I n d . Eng. Chem. Res. 1990,29, 1013-1019
1013
The Fluidized Bed Catalytic Reactor: A Learning Model for Fast Reaction Richard G. Pigeon and James J. Carberry* Laboratory of Catalysis, Department of Chemical Engineering, University of Notre Dame, Notre Dame, Indiana 46556
The two-phase model of the bubbling fluidized bed catalytic reactor is modified in anticipation of rapid reaction occurring not in series but simultaneously with mass transport between lean and dense phases. Thus is invoked an intraphase effectiveness factor governed by chemical and physical kinetics. There emerges a fluid bed efficiency (relative to fixed bed plug flow behavior) which can, in principle, be ascertained by a novel gradientless laboratory reactor strategy suggested here. The telling influences of bubble size and feed velocity relative to that of minimum fluidization are explicated in terms of conversion and yield for a linear triangular catalytic reaction network. This “learning” model teaches that (a) bubbles and their growth are detrimental to space time conversion and yield of intermediates and as a consequence (b) a well horizontally baffled fluid bed operated at high velocities such that continuous “snakes” as opposed to “bubbles” are created grants superior fluid bed performance.
Introduction It is meet and just that we salute Hugh Hulburt in this collection of papers which reflects our indebtedness to him as a gentleman, scholar, and teacher. Some years ago (Hulburt, 1967), he incisively struck a fine philisophical chord with regard to nature’s balance between the macro- and microscopic. In terms of our calling, his insight taught and indeed teaches us that our celebrated continuity equations for reacting systems can be properly viewed as reactor = reactions lhs = rhs
(1)
The left-hand side (ihs) defines the global, macroscopic scale, the right-hand side (rhs) the local, microscopic scale. Hugh Hulburt respected and contributed to the clarification of both sides of eq 1. In that spirit, we address the tantalizing issue of fluidized bed catalytic reactor modeling. In this complex case, we must give proper, indeed careful attention to both the rhs and lhs; i.e., an instructive if not realistic model of the reactor per se must be fashioned, and as well, a model of chemical-physical kinetics (rhs) is required if meaningful analyses and predictions of real reactor behavior are to be realized. Alas, can one expect any model of a multiphase reactor (e.g., trickle, fluid beds) to be of predictive potency at this time? Surely not! Nevertheless, as Shinnar (1978) teaches us, reactor models can be (a) predictive (Le., design models) and/or (b) instructive (i.e., learning models). Prophets and predictive models of reality are far more scarce than are existentialists and instructive (learning) models, particularly in the case of multiphase reactors (not to mention multifaceted society). We herein set forth a “learning” model. The Learning Model vs the Predictive Model. Shinnar’sdistinction between the learning (instructive) and predictive (design) models has its fruitful precedents. Surely the CSTR, while rarely encountered on the plant (industrial) scale, exhibits, nevertheless, behavior that is instructive in general terms (e.g., stability, multiplicity), which teachings prove of qualitative though not quantitative value to those who are obliged to predict the behavior of far more complex reactor networks. The “film“ theory of heat, mass, and momentum transport is surely quite primitive, indeed naive. Said 0888-5885/90/2629-1013$02.50/0
model is rooted in unrealistic fluid mechanical theses. Yet while worthless as a predictive model, film theory proves of signal merit as an agent of qualitative instruction: A learning model which in due time inspired the creation of more sophisticated and thus more predictive models (Reynolds analogy, Prandtl-Taylor model, that of Von Karman, and, of course, the model rooted in boundary layer theory). In the case of fluid bed modeling, a challenging array of as yet unresolved problems deny creation of a predictive (design) model at this time. The learning model set forth here addresses but a few issues: (1) the influence of simultaneous intraphase transport and reaction upon conversion and yield/selectivity for rapid reaction; (2) the influence of bubble-free vs bubbling behavior of the lean phase and velocity relative to that at minimum fluidization upon conversion/ yield. To examine these matters an