Werther - Fluidized Bed Reactors 4b1f54

Article No : b04_239

Article with Color Figures

Fluidized-Bed Reactors JOACHIM WERTHER, Hamburg University of Technology, Hamburg,

1. 1.1. 1.2. 1.3. 2. 2.1. 2.2. 2.3. 2.4. 2.5. 2.6. 2.7. 2.8. 2.9. 2.9.1. 2.9.2. 2.9.3. 2.10. 2.11. 3. 3.1. 3.2. 3.3. 3.4. 3.5.

Introduction. . . . . . . . . . . . . . . . . . . . . . . . The Fluidization Principle . . . . . . . . . . . . . Forms of Fluidized Beds . . . . . . . . . . . . . . Advantages and Disadvantages of the Fluidized-Bed Reactor . . . . . . . . . . . . . . . . Fluid-Mechanical Principles . . . . . . . . . . . Minimum Fluidization Velocity . . . . . . . . . Expansion of Liquid–Solid Fluidized Beds. Fluidization Properties of Typical Bed Solids State Diagram of Fluidized Bed . . . . . . . . . Gas Distribution . . . . . . . . . . . . . . . . . . . . Gas Jets in Fluidized Beds . . . . . . . . . . . . . Bubble Development . . . . . . . . . . . . . . . . . Elutriation . . . . . . . . . . . . . . . . . . . . . . . . . Circulating Fluidized Beds. . . . . . . . . . . . . Hydrodynamic Principles . . . . . . . . . . . . . . . Local Flow Structure in Circulating Fluidized Beds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design of Solids Recycle System . . . . . . . . . Cocurrent Downflow Circulating Fluidized Beds (Downers) . . . . . . . . . . . . . . . . . . . . . Attrition of Solids . . . . . . . . . . . . . . . . . . . Solids Mixing in Fluidized-Bed Reactors . . Mechanisms of Solids Mixing . . . . . . . . . . Vertical Mixing of Solids . . . . . . . . . . . . . . Horizontal Mixing of Solids . . . . . . . . . . . . Solids Residence-Time Properties . . . . . . . Solids Mixing in Circulating Fluidized Beds

320 320 321 322 322 322 324 324 325 326 327 328 329 330 330 333 334 334 335 337 338 338 339 340 340

Symbols (see also ! Principles of Chemical Reaction Engineering and ! Model Reactors and Their Design Equations) a:

A0: Ar: At: b:

volume-specific mass-transfer area between bubble and suspension phases, m1 cross-sectional area of orifice, m2 Archimedes number, defined by Equation (5) cross-sectional area of reactor, m2 parameter def. by Equation (54)

2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim DOI: 10.1002/14356007.b04_239.pub2

4. 4.1. 4.2. 5. 6. 7. 8. 8.1. 8.2. 8.3. 8.4. 8.5. 9. 9.1. 9.2. 9.2.1. 9.2.2. 9.3. 9.3.1. 9.3.2. 10.

cv: cb: cc: cj: Cb: Cd: d o:

Gas Mixing in Fluidized-Bed Reactors . . . Gas Mixing in Bubbling Fluidized Beds. . . Gas Mixing in Circulating Fluidized Beds . Heat and Mass Transfer in Fluidized-Bed Reactors. . . . . . . . . . . . . . . . . . . . . . . . . . . Gas-Solid Separation . . . . . . . . . . . . . . . . . Injection of Liquid Reactants into Fluidized Beds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Industrial Applications . . . . . . . . . . . . . . . Heterogeneous Catalytic Gas-Phase Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . Polymerization of Olefins. . . . . . . . . . . . . . Homogeneous Gas-Phase Reactions . . . . . . Gas–Solid Reactions. . . . . . . . . . . . . . . . . . Applications in Biotechnology . . . . . . . . . . Modeling of Fluidized-Bed Reactors . . . . . Modeling of Liquid–Solid Fluidized-Bed Reactors. . . . . . . . . . . . . . . . . . . . . . . . . . . Modeling of Gas–Solid Fluidized-Bed Reactors. . . . . . . . . . . . . . . . . . . . . . . . . . . Bubbling Fluidized-Bed Reactors . . . . . . . . . Circulating Fluidized-Bed Reactors . . . . . . . New Developments in Modeling FluidizedBed Reactors . . . . . . . . . . . . . . . . . . . . . . . Computational Fluid Dynamics . . . . . . . . . . Modeling of Fluidized-Bed Systems . . . . . . . Scale-up . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . .

340 341 341 341 343 343 344 344 347 347 348 352 354 354 354 355 356 357 357 358 359 361

solids volume concentration bubble attrition rate constant, defined by Equation (50), s2/m4 cyclone attrition rate constant defined by Equation (51), s2/m3 jet attrition rate constant, defined by Equation (52), s2/m3 concentration in bubble phase, kmol/m3 concentration in suspension phase, kmol/m3 orifice diameter, m

320

Fluidized-Bed Reactors

d p:

Sauter diameter, defined by Equation (6), m diameter of particle size class i, m dpi: bed diameter, m dt: local bubble volume equivalent sphere dv: diameter, m initial bubble diameter, m dv0: D: coefficient of molecular diffusion, m2/s lateral solids dispersion coefficient, m2/s Dsh: vertical solids dispersion coefficient, Dsv: m2/s Froude number, defined by Frp: Equation (29) solids mass flow rate, based on reactor Gs: cross-sectional area, kg m2 s1 h: height above distributor level, m height above distributor where bubbles h o: are forming, m gas-to-solid heat transfer coefficient, W hgs: m2K1 hwb: wall-to-bed heat transfer coefficient, W m2K H: expanded bed height, m Hmf: bed height at minimum fluidization, m mass-transfer coefficient, m/s kG: L: jet length, m mass of elutriated solids, kg m a: mass flow due to attrition, kg/s m_att: bed mass, kg mb: solids mass flow, g/s m_s: number of ages through cyclone np: p: pressure, Pa Per, c: Peclet number, defined by Equation (43) cumulative mass distribution Q3: attrition rate, defined by Equation (33), r a: s1 rj: reaction rate, based on catalyst mass, kmol kg1 s1

1. Introduction 1.1. The Fluidization Principle In fluidization an initially stationary bed of solid particles is brought to a ‘‘fluidized’’ state by an upwardstreamofgasorliquidassoonasthevolume flowrateofthefluidexceedsacertainlimitingvalue V_mf (where mf denotes minimum fluidization). In

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Re: S v: t: TDH: u: ub: u c: umf: uo: usl: ut: V_b: V_mf: V_o: xi: a: Dpd: e: eb: ei: emf: k *: l: m: n: nij: r f: r s: q: q b: y:

Reynolds number volume-specific surface area of particles, m1 time, s transport disengaging height, m superficial fluidizing velocity, m/s local bubble rise velocity, m/s velocity at cyclone inlet, m/s superficial minimum fluidizing velocity, m/s jet velocity at orifice, m/s slip velocity, defined by Equation (27), m/s single particle terminal velocity, m/s visible bubble flow, based on bed area, m3 m2 s1 minimum fluidizing flow rate, m3/s flow rate of gas issuing from orifice, m3/s mass fraction of particle size fraction i in bedmaterial velocity ratio, defined by Equation (14) pressure drop of the gas distributor, Pa bed porosity local bubble gas holdup porosity of catalyst particle bed porosity at minimum fluidization elutriation rate constant, kg m2 s1 average life time of a bubble, s solid-to-gas mass flow ratio kinematic viscosity, m2/s stoichiometric number of species i in reaction j fluid density, kg/m3 solids density, kg/m3 stress history parameter, defined by Equation (54) parameter, defined by Equation (23) pressure ratio, defined by Equation (28)

the fluidized bed, the particles are held suspended by the fluid stream; the pressure drop Dpfb of the fluid oningthroughthefluidized bed isequal to the weight of the solids minus the buoyancy, dividedbythecross-sectionalareaAt ofthefluidized-bed vessel (Fig. 1): Dpfb ¼

At H ð1eÞ ðrs rf Þ g At

ð1Þ

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321

Figure 1. Pressure drop in flow through packed and fluidized beds

In Equation (1), the porosity e of the fluidized bed is the void volume of the fluidized bed (volume in interstices between grains, not including any pore volume in the interior of the particles) divided by the total bed volume; rs is the solids apparent density; and H is the height of the fluidized bed. In many respects, the fluidized bed behaves like a liquid. The bed can be stirred like a liquid; objects of greater specific gravity sink, whereas those of lower specific gravity float; if the vessel is tilted, the bed surface resumes a horizontal position; if two adjacent fluidized beds with different bed heights are connected to each other, the heights become equal; and the fluidized bed flows out like a liquid through a lateral opening. Particularly advantageous features of the fluidized bed for use as a reactor are excellent gas– solid in the bed, good gas–particle heat and mass transfer, and high bed–wall and bed– internals heat-transfer coefficients. The fluidization principle was first used on an industrial scale in 1922 for the gasification of finegrained coal [1]. Since then, fluidized beds have been applied in many industrially important processes. The present spectrum of applications extends from a number of physical processes, such as cooling–heating, drying, sublimation–desublimation, adsorption–desorption, coating, and granulation, to many heterogeneous catalytic gasphase reactions as well as noncatalytic reactions. What follows is a survey of the fluid mechanical principles of fluidization technology, gas and solid mixing, gas–solid in the fluidized bed, typical industrial applications, and approaches to modeling fluidized-bed reactors. Further information is given in textbooks (e.g.,

[2]) and monographs (e.g., [3–8]). Summary treatments can also be found in [9–19]. Other useful literature includes reports of the Engineering Foundation Conferences on Fluidization [20–22], the Circulating Fluidized Bed Conferences (e.g., [23–25], and – for use of the fluidized bed in energy technology – the Fluidized Bed Combustion Conferences (e.g., [26–28]).

1.2. Forms of Fluidized Beds As the volume flow rate V_ or the superficial velocity u ¼ V_/At of the fluid increases beyond the value V_mf or umf (Fig. 2 A) corresponding to the minimum fluidization point, one of two things happens: in fluidization with a liquid, the bed begins to expand uniformly; in fluidization with a gas – a process of greater industrial importance and the one discussed almost exclusively in the following material – virtually solids-free gas bubbles begin to form (Fig. 2 B). The local mean bubble size increases rapidly with increasing height above the grid because of coalescence of the bubbles. If the bed vessel is sufficiently narrow and high, the bubbles ultimately fill the entire cross section and through the bed as a series of gas slugs (Fig. 2 C). As the gas velocity increases further, more and more solids are carried out of the bed, the original, sharply defined surface of the bed disappears, and the solids concentration comes to decrease continuously with increasing height. To achieve steady-state operation of such a ‘‘turbulent’’ fluidized bed (Fig. 2 D), solids entrained in the fluidizing gas must be collected

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Figure 2. Forms of gas–solids fluidized beds

and returned to the bed. The simplest way to do this is with a cyclone integrated into the bed vessel and a standpipe dipping into the bed. A further increase in gas velocity finally leads to the circulating fluidized bed (Fig. 2 E), which is characterized by a much lower average solids concentration than the previous systems. The high solids entrainment requires an efficient external solids recycle system with a specially designed pressure seal (shown as a siphon in Fig. 2 E).

1.3. Advantages and Disadvantages of the Fluidized-Bed Reactor The major advantages of the (gas–solid) fluidized bed as a reaction system include 1. Easy handling and transport of solids due to liquid-like behavior of the fluidized bed 2. Uniform temperature distribution due to intensive solids mixing (no hot spots even with strongly exothermic reactions) 3. Large solid–gas exchange area by virtue of small solids grain size 4. High heat-transfer coefficients between bed and immersed heating or cooling surfaces 5. Uniform (solid) product in batchwise process because of intensive solids mixing

Set against these advantages are the following disadvantages: 1. Expensive solids separation or gas purification equipment required because of solids entrainment by fluidizing gas 2. As a consequence of high solids mixing rate, nonuniform residence time of solids, backmixing of gas, and resulting lower conversion 3. In catalytic reactions, undesired by or broadening of residence-time distribution for reaction gas due to bubble development 4. Erosion of internals and attrition of solids (especially significant with catalysts), resulting from high solids velocities 5. Possibility of defluidization due to agglomeration of solids 6. Gas–solid countercurrent motion possible only in multistage equipment 7. Difficulty in scaling-up Table 1 compares the fluidized-bed reactor with alternative gas–solid reaction systems: fixedbed, moving-bed, and entrained-flow reactors.

