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Review article

Scale-up of fluidized-bed combustion A review

Bo Leckner a, Pal Szentannai b, Franz Winter c,

a Department of Energy and Environment, Chalmers University of Technology, Gteborg, Swedenb Department of Energy Engineering, Budapest University of Technology and Economics, Budapest, Hungaryc Institute of Chemical Engineering, Vienna University of Technology, Vienna, Austria

a r t i c l e i n f o

Article history:Received 7 October 2010Received in revised form 17 March 2011Accepted 28 April 2011Available online 13 May 2011

Keywords:

FBCFluidized-bed combustorFluid dynamic scalingCombustion scalingBoiler design

a b s t r a c t

Methods for scaling of fluidized-bed combustors are reviewed. It is found that a general scaling method-ology, including simultaneously fluid-dynamic and combustion scaling, cannot be applied in practicalscaling tests. Simplifications are needed. The approach followed here is to differentiate between fluid-dynamic scaling, combustion scaling, both related to the basic equations describing the phenomena,and boiler scaling that means scale-up from one boiler size to another, where established design ele-ments can be utilized in the scaling procedure.

2011 Elsevier Ltd. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29512. Fluid-dynamic scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29533. Combustion scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2954

3.1. General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29543.2. The horizontal scaling problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29563.3. The vertical scaling problem riser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29573.4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29583.5. Application of the vertical scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29583.6. The impact of the cyclone. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29593.7. The vertical scaling problembubbling bed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29603.8. Concluding remark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2960

4. Boiler design scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29615. Conclusions and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2963

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2964

1. Introduction

Scaling methods have been used with success in engineeringapplications to transfer information from equipment of one sizeto another similar equipment having a different size. Mathematical

modelling is the most basic approach to scale-up, but often also themost complex one. Even though mathematical expressions can beformulated to be generally valid, it may be difficult to solve themeven with present computational means. A step towards simplifi-cation is to convert the mathematical expressions describing theprocess into a dimensionless form, thereby deriving dimensionlessnumbers, which contain the decisive parameters to be scaled. Thedimensionless numbers are equally valid for both small and large

0016-2361/$ - see front matter 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.fuel.2011.04.038

Corresponding author.

E-mail address: [email protected](F. Winter).

Fuel 90 (2011) 29512964

Contents lists available at ScienceDirect

Fuel

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / f u e l
http://dx.doi.org/10.1016/j.fuel.2011.04.038mailto:[email protected]://dx.doi.org/10.1016/j.fuel.2011.04.038http://www.sciencedirect.com/science/journal/00162361http://www.elsevier.com/locate/fuelhttp://www.elsevier.com/locate/fuelhttp://www.sciencedirect.com/science/journal/00162361http://dx.doi.org/10.1016/j.fuel.2011.04.038mailto:[email protected]://dx.doi.org/10.1016/j.fuel.2011.04.038

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geometrically similar applications within the domain of validity ofthe mathematical expressions themselves. These dimensionlessnumbers or groups of parameters form the basis for scaling fromone size to another. The simple cases of developed flow throughtubes characterized by Reynolds number, or heat transfer charac-terized by Nusselts number, being a function of the Reynolds andPrandtl numbers, are well known examples of successful scaling.

These ideas were applied to boilers [1], but the procedure ofscaling requires a description of both fluid-dynamics, chemicalreactions and heat transfer in a complex geometry, and the ef-fort referred to resulted in such a great set of dimensionlessnumbers that it did not prove useful for scaling. It appears thatscaling by means of dimensionless criteria could not be carriedout in a rigorous way in complex cases, and simplifying compro-mises are necessary to make this method technically useful. If a

rigorous solution is sought, mathematical modelling is a morepromising route, although complexity and long computationtimes are obvious obstacles also for this route, particularly inthe two-phase medium of a fluidized bed where combustionand heat transfer take place. However, scaling by means ofdimensionless criteria may be feasible if the rigorous treatmentis somewhat relaxed, and the scaling task is carried out withsome compromises. A first procedure to be tried could be to dif-ferentiate between fluid-dynamic scaling, combustion scaling,and boiler-design scaling; a division of approaches that will befollowed below where a survey of scaling will be presented: areview which does not have the purpose of including all previ-ous work, but rather to relate the various scaling methods inan overview aiming at illustrating fluidized-bed combustionscaling.