admittedly simple model is invoked which, while marked by prudent comprimises with an ill-defined reality, attempts to focus upon the two key design factors noted above. Background. Fluidization and fluid bed catalytic reactor analyses and design have been subjects of keen concern for some time (Zenz and Othmer, 1960; Davidson and Harrison, 1963; Kunii and Levenspiel, 1969; Rowe and Yates, 1986; Squires et al., 1985; Kunii and Toei, 1984: to cite representative sources). Indeed an excellent review of the history of fluid bed development is set forth by Squires et al. (1985), while Bolthrunis (1988),Johnsson et al. (1987), and Avidan and Edwards (1986) provide telling critiques of conventional wisdom regarding fluid bed behavior. It would seem that we are witness to two worlds of fluidization: the academic and real. Bubbling bed models, which envisage a lean (bubble) phase passing through a solids-rich continuous dense (emulsion) phase, have been the concern of academics-a not idle concern insofar as signal fluid mechanical insights have issued from such enquiries. However, as practitioners have noted (Bolthrunis, 1988; Avidan and Edwards, 1986),most fluid bed reactors operate at gas velocities relative to that of minimum fluidization, uo/umf,well beyond those anticipated by bubbling bed models (i.e., uo/umfca. 2-10). Further, real fluid bed reactors are generally baffled and operate at uo/,u, > 20, conditions that give rise to fast or turbulent behavior as opposed to bubbling fluid bed behavior (Squires et al., 1985). 0 1990 American Chemical Society
1014 Ind. Eng. Chem. Res., Vol. 29, No. 6, 1990
A number of models of the fluidized bed catalytic reactor have been developed in the wake of the appearance of fluid bed catalytic cracking (May, 1959: Van Deemter, 1961). The Davidson-Harrison (D-H) model (1963),rooted in the then known fluid mechanics encountered in fluidization, defined the bed in terms of a solids-free bubble phase and a solids-rich particulate (dense, emulsion) phase. Reactant gas is assumed to be distributed between these phasesthat in the particulate phase at minimum fluidization velocity, the balance appearing in the bubble phase. Exchange is visualized to occur between phases as the gas passes upward through the fluidized bed. Reaction is assumed to occur only in the particulate, solids-rich phase. The D-H model anticipates both plug flow or CSTR behavior in the particulate phase. Another model of interest is that of Kunii and Levenspiel (K-L) (1969) in which rising bubbles are essentially viewed as batch reactors of residence time in the bed dictated by bubble rise velocity and bed height. During the bubble’s rise, reactant is transported from the bubble to the cloud-wake phase to react, the unreacted species then being transported to the emulsion (particulate) phase wherein further reaction occurs. The D-H and K-L models are, of course, but two amongst others that have been offered, and we cite these two since the essential features of all extant models are found in D-H and K-L developments. A comprehensive outline of fluid bed modeling is available (Doraiswamy and Sharma, 1984),and recent work contrasts models with data (Johnsson et, al., 1987). What is quite apparent in reviewing existing models is the implicit assumption that transfer between bubble (lean) and particulate (dense or emulsion) phases occurs in series with reaction (Carberry, 1976). Therein the need for a model of fluid bed simultaneous reaction-transport was ennunciated. Obviously the series transport-reaction assumption (implicit or explicit) is only valid for low reaction velocity as is taught in treatments of the gas-liquid reaction (Bridgwater and Carberry, 1967). The analogy between the fluid bed and gas-liquid reactors is not an idle one. For the classic Van Krevelen-Hoftiier plot of enhancement of gas absorption due to liquid phase reaction makes it evident that the series transport-reaction postulate is only valid a t small ( 3. Series transport-reaction models fail to reveal this inevitable behavior with increasing catalytic reaction vigor. So, for example, when both phases are in plug flow and
f=
0,
+ (9
[ [
X, = V - ( V - 1) exp -E-kOo
For $I > 3, tanh 4
-
1.0 and eq 29 becomes (32)
Ind. Eng. Chem. Res., Vol. 29, NO. 6, 1990 1017
-
For small Bi relative to 4 E 1/42/Bi
-
l/Dao = K,/k
then
For Bi
>4
exp(-( kKd)’/2v6,)]]/v
(34)