2. Fluid-Mechanical Principles 2.1. Minimum Fluidization Velocity The minimum fluidization point, which marks the boundary between the fixed- and the fluidized-bed

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323

Table 1. Comparison of gas–solid reaction systems [2, 18]

conditions, can be determined by measuring the pressure drop Dp across the bed as a function of volume flow rate V_(Fig. 1). Measurement should always be performed with decreasing gas velocity, by starting in the fluidized condition. Only for very narrow particle-size distributions, however, does a sharply defined minimum fluidization point occur. The broad size distributions commonly encountered in practice exhibit a blurred range; conventionally, the minimum fluidization point is defined as the intersection of the extrapolated fixed-bed characteristic with the line of constant bed pressure drop typical of the fluidized bed (Fig. 1). The measurement technique already contains the possibility of calculating the minimum fluidization velocity umf: The pressure drop in flow

through the polydisperse fixed bed at the point u ¼ umf, given, for example, by the Ergun relation [29] (! Fluid Mechanics), is set equal to the fluidized-bed pressure drop given by Equation (1). From the Ergun relation Dp ð1eÞ2 1e huþ0:29Sv 3 rf u2 ¼ 4:17 S2v e3 h e

it follows umf ¼ 7:14 ð1emf Þn Sv 2 3 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 3 emf ðr r Þ g 1 7 6u 4t1þ0:067 s f2 3 15 rf n Sv ð1emf Þ2

ð2Þ

Accordingly, to calculate umf, the characteristics of the gas (rf, n), the density rs of the particles,

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the porosity emf of the bed at minimum fluidization, and the volume-specific surface area Sv of the solids must be known. The specific surface area defined by Sv ¼

surface area of all particles in the bed volume of all particles in the bed

(this takes into only the external area, which governs hydraulic resistance, not the pore surface area as in porous catalysts) cannot be determined very exactly in practice. Hence umf should not be calculated on the basis of the measured particle-size distribution of a representative sample of the bed solids; instead, it is better measured directly. Equation (2) can be employed advantageously to calculate umf in an industrial-scale process on the basis of minimum fluidization velocities measured in the laboratory under ambient conditions [30]. An equation from WEN and YU [31] can be used for approximate calculations: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Remf ¼ 33:7 ð 1þ3:6 105 Ar 1Þ

ð3Þ

where Remf ¼ Ar ¼

umf dp n

gdp3 n2

ð4Þ

rs rf rf

ð5Þ

Here the surface mean or Sauter diameter calculated from the mass–density distribution q3 (d) of the particle diameters dp ¼

1 dR max

d 1

ð6Þ

u ¼ en ut

ð7Þ

according to RICHARDSON and ZAKI [33]. Here ut is the terminal velocity of isolated single particles; the exponent n is given as follows, provided the particle diameter is much smaller than that of the vessel: 8 4:65 > > < 4:4 Re0:03 t n¼ 0:1 > > 4:4 Ret : 2:4

0 < Ret 0:2 0:2 < Ret 1 1 < Ret 500 500 < Ret

ð8Þ

The Reynolds number used above is calculated via the single-particle terminal velocity ut: Ret ¼

ut dp n

ð9Þ

2.3. Fluidization Properties of Typical Bed Solids In fluidization with gases, solids display characteristic differences in behavior that can also affect the operating characteristics of fluidizedbed reactors. GELDART has proposed an empirically based classification of solids into four groups (A to D) by fluidization behavior [34]. The parameters employed are those crucial for fluidization properties: the mean particle diameter (dp) and the density difference (rs rf) between solid and fluid. Figure 3 shows the Geldart diagram with the interclass boundaries theoretically established by MOLERUS [35].

q3 ðdÞdðdÞ

dmin

should be used for the characteristic particle diameter dp. Both the Ergun approach and the Wen and Yu simplification have been confirmed experimentally over a wide range of parameters. More recently, Vogt et al. [32] found that Equations (2) and (3) are also applicable to high-pressure fluidized beds in which the fluid is under supercritical conditions

2.2. Expansion of Liquid–Solid Fluidized Beds The uniform expansion of a bed on fluidization with a liquid can be described by

Figure 3. Geldart diagram (boundaries according to MOLERUS [35]) For explanation see text

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Solids of Group C are very fine-grained, cohesive powders (e.g., flour, fines from cyclones and electrostatic filters) that virtually cannot be fluidized without fluidization aids. The adhesion forces between particles are stronger than the forces that the fluid can exert on the particles. Gas flow through the bed forms channels extending from the grid to the top of the bed, and the pressure drop across the bed is lower than the value from Equation (1). Fluidization properties can be improved by the use of mechanical equipment (agitators, vibrators) or flowability additives, e.g., Aerosil. Solids of Group A have small particle diameters (ca. 0.1 mm) or low bulk densities; this class includes catalysts used e.g., in the fluidizedbed catalytic cracker. As the gas velocity u increases beyond the minimum fluidization point, the bed of such a solid first expands uniformly until bubble formation sets in at u ¼ umb > umf. The bubbles grow by coalescence but break up again after ing a certain size. At a considerable height above the gas distributor grid, a dynamic equilibrium is formed between bubble growth and breakup. If the gas flow is cut off abruptly, the gas storage capacity of the fluidized suspension causes the bed to collapse rather slowly.


325

2.4. State Diagram of Fluidized Bed Whereas the onset of the fluidized state can be described by the minimum fluidization velocity, the bed operating range and the gas velocity needed to create a given fluidized state can be estimated with the help of the fluidized-bed state diagram (Fig. 4) devised by REH [36]. This plot shows the fluid mechanical resistance characteristics of the fixed bed, fluidized bed, and pneumatic transport. The ordinate is the quantity 3 u2 rf 4 g dp ðrs rf Þ

and the abscissa is the Reynolds number Rep formed with the fluidization velocity u and the particle diameter dp. The state parameter in the fluidized-bed region is the mean bed porosity e. The use of the diagram is facilitated by an auxiliary grid with lines of constant M and constant Archimedes number. While the dimensionless groups plotted as ordinate and abscissa each contain both the particle diameter and the fluidization velocity, this is not the case with the parameters Ar and M defined by Ar ¼

g dp3 ðrs rf Þ n2 rf

ð10Þ

Group B Solids have moderate particle sizes and densities. Typical representatives of this group are sands with mean particle diameters between ca. 0.06 and 0.5 mm. Bubble formation begins immediately above the minimum fluidization point. The bubbles grow by coalescence, and growth is not limited by bubble splitting. When the gas flow is cut off abruptly, the bed collapses quickly. Group D includes solids with large particle diameters or high bulk densities; examples are sands with average particle diameters > 0.5 mm. Bubbles begin to form just above the minimum fluidization point, but the character of bubble flow is markedly different from that in group B solids: group D solids are characterized by the formation of ‘‘slow’’ bubbles (Section 2.7). On sudden stoppage of the gas flow, the bed also collapses suddenly.

color fig

Figure 4. Reh status diagram with status points S and S1–S4 (for explanation, see text)

326 M¼

Fluidized-Bed Reactors u3 rf g n ðrs rf Þ

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The Reh status diagram can answer a number of practical questions. If, for example, the properties of the gas (rf, v) and the solid (dp, rs ) and the fluidization velocity u are given, the calculation of Ar and Rep yields, via the status point S in the diagram (Fig. 4), the average voidage e in the fluidized bed. Taking the line M ¼ const. through S at the intersection with the line e ! 1 at S1 gives information on the particle size which is just elutriated when a particles with a size distribution are fluidized, and the intersection of the same line with the fixed-bed limit e ¼ 0.4 (S2) indicates the particle size at which fluidization will break down if agglomeration occurs. The line Ar ¼ const. through S can be used to find the minimum fluidization velocity at S3 or – as a measure of the upper limit of fluidization – the maximum fluidizing velocity at S4. An important practical point is that the state diagram implies a classification scheme that

relates various fluidized-bed systems to one another [37, 38] (Fig. 5). When a new fluidized-bed process is being designed, the position of the state point in the diagram will identify related fluidized-bed systems with potentially similar operating problems.

2.5. Gas Distribution The gas distribution device must satisfy the following requirements: 1. Ensure uniform fluidization over the entire cross section of the bed (especially important for shallow beds) 2. Provide complete fluidization of the bed without dead spots where, for example, deposits can form 3. Maintain a constant pressure drop over long operation periods (outlet holes must not become clogged)

Figure 5. Reh’s fluidized-bed state diagram with operating regions of different reaction systems a) Circulating fluidized bed; b) Fluidized-bed roaster; c) Bubbling fluidized bed; d) Shaft furnace; e) Moving bed

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Often, the gas distributor design must also prevent solids from raining through the grid both during operation and after the bed has been shut off. Porous plates of glass, ceramics, metal, or plastic are commonly used as gas distributors in laboratory apparatus; a variety of designs are used in pilot-plant and full-scale fluidized-bed reactors (see Fig. 6). Many more designs can be found, for example, in [2] and [39]. The principal requirement – uniform distribution of fluidizing gas over the bed cross section – can be met if the pressure drop Dpd across the gas distribution grid is large enough. Suggested values for the ratio Dpd/Dpfb are 0.1–0.3 (with a minimum Dpd of 3.5 kPa) [40], 0.2–0.4 [41], and > 0.3 [42]. For a given pressure drop Dpd the gas velocity in the nozzle uo can be calculated from Dpd ¼

ro CD u2o 2

where ro is the gas density in the orifice and CD is the drag coefficient. Applying the continuity equation : V ¼ No Ao uo

either the number of nozzles No or the crosssectional area of the individual nozzle Ao can be calculated for a given gas flow rate V_. Problems related to the design of gas distributors are attrition of solids (see Section 2.11),

Figure 6. Industrial gas distributors A) Perforated plate; B) Nozzle plate; C) Bubble-cap plate


327

erosion, and back-flow of solids. Erosion may occur at the distributor plate and at neighboring nozzles or walls due to gas jets as well as at the nozzle itself. Back-flow of solids into the windbox is caused by pressure fluctuations. In order to prevent this either the design pressure drop has to be larger than the pressure fluctuations or – if this is not feasible for economic reasons – a design must be chosen which tolerates short periods of gas flow reversal without permitting the solids to penetrate into the windbox. For the latter case the bubble cap design has turned out to be advantageous [43]. In the operation of fluidized-bed reactors, the quadratic response (Dpd u2) of industrial gasdistributor designs must be kept in mind, because even if the fluidization velocity is lowered only slightly, an unacceptably low pressure drop across the gas distributor may occur. Industrial experience with different distributor designs, practical design rules, and a discussion of distributor-related problems, such as weepage into the windbox and erosion by grid jets and at grid nozzles, has been compiled in [44].

2.6. Gas Jets in Fluidized Beds Gas jets can form at the outlet openings of industrial gas distributors and also where gaseous reactants are itted directly into the fluidized bed. A knowledge of the geometry of such jets, in

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particular the depth of penetration, is important for the implementation of chemical operations in fluidized-bed reactors, and not just from the standpoint of reaction engineering. It is also vital for reasons of design: the strongly erosive action of these jets means that internals, such as heatexchanger tubes, must not be located within their range. The literature contains many empirical correlations for estimating the mean depth of jet penetration L (e.g., [2–4]); these must, however, be used with care and, whenever possible, only within the range of parameter values for which they were derived. By way of example, MERRY gives the following correlations for vertical gas jets [45]: " 2 0:2 # L r do 0:3 uo ¼ 5:2 f 1:3 1 rs dp gdo do

ð12Þ

and for horizontal jets [46]: #0:4 " L ro u2o ¼ 5:25 ð1eÞ rs g dp do

ðÞ dp do

rf

ðr Þ s

0:2

0:2

ð13Þ

4:5

Here do is the diameter of the outlet opening, uo is the outflow velocity, and ro is the density of the jet gas.

2.7. Bubble Development For many applications, especially physical operations and noncatalytic reactions, the state of a fluidized bed can adequately be described in of a single quantity averaged over the entire bed, such as the mean bed porosity e. In contrast, the design of fluidized-bed catalytic reactors requires that local fluid-flow conditions also be taken into . The local fluid mechanics of gas–solid fluidized beds are determined by the existence of bubbles, which influence the performance of fluidized-bed equipment in several ways: the stirring action and convective solids transport by the rising bubbles are helpful; the resulting intensive solids motion produces a uniform temperature throughout the fluidized bed and rapid heat transfer between the bed and the heating or cooling tubes submerged in it. The bubbles and

the motion of solids that they cause, however, also have some drawbacks: attrition of solid particles, erosion of internals, and increased solids entrainment by bubbles bursting at the bed surface. The existence of bubbles is particularly detrimental in the case of a heterogeneous catalytic gas-phase reaction, because the by of reactant gas in the bubble phase limits the conversion achieved in the fluidized bed. The ultimate cause of bubble formation is the universal tendency of gas–solid flows to segregate. Many studies on the theory of stability (e.g., [3, 4]) have shown that disturbances induced in an initially homogeneous gas–solid suspension do not decay but always lead to the formation of voids. The bubbles formed in this way exhibit a characteristic flow pattern whose basic properties can be calculated with the model of DAVIDSON and HARRISON [47]. Figure 7 shows the streamlines of the gas flow relative to a bubble rising in a fluidized bed at minimum fluidization conditions (e ¼ emf). The characteristic parameter is the ratio a of the bubble’s upward velocity ub to the interstitial velocity of the gas in the suspension surrounding the bubble: a¼

ub umf= emf

ð14Þ

The case a > 1 is typical for solids of Geldart groups A and B. The gas rising in the bubble flows downward again in a thin layer of suspension (‘‘cloud’’) surrounding the bubble. An important point for heterogeneous catalytic gas-phase reactions is that the presence of a boundary between bubble gas and suspension gas leads to the existence of two distinct phases (bubble phase and suspension phase) with drastically different gas–solid .