Nomenclature

Aexternal external particle surface area (m2)

ab specific bubble surface area (m2)

A cross section surface area (m2)

Ar Archimedes number Arqfqpqfd

3pg

l2 ()a1, a2 coefficientsc concentration (mole/m3), particle concentration qp

(1 e) (kg/m3)C dimensionless concentration, c/c0 ()CFB circulating fluidized bedD diffusion or dispersion coefficient (m2/s), riser diameter,

cyclone diameter (m)Dx diameter of vortex finder (m)Da Damkhler number, Da Rxuc or

Rx2

Dc ()d particle dimension (m)dp,50 cut size (m)f() functionFr Froude number, Fr u

2

gL ()

G solids flux (kg/(m2 s))g acceleration due to gravity (m/s2)

Hu lower heating value (MJ/kg)L height of riser, length (m)k transfer coefficient, reaction rate coefficient (m/s)K effective reaction coefficient ()M molecular mass (kg/k mol)NTU number of transfer units ()n circulation number ()N number ()m mass fraction() or mass (kg), coefficient related to g ()P pressure (Pa)PC Pulverized coalPe Pclet number Pe = ReSc= Lu/D ()PSD particle size distributionq surface power (MW/m2), defined in Eq. (42)Q power (W)

R chemical reaction rate (1/s) or (kg/(m2

s))Re Reynolds number, Re = quL/l (-)Sc Schmidt number, Sc= l/(qD) ()Sh Sherwood number, Sh = kdiff dp/D ()

Stk Stokes mumber, Stk d

2p;50uinDq18lDcykl

()

t time (s)x,x distance (bold is vector) (m)yv gas yield (kg gas/kg combustible)u, u superficial velocity (bold is vector) (m/s)U, U dimensionless velocity (bold is vector) ()vr,CS radial gas velocity in cyclone (m/s)vhCS tangential gas velocity in cyclone (m/s)

Z dimensionless vertical coordinate ()z vertical coordinate (m)

Greek lettersb dimensionless velocity ()D differencee voidage ()g cyclone efficiency ()u sphericity ()l viscosity (kg/m s)q density (kg/m3)rc volume concentration of char in the solids phase (m

3/m3)

s time, time constant (s)

Index0 Standard conditionsavg averageb bubblebe bubbleemulsionc carbonchar charcycl cyclonedev devolatilizationdiff diffusivee external, emulsion, equivalentf fluid, gasgg gasgasgs gassolidh horizontali species, numberin entrancekin kineticmf minimum fluidizationN number of particle size fractionsox oxygenp particler risers solidt terminal, transportu lowerv vertical, actualz coordinateI, II plant I and IIp,50 cut size1 far from a surface

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2. Fluid-dynamic scaling

In the two-fluid model of two-phase flow, the flow is treated asinterpenetrating gaseous and particle media connected bycoupling terms that express the interaction between the phases.These equations together with constitutive relationships andboundary conditions have been used to derive similarity criteria

in the form of dimensionless numbers for fluidized beds. The com-prehensive work of Glicksman and coworkers together with analo-gous work by other researchers in this area is summarized in areview by Glicksman et al. [2], where the dimensionless numbersare derived and presented. The set of dimensionless parametersobtained from the equations, is called the full set, and is written as

u20gL

;qpqf

;qpu0d

2p

lL;qfu0L

l;

G

qpu0;geometry;u; PSD 1

This set of criteria can be expressed in various ways by manip-ulating the parameters, for instance, in the form of Reynoldsnumbers

u20

gL

;qp

qf;qpu0dp

l

;qfu0L

l

;G


or with Archimedes number (qp % qp qf)

u20gL

;qpqf

;qfqpd

3pg

l2;qfu0L

l;

G


but the same set of parameters is involved in all cases:

Superficial gas velocity u0. Surface mean particle diameter dp. Riser dimension L, often the risers hydraulic diameter D is used. Particle density qp. Gas density qf. Gas viscosity l.

External solids circulation flux G.

In addition, g acceleration due to gravity is included, but thisquantity is constant in the present application.

The dimensionless parameters should be similar in a model bedand in a target application. Moreover, the geometries of the modelbed and the target application should be similar, as well as thesphericities u of the bed particles and the particle-size distribu-tions (PSD) of the bed materials.

