3 Fluidized Bed Reactors: A Review D. L . PYLE
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Department of Chemical Engineering and Chemical Technology, Imperial College, London, S.W. 7, England
Recent work relevant to the development of models for analyzing and designing fluidized bed reactors is reviewed. Special attention is placed on attempts to develop mechanis tic models, and the various features of the existing models are compared and contrasted and related to other experi mental and theoretical studies. In general it appears that most effort has been placed on the study of single bubbles and on attempts to correlate reactor performance in terms of these studies. In practice, as experimental studies show, many of the important characteristics offluidizedreactors can be explained only in terms of more complex models accounting for bubble interactions, coalescence, and growth. Although it is now possible to explain qualitatively, at least, many of the features of such reactors, much more theoretical and critical experimental work is needed before a priori design methods can be used with confidence.
' " p h e analysis of fluidized bed reactors provides one of the clearest ^ examples we have of the complex interaction between different physi cal and chemical processes that typify chemical engineering. This review attempts to describe some of the characteristic features of gas fluidized beds, particularly those which seem to have the most important effect on their operation as chemical reactors. It is intended to provide a reasonable background to the field although it is not a comprehensive literature survey. Even a superficial study of a fluidized bed i n operation reveals its essential complexity. Bubbles form, at an apparently unpredictable rate, and subsequently grow—perhaps to the same dimensions as the b e d itself—coalesce, and split. There is clearly a flow of gas through the bubbles and a consequent interchange with the bed. The particles move up and down and around as the bubbles pass; a fraction of the particles 106 In Chemical Reaction Engineering; Bischoff, K.; Advances in Chemistry; American Chemical Society: Washington, DC, 1974.
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may be steadily elutriated from the bed. What is more, the behavior of a bed w i l l depend strongly on many variables: particles, gas flow, bed diameter, distributor design. The questions that must ultimately be answered are ( 1 ) whether all the relevant features of bubbling fluidized beds are understood and can be built into reactor models, and (2) which features are important or critical for satisfactory reactor design and operation. This review was prepared with these questions i n mind although the choice of topics for discussion was quite selective. A number of different types of reaction are commonly carried out i n fluidized reactors: gas-phase reactions, solid-catalyzed reactions, and reactions involving reaction within and between the gas and solid phases. Catalytic reactions are probably the most common in chemical engineer ing, but in all these cases, and particularly the last two, what is important is the contact time distribution between the two phases. For heterogene ous reactions the contact time distribution plays the same role as the residence time distribution for homogeneous reactions. The problems discussed below are those which have a particular influence on the con tact time distribution. W h e n attempts failed to describe fluidized bed reactors i n the con ventional terms of a reactor with dispersion, a series of papers i n the 1950's developed a model for a fluidized bed which recognized that many of the problems and contradictions i n the operation, and particularly scale-up, of fluidized reactors stemmed from their two-phase character ( 1 - 5 ) . It is the presence of bubbles, and their effect on gas/solid con tacting and mixing, that lies at the root of the bed's behavior and gives rise to the great difference between the R . T . D . (which is easily measured) and the C . T . D . (which is not). For example, May's model (6), which today with a much more detailed knowledge of the fluid mechanics i n volved, is known to be essentially correct, described the bubbling bed as a two-phase system, characterized by an interchange between the bubbles and the emulsion or dense phase, and by mixing within the emulsion phase (Figure 1). The bubble phase, which is free of particles, is i n essentially plug flow, and the gas mixing i n the dense phase is charac terized by a dispersion coefficient. W i t h these assumptions, material bal ances on the two phases lead to: C)
dy and
^ ^ - ψ . ψ *
(1)
b
+ Τν. (C
b
-
C) p
- KV C P
P
= 0
(2)
Although we shall examine the mechanics of the two-phase system i n
In Chemical Reaction Engineering; Bischoff, K.; Advances in Chemistry; American Chemical Society: Washington, DC, 1974.
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more detail later, it is worth noting that May's model gives a reasonable account of the effects of gas interchange on reactor performance. What is probably the least satisfactory aspect of the theory and those preceding it is its reliance on experimental values for the various parameters i n the model. T h e only exception is what is now known as the two-phase theory, which proposes that all the gas i n excess of that required just to fluidize the bed flows through the bed as bubbles. The most significant improvement of the various bubble-type models developed since then is the ability to begin at least to forecast some of the parameters and par ticularly the rate of interchange between the phases. May's model was developed b y van Deemter ( 7 ) , and more recently b y Mireur and Bischoff (8) to enable the parameters of the two-phase model to be assessed from tracer and reactor experiments; v a n Deemter (9) a n d Bailie (JO) have also developed this type of model to include the presence and interchange of particles within both phases. Although these methods have probably not yet been sufficiently exploited I want to concentrate more on the developments i n predicting a priori the performance of a particular reactor.