Figure 7. Gas flow for isolated rising bubbles in the Davidson model [47]

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If a < 1, some of the gas in the suspension phase undergoes short-circuit flow through the bubble, while only part of the bubble gas recirculates through the suspension. This type of flow is typical for fluidized beds of coarse particles (Geldart group D). Under the real operating conditions of a fluidized-bed reactor, a number of interacting bubbles occur in the interior of the fluidized bed. As a rule, the interaction leads to coalescence. As detailed studies have shown, this process is quite different from that between gas bubbles in liquids because of the absence of surface-tension effects in the fluidized bed [48, 49]. For predicting mean bubble sizes in freely bubbling fluidized beds, a differential equation for bubble growth should be used in the case of Geldart group A and B solids [50]: d dv ¼ dh

13 2eb dv 9p 3l ub

ð15Þ

with the following boundary condition at h ¼ ho: 8 1=3 > > 0:008eb : 2 dv0 < Vo ¼ 1:3 > m > : g

ð Þ

b ¼


329

3:2 dt0:33 0:05 dt 1 m; Geldart group A 3:2 dt0:5 0:1 dt 1 m; Geldart group B

ð20Þ

Outside these limits, b is taken as constant. The differential equation (Eq. 15) describes not only bubble growth by coalescence but also the splitting of bubbles (second term on the righthand side [51]). The crucial parameter here is the mean bubble lifetime l: l 280

umf g

ð21Þ

In practice, bubble growth is limited not only by the splitting mechanism based on the particlesize distribution of the bed solids, but also by internals (screens, tube bundles, and the like) that cause bubbles to break up. Computational techniques for estimating this process are given in [52, 53]. HILLIGARDT and WERTHER have derived a corresponding bubble-growth model for coarse-particle fluidized beds (Geldart group D) [50]. An example of a measured and calculated bubble-growth curve is presented in Figure 8.

porous plate 0:2

industrial gas distributor

ð16Þ

where ho is the height above the grid where the bubbles form (for a porous plate, ho 0; for a perforated plate, ho ¼ L; for a nozzle plate, ho is the height of the outlet opening above the plate; and for a bubble-cap plate, ho is the height of the lower edge of the cap above the plate). V_0 is the volume flow rate of gas through the individual grid opening. The local volume fraction of bubble gas eb is given by : eb ¼ V b =ub

2.8. Elutriation When bubbles burst at the surface of the fluidized bed, solid material carried along in their wake is ejected into the freeboard space above the bed. The solids are classified in the freeboard; particles whose settling velocity ut is greater than the gas velocity fall back into the bed, whereas particles with ut < u are elutriated by the gas

ð17Þ

and the visible bubble flow V_b is : V b 0:8 ðuumf Þ

ð18Þ

The upward velocity ub of bubbles depends not only on the bubble size but also on the diameter dt of the fluidized bed: where pffiffiffiffiffiffiffi : ub ¼ V b þ0:71_sb s_ gdv

ð19Þ

Figure 8. Bubble growth in a fluidized bed of fine particles (Geldart group A; data points from [54], calculation from [50])

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Figure 9. Schematic drawing of fluidized bed and freeboard

stream. As a result, both the volume concentration of solids cv and the mass flow rate of entrained solids in the freeboard show a characteristic exponential decay (Fig. 9). With increasing height above the bed surface, the ‘‘transport disengaging height’’ (TDH) is finally reached. Here the increased local gas velocities due to bubble eruptions have decayed, and the gas stream contains only particles with ut < u. When the TDH can be reached in a fluidized-bed reactor, this is associated with minimum entrained mass flow rates and solids concentrations, and hence with minimum loading on downstream dust collection equipment. Design of the dust collection system requires knowledge of the entrained mass flow rate Gs and the particle-size distribution of the entrained solids. For the design of the fluidized-bed reactor, the distribution cv (h) of the solids volume concentration and, for gas– solid reactions, the local particle-size distribution as a function of height in the freeboard must be known. For solids of Geldart group A, the TDH can be estimated with the diagram shown in Figure 10 [55]. The following relation is given for the TDH of Geldart group B solids as a function of the size dv of bubbles bursting at the bed surface [56]: TDH ¼ 18:2 dv

ð22Þ

Equation (25) was, however, derived for a bench-scale unit and may not scale to plant-size equipment. The mass flow rate Gs of entrained solids per unit area leaving the fluidized-bed reactor is the

Figure 10. Estimation of transport disengaging height (TDH), according to [55] umb ¼ Fluidization velocity at which bubble development begins

sum of contributions from the entrainable particle size fractions (ut < u): Gs ¼

X

xi k*i

ð23Þ

i

Here xi is the mass fraction of particle-size fraction i in the bed material and k*i is the elutriation rate constant for this fraction. The literature contains a number of empirical correlations for estimating k*i (e.g., [2–4]). More physical-based are the elutriation models of WEN and CHEN [57] and of KUNII and LEVENSPIEL [2, 58], which enable not only calculation of the exiting mass flow rate but also estimation of the concentration versus height cv (h) in the freeboard. The model by SMOLDERS and BAEYENS additionally takes the effect of variable freeboard geometry into [59]. A literature survey on the factors affecting elutriation and the available modeling tools is given in [60].

2.9. Circulating Fluidized Beds 2.9.1. Hydrodynamic Principles In REH’s state diagram of the fluidized bed [36], the circulating fluidized bed (CFB) is located above the single-particle suspension curve for

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Fluidized-Bed Reactors u Frp ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðrs rf Þ gdp r

331 ð26Þ

f

The dimensionless pressure drop y is the ratio of the pressure drop Dp along the flow path Dh to the maximum possible value for ascending flow (the value that would be attained if the pipe cross section were filled with solids corresponding to the concentration at the minimum fluidization point). The parameter of the family of curves is a volume flow rate ratio Figure 11. Fluidized-bed state diagram, according to [61]

Re < 10 and porosities e greater than about 0.8 (dashed line in Fig. 5). The shortcoming of this diagram is that it does not show an important parameter in the operation of a circulating fluidized bed: the circulating solids mass flow rate per unit area Gs. The diagram of Figure 11 [61] attempts to remedy this by plotting the mean slip velocity usl between gas and solids 2

u ðGs =rs Þ usl ¼ e 1e

ð24Þ

versus the mean solids concentration cv ¼ 1 e, with Gs as the parameter. The limiting conditions are high solids concentration (bed at minimum fluidization) and cv ! 0 with usl ¼ ut (isolated single particle). In the circulating fluidized-bed region, slip velocity increases with increasing Gs and can become much higher than the single-particle settling velocity (the physical justification for this statement comes from the formation of strands or clusters of particles). In the entrained-flow region the slip velocities again decrease with decreasing solids concentration. The fluidized-bed state diagrams discussed thus far, as well as others (e.g., [62, 63]), are suitable mainly for the qualitative interpretation of flow phenomena. A diagram proposed by WIRTH (e.g., [11, 64, 65]) also provides quantitative assistance in the design of circulating fluidized beds. The schematic in Figure 12 applies to a given gas–solid system described by a constant value of the Archimedes number Ar. The ordinate is the dimensionless pressure drop of the fluidized bed y¼

Dp ðrs rf Þ ð1emf Þ g Dh

the abscissa is the particle Froude number

ð25Þ

m rf rs ð1emf Þ

ð27Þ

where m is the ratio of solid-to-gas mass flow rates. The limiting curve bounds the region of stable, vertically upward gas–solid flow on the low gas velocity side. Figure 13 shows how the state diagram of Figure 12 is constructed for a circulating fluidized bed with siphon recycle. If solids holdup in the recycle line and siphon is ignored, this case represents operation with a constant bed mass independent of velocity. At high gas velocities and if acceleration effects are neglected, the bed material is distributed uniformly over the total height Hcfb of the fluidized bed (Fig. 13 C). The circulating fluidized bed then exhibits a single steady-state section with a constant pressure gradient (Dp/Dh). This pressure gradient can be calculated from the bed mass as

Figure 12. State diagram for the circulating fluidized bed with siphon, according to WIRTH [64] Ar ¼ const., parameter of family of curves is the volume flow rate ratio m rf/(rs (1 emf)); Frp¼ particle Froude number for superficial minimum fluidization velocity (pumf), singleparticle terminal velocity (pt), and transport velocity (pT), respectively

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Figure 13. Pressure profile in the circulating fluidized bed with siphon, according to WIRTH [64] A) Frpumf < Frp < Frpt ; B) Frpt < Frpmax ; C) Frp > Frpmax

yhom ¼

ðrs rf ÞgHmf ð1emf Þ Hmf ¼ ðrs rf ÞgHcfb ð1emf Þ Hcfb

ð28Þ

where Hmf is the bed height at minimum fluidization. The states identified by yhom to the right of the bounding curve in Figure 12 are accessible by increasing the gas velocity (corresponding to increasing Frp). With increasing Frp the volume flow ratio increases; that is, relatively more solids are elutriated (and thus circulated). If Frp is allowed to drop below the limit Frpmax (Fig. 13 B, Fig. 12) two steady-state sections appear in the riser tube: the one in the lower part is marked by a high pressure gradient, that in the upper part by a lower gradient. Figure 13 illustrates the physical significance of these two pressure gradients. In practice, the transition between the two linear regions takes place gradually. The height of the transition zone corresponds to the transport disengaging height (TDH). The picture changes further if the gas velocity declines to values lower than the settling velocity ut of a single isolated particle. In this case (for Frp < Frpt, Fig. 13 A, Fig. 12), no more solids can be elutriated, and the pressure gradient in the upper linear region vanishes. All the solid material is now in the form of a bubbling or turbulent fluidized bed. The solids concentrations averaged over the tube cross section (1 e) can be calculated from the dimensionless pressure drop: 1e ¼ ð1emf Þ y

ð29Þ

Besides the pressure and solids concentration profile, the circulating mass flow rate of solids Gs At is important for the design of the circulating fluidized bed. In particular, the design of the solids collection and recycle system depends very much on this quantity. The mass flow rate of solids depends on the flow regime. At gas velocities such that two steady-state sections are present in the bed vessel (i.e.,Frpumf < Frp < FrpT), the mass flow rate of entrained solids depends on the physics of the gas–solid flow. Figure 14 plots the

Figure 14. Elutriation diagram when the circulating fluidized bed contains two steady-state sections, according to WIRTH [64]

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dimensionless solids mass flow rate versus Frp, with the Archimedes number as parameter. For a given Ar, the flow rate tends to zero as Frp! Frpt and reaches a maximum at Frp ¼ FrpT. The slope of the elutriation curve becomes greater with increasing Ar; that is, the coarser the particles, the greater is the relative change in the circulating mass flow rate of solids with a change in gas velocity. At high gas velocities in the circulating fluidized bed (i.e., when a single steady-state section exists), the entrained mass flow rate depends on the particle Froude number and the solids holdup. More detailed information about the application of Wirth’s theory in practice may be found in [11]. Whereas WIRTH’s analysis of the circulating fluidized bed starts from the pneumatic transport condition, the models of RHODES and GELDART [66], as well as KUNII and LEVENSPIEL [2, 58], are based on the bubbling fluidized bed and describe the circulating fluidized bed as a limiting case of a bubbling bed with a very high rate of solids entrainment. 2.9.2. Local Flow Structure in Circulating Fluidized Beds The Wirth state diagram, as a first step toward the local characterization of flow regimes in a circulating fluidized bed, describes the vertical profile of the solids concentration. In the lower section of a circulating fluidized bed a dense region exits near the gas distributor. It has been observed that in this bottom zone bubble-like voids coexist with a surrounding dense suspension. The solids volume concentration is higher at the wall (cv 0.4) then in the center (cv 0.15) of the bottom zone [67]. The splash zone which links the bottom zone to the upper dilute zone is characterized by violent gas–solid mixing. Many recent experimental studies with various measurement techniques (e.g., X-ray tomography [68], capacitance tomography [69] and fiber-optical probes [70]) have shown that the upper section of the circulating fluidized bed exhibits characteristic horizontal profiles, with the concentration cv, wall near the vessel wall always significantly higher than the value cv averaged over the vessel cross section; for example, cv, wall ¼ 2.3 cv [71]. Local measurements of the solids concentration and solids velocity show that upward-


333

Figure 15. Schematic diagram of flow structure in a circulating fluidized bed

flowing regions of low solids concentration and downward-flowing aggregates of high solids concentration alternate in time at every point inside the fluidized bed, with downward-moving aggregates (strands, clusters) predominating near the wall and upward-moving regions of low suspension concentration predominating in the central zone. However, no significant downward flow of solids near the wall was observed in highdensity circulating fluidized beds, e.g., [72]. The picture of the local flow structure in a circulating fluidized bed, as derived from these observations, is shown schematically in Figure 15. A modeling approach which is based on the local flow structure of the CFB is the energyminimization multiscale (EMMS) model [73]. It considers the tendency of a fluid in a gas–solid two-phase flow to through the particulate layer with least resistance and the tendency of the solids to maintain least gravitational potential. Least resistance means that the volume-specific energy consumption for suspending and transporting solids is minimized, and minimization of the gravitational potential is equivalent to the requirement that the local mean voidage e attains a minimum. The model has been applied as a description of fluid-mechanical phenomena in CFB risers of different sizes [74, 75] but also for the prediction of flow patterns of gas and solids in industrial-scale units, such as a CFB boiler [76] and a petrochemical processing unit [77]. Another promising line of development is the introduction of the EMMS concept into computational fluid dynamical calculations of multiphase flows; first results obtained with a drag model based on the EMMS model are encouraging [78].