The full set of scaling parameters Eqs. (1)(3) results in a uniqueset of values of particle diameter and density as well as of thedimensions of the bed. It may be difficult to satisfy all criteria ina scale model. Therefore Glicksman et al. [2] suggested a simplifiedset of scaling parameters, valid in the low as well as in the highparticle Reynolds number ranges and with some approximationalso in the region between these cases

u20gL

;qpqf

;u0umf

;G


and even more simplified in the viscous limit

u20gL

;u0umf

;G


In the simplified expressions, an analysis of the correlation forthe drag force allows removing the dependence on dp/L, and theArchimedes number is substituted by u0/umf. Furthermore, in theviscous set of dimensionless numbers, gas-phase inertia is as-sumed to be negligible compared to viscous forces, and qf/qp is

omitted. As can be seen, these sets of dimensionless criteria consistof five, four or three parameter groups to be set equal in a scale

model and in the target plant. Moreover, the geometries of theplants should be similar, and in all three cases some conditions(u, PSD) are imposed on the particles used.

Among several alternative proposals of fluid-dynamic scaling-laws, that of Horio and coworkers [3] should be mentioned.According to Glicksman, this scaling technique, although derivedin an entirely different manner, is equivalent to the simplified setof parameters.

There are several examples of scaling in Ref. [2], but here a fewindependent experiences will be shown from scaling of a 12 MWthboiler using a cold, 1/9th down-scaled plastic model fluidized withair, where visual observations and measurements could be madeconveniently. In one of these works [4], the purpose was to inves-tigate the performance of several furnace exit configurations. Theother work [5] was a study of the dispersion of gas in the two-phase suspension of a fluidized-bed riser. Fig. 1 presents a viewof the boiler and the down-scaled model. The boiler was operatedwith low-ash wood chips using only primary air in order to sim-plify the scaling situation as much as possible. As usual, theamount of fuel in a fluidized-bed combustor is low and does notinfluence the fluid-dynamic behavior of the bed, and, conse-quently, the size of the fuel particles is not accounted for.

The scaling followed the simplified scaling law, Eq. (4). Scalingaccording to the full scaling law would have required bed particlesthat were not available. Even with the simplified scaling criteriaperfect particles could not be found, and those attained with ironand steel particles in [4] deviate to some extent from the numberstheoretically derived, as seen in Table 1. Slightly better bronze par-ticles with a size of 0.06 mm and a density of 8800 kg/m3 wereused in [5].

The table illustrates how closely the desired data of the scalinglaw (column Eq. (4) in the table) could be approached. The sizedistributions were made reasonably similar by sieving and by thefact that the boiler was operated with low-ash wood chips of bestquality, thereby maintaining the size distribution and the particledensity of the initial bed (the bed was not affected by ashes). It

is not a simple task to find perfectly suitable particles. In the pres-ent case the selected iron and steel particles deviate slightly fromthe target density and they had some irregularities in their surfacestructure. As seen from Fig. 2: the surfaces were rather rough andthe particles were far from spherical.

Fig. 1. (a) The 12 MW boiler at Chalmers University. (b) The 1/9 th plastic model ofthe boiler operated under ambient conditions [4].

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The iron particles in the scaled bed (the model) representedvery well the solids volume concentration along the height of theboilers furnace and coincided with the concentrations measuredthere. Also the solids flux and the pressure fluctuations in thebed were quite similar in the model and in the boiler. For some stillunknown reason, the net solids flux of the steel particles, as well asthe corresponding density profile in the upper part of the columnof the model were lower than for the sand used in the boiler andfor the iron particles in the model. However, in the lower part ofthe riser the agreement between model and boiler was good, notonly with the iron but also with the concentration of steel particles,

as well as in terms of pressure fluctuations. In the case of disper-sion measurements [5] no problems were reported, and goodagreement between model and furnace was obtained, as illustratedby the example in Fig. 3.

Also in the development of future large-scale circulating fluid-ized-bed (CFB) boilers cold modelling is carried out, where highimportance has been given to hydrodynamic similarities in thedevelopment of cyclone configurations [6] as seen in Fig. 4. Noother information regarding the scaling was given, however. Simi-lar studies have been made by others, e.g. [7].

3. Combustion scaling

3.1. General

In the fluid dynamic case, the problem often consists in trans-ferring information from a cold (room temperature) small-scale

Table 1

Scaling data corresponding to the case in Fig. 1.

Quantity Unit 12 MW CFB According to scaling law

Eq. (4) Iron particles Steel particles

Temperature C 850 20 20 20Superficial velocity m/s u0 u01/3 u01/3 u01/3Particle diameter lm ds dp019 dp 0.18 dp0.15

305 57 56 46Riser dimension m L L/9 L/9 L/9Solid density kg/m3 qp qp3.7 qp3.0 qp3.1

2600 9720 7860 8027Gas density kg/m3 0.31 1.19 1.19 1.19Gas viscosity m2/s 1.45 104 1.72 105 1.72 105 1.72 105

Solids circulation flux kg/m2 s G G1.25 G1.01 G1.03

Fig. 2. Photos of solids in boiler and model. From [4].