Bubble or Lean Phase^ eTs^
Dense Phase •U
ι
t
Bubbling
y
t
t
General Two Phase
Figure 1.
Two-phase models
Lanneau (11) attempted to measure bubble velocities and to incor porate these into a model of a chemical reactor. H i s model allowed for either upwards flow of gas i n the dense phase or for the possibility of downwards flow and backmixing of gas (following simply from a conti nuity argument). T h e gas crossflow or interchange between the two phases was held to be largely caused by the consequence of solids inter change and was predicted to be, per unit volume of reactor,
ε
_ VuPbUb _! " VçH S
In Chemical Reaction Engineering; Bischoff, K.; Advances in Chemistry; American Chemical Society: Washington, DC, 1974.
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Gas Interchange from Basing Bubbles The work b y Orcutt, Davidson, and Pigford (12), subsequently developed b y Davidson and Harrison (13) was really the first to include results which had become available on the relation between bubble rising velocity and the bubble size and gas velocity. I n this theory the bubble rising velocity is considered proportional to the square root of the bubble radius, which is consistent with the assumption that the particles move around the essentially spherical bubbles like an inviscid liquid. Davidson (14) developed a simple theory for the gas and particle motion around a bubble using this assumption and the assumption of constant voidage fraction, and this theory was used to predict the rate of gas throughflow through a bubble of diameter d . A diffusional flow was added to the convective term, and the basis for this theory was the assumption that resistance to diffusion resided i n a gas film inside the bubble, as developed by Baird and Davidson (15). W e return later to a comparative assess ment of the various theories for interchange between the phases. F o r the moment we note that Davidson's theory at that time took no account of resistance to diffusion within the particulate phase nor of the interaction between the convective flow or the rate of any reaction proceeding i n the dense phase and this diffusional term. The other point which should be noted is that the significance of this interchange depends on a = U /u , which is the ratio between the bubble velocity and the interstitial gas velocity at incipient fluidization. As Davidson (14) showed, and subse quent experiments have confirmed, the gas flow relative to a rising bubble depends strongly on a (Figure 2 ) . F o r air fluidization, systems with throughflow—i.e., a < 1—are usually confined to large particles ( > 4 0 0 500 microns), or "teeter beds" to use Squires' (16) terminology, except possibly for conditions very close to the distributor i n beds offineparb
b
Gas (a)
Particles a < 1
Figure 2.
(b)
oc>1
Flow around bubbles in fluidized beds
In Chemical Reaction Engineering; Bischoff, K.; Advances in Chemistry; American Chemical Society: Washington, DC, 1974.
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tides. M a n y situations of industrial importance, particularly catalytic cracking units, operate with large values of a—i.e., with gas clouds sur rounding the bubble. In this latter case, the throughflow predicted by Davidson, and used by Davidson and Harrison, represents the rate at which gas circulates between the bubble void and the surrounding gas cloud. It is not, strictly speaking, the correct interchange between the bubble phase and the surrounding dense phase. It, or a more rigorous version of it, would appear to be the correct term to use i n the analysis of the teeter bed reactor. Since most of the subsequent work on reactor modeling has been based on this model, with the incorporation of later experimental results on bubble and wake shape or on a more refined model of the gas and particle flow (17) it is suitable to consider i n more detail the mechanism of gas interchange between bubbles and the surrounding gas phase. For the moment let us confine ourselves to bubbles rising i n an essentially infinite medium; the important and frequently encountered case of slug ging is dealt with briefly later. Considering first the case a < 1 (Figure 2), a modification of D a v i d sons theory should be appropriate. It is found experimentally (18) that bubbles carry up with them a wake which occupies around J—i of the bubble volume. Clearly this w i l l contribute to any catalytic or gas-solid reaction. The effect of the wake on the gas flow i n and around the bubble is as yet unknown. Assuming that Davidson s or Murray's analysis is an adequate representation, the convective contribution to the gas exchange rate is q = ? xC/ D 0
e
(3a)
2
or (3b)