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the mass flow rate of the solids can be regulated by varying the gas supplied to the standpipe. Because the solids path does not contain any sort of mechanical closure, the characteristic pressure distribution plotted in Figure 17 is obtained. The distribution of solids between the fluidized bed and the recycle line is directly related to this pressure distribution. Operating properties differ from one recycle design to another [79].

Figure 16. Design options for solids recycle A) Siphon; B) L-valve

2.9.3. Design of Solids Recycle System Solids carried over with the fluidized gas are generally collected in cyclones. In the case of bubbling beds, the solids can easily be returned to the bed through the standpipe of the cyclone, which dips directly into the bed. Due to the large amounts of circulating solids, circulating fluidized beds require very large cyclones arranged beside and outside the bed, with special ‘‘valves’’ needed to connect the standpipe to the bed vessel. Figure 16 shows two design options, the siphon and the L-valve. With the siphon, the solids are fluidized (i.e., enabled to flow back into the reactor). In the L-valve design,

2.10. Cocurrent Downflow Circulating Fluidized Beds (Downers) A certain drawback of circulating and bubbling fluidized beds when applied for gas-phase reactions is the backmixing which inevitably occurs in the gas phase. In bubbling fluidized beds it is the bubble-induced solids circulation, and in circulating fluidized beds the downflow of solids in the wall zone, which entrains gas in the upstream direction and thus lowers the yield of a catalytic reaction or gives rise to undesired consecutive or side reactions. These disadvantages caused by the hydrodynamic effects of both gas and solids flowing against gravity could be overcome in the so-called downer reactor, in which the flow directions of both gas and solids are downward, i.e., in the same direction as gravity [80]. Another incentive is the possibility

Figure 17. Pressure distribution in solids recycle system of a circulating fluidized bed a) Fluidized bed; b) Return leg

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of realizing short times between gas and solids of around or even below one second. Downer systems have been intensely studied [80]. Hydrodynamics [81, 82], gas mixing [83], and solids mixing [84, 85] have been investigated both experimentally and by numerical simulation [86]. It has been found that the hydrodynamics of the downer are also characterized by a wall zone of increased solids concentration. However, axial and radial gas-solids flow structures are much more uniform than in conventional fluidized beds. Another result is that the length of the flow development zone is much shorter for the downer than for the riser, which means that reactions with very short times can be carried out under near-plug-flow conditions. However, the solids feeding process and the geometry of the entrance region are critical points that deserve special attention [87]. The patent and open literature suggest various applications for downer reactors, e.g., residual oil cracking [88], coal pyrolysis [89], and biomass pyrolysis [90]. The catalytic pyrolysis of heavy feeds for the production of light olefins has been investigated on the laboratory scale with promising results [88]. However, no large-scale industrial process has emerged yet.

2.11. Attrition of Solids The attrition of solid particles is an unavoidable consequence of the intensive solids motion in the fluidized bed. The attrition problem is especially critical in processes where the bed material needs to remain unaltered for the longest possible time, as in fluidized-bed reactors for heterogeneous catalytic gas-phase reactions. Catalyst attrition is important in the economics of such processes and may even become the critical factor. Catalyst attrition in fluidized-bed reactors occurs normally as surface abrasion (Fig. 18) which means that surface asperities are abraded and edges of the catalyst particles are rounded off. Fragmentation may also play a role, especially for some fresh catalyst particles which on entering the reactor may simply be crushed into pieces. If in an industrial process extraordinarily high catalyst losses are observed it is advisable to examine catalyst samples under the scanning electron microscope. If the sample contains many fragments this could be an indication of


335

Figure 18. Attrition modes and their effects on the particle size distribution (q3 ¼ mass density distribution of particle sizes dp)

a wrong design (e.g., too high a velocity at the cyclone inlet or at the distributor). When deg catalytic fluidized-bed processes, the attrition performance of candidate catalysts should be tested under standardized conditions in the process development stage. This test can be performed in a small laboratory apparatus; it consists essentially of an extended fluidization test in which the mass of solids carried out of the bed is recorded as a function of time. Figure 19 presents a typical test result: during the first hours of testing, both the attrited material and the fine fraction of the bed material are elutriated. Only after a relatively long operating period is a quasi-steady state attained. The

Figure 19. Result of an attrition measurement

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attrition rate ra in this steady state can be defined as ra ¼

1 Dma mb Dt

ð30Þ

where ma is the elutriated mass and mb the bed mass. Usually ra is expressed as percentage per day; for relatively attrition-resistant, fluidizedbed catalysts, it is of the order of 0.2 % per day [9]. Many standard test apparatuses have been proposed for comparative attrition tests (e.g., [91, 92]), but all such equipment has been suitable only for comparative studies of different catalysts under consideration for the same process. The attrition measured in large-scale equipment can be far different from the values measured in a test apparatus. A number of sources can be identified for catalyst attrition in industrial fluidized-bed reactors: 1. Jet attrition at gas distribution grid openings and nozzles where gaseous reactants are itted to the bed 2. Bubble attrition in the bed due to solids motion caused by bubbles 3. Attrition in cyclones 4. Attrition in pneumatic conveying lines, such as those between reactor and regenerator beds Empirical correlations are available for the attriting action of a gas jet in the fluidized bed [93] and for the size reduction effect of solids motion in the bed [94, 95]. WERTHER and coworkers [96] employ the laboratory apparatus shown schematically in Figure 20 which enables separate study of the attrition due to jets from nozzles of various diameters and that due to bubbles. Under steady-state conditions the jet-attritionrelated mass production of fines per unit time for a gas distributor with a number no of orifices from mother particles with diameter dp,i which are present in the catalyst inventory with a mass fraction DQ3i is proportional to the particle size dpi, the mass fraction DQ3i, the density ro of the gas issuing from the orifice, the square of the orifice diameter do, and to the cube of the jet exit velocity uo [97, 98]: m att; jet;i ¼ cj n0 dpi DQ3i r0 d02 u30

ð31Þ

Figure 20. Experimental measurement

apparatus

for

attrition

Attrition due to the bubble induced solids movement is given by [98] m att; bubble;i ¼ cb dpi DQ3i mb ðuumf Þ3

ð32Þ

where mb denotes the bed mass which contains bubbles (i.e., which is located outside the jet-dominated grid region). Equation (32) also denotes the mass production of attrited fines which is resulting from the size fraction dpi in the bed. The stress on the catalyst particles will be different in with a gas jet, in the bulk of the bubbling fluidized bed, and during its age through a cyclone. Recent investigations of cyclone-induced catalyst attrition [99–101] have shown that the mass flow of attrited fines which is produced by attrition inside the cyclone when a solids mass flow m_cDQ3ci of particles of the size fraction dpi enters the cyclone is given by u2c m att; c;i ¼ cc m c DQ3ci dpi pffiffiffiffiffi mc

ð33Þ

where uc is the gas velocity at the cyclone inlet, and mc the solids loading of the incoming gas flow mc ¼

m c rc uc Ac

ð34Þ

where rc is the density of the inflowing gas, and Ac the cross-sectional area of the cyclone inlet.

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Figure 21. Dependence of attrition on time (bubble- and jetinduced attrition) and number of ages np through a cyclone.

Equations (31)–(34) describe the catalyst attrition under conditions of steady state, i.e., when the particles are more or less rounded off (Fig. 18). To describe also the initial breakage and attrition of fresh catalyst particles, it is necessary to follow the fate of the particles on their introduction into the reactor, which is possible with population balance models (cf. Section 9.3.2). Klett et al. [102] and Hartge et al. [103] have defined a stress history parameter 8 * t=tj for jet--induced attrition > > < ¼ t=tb* for in--bed attrition > > : np =n*p for attrition in cyclones

ð35Þ

where the definition of the characteristic parameters tj*, tb*, and np* can be taken from Figure 21, np is the number of ages of a given particle through the cyclone, and tb and tj are the time periods during which the particle is subjected to bubble and jet stress, respectively. If it is assumed that the effects of the different stress mechanisms on the catalyst particles are additive, a uniform treatment of the overall stress history for all three attrition mechanisms is given by m att ðÞ ¼ m att;¥

1:1 b 1

1:11=b > 1:11=b

ð36Þ

The parameter b is characteristic of a given catalyst. Figure 22 shows measurements with FCC catalyst [103] which lead to b ¼ 1.16. Equation (36) allows the description of the stresshistory-dependent attrition rate and can be used for the simulation of fluidized bed reactors (see Section 9.3.2).

337

Figure 22. Dimensionless attrition rate of FCC catalyst as a function of stress history.

A variety of approaches exist for reducing attrition in industrial fluidized-bed reactors. The jet attrition action can be controlled with special gas distributor designs ([9]; e.g., by the use of bubble caps, Fig. 6) such that gas jets do not issue directly into the bed at high velocity. Attrition due to bubbles can be lowered by limiting bubble growth (avoiding high gas velocities and large bed heights; use of fine catalysts with low umf, as implied by Eqs. 18 and 24). Attrition in cyclones can be prevented, in the simplest case, by replacing the cyclones with devices such as filters. Attrition can also be minimized by cutting back the load on the cyclone, for example, by placing the cyclones above the TDH. Relatively high catalyst attrition also occurs in circulating fluidized beds where very large quantities of solids must be collected in the cyclones.

3. Solids Mixing in Fluidized-Bed Reactors The intensive solids mixing typical of fluidizedbed reactors has several effects on performance. In catalytic reactions, the large-scale vertical solids mixing results in a transport of the gas components, adsorbed to the catalyst, so that the gas phase is backmixed and the conversion and selectivity are impaired. In noncatalytic gas– solid reactions, the mean solids residence time and residence-time distribution, as well as the propagation behavior of the solids from individual feed points, play a role. In general, fast and strongly exothermic reactions require fairly vigorous solids mixing to prevent temperature peaks near the reactant inlet.

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Figure 23. Solids mixing in bubbling fluidized beds due to particle drift (A) and wake transport (B) a) Cloud; b) Wake

3.1. Mechanisms of Solids Mixing The wake of the rising bubbles produces a rather slight upward and lateral drift of the particles (Fig. 23 A) [104]. In addition, solid particles are drawn upward in the wake, portions of the wake are shed at irregular intervals during bubble motion, and new portions of solids are taken into the wake (Fig. 23 B). Solids transport in the wake is essentially the reason that vertical solids mixing is from one to two orders of magnitude better than horizontal mixing. For reasons of continuity, the upward transport of particles by bubbles is coupled with a downward movement in the suspension phase that surrounds the bubbles. Measurements of the local bubble-gas flow have shown that the rising bubbles are not distributed evenly over the bed cross section. As a typical example, Figure 24 A gives a plot of the radial distribution of the bubble-gas flow at three heights above the grid in a fluidized bed 1 m in diameter. The profile is comparatively flat in the bottom zone but exhibits a steeper slope as the height increases, with an annular zone of preferentially rising bubbles. The resulting circulation of the solids also features an annular region of upward transport in the wakes with predominantly downward motion of the solids in the center and at the periphery of the bed (Fig. 24 B). The large-scale solids circulation can be reinforced by uneven distribution of the fluidized gas over the distributor cross section [106]. Figure 25 presents examples of industrial fluid-

Figure 24. A) Radial distribution of bubble-gas flow; B) Relationship between bubble distribution and solids circulation [105] dt ¼ 1 m, quartz sand, umf ¼ 0.013 m/s, u ¼ 0.2 m/s, Hmf ¼ 0.5 m, V_b ¼ visible bubble flow

ized-bed furnaces in which forced circulation of the solids is employed to improve coal burnup.

3.2. Vertical Mixing of Solids The propagation behavior of the solids in a fluidized bed can be described by a number of models (e.g., [2, 109]). Most commonly used is the dispersion model, in which solids transport is described by a diffusion law. The numerical value of the dispersion coefficient Dsv for solids mixing in the vertical direction increases with increasing gas velocity because of the growth in the number and size of bubbles. The following simple empirical correlation is given for fine particles (Geldart groups A and B) [2]:

Dsv u ¼ 0:06þ0:1 2 m =s m=s

ð37Þ

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339

Figure 25. Fluidized-bed furnaces with forced circulation of solids A) According to [107]; B) According to [108]

For a plant-scale fluidized bed (0.9 1.26 m2 in plan, bed height 4 m) equipped with a bundle of horizontal tubes, a very similar relation was derived for a solid of Geldart group B [110]:

Dsv uumf ¼ 0:056 2 m =s m=s

ð38Þ

Because solids circulation becomes more marked in larger-diameter fluidized beds, the dispersion coefficient increases rapidly with increasing bed diameter dt (Fig. 26). For this case the following expression is found [2]: 0:65 Dsv dt ¼ 0:030 2 m =s m

coworkers model the horizontal propagation of coal in a fluidized-bed furnace, describing the carbon conversion in of a simple first-order reaction (rate constant k with dimension s1) [113]. The crucial parameter is the ratio k d2t /Dsh between the rate of the chemical reaction and the rate of dispersive mass transport. For high values of k (fast reaction), large reactor diameters dt, and low values of the dispersion coefficient Dsh, the

ð39Þ

The above correlations can provide only rough values. Other effects observed in practice include, in particular, a significant effect of particle-size range [111, 112].