Fig. 3. Comparison of gas concentration profiles resulting from tracer gas injectionin the boiler and in the scale model. The fluidization velocity was 3.25 m/s and the

injection height 4.7 m from the bottom in the boiler. The corresponding data in thescale model were 1.1 m/s and 0.52 m. The Pclet number Pe = 400. From [5].

Fig. 4. Scaled-down test facility operated at room temperature to investigate

cyclone performance (particularly the distribution of solids between the treecyclones) for a 600 MWe CFB boiler [6].


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model to a larger fluidized-bed boiler operated under hot condi-tions (800900 C), and in some applications, even at high pres-sure. In contrast, in combustion scaling, combustion usually takesplace both in the small and the large plants. Then, the chemicalreactions related to combustion and their progress in the combus-tor play the most important role. Usually, significant parameterscan be kept the same in the small and the large-scale plants, andthis is already a great step towards scaling. Such parameters are:bed temperature (assumed constant in the entire bed), total ex-cess-air ratio, primary-air stoichiometry, fuel and bed material(including particle size and size distribution). Also the fluidizationvelocity should be kept at about the same level in the devices to becompared.

If the just mentioned operation similarities are fulfilled, thedimensions height L or width D of the vessel and the criterionG/(qpu0) are the only remaining parameters from the fluid dynamicscaling that have to be adjusted. The others are already similar. Thelatter criterion to be determined actually represents the particlevolume concentration cp(L) in the upper part of the riser, as canbe seen from Eq. (6), valid for rather disperse flow, which is nottoo much affected by particleparticle interaction (clusters)

Gqpu0

qp1 eu0 ut

qpu0% 1 e cpL 6

If the average particle density in the riser

cp DP

gqpL7

is used instead of the exit density to represent the particle density(particle concentration) in the riser, an observable quantity is ob-tained, since not only the particle solid density qp, the height ofthe riser L, but also the pressure drop over the riserDP, can be mea-sured. Two geometrically similar plants, plant I and plant II, wouldtend to behave in a similar way if their average particle concentra-tions are the same in both plants, cp;I cp;II. Combination of Eqs. (6)

and (7) leads to the conclusion that the pressure drop over thecombustion chamber DP can substitute G as a scaling parameterfor boiler scaling. This is an advantage, because DP (or bed inven-tory), is an independent parameter, whereas G is dependent andnot independent as it might be in chemical CFB reactor scaling withparticles of Class A. Following Knbig et al. [8], a scaling criterioncould be derived from Eq. (7) as

DPI LIDPII=LII 8

Qi et al. [9] derived Eq. (6) in a different way but their conclu-sion is the same: the relationship is only valid for a non-clusteringsituation (when the particles can be regarded as single, not influ-enced by surrounding particles), and it has to be corrected if re-lated to an average riser concentration. The correction factor was

shown to be the Froude number Fr= u2o/(gL), Fr

0.3

, which, however,is included in the scaling criteria Eqs. (1)(5) and is identical inCases I and II, so the resulting Eq. (8) is valid.

The remaining similarity criterion, expressing that the devicesto be compared are geometrically similar, cannot be fulfilled inall cases. There are three common situations:

(1) Tests are made in a laboratory device with the purpose ofobtaining information on the combustion and related chem-ical reactions in a full-scale boiler. In this case, the widthdimension D of the laboratory device is usually much smal-ler than that of the full scale, while the height dimension, atleast within reasonable limits, can be subjected to somescaling strategy. In general L/D is >30 in the laboratory

equipment, while boilers have L/D < 10, because of the dif-ference in width, D. There are many tests published from

such equipment. In Ref. [8], for instance, an effort was madeto compare the combustion performance of a narrow test rig(0.1 m inner diameter) and a wider boiler (1.6 1.6 m crosssection) observing scaling conditions. Even if it is obviousthat the fluid dynamics were not scaled in the horizontaldirection of the test tube, relevant information could beobtained reasonably well on reactions that take place inthe vertical sense of the equipment, compared with corre-sponding reactions in a boiler, because the residence timeswere of similar magnitude.

(2) In a different approach, information from a small-scale testcan be applied to a larger boiler; this is the chemical similar-ity, which allows results from bench scale reactors to beapplied in large-scale equipment [10].

