donors of t h e P e t r o l e u m R e search Fund, a d m i n i s t e r e d by t h e A m e r i c a n C h e m i c a l Society, for s u p p o r t of t h i s research.
Performance Analysis of a Fluidized Bed Reactor. II. Observed Reactor Behavior Compared with Simple Two-Phase Models Claude Chavarie and John R. Grace* Department of Chemical Engineering, McGill University, Montreal, Canada H3C 3G 1
The catalytic decomposition of ozone was monitored in a two-dimensional fluidized bed reactor. Experimental concentration profiles were obtained for both the dense phase and the bubble phase. Overall conversions were also measured. The experimental data were compared to predictions from six simple physical models which take account of the two-phase nature of gas fluidized beds, where one parameter, at most, was fitted. On statistical grounds, all of the models fail to represent the observed reactor behavior. A useful approximation of the reactor performance is, nevertheless, provided by the bubbling bed model of Kunii and Levenspiel.
Introduction The hydrodynamic behaviour of the fluidized bed used in this work was described in Part I. Part I1 analyzes the performance of the same fluidized bed as a chemical reactor and compares the reactor data with predictions from six of the more popular two-phase chemical reactor models. These models represent a broad range of basic assumptions (Grace, 1971). For example, clouds and/or wakes are assumed in some models and not in others; a single average bubble diameter is assumed in some models while others allow for changes in bubble size with height; some models rely on the two-phase flow distribution suggested by Toomey and Johnstone (1952) while others neglect the percolation of gas through the dense phase; five different interphase mass transfer mechanisms are employed. The fundamental assumptions of each model have been respected in the present paper, although minor modifications are necessary to adapt the models to two-dimensional systems. The objectives of the present paper are (i) to present experimental concentration profiles for the fluidized bed under conditions identical to those described in Part I, (ii) to observe how well the six representative models predict the concentration profiles and overall conversions, and (iii) to lay the grounds for model improvements to be discussed in Part 111.
nitrate provided a reliable catalyst. The activity of the catalyst was varied by changing the relative amounts of alumina particles and inert beads. The activity was measured before, during, and after each run by feeding samples of solids to a fixed bed reactor. The materials of the reactor and auxiliary equipment were carefully chosen to prevent attack by ozone or poisoning of the catalyst particles. The fluidizing gas consisted of air containing less than 1% ozone by volume generated by a Model 03B6-0 ozone generator manufactured by Ozone Research and Equipment Corporation. Bubble phase ozone concentrations were measured by passing a 254-pm uv beam and a reference beam through a pair of quartz windows (there were 54 pairs in all) and measuring the intensity of the beams with a DuPont 400 photometric analyzer connected to a high-speed recorder. The reference beam allowed correction for particle showering through the bubbles. Withdrawal of gas samples through porous disks located throughout the bed allowed dense phase ozone concentrations to be measured. Samples were withdrawn intermittently, between the arrivals of bubbles a t the sample point. Inlet and outlet concentrations were also measured using uv absorption. Full experimental details including a discussion of errors have been reported elsewhere (Chavarie, 1973; Chavarie and Grace, 1972).
Experimental Apparatus The catalytic decomposition of ozone is particularly well-suited to the objectives of the present work since the reaction is very nearly first order, may be analyzed using uv absorption, and has appreciable rates of reaction at room temperature. A mixture of glass beads and porous alumina particles which had been impregnated with ferric
Experimental Profiles Figure 1 shows typical concentration profiles and illustrates the reproducibility of the data (pure error = 1 X the runs having been carried out on three different days. Profiles were obtained for superficial gas velocities, U , of 12.7, 16.5, and 22.8 cm/sec and catalyst activities, k , of 0.063, 0.09, and 0.20 and 0.4 sec -I. The height of the Ind. Eng. Chem., Fundam., Vol. 14, No. 2 , 1975
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