3.3. Horizontal Mixing of Solids In gas–solid reactions, the propagation behavior of the solids in the horizontal direction is important if, for example, the solid material is fed into the bed at isolated feed points. WERTHER and

Figure 26. Vertical solids dispersion in fluidized beds of fine particles (Geldart groups A and B) [2]

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local carbon concentration in the bed exhibits a rather steep horizontal profile, resulting in a significantly nonuniform distribution of gas emissions over the bed cross section. On the basis of KUNII and LEVENSPIEL’s model of bubble-induced solids mixing [114], an expression has been derived for calculating the horizontal dispersion coefficient Dsh averaged over the bed height H, given local bubble properties (bubble diameter dv, bubble-gas holdup eb) [115]: Dsh ¼ 0:67 103 þ0:023

1 H

ZH 0

eb qffiffiffiffiffiffiffiffiffiffi3 g dv dh 1eb

ð40Þ

This correlation holds for solids of Geldart groups B and D with Archimedes numbers between 8 600 and 58 000.

3.5. Solids Mixing in Circulating Fluidized Beds The circulating fluidized bed exhibits a complex gas–solid flow pattern as discussed in Section 2.9. Different regions can be discriminated with respect to the prevailing mechanisms of solids motion and mixing. An extensive survey on experimental findings in solids mixing is given in [116]. In the upper diluted zone of the circulating fluidized bed, clusters are formed with mainly upward flow in the core and predominantly downwards motion near the wall. While the wall region can be modeled by a plug-flow approach, the core region exhibits radial gradients. The Peclet number characterizing radial solids mixing in the core region Per; s ¼

3.4. Solids Residence-Time Properties Many applications of fluidization technology involve continuous processing of solids. Important considerations in such cases are not only the mean solids residence time but also the residence-time distribution. Whereas all elements have the same residence time in a plug-flow system, a stirred tank exhibits a broad distribution of residence times. To a good approximation, the residence-time properties of the fluidized bed with respect to the solids are the same as those of a stirred tank. The mean residence time t is the ratio of the solids mass mb in the reactor to the solids throughput m_s: mb t¼ : ms

ð41Þ

The mass fraction dms/mb of solids having a residence time between t and t þ dt is dms 1 t ¼ e t dt mb t

ð42Þ

Similarly, the fraction f of solids having a residence time less than t in the bed is calculated as f ¼ 1e

t=t

ð43Þ

The residence-time distribution can be narrowed by placing a number of fluidized beds in series. Multistage systems of this type are used, for example, in fluidized-bed drying [18].

uc 2R* Dr; s

increases from 150 to 300 with increasing solids volume concentrations [117]. A recent investigation of solids mixing in the bottom zone with solid carbon dioxide as a tracer showed that in this zone solids are almost ideally mixed in the vertical direction but lateral mixing is limited with dispersion coefficients of about 0.1 m2/s which corresponds to Peclet numbers of around 40, [118]. Counteracting to solids mixing, segregation occurs in applications using particles of a broad size distribution and/or different densities. Easily fluidized particles tend to be elutriated while others tend to sink. A dynamic equilibrium between solids mixing and segregation is established, causing a spatial distribution of particles with significantly different solids properties, as was shown in an experimental study with a mixture of iron powder and quartz sand with a broad particle size distribution [119].

4. Gas Mixing in Fluidized-Bed Reactors The mixing and residence-time distribution of the gas are particularly important for catalytic reactions but are also significant for gas–solid reactions when gaseous reactants are to be converted to the greatest possible extent in fluidized beds (e.g., reduction of fine-grained iron ores to sponge iron with gaseous reductants [18]). Gas

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mixing is closely linked to the motion and mixing of the solids in the bed.

4.1. Gas Mixing in Bubbling Fluidized Beds If the flow and mixing of gas in the bubbling fluidized bed are described by a simple one-phase dispersion model, the coefficients Dgv and Dgh of gas dispersion in the vertical and horizontal directions have similar numerical values and follow trends similar to those of the solids dispersion coefficients. By way of example, Figure 27 shows the effect of fluidized-bed diameter dt on vertical gas dispersion. The increase in dispersion coefficient with vessel diameter might be attributable to the formation of large-scale solids circulation patterns, which becomes more marked in larger equipment. As in the solids case, the coefficients of horizontal gas dispersion are a factor of 10–100 lower than those of vertical gas dispersion. A single-phase dispersion model gives only a rough description of gas mixing in bubbling fluidized beds. A more exact description comes from models that take of local flow conditions in the bed, especially the presence of bubbles (see Chap. 9).


which are summarized in [120]. The bubbles in a bubbling fluidized bed influence the gas residence-time distribution and mixing directly through the by action of the bubble-gas flow and gas exchange between the bubbles and the surrounding suspension phase, and also indirectly through the solids motion that they induce. In the circulating fluidized bed, on the other hand, the gas-mixing properties are controlled by segregation due to the formation of solid aggregates (jets, clusters) and the rapid downward movement of solids strands predominantly near the wall. GRACE and coworkers, for example, show that a single-phase dispersion model cannot describe the tracer gas residence-time distributions that they measured [121]. They propose instead a two-phase model featuring exchange between a wall zone with stagnant gas and a core zone with plug flow. For the case of horizontal gas mixing, WERTHER and coworkers [122, 123] have shown that, for the bed solids they used (quartz sand, dp ¼ 0.13 mm, Geldart group B), horizontal gas mixing in the top part of the circulating fluidized bed in the core zone can be described by the model of turbulent single-phase flow [124]. The Peclet number Per; c ¼

4.2. Gas Mixing in Circulating Fluidized Beds Only a few detailed studies of gas mixing in circulating fluidized beds have been published,

341

uc 2R* Dr; c

ð44Þ

(defined in of uc, the superficial velocity in the core zone; R*, the radius of the core zone; and Dr, c, the horizontal dispersion coefficient in the core zone) has a value of 465, which is in fairly good agreement with values measured in singlephase flows [125]. This value is independent of the solids circulation rate Gs. The circulating fluidized bed thus exhibits no especially intensive horizontal gas mixing, at least in the upper section where solids concentrations are relatively low.

5. Heat and Mass Transfer in Fluidized-Bed Reactors

Figure 27. Vertical gas dispersion in a fluidized bed of solids of Geldart group A (measurements by various workers; [2])

Fluidized-bed reactors exhibit a uniform temperature distribution even in case of highly exothermic or endothermic reactions. Approximations of the heat transfer rates are necessary for the design and control of fluidized-bed reactors in

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order to determine the appropriate design of internals for cooling or heating and to estimate the changes in the performance with changing operating conditions. However, up to now there is no general theory on heat and mass transfer in fluidized beds. Numerous correlations for the calculation of heat and mass transfer coefficients are reported in the literature. Since these correlations are mainly based on experimental investigations performed under laboratory conditions, they may be different to the situation in large-scale reactors. Details on models of heat and mass transfer with their respective range of application are given in related surveys, e.g., [14–17, 126, 130]. Fluid-to-Particle Heat and Mass Transfer. Since the particle surface area is very large, fluidto-particle heat and mass transfer is rarely a limiting factor in the design and operation of fluidized bed reactors. The heat-transfer coefficients of fluidized-beds range between characteristic values for flow through a fixed bed and flow around a single particle [127]. Fixed bed (Rep > 80) Nu ¼

hgs dp 0:33 ¼ 2þ1:8 Re0:5 p Pr lg

Single particle Nu ¼

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magnitude larger than for gases alone [126]. For single phase flow a stagnant gas layer is established at the wall causing a hindered heat transfer. This layer is disrupted by solids transported at the wall. The solids adsorb heat and are mixed into the fluidized bed [9]. An example of the time-averaged local heat transfer along the circumference of a tube immersed horizontally in a fluidized bed is given in Figure 28. It exhibits lower values of the heattransfer coefficient below the tube due to a gas gap caused by bubbles and lower values on top of the tube because of solids being at rest. With intensified mixing this effect becomes less significant. The dependence of the heat-transfer coefficient on the superficial gas velocity is illustrated in Figure 29. Fluidized beds of fine particles yield a larger heat-transfer coefficient than coarse particles. According to MOLERUS and WIRTH [126], different transfer mechanisms can be identified. In case of fine particles, solids act as agents transporting heat between walls and bed, whereas gas convective transport is the mechanism dominating the heat transfer of coarse particles. The heat-transfer coefficient of particles of intermediate sizes exhibits a maximum due to the superposition of these two transport mechanisms. Heat-transfer rates in circulating fluidized beds are lower than in bubbling fluidized beds due to

hgs dp 0:33 ¼ 2þ0:6 Re0:5 p Pr lg

where hgs is the gas–solid heat-transfer coefficient, dp the particle size, and lg the thermal conductivity of gas. The mass transfer coefficient can be determined applying the analogy of heat and mass transfer by replacing in the above formulas the Nusselt number Nu by the Sherwood number Sh and the Prandtl number Pr by the Schmidt number Sc. For particle Reynolds numbers below 100 and for fine particles, the transfer coefficients are significantly lower than estimated by the above formulas. If necessary, the effect of adsorption in mass transfer and of radiation in heat transfer needs to be taken into additionally. Heat Transfer to Submerged Surfaces. Heat-transfer coefficients between fluidized bed and submerged surfaces are one or two orders of

Figure 28. Local heat-transfer coefficient around a 35 mm diameter tube immersed horizontally in a fluidized bed of 0.37 mm alumina particles operated at a superficial gas velocity of 0.8 m/s and a temperature of 500 C, adapted from [128]

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Figure 29. Heat-transfer coefficients determined with a tube immersed vertically in a fluidized bed of glass beads of different size operated at ambient conditions, adapted from [129, 126]

reduced solids volume concentrations and are dominated by clusters and strands [130]. The heat-transfer coefficient increases with increasing pressure [131] and temperature. The effect of radiation has to be considered for temperatures above 500 C, but opaque particles can form an effective radiation shield [132].

6. Gas-Solid Separation The fluidizing gas inevitably carries fine catalyst particles by entrainment to the reactor exit. Not only for environmental reasons (i.e., to minimize emissions) is it necessary to separate the solids from the gas. It may also be necessary to stop the main reaction and to avoid unwanted side or consecutive reactions or to protect following process steps or machines from particle-laden streams. In fluidized-bed technology cyclones are mostly used for this purpose. KNOWLTON [133] has given a survey on the state of the art of cyclone design and application in fluidizedbed reactors. The cyclone should not be considered as a separate apparatus following the fluidized bed but should be seen as an integral part of the fluidized-bed process. The reason is that, not only in circulating fluidized beds but also in bubbling or turbulent fluidized beds, the catalyst particles which are recovered in the cyclone are recycled to the fluidized bed. The collection efficiency of the cyclone is thus responsible for maintaining the particle size distribution in the bed inventory, which in turn determines the

fluidized-bed fluid mechanics and the chemical performance of the bed as a reactor. The interrelation between fluidized bed and cyclone is discussed in Section 9.3.2. The influence of cyclone performance on the overall process performance is increasingly considered. For example, PULUPULA et al. [134] investigated the role of cyclones in the regenerator system of a commercial FCC unit. ARNOLD et al. [135] were able to trace the deterioration of plant performance in the ALMA maleic process back to problems with cyclone efficiency. A change of the cyclone design improved the particle size distribution of the bed inventory and consequently bed hydrodynamics and chemical conversion. SMIT et al. [136] report on cyclone performance in turbulent fluidized-bed Synthol reactors for Fischer–Tropsch synthesis. Carbon deposition on the catalyst particles influences the bed hydrodynamics, which in turn, via the elutriation mechanism, influence cyclone performance.

7. Injection of Liquid Reactants into Fluidized Beds The injection of reactants in liquid form into the bed was already an essential part of the first fluidized-bed catalytic process. In the FCC process (Section 8.1) crude oil is injected at the base of the reactor and evaporated in with the hot catalyst particles. The direct heat transfer is very efficient and avoids a separate evaporator for the feed. The cooling action of the evaporating reactant is a further advantage in the case of an

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exothermal reaction. Liquid-feed injection is therefore practiced not only in the FCC process but also, for example, in the syntheses of aniline (! Aniline, Section 3.2.), caprolactam (! Caprolactam, Section 4.1.4.), and melamine (! Melamine and Guanamines, Section 4.1.) and in BP Chemicals’ Inovene process [137] for the gasphase production of low-density polyethylene. Despite its industrial significance knowledge about the mechanisms of liquid mixing and evaporation in the fluidized bed is relatively scarce. Investigations with nonvaporizing horizontal gas–liquid spray jets have shown that with proper design of the injection nozzle it is possible to penetrate over several decimeters into the bed before the jet breaks up [138, 139]. On the other hand, it was found that under vaporizing conditions for atomizer nozzles with spray angles between 20 and 120 the injected liquid wetted the bed particles and subsequently evaporated from their surface while the particles were mixing in the bulk of the bed [140, 141]. This latter mechanism helps to transport the reactant away from the location of the nozzle and thus contributes to equalization of the feed distribution inside the reactor. The special case that a large oil droplet impinges on a smaller hot catalyst particle was recently investigated in a 3D direct numerical simulation to analyze droplet–particle collisions in the Leidenfrost regime [142]. The calculations were carried out for conditions prevailing near the feed nozzle in an FCC riser. Vapor layer pressure induced by evaporation and the droplet surface tension are the driving forces for droplet recoiling and rebounding. The time for a FCC particle and an oil droplet turned out to be about 140 ms.