(3) Experience from a small boiler is to be transferred to a largerboiler. In this case, the width is already quite large and thedifferences are probably not so important, as long as it iswider than the largest scale affecting the fluid dynamics,for instance, the size of the largest bubbles. The bubblesare limited in size by the height of the bottom bed, whichis smaller than the width of the furnace even in a small boi-ler, so this criterion is usually fulfilled. Then, the fluiddynamics may not be perfectly scaled, but the devicesbehave in sufficiently similar way to make other scaling cri-teria more important than those of fluid dynamics. This sim-ple line of thought is contradicted by recent computations ofthe effective dispersion coefficient in the bed, showing thatthe dispersion coefficient continues to rise with bed widthup to a width of about six meters [11]. However, this findingstill requires experimental verification.

For the combustion reactions, the mixing, bringing fuel andreactant together, and the times of reaction are the important pro-cesses. A reacting fuel particle is transported both in the horizontaland in the vertical directions in the furnace, while the oxygen inthe gas, serving as fluidization medium, is flowing essentially in

the vertical direction through the furnace, and at least initially,evenly distributed over the cross section. Hence, processes bothin the horizontal and in the vertical direction are of significancefor combustion scaling.

For combustion scaling, the works of Damkhler [12] in 1936,Zeldovich [13] and Thiele [14] in 1939 are useful. These worksessentially came to the same conclusion, but the latter two authorsfocused on the treatment of single catalyst particles, while Dam-khlers approach was more general and also included chemicalconversion compared with the transport processes in a reactor,both from a thermal and from a chemical point of view, the latterbeing the one of importance here. In addition to the fluid-dynamicequations, a dimensionless equation is formulated for mass trans-port of a species i (here representing gas or solid fuel components

with a dimensionless concentration Ci) that is produced or con-sumed by a chemical reaction, as expressed by a source term.The three-dimensional mass-transport equation can be writtenfor steady state in two equivalent ways

divUCi 1

Peidivgrad Ci Dai;I 9

or

PeidivUCi divgrad Ci Dai;II 10

where Da is the Damkhler number, expressing the ratio of thechemical reaction rate Ri to the rate of transport by convection

c0u0/x0 or by diffusion c0Di=x2

0. Consequently, Dai,I = Dai,v = Rix0/(c0u0) and Dai;II Dai;h Rix20=Dic0), the first and the second


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Damkhler numbers [12], which are later used in the relevant

directions and then called vertical (index v) and horizontal (indexh) Damkhler numbers. Pei = ReSc=x0u0/Di is the Pclet number,the product of the Reynolds and the Schmidt numbers, expressingthe ratio of transport by convection to transport by diffusion. Notethat Dai,v = Dai,h/Pei. U is the dimensionless local averagevelocity vector. In a general way, the Damkhler criterion can beexpressed as

Da transport time=reaction time 11

The Damkhler criterion can be related to burn-out of char orgas rising in the vertical direction through the furnace, and alsoto the processes in the horizontal direction. Only the horizontaland vertical components of the equations are treated here.

Similar relationships are valid for heat transfer, but this is not

important in the present context, as the temperature is given andassumed constant in the entire bed.

The solid fuel is added from one or several feed points at thewall of the furnace and the fuel particles that are not instanta-neously carried away by the gas are spread over the cross-sectional area of the furnace. Fuel and oxygen (air) are likelynot well mixed over the cross section of a large boiler, as illus-trated in Fig. 5, showing how the spread of fuel from a feed pointinto the fluidized bed meets the evenly distributed fluidizationgas. This leads to a potential maldistribution of fuel that becomesmore severe as the size of a combustor increases and the fuelparticles have to be transported longer distances. It is the aim ofa designer to reduce this inconvenience as much as reasonable,for instance, by choosing a suitable number of fuel feed points.

There is also a contribution to the horizontal distribution of fuelfrom the char in the return material separated by the cyclones,and although this smoothes the fuel distribution, it is clear thatthe problem needs more care the larger the boiler is. This is thehorizontal scale-up problem.

The volatiles from the fuel and the gaseous combustion prod-ucts are released from the fuel particles and carried upward bythe fluidization gas. Also small char particles may be captured bythe vertical gas stream and brought upward while they burn. Even-tually, if they do not have time to burn, the particles reach the par-ticle separator (usually one or several cyclones). The coarser fuelparticles of a size that could be carried by the gas stream are sep-arated by the cyclone