or by eq 33 k(observed) = Kl and by eq 34 k(observed (k(true)V2the apparent activation energy can be near zero or equal to about one-half the intrinsic value. When, of course, the reaction velocity in the dense, emulsion phase achieves very high values, the presence of even small quantities of catalytic solids in the lean phase 0 but f f 0, becomes important. Then when E v- 1 V (35) xp= 1 exp[ -f;kdo]
[y ]
0.8 ’
,
O
i
=
-
in which case normal intrinsic activational energy is made manifest. If then, with increasing temperature an apparent overall, global rate coefficient is extracted from the data, its (the rate coefficient) temperature dependency may well exhibit rather bizarre behavior for the multiphase fluid bed. Model Predictions There is provided by K-L a prediction of conversion for ozone decomposition as measured by Kobayashi (Carberry, 1976). In terms of our model, V = 6.3, ud = 2.1, and d b = 3.7 (assumed by K-L to fit the data); so according to the K-L model, X, = 0.73, and according to our model, X, = 0.6. In fact, our simple model reveals an overall effectiveness of E z 0.6. Should we assume d b = 2 cm, all other other conditions being the same, we find Bi = 2.2, Kd = 5, 4 = 0.6, i j = 0.9, qo = 0.86, E = 0.76, X, = 0.76, X , / X , * = 0.9, where X /X,*= (fluid bed/homogeneous CSTR)conversion. %he teaching here is that a simultaneous transport-reaction model of the fluid bed admits to proper conversion predictions at smaller bubble size than is required in series reaction-transport models (D-H, K-L). Again we see that fluid bed performance, in terms of conversion can be poorer than that in a simple homogeneous CSTR governed by eq 24b. The critical difference between a bubble (lean-phase discontinuous) bed and a snake (lean-phase continuous) situation to be expected at large (>25) values of V is, of course, naught but a reflection of the telling influence of ul upon Bi and Kd and, for a given reaction vigor, upon E. If, for example, in the ozone decomposition study clever baffling had generated a continuous lean (snake) phase, or quite small bubble diameter, our simple model would predict for the parameters employed in the K-L analysis Bi = 5.3, Kd 1.03, 4 = 1.4, i j = 0.63, To = 0.81, E = 0.5, X, = 0.965, and Xp/X,* = 1.15. Insofar as the existance of bubbles prompts a rise velocity N (gdb)ll2 in excess of u, - ud, the meaning of “bypassing” in bubbling fluid beds is made evident. Elimination of bypassing is realized by, for example, the following: (1)redispersion (via baffling and other modes
tfil
Iv.IM)j o CSTR
0.01 0
I
I
I
4
I
I
I
> k3. The latter assertion justifies the postulate that whereas intraphase (dense, emulsion phase) effectiveness for consumption of A can be equal to or less than unity, that of reaction step 3 (B C) can be assumed to be unity. For the lean phase quite poor in catalyst (f = 0)
-
~1
dA/dy = KI(A - a )
~1
dB/dy = KI(B - b)
(37)
1018 Ind. Eng. Chem. Res., Vol. 29, No. 6, 1990 lop
For the dense phase u d da/dy = -ri(kl ud
f
k2)a
db/dy = qk,a - k3b
i
i
As before ii=--
tanh 4 '%
4
but
'\
The yield of B is
Y=
( V - l)B/A,
V where, of course, A, is the reactant feed concentration. Integration of eqs 37 and 38 grants B/A, (lean) =
*[
K, - 1 exp( - $k,*,)
2
16
20
12
16
20
+ b/A,
- exp( - ~ k 3 0 0 ) ]
1.0,
0.8
5F 0.6 4 F
i 3 2 0.4 0 0
(41) where I?, = kl/(kl + k2) and R3 = k3/(k1 f k J . Conversion of A and yield of B (eq 37) is displayed in Figure 3 for the noted values of V and two values of bubble or snake diameters. More instructive is Table I which the maximum yield of B and the conversion at that maximum are tabulated as are the corresponding values of ke,, Le., (k, + k2)Bo. All computations are based upon k, = 0.9 s-l, k2 = 0.1 s-l, k3 = 0.1 s-l, and eD = 0.1. A wide range of values of V and lean phase db and d, is set forth, and predictions based upon homogeneous PFR and CSTR models are also indicated. Our learning model teaches in the case of yield of intermediate that the bubbling and snake bed grant comparable performance, but a greater reactor depth is required for the bubbling condition. As with conversion, the superior, near PFR, yield is predicted for high values of V and small values of d. To elevate a learning model, such as ours, to the more lofty predictive level of reality requires more data for yield/selectivity-sensitive reaction networks as catalyzed in fluid beds under realistic circumstances. Furthermore, far more refined interphase-intraphase transport coefficient studies and correlations are needed for flow conditions that mark real fluid bed reactors.