8. Industrial Applications In this chapter the industrial uses of fluidized-bed reactors are classified as follows: 1. 2. 3. 4. 5.

Heterogeneous catalytic gas-phase reactions Polymerization of olefins Homogeneous gas-phase reactions Gas–solid reactions Biotechnology applications

In each of these areas, the most important applications are listed and a few typical examples

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are analyzed in more detail. For further descriptions of processes, the reader is referred to relevant articles in the A series. Complete descriptions of industrial uses of the fluidized-bed reactor can also be found in [2, 10, 18, 19].

8.1. Heterogeneous Catalytic Gas-Phase Reactions The fluidized-bed reactor offers the following principal advantages over the fixed-bed reactor for heterogeneous catalytic gas-phase reactions: 1. High temperature homogeneity, even with strongly exothermic reactions. 2. Easy solids handling, permitting continuous withdrawal of spent catalyst and addition of fresh if the catalyst rapidly loses its activity. 3. Ability to operate in the explosion range, provided the reactants are not mixed until they are inlet to the fluidized bed. This is because the high heat capacity of the bed solids, together with intensive solids mixing, prevents the propagation of explosions. Catalytic Cracking. (! Oil Refining, Section 3.2.). The ease of solids handling was the basic reason for the success of catalytic cracking of long-chain hydrocarbons in the fluidized bed (Fig. 30). The cracking reaction is endothermic and involves the deposition of carbon on the catalyst surface, which quickly renders the catalyst inactive. Accordingly, the catalyst must be continuously discharged from the reactor and regenerated in an air-fluidized regenerator bed (b), where its carbon loading is lowered from 1–2 to 0.4–0.8 wt %. The combustion in this bed simultaneously furnishes the heat required for the cracking reactor; the catalyst acts as a heat carrier. The temperature in the regenerator is 570–590 C and in the reactor, 480–540 C [2]. In a stripper, steam is itted to remove hydrocarbons adhering to the catalyst before it is forwarded to the regenerator. With the advent of high-activity zeolite catalysts in the 1960s, the bubbling fluidized bed, operated at gas velocities between 0.31 and 0.76 m/s [2], was replaced by the riser cracker (Fig. 31), in which the oil fed in at the bottom of the riser (c) is vaporized in with the hot catalyst and the mixture of oil vapors and

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of the order of a few seconds and the narrow gas residence-time distribution, the high activity of the zeolite catalyst is optimally utilized and a higher gasoline yield is achieved [2, 10]. Synthesis of Acrylonitrile. The crucial factor in the successful use of the fluidized-bed reactor for the synthesis of acrylonitrile by the ammonoxidation of propene (Sohio process) (! Acrylonitrile) was reliable control of this strongly exothermic reaction: C3 H6 þNH3 þ3=2 O2 ! C3 H3 Nþ3 H2 O DH r ¼ 515 kJ=mol of acrylonitrile:

Figure 30. Fluid catalytic cracking process (Kellogg-Orthoflow system; according to [143, 144]) a) Reactor; b) Regenerator

The reaction is carried out at a bed temperature of 400–500 C and gas time of 1– 15 s [145] or 5–20 s [2]. Figure 32 is a schematic of the reactor. Air is fed to the bottom of the fluidized-bed vessel. The reactants ammonia and propene are fed in through a separate distributor (b). Catalyst regeneration by carbon burnoff occurs in the space between the air distributor and the feed-gas distributor. The heat of reaction is removed by bundles of vertical tubes (a) inside the bed (horizontal tubes are used in other designs [146]).

cracking gas transports the catalyst up through the riser. In the reactor bed (a), solids are collected before ing through the stripper (b) to the regenerator (f). By virtue of the short time

Figure 31. Riser cracking process (UOP system), [2] a) Reactor; b) Stripper; c) Riser; d) Slide valve; e) Air grid; f) Regenerator

Figure 32. Synthesis of acrylonitrile (Sohio process) [2] a) Cooler with internals; b) Distributor

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Fischer–Tropsch Synthesis. The Fischer– Tropsch synthesis of hydrocarbons is used on a large scale for fuel production in the Republic of South Africa [149]. Synthesis gas generated from coal in Lurgi fixed-bed gasifiers enters the Synthol reactor (Fig. 33), where it is reacted over an iron catalyst at ca. 340 C. The reactor works on the principle of the circulating fluidized bed. The mean porosity in the riser is 85 %, and the gas velocity varies between 3 and 12 m/s [2]. Reaction heat is removed by way of heat-exchanger tube bundles placed inside the riser. However, experience has shown that this reactor is costly, relatively expensive to operate and maintain, and scale-up to the size of the reactors in operation is probably close to the maximum achievable for operation at 350 C and 2.5 MPa. Therefore, in the 1990s the 16 circulating fluidized-bed reactors operating at Sasol’s Secunda site were replaced by eight turbulent fluidized-bed reactors each of 10.7 m diameter, which achieve a higher per- syngas conversion [150].

Figure 33. Fischer–Tropsch synthesis in the Synthol reactor [2, 147] a) Hopper; b) Standpipe; c) Riser; d) Cooler (coil); e) Reactor; f) Gooseneck

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Different process routes have been developed for the synthesis of maleic anhydride. The Mitsubishi process [152, 153] used the naphtha cracker C4 fraction. The ALMA process uses n-butane as feedstock [154, 155]. A more recent development is the Du Pont process, which is also based on n-butane but uses a circulating fluidized bed as reactor (Fig. 34) [156]. It is based on a vanadium phosphorus oxide (VPO) catalyst which oxidizes n-butane to maleic anhydride by a redox mechanism on its surface layers [157]. In the riser n-butane is selectively oxidized by the oxidized catalyst. In the fluidized-bed regenerator the spent catalyst is reoxidized. Since 1996 a commercial plant has been operating in Asturias, Spain [158]. Other Processes. Other catalytic reactions carried out in fluidized-bed reactors are the oxidation of naphthalene to phthalic anhydride (! Phthalic Acid and Derivatives) [2, 10, 151]; the ammoxidation of isobutane to methacrylonitrile [2]; the reaction of acetylene with acetic acid to vinyl acetate [2]; the oxychlorination of ethylene to 1,2-dichloroethane (! Chlorinated Hydrocarbons) [2, 10, 159, 160]; the chlorination of meth-

Figure 34. The Du Pont maleic anhydride process [158].

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ane [2]; the reaction of phenol with methanol to cresol and 2,6-xylenol [2, 161]; the reaction of methanol to gasoline [162, 163]; the synthesis of phthalonitrile by ammoxidation of o-xylene (! Phthalic Acid and Derivatives) [164]; the synthesis of aniline by gas-phase hydrogenation of nitrobenzene (! Aniline, Section 3.2.) [165]; and the low-pressure synthesis of melamine from urea (! Melamine and Guanamines) [166]. An overview on the various fluidized-bed catalytic processes has been given [167].

8.2. Polymerization of Olefins The gas-phase polymerization of ethylene in the fluidized bed was developed by Union Carbide (Unipol process [168]; see Fig. 35) (! Polyolefins). The reaction gas (ethylene and its comonomers butene or hexene) fluidizes the bed at 75– 115 C and 20–30 bar. Extremely fine-grained catalyst is metered into the bed. Polymerization occurs on the catalyst surface and yields a granular product with diameter ranging from 0.25 to 1 mm. Ethylene conversion is comparatively low, 2 % per ; so the reaction gas is recycled. The heat of reaction is removed by cooling the


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recirculating gas. The catalysts used have such a high activity that more than 105 parts by volume of polymer can be produced per unit weight of active substance in the catalyst [2]. Because of the high degree of catalyst dilution in the granular polymer, the catalyst need not be removed from the product. In the process developed by BP Chemicals, prepolymers with a diameter from 0.2 to 0.25 mm rather than catalyst particles are fed into the fluidized bed [169]. Mitsui Petrochemical Industries has developed a process for the gas-phase fluidized-bed polymerization of propene (! Polyolefins); a plant using this process came on stream in 1984 [170]. The Unipol–Shell process was tly developed by Union Carbide and Shell and commissioned in 1986. Burdett et al. [171] have given a broad overview on this still-developing technology, which presents many challenges for the engineer. One of the biggest problems is the stickiness of the particles under the operating conditions of the process, which has often led to particle sintering with subsequent defluidization of the bed. Seville et al. [172] monitored the motion of particles in a scaled polymer reactor and studied the sintering kinetics in order to determine a safe operating window. Cai and Burdett [173] developed a model of single-particle polymerization in the fluidized bed to simulate particle growth and particle-temperature evolution with the residence time of a catalyst particle in the reactor.

8.3. Homogeneous Gas-Phase Reactions

Figure 35. Gas-phase polymerization of ethylene (Unipol process) [2] a) Compressor; b) Cooler; c) Catalyst feed hopper; d) Reactor; e) Separator

The decisive advantage of the fluidized bed for homogeneous gas-phase reactions is the ability to carry large quantities of heat into or out of the reactor by using direct heat exchange via the bed solids. An example is the Exxon fluid coking process (Fig. 36; [2, 18, 174, 175]), which converts heavy residual oils to petroleum coke and gas-oil. The reactor (d) and heater (e) beds are connected in a single solids loop. The bed material is coke generated in coking at 480–570 C, which grows to spherical particles 0.1–1 mm in diameter in the reactor. The coke is discharged continuously from the reactor and heated to 500– 690 C by partial combustion in the heater. The hot coke stream then transports the heat needed

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sions can be reduced. If limestone is added to the bed, the calcination reaction CaCO3 ! CaOþCO2

yields CaO, which can bind in situ the SO2 produced in combustion: SO2 þCaOþ1=2 O2 ! CaSO4

Figure 36. Fluid coking process [2, 18] a) Slurry recycle; b) Stripper; c) Scrubber; d) Reactor; e) Heater; f) Quench elutriator

for the endothermic coking reaction into the reactor. Excess coke is removed as a coarse fraction in a classifier connected to the heater. Fluid coking is used, e.g., for refining bitumen from the Athabasca tar sands in Canada. To make efficient use of the product coke, Exxon combined the fluid coking process with a fluidizedbed gasification reactor [2, 175]. This FlexiCoking process was first implemented in 1976 in Japan; the daily capacity of one plant is ca. 3400 t of vacuum residue. The bed solids also find use as heat-transfer agents in the thermal cracking of naphtha, a process carried out in the Lurgi sand cracker [2, 18, 176]. The solids circulating between the reactor and the heater consist of coarse sand particles (ca. 1 mm in diameter). When the coke deposit produced in cracking is burned off the particle surface with air, the solids are heated to 800–850 C and can thus deliver the heat required for endothermic cracking. The temperature in the reactor is ca. 700–750 C. Other thermal cracking processes include the BASF Wirbelfliess process [2, 18, 177], and the Kunii–Kunugi process [2].

8.4. Gas–Solid Reactions Coal Combustion. The high heat capacity of the fluidized bed permits stable combustion at low temperature (ca. 850 C), so that the formation of thermal and prompt nitrogen oxides [178] can be suppressed and total nitrogen oxide emis-

During the 1980s the fluidized bed was established in power-plant engineering. The unit size rapidly increased from 5 MWe in 1970 to about 350 MWe during this time [179]. Meanwhile (ca. 2006) some 500 power plants are in operation worldwide. By far the majority of these plants operate with circulating fluidized beds. As an example, Figure 37 shows a Lurgi design. The staged ission of the combustion air minimizes NO production from nitrogen in the fuel in the lower part of the combustion chamber. The ission of secondary air completes the combustion in the upper part of the chamber by oxidizing most of the CO. Some of the circulating solids are led through the external fluidized-bed cooler, which enhances the flexibility of control and permits load variation over a wide range. More recent developments aim at even larger capacities with a further enlargement of the combustion chamber and making use of supercritical steam conditions and once-through boiler design. One problem associated with the size enlargement is the distribution of both the coal and the secondary air from the sidewalls over the cross section of the combustion chamber. Since the lateral mixing of gas and solids in a circulating fluidized bed is quite slow, sufficient numbers of feed ports for the coal and air injection nozzles have to be arranged on the sidewalls. The ‘‘pantsleg’’ design shown in Figure 38 is one possibility to provide sufficient lateral mixing at the bottom of the combustion chamber. A first 450 MWe unit is being built in Lagisza/Poland [181] and 600 MWe CFB combustors are in the design phase [182]. If a fluidized-bed furnace running under a pressure of 12–16 bar is linked to a gas turbine, the efficiency of the power plant can be markedly enhanced [183]. At the same time, however, this concept imposes severe requirements on gas cleaning [184]. Pressurized fluidized-bed combustion has been tested in several large experimental plants (e.g., [186]). In the meantime

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Figure 37. Power plant with circulating fluidized-bed furnace (Lurgi process) [180] a) Circulating fluidized-bed reactor; b) Recycling cyclone; c) Siphon; d) Fluidized-bed heat exchanger; e) Convective ; f) Dust filter; g) Turbine; h) Stack

several plants of the 80 MW range are in commercial operation. Recently, a pressurized fluidized-bed combustor with an electrical power of 360 MW was erected by ABB Carbon [185] (Fig. 39); these units employ bubbling fluidized beds [187, 188]. Pressurized fluidized-bed boi-

lers employing circulating fluidized beds are still under development (e.g., [189]). For further details on fluidized-bed combustion systems see the proceedings of the Fluidized Bed Combustion Conferences [25] and a monograph [190].