Experimental Assessment: A Tentative Suggestion A barometer of fluid bed catalytic reactor efficiency relative to that of a fixed bed of the same catalyst can be ascertained experimentally by use of an external recycle reactor (CSTR) which when operated in up-flow provides CSTR fluid bed data, while in down-flow fixed bed data are obtained. We then have CSTR conversion (and selectivity) data which directly contrast fixed and fluid bed behavior under gradientless conditions. Since such a laboratory network grants observed R , simply in terms of CSTR material balance, then, in principle, an extimate of Kl provides
0.2
0.0
0
4
8
ko80
Figure 3. Concentrations vs k9 for a triangular network (eq 36) for (a, top) bubbling and (b, bottom) snake fluid bed (eD = 0.1). kl = 0.9 s-'; k2 = 0.1 s-'; k3 = 0.1 s-'. Table I. [Y/X]k,O, for Diverse Values of db,d,, and V 0 V dbr cm 10 100 300 Bubbling Bed 1 0.6163/0.9276 (8.4) 0.6794/0.9176 (3.2) 0.6846/0.9229 (2.9) 10 0.4975/0.8763 (35) 0.5566/0.8701 (7.2) 0.5675/0.8750 (5.1) 100 0.1624/0.7086 (415) 0.1809/0.6839 (57) 0.1852/0.6842 (30) V d,, cm 10 100 300 Snake Bed 1 0.6232/0.9117 (2.3) 0.6792/0.9157 (2.6) 0.6846/0.9227 (2.7) 10 0.4602/0.8419 (4.7) 0.5504/0.8623 (4.3) 0.5658/0.8756 (4.2) 100 0.1368/0.6519 (19.6) 0.1725/0.6677 (18.8) 0.1817/0.6830 (18.0) nominal max vield conv at max vield contact time 0.6968 0.9257 2.6 PFR CSTR 0.5772 0.7619 3.2 Note: Y is the maximum yield of B and X is the conversion at that maximum yield. k,BO is (k, + k2)Bo. The PFR and CSTR results are for the simple homogeneous analogues. Rate coefficients are those cited in Figure 3.
Note that by Figure 1 qqo can be estimated for a given CSTR conversion, X,contact time, Bo, and an estimate of K,, i.e., the observable, Obs. Division of Obs by qq0 grants k, since @/Bi = k,/K,. Given the complexities of fluidization and fluidized bed reactors, surely experimental comparisons with the far better understood fixed bed under well-defined conditions are of critical importance, particularly as influenced by V and baffling. The most unambiguous of the "well-defined conditions" is, of course, the globally gradientless one as is to be found with the open-loop external recycle reactor. The extension
Ind. Eng. Chem. Res., Vol. 29, No. 6, 1990 1019 of the concept to a fluidized bed system presents no difficulties, in principle. As noted, in the open-loop recycle mode, operation in upflow provides fluid bed CSTR data, while down-flow grants fixed bed CSTR data; hence for identical feeds since R = A,X/B R(up-flow) Xf/df = -= qvo = E (43) R(down-flow) X,/B,
or fluid bed reactor efficiency is, for identical feed and volume of catalyst, Xf Uf E = s/vo = -(44) uo where uf is the velocity in up-flow required to achieve a conversion in the fluid bed, XI. Fixed bed (down-flow) conversion (X,) is that realized at velocity u,.
x,
Discussion and Conclusions The learning model set forth in this essay is one which, while hardly deserving to be termed a predictive one, does exhibit trends noted by practioners, e.g., the merits of operation at high values of V and small values of “average” bubble size or indeed the advantages of discouraging bubble formation per se by clever horizontal baffling. Surely bubble formation is the prime cause of the well-known phenomenon that plagues fluid bed reactors-bypassing: an event minimized by operation at high values of V, baffling, and/or staging. Unhindered bubble growth can, according to our model, lead to reaction quenching since at high reaction vigor q l/f$and Tj becomes proportional to db4/4. It follows that redispersion of growing bubbles may cause a marked “jump” in local reactivity-that is, q 0 with increasing bubble size and then q 1.0 in the wake of bubble size reduction by local redispersion. Our model does not address bubble (or snake) growth nor redispersion within the fluid bed, yet the analysis does suggest a quenching potential due to bubble growth and/or coalescence, followed by ignition due to redispersion. The evolution from a learning to a predictive model will, as Hugh Hulburt taught us so well, require more thoughtful experimentation focused upon the lhs and rhs, the reactor and the reactions.