Figure 38. Furnace cross section of a large CFB combustor (after [179])

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Figure 39. Power plant with pressurized fluidized-bed combustor (ABB design) [187] a) Pressurized fluidized-bed boiler; b) Cyclone; c) Gas turbine; d) Economizer; e) Ash removal; f) Fuel feed; g) Feed-water tank; h) Steam turbine; i) Condenser; j) Bed material hopper

Waste Incineration. The incineration of municipal sewage sludge in fluidized-bed furnaces is now practiced in many facilities [191]. The total amount of sludge thermally treated in in 1996 was 513 000 t (dry basis) [192]. Figure 40 is a diagram of an incinerator. Moist, centrifuged sludge is fed from above to the fluidized bed by means of piston pumps. The fluidizing air is preheated in an oil-fired muffle before reaching the furnace. Fuel oil, used as a supplemental fuel, is metered directly into the bed. Developments in sludge incineration have achieved energy autarky by recovering waste heat and utilizing it to predry the sludge so that self-sustaining combustion is possible [194–196]. Later, the more stringent emission limits set forth in the 17th Bundesimmissionschutzverordnung (BImSchV, regulation in the Federal Republic of concerning the limitation of immissions) may necessitate staged combustion (as in power generation), particularly to control NOx emissions [197, 198]. For the incineration of municipal waste, a furnace with a ‘‘rotating’’ fluidized bed has been developed. The inclined distribution grid in this design generates two rollerlike flows of circulat-

Figure 40. Fluidized-bed furnace for municipal sludge incineration (Uhde system) [193]

ing bed solids, leading to rapid and efficient mixing of the waste in the bed [199]. Coal Gasification. A number of fluidizedbed processes have been developed for gasifying

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Figure 41. Concept for cogeneration power plant based on high-pressure gasification in circulating fluidized bed [185] a) High-pressure CFB gasification; b) Gas cleaning; c) CFB combustion; d) Waste-heat boiler; e) Gas turbine; f) Steam turbine

coal (! Gas Production; e.g., [2]). Interest in these processes for cogeneration power plants has recently become more intense. In the cogeneration system shown in Figure 41, high-pressure gasification is combined with combustion in a circulating fluidized bed; efficiencies of more than 40 % are expected, depending on the available gas turbine technology [180]. The Rheinische Braunkohlenwerke company has developed a high-temperature Winkler (HTW) process based on Winkler gasification (Fig. 42) [200]. The pressure (ca. 10 bar) and temperature (ca. 1100 C) are higher than in the Winkler process; coal is gasified with oxygen and steam. Recycling of solids from the cyclone to the fluidized bed results in a much higher carbon conversion than in the Winkler process. Gasification of Solid Waste. In comparison with incineration, the gasification of solid waste offers the advantage of a smaller volume of offgas, so the cleaning system can be made smaller. In the Japanese Pyrox process, heat required by the gasification reactor is supplied by sand heated in a fluidized-bed furnace, so that a high-Btu-gas can be generated [2]. A cement kiln plant at Ruedersdorf in is operated with a biomass gasification reactor. This circulating fluidized-bed reactor designed by Lurgi supplies fuel gas for the calciners [201].

Calcination. The calcination of aluminum hydroxide in the Vereinigte Aluminiumwerke (VAW)/Lurgi circulating fluidized-bed process features an overall thermal efficiency of more than 70 %, which is achieved through downstream heat recovery from the calcined alumina and the off-gas [18, 202–204]. The circulating fluidized bed proper (c) is coupled to two venturi fluidized beds (a), in which the moist hydroxide is first dried and heated by direct with the off-gas before it is forwarded to the calcination furnace (see Fig. 43). The five-stage fluidizedbed cooler (d) downstream of the furnace serves to preheat the combustion air. A furnace 3.8 m in diameter and 20 m tall, with a fluidization velocity of 3 m/s and mean particle diameter of 0.04– 0.05 mm, produces more than 500 t/d of Al2O3 [18]. Other applications include the calcination of limestone (in multistage fluidized-bed furnaces), lime muds, and crude phosphates [2, 18]. Roasting Processes. Fluidized-bed roasting follows the general reaction equation Metal sulfideþAtmospheric oxygen !Metal oxideþSulfur dioxide

This is one of the earliest industrial uses of fluidization. Many such processes are used in the roasting of pyrite, zinc blende, and other sulfide

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Figure 42. Flow sheet of HTW demonstration plant [200] a) Coal lock hopper system; b) Gasifier; c) Cyclone; d) Ash lock hopper system; e) Raw gas cooler; f) Wet dust separator; g) Carbon monoxide conversion

ores. Bubbling fluidized beds with gas velocities between 0.5 and 2.3 m/s [2] are employed; heat generated by the exothermic roasting reaction is removed by tube banks immersed in the bed, via a solid heat-transfer agent, or by simple water injection. Roasting furnaces are available in very large sizes (bed diameters up to 11 m) with capacities of several hundred tonnes of ore per day [2, 18].

Other Processes. Fluidized-bed processes for the production of high-purity silicon and activated carbon and the chlorination and fluorination of metal oxides are described in [2]. A detailed description of TiO2 synthesis in a fluidized-bed reactor and a survey of the use of fluidized-bed processes in the production of nuclear fuels are given in [10].

Iron Ore Direct Reduction. (! Iron). For the direct reduction of iron ore, Lurgi has developed two processes [205]. Hydrogen is applied as reductant in the Circored process, coal gas is used in the Circofer process. A plant for the Circored process has been built in Trinidad with a capacity of 500 000 t iron briquette per year [206]. Applying two stages, a circulating fluidized-bed reactor reduces the preheated iron ore (800 C) at 630–650 C to a degree of metallization of 65– 85 % and a bubbling fluidized-bed reactor proceeds at temperatures up to 680 C to achieve a degree of metallization of 93–95 % (see Fig. 44). The metallized product is then transported to the hot briquetting unit. At a pressure of 4 bar, the process gas is recycled to a gas cleaning unit and made up with hydrogen.

8.5. Applications in Biotechnology A comprehensive survey of the use of fluidizedbed reactors in biotechnology is given in [10, 207]. Liquid–Solid and Liquid–Gas–Solid Systems. are used in aerobic and anaerobic wastewater treatment (nitrification and denitrification); the microorganisms are grown as a biofilm on particulate s to prevent their entrainment from the reactor with the fluidizing medium. The advantages of the fluidized-bed reactor over the fixed-bed reactor include higher capacity per unit volume and less susceptibility to plugging [208]. A study showing the potential of liquid–solid circulating fluidized beds in

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Figure 43. Fluidized-bed calcination of aluminum hydroxide (VAW/Lurgi system) [18] a) Venturi fluidized bed; b) Cyclones; c) Fluidized-bed furnace; d) Fluidized-bed cooler; e) Recycle cylone; f) Electrostatic precipitator

biotechnological processes such as fermentation has been published recently [209]. Full-scale fluidized-bed biogas production reactors have come on stream since 1984 [210, 211]. The process consists of two stages, acidification and methanation. Sand particles 0.1–0.3 mm in diameter serve as for the microorganisms; at fluidization velocities of 8– 20 m/h, the biofilm grows to a thickness of 0.06– 0.2 mm on these particles. The reactors are large devices with diameters of 4.6 m and bed heights of 21 m. Gas–Solid Systems. Gas–solid fluidizedbed fermenters have been investigated on a pilot scale for the growth of Saccharomyces cerevisiae [212], the production of ethanol with S. cerevisiae [213, 214], and the enrichment of glutathione in yeast by S. cerevisiae [214, 215]. In these

applications, the substrate is metered into the bed in liquid form. A process used in Japan for the culture of Aspergillus sojae on wheat groats employs a solid substrate [216, 217]. The latter process is in service on a plant scale (bed mass 500 kg, bed diameter 1.5 m). The reactor (Fig. 45) contains an agitator (c) just above the distributor (d), as well as a rotating separator (a) in the top of the vessel. Water is sprayed onto the bed from above to maintain the proper moisture level; electrodes (b) dipping into the bed measure this parameter. The moisture content of the solids is generally a critical parameter for the fluidizedbed fermenter; the bioreactions extinguish if it becomes too low, whereas the particles agglomerate and fluidization is disrupted if it becomes too high. Sterilized air is used for fluidization. Seed spores of the microorganisms are fed into the bed via the ejector (e). This system achieves a

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Figure 44. Flow sheet of Lurgi Circored process [206] a) Preheater; b) Cyclone; c) First stage reactor; d) Second stage reactor; e) Briquetting unit; f) Gas cleaning unit

considerable gain in cell yield and an enrichment of certain enzymes by a factor of 5–15 over conventional fixed-bed cultures. The generated biomass forms the basis for soy sauce production.

9. Modeling of Fluidized-Bed Reactors 9.1. Modeling of Liquid–Solid Fluidized-Bed Reactors An expansion formula of the Richardson–Zaki type, Equation (7), describes the hydrodynamics of liquid–solid fluidized beds fairly well [218]. The difficulty in modeling this kind of reactor for bioreactions thus lies not so much in determining the flow and mixing conditions in the fluid as in describing the diffusion processes in the biofilm and the kinetics of the biological reactions [219]. In view of the small number of experimental studies reported thus far, no final judgment can be made on the suitability of various models [208].

9.2. Modeling of Gas–Solid Fluidized-Bed Reactors Figure 45. Solid-state fermentation of Aspergillus sojae in the fluidized bed (adapted from [216]) a) Separator; b) Electrode; c) Agitator; d) Distributor; e) Ejector

Exhaustive literature surveys can be found in [2, 9, 10, 220]. [221]. Many models exist in the literature, which are classified in the cited

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references under various schemes. The available information can be summed up as follows: No generally accepted model of the fluidizedbed reactor exists; instead, many models have been proposed on the basis of more-or-less extensive experimental findings for various applications. Any fluidized-bed reactor model can be broken down into separate components that describe, with varying degrees of accuracy, the hydrodynamics (depending on solid properties, operating conditions, and geometry), gas–solid , and reaction kinetics. The essential point is that the reactor geometry effect, which is important for scale-up (Chap. 10), manifests itself in the flow conditions and must therefore be included in the hydrodynamic part of the model. Before a reactor model found in the literature can be applied to a given problem, the designer must determine whether numerical values are available for all model parameters, that is, whether the model is appropriate for design calculations or is a ‘‘learning model’’ [222] in which the numerical values of important parameters can be determined only after the model is adapted to actual test results. Reaction kinetics may be determined in a fixed-bed reactor, provided measurements are performed under conditions comparable to those that prevail in the fluidized-bed reactor (e.g., the same solids composition and particle-size distribution, the same activity state in the case of catalysts) [223]. However, the kinetic parameters can also be determined directly by measurements in a bench-scale fluidized-bed apparatus [224]. 9.2.1. Bubbling Fluidized-Bed Reactors By far the majority of fluidized-bed reactor models described in the literature deal with reactions in bubbling fluidized beds [2, 9, 10, 225, 226]. For a specific application, modeling depends on the bubble flow regime. For slow-bubble systems (Fig. 7, left), the short-circuit flow of gas through the bubbles must be taken into [227]. For fast-bubble systems (Fig. 7, right), the species have to be balanced separately in the bubble and suspension phases. If models from the literature are employed, it should be taken into that those devised in the past, when adequate computing hardware was


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not available, often sought to obtain analytical expressions for the degree of conversion of a single reaction (usually taken as first-order). The simplifying assumption of a single ‘‘effective’’ bubble size for the entire fluidized bed was therefore made [2], or the mass-transfer area between the bubble and suspension phases was taken as uniformly distributed over the height of the bed (HTU or NTU concept, where HTU denotes height of transfer unit and NTU denotes number of transfer units [228]. Today, in view of the computing power available at the PC level, the recommended procedure is to start from local mass-transfer relations, write balance equations for the differential volume element of the reactor, and then numerically integrate these equations. Figure 46 presents a model used by WERTHER for a constant-volume reaction [224, 229]. Here the simplifying assumption is that flow through the suspension phase is at the minimum fluidization velocity umf. For a heterogeneous catalytic gas-phase reaction, the material balances for species i in the unsteady-state cases are as follows: Bubble phase eb

dCbi dCbi ¼ ½uumf ð1eb Þ dt dh

ð45Þ

kG;i aðCbi Cdi Þ

Suspension phase ð1eb Þ½emf þð1emf Þei

dCdi dCdi ¼ umf ð1eb Þ dt dh þkG;i aðCbi Cdi Þ þð1eb Þ ð1emf Þrs

M X ni;j rj j¼1

ð46Þ

In Equations (45) and (46) the following simplifying assumptions have been made: 1. Plug flow through the suspension phase at an interstitial velocity (umf/emf) 2. Bubble phase in plug flow, bubbles are solids free 3. Reaction in suspension phase only 4. Constant-volume reaction (see [224] for handling a change in number of moles) 5. Sorption effects neglected (see [229] for handling sorption)

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Figure 46. Two-phase model of the fluidized-bed reactor

Here ei is the porosity of the catalyst particles; a is the local mass-transfer area per unit of fluidized-bed volume, which can be calculated as a¼

6eb dv

ð47Þ

for spherical bubbles; rj is the rate of partial reaction j per unit mass of catalyst; and nij is the stoichiometric number of species i in reaction j. The relation kG;i ¼

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi umf 4Di emf ub þ 3 pdv

of the few exceptions; here the model must take of the propagation of coal from the feed point if the furnace emission behavior is to be described correctly [232, 234].

ð48Þ

proposed by SIT and GRACE [230] has proved useful for describing the mass-transfer coefficient kGi associated with component i in mass transfer between the bubble and suspension phases; Di is the molecular diffusion coefficient of species i. The freeboard space above the bubbling fluidized bed must be considered in the reactor model if the entrainment rate is high and the reactions in the freeboard are not quenched, for example, by cooling. Most fluidized-bed models include concentration profiles only for the vertical direction. This one-dimensional modeling is acceptable when the reactants are itted uniformly over the bed cross section. If, however, reactants are metered into the bed at individual feed points, threedimensional modeling may become necessary. Such models have been devised for the combustion of coal in bubbling fluidized beds [232–234]. As a rule, the modeling of solids behavior in bubbling fluidized-bed reactors is based on that in stirred tanks. Fluidized-bed combustion is one

Temperature Homogeneity is a virtually fundamental property of the fluidized-bed reactor. Even so, one exception is industrially important: in high-pressure fluidized-bed furnaces, the high energy density can cause local hot spots near the fuel injection points [235]. Reactor models that take care of this have been described, e.g., in [236]. 9.2.2. Circulating Fluidized-Bed Reactors In the early days of circulating fluidized-bed reactor modeling, negligible axial dispersion and laterally uniform flow structure were believed to characterize these systems. Thus, simple plugflow models were used [237]. This approach was found to oversimplify the behavior of circulating fluidized-bed reactors, because a significant amount of axial dispersion was observed. As a result, the plug-flow model has often been modified by adding a dispersion term to the balance equations. Axial dispersion coefficients have been determined by many authors who measured the residence time distribution of tracer gases [238, 239]. Typical values of Peclet numbers they found are on the order of 10. By means of a model reaction it has been proved that in many cases circulating fluidizedbed reactors cannot be characterized by solely considering mixing phenomena [240]. Instead,

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the presence of mass-transfer limitations and bying was found to have a significant influence. In analogy to low-velocity fluidized beds a detailed description of the local flow structure within the reaction volume must serve as a basis for appropriate reactor modeling. The highly nonuniform flow structure of circulating fluidized beds described in Section 2.9.2 has led to reactor models which separately deal with different axial zones. The bottom zone–if it exists under the given operating conditions–can be described by models whose basic approaches were originally developed for modeling of bubbling fluidized beds [241]. Modeling of the upper section of the circulating fluidized bed is in most cases based on a proper description of the heterogeneous core–annulus flow structure [242–244]. These state-of-the-art models are one-dimensional and define two phases or zones which are present at every axial location: 1. A dense phase or annulus zone: high solids concentration, gas stagnant or moving downwards 2. A dilute phase or core zone: low solids concentration, gas flowing quickly upward. Similar to the situation in bubbling fluidized beds, the two phases exchange gas with each other and are modeled by separate equations which are obtained from mass balances for each component in each phase. Today’s models still suffer from the problem that not all fluid-mechanical variables can be predicted on the basis of the operating conditions. Instead, reasonable estimations or measurements in cold-flow models are used to obtain numerical values for many variables. A common feature of all models for the upper part of circulating fluidized beds is the description of the mass exchange between dense phase and dilute phase. In analogy to low-velocity fluidized beds the product of the local specific mass transfer area a and the mass-transfer coefficient k may be used for this purpose. Many different methods for determination of values for these important variables have been reported, such as tracer-gas backmixing experiments [241], non-steady-state tracer-gas experiments [245], model reactions [244] and theoretical calculations [243].


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Similar to the bubbling fluidized-bed reactor, the solids behavior of the circulating fluidizedbed reactor can usually be described as completely mixed. This does not hold for riser reactors with very high gas velocities, such as those used in FCC risers (u > 10 ms1). Here, better modeling results will be obtained by assuming dispersed plug flow of solids [239]. Like for bubbling fluidized beds, it can be assumed that circulating fluidized beds exhibit a high degree of temperature homogeneity even in the case of highly exothermic reactions. However, in the case of very large circulating fluidized beds for coal combustion, significant horizontal and vertical temperature profiles have been observed inside the combustion chambers [246]. Despite the many uncertainties, circulating fluidized bed reactors have been modeled successfully. For example, three-dimensional gas and solids concentration profiles were calculated in circulating fluidized-bed boilers with local injection of reactants [247] and coal feeding via discrete feeding points [248].

9.3. New Developments in Modeling Fluidized-Bed Reactors 9.3.1. Computational Fluid Dynamics The models described above follow the ‘‘classical’’ chemical engineering approach which replaces the complex particle–fluid interaction in the fluidized bed by idealized configurations (plug flow, stirred tank, either valid overall or in regions) with mixing and mass-transfer coefficients describing the transport of matter. However, more recently, there has been a strong tendency to model the fluid mechanics of fluidized-bed reactors from first principles. The problem of computational fluid dynamics (CFD) modeling in this area is that the particle–particle and particle–fluid interaction must be considered on the particle scale, while the reactor performance must be described on a much larger scale, typically on the order of several meters. This leads to computational difficulties and problems with available computing capacities. At present (ca. 2006) there is no generally accepted CFD model of the fluidized-bed reactor available, but rapid progress can be seen in this area [249–253].

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A promising approach appears to be multiscale modeling strategy [254]. The idea essentially is that fundamental models which take into the relevant details of fluid–particle (lattice Boltzmann model) and particle–particle (discrete-particle model) interactions are used to develop closure laws to feed continuum models which can then be used to simulate the flow structures on a larger scale. Figure 47 illustrates this approach, which finally leads to the discrete-bubble model and should be applicable to the large industrial scale of the bubbling fluidized-bed reactor. The multiscale methodology [255] still requires development work but provides a good chance to arrive at more realistic fluidized-bed reactor models in the not too far future. 9.3.2. Modeling of Fluidized-Bed Systems Another line of development is the modeling of fluidized-bed reactor systems. Whereas previously the isolated fluidized bed was modeled,

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the focus now is on the coupling between the fluidized bed and the cyclone for catalyst recovery and recycle [256] or even on the coupling between two fluidized-bed reactors [257], e.g., reactor–regenerator systems as are used in the FCC and maleic anhydride processes. As an example, Figure 48 shows a fluidizedbed coupled with a cyclone and its translation into the model system. Attrition leads to a loss of material from the system, which requires the addition of fresh catalyst after some time (Fig. 49). A population balance model which considers the changes in the catalyst particle size intervals allows the change in the catalyst inventory with time to be followed. We see that it takes several weeks for the system to reach a quasisteady state. As a consequence of attrition and incomplete separation in the cyclone, the mean particle diameter in the bed increases with time, and this leads to larger bubbles and a reduced area of mass transfer between bubbles and the surrounding suspension in the bed. As a further consequence the conversion rate of a simple first-order reaction falls off with time. Finally, Figure 50

color fig

Figure 47. The multiscale approach for CFD modeling of fluidized-bed reactors [254].

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Figure 48. Fluidized-bed reactor model system [256]

Figure 49. Reactor behavior as a function of operating time [256]

shows that improvements in the efficiency of the solids-recovery system are able to increase the conversion rate again, which is in agreement with large-scale industrial experience [258, 259].

10. Scale-up Typical diameters of bench-scale fluidizedbed reactors are roughly 30–60 mm, and of

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Internals. Whereas the laboratory fluidized bed is generally operated with no internals, plant equipment often must contain bundles of heatexchanger tubes. Screens, baffles, or similar internals are frequently used to redisperse the bubble gas in industrial reactors. The mass-transfer area is thus increased relative to the fluidized bed without internals; the extra area can be utilized to partially offset the conversion-reducing effects of bed diameter and gas distributor [263]. Figure 50. Influence of the Sauter diameter on the chemical conversion of a simple first-order reaction [256].

pilot-scale units 450–600 mm, which should allow a reliable scale-up [9]. Full-scale fluidized-bed reactors used in the chemical industry have diameters up to ca. 10 m. Circulating fluidized bed combustors are even bigger with bed cross-sectional areas reaching 200 m2 [261]. As equipment size increases, characteristic changes take place in the gas–solid flow that can decisively affect reactor performance. Such changes result either directly from the geometry or indirectly from design changes made as the unit is enlarged. In particular, experience has shown that the following factors affect the performance of bubbling fluidized beds during scale-up [262]: Bed Diameter. According to Equation (22), the mean upward bubble velocity increases as the bed diameter dt increases. As a result, the bubbles have a shorter residence time in the bed; hence the exchange area between the bubble and suspension phases is smaller, so conversion is reduced [263]. In case of circulating fluidizedbed combustors, measurements have shown that the downwards velocity of solids in the wall zone increases drastically with increasing size of the combustor [260]. Grid Design. In the laboratory, porous plates are the preferred type of gas distributor because of the ease of working with them. Gas distribution becomes worse when these are replaced by industrial distributor designs; thus the exchange area between the bubble and suspension phases is reduced, again with consequently lower conversion [43].

Catalyst Particle-Size Distribution. Bubble growth is influenced by the proportion of fines in the particle-size distribution of the bed (usually measured as the weight fraction < 0.044 mm) or by the mean grain size dp (via umf, Eq. 18). If the content of fines increases, bubbles collapse sooner and the equilibrium bubble size becomes smaller, with a resultant greater bubble–suspension mass-transfer area. This effect generally is fully developed only in the plantscale reactor, where bubbles can grow without the hindrance of vessel walls. Thus, in principle, the performance of catalytic fluidized-bed reactors can be controlled by modifying the catalyst particle-size distribution [112, 264]. The recommended content by weight of fines (< 0.044 mm) for ‘‘good fluidization’’ is 30–40 % [265], but maintaining this high a fines content in the system over a long span of time requires a very efficient solids recovery system. Lateral Mixing of Reactants. On a laboratory scale, reactants experience compulsory uniform distribution over the bed cross section. In plant equipment, on the other hand, reactants often arrive in the reactor via individual feed points. The resulting uneven distribution of reactants can have a marked effect on reactor performance, which has been shown for the effect of coal feeding on the emission properties of fluidized-bed furnaces [248]. Secondary Reactions in the Freeboard. In a bench-scale apparatus, the fluidized gas is rapidly cooled by the vessel wall in the freeboard space after leaving the bed, so secondary reactions in the freeboard are often negligible. Such is not the case in the plant-scale reactor. The action of wall cooling is not significant here, and the entrainment rate is high because of the higher

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fluidization velocities common in full-scale equipment. Both effects – lack of cooling and high solids concentration in the freeboard – may lead to marked secondary reactions in the freeboard of industrial fluidized-bed reactors. In the case of a system of consecutive reactions where the desired product is formed as an intermediate, the freeboard reactions will generally lower the selectivity. The effect of freeboard reactions has been demonstrated for the example of NO and CO emissions from a fluidized-bed furnace [232]. Catalyst Attrition. Catalyst attrition is minimal in laboratory apparatus, because of the use of porous plates as gas distributors, as well as the low gas velocities and bed depths. Attrition is necessarily greater in industrial reactors. To reduce this risk in scale-up, the attrition tests described in Section 2.11 should be carried out and the results converted to the full-scale conditions with the aid of Equations (34), (35) and (36). Other Factors. In addition to the factors just listed, many other effects become apparent when a fluidized-bed reactor is scaled up that are difficult to calculate. Examples are the risk of nonuniform gas distribution over very large cross sections in shallow fluidized beds; the formation of deposits in the bed; the fouling of heatexchange surfaces; and catalyst aging and poisoning. On the whole, accordingly, the scale-up of fluidized-bed reactors is a complex process, commonly requiring a large amount of pilotscale experimentation. Current knowledge about the fluid mechanics in the fluidized bed, however, enables simulation calculations of many of the scale-up effects, so the amount of testing during process development may be decreased and the risk can be at least limited.

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