-
-
-
Nomenclature a , b = species concentrations in the dense phase A , B = species concentrations in the lean phase Bi = Biot number, eq 22 B = bulk concentration of co-reactant in gas-liquid reaction Cy = average concentration D = molecular diffusivity db = bubble diameter d, = snake diameter Da, = Damkohler number, qk/KI e = bed void fraction E = fluid bed overall effectiveness relative to the fixed bed 707
f = fraction of catalyst in the lean (bubble or snake) phase relative to the emulsion phase g = gravitational constant
H = Hatta number for gas-liquid reaction k = reaction rate coefficient ke = physical mass-transfer coefficient K = fluid bed mass-exchange coefficient R = rate coefficient ratio n = number of CSTRs R = global reaction rate tanh = hyperbolic tangent u = fluid velocity
V = ratio of fluid velocity to that of minimum fluidization, Uo/Ud
w = lean-phase velocity, uI/ud = ub/u,-Jfor bubble bed X = conversion of key reactant y = axial distance in fluid bed Y = yield, B / A o Greek N o t a t i o n 7 = effectiveness factor 0 = contact time, y/u, 6 = fluid bed Thiele modulus, (k,/Kd)’/2
Subscripts
b = bubble br = bubble rise c = catalyst d = dense (emulsion) phase 1 = lean phase mf = minimum fluidization o = feed or overall s = snake y = bed height
Literature Cited Avidan, A.; Edwards, M. Modeling and Scale-up of Mobil’s Fluid Bed MTG Process. 5th Int. Conf. on Fluidization, Elsinore, Denmark, May 18-23, 1986. Bolthrunis, C. 0. An Industrial Perspective on Fluid Bed Reactor Models. Chem. Eng. Prog. 1988, No. 5,51-54. Bridgwater, J.; Carberry, J. J. Theory of Gas-Liquid Reactions. Br. Chem. Eng. 1967, 12, 58-63. Bukur, D. G.; Wittmann, C. V.; Amundson, N. Analysis of a Model for a Nonisothermal Continuous Fluidized Bed Catalytic Reactor. Chem. Eng. Sci. 1974,29, 1173-1192. Carberry, J. J. Chemical and Catalytic Reaction Engineering; McGraw-Hill: New York, 1976. Carberry, J. J. Remarks Upon the Modelling of Heterogeneous Catalytic Reactors. Chem. Eng. Technol. 1988,11, 425-431. Davidson, J. F.; Harrison, D. Fluidised Particles; Cambridge University Press: New York, 1963. Doraiswamy, L. K.; Sharma, M. M. Heterogeneous Reactions; J. Wiley: New York, 1984;Vol. I. Hulburt, H. P. C. Reilly Lecture, University of Notre Dame, IN, 1967. Johnsson, J. E.; Grace, J. R.; Graham, J. J. Fluidized-Bed Reactor Model Verification on a Reactor of Industrial Scale. AZChE J. 1987, 33 (4),619-627. Krambeck, F. J.; Avidan, A.; Lee, C. K.; Lo,N. M. Predicting Fluid Bed Reactor Efficiency Using Adsorbing- Tracers. AIChE J. 1987, 33 (lo),1727-1734. Kunii, D.; Levenspiel, 0. Fluidization Engineering; J. Wiley: New York, 1969. Kunii, D., Toei, R., Eds. Fluidization, Proc. 4th Intl. Conf. AIChE; Engineering Foundation: New York, 1984. May, W. G. Fluidized Bed Reactor Studies. Chem. Eng. h o g . 1959, 55 (12),49-55. Rowe, P.; Yaks, J. G. Fluidised Bed Reactors. In Chemical Reaction and Reactor Engineering; Carberry, J. J., Varma, A., Eds.; M. Dekker: New York, 1986; Chapter 7. Shaikh, A.; Carberry, J. J. Transport Effects in Catalytic Fluidized Bed Reactors. Chem. Eng. Technol. 1990, in press. Shinnar, R. Chemical Reactor Modeling-The Desirable and the Achievable. Chemical Reactor Engineering Reuiews-Houston; ACS Symposium Series 72;American Chemical Society: Washington, DC, 1978;pp 1-36. Squires, A. M.; Kwauk, M.; Avidan, A. Fluid Beds: At Last, Challenging Two Entrenched Practices. Science 1985,230,1329-1337. Van Deemter, J. J. Mixing and Contacting in Gas-Solid Fluidized Beds. Chem. Eng. Sci. 1961, 13,143-150. Werther, J. Modeling and Scale-up of Industrial Fluidized Bed Reactors. Chem. Eng. Sci. 1980, 35, 372-379. Zenz, F. A.; Othmer, D. F. Fluidization and Fluid-Particle S y s t e m ; Reinhold: New York, 1960. I
Received for review August 29, 1989 Revised manuscript received January 16, 1990 Accepted January 29, 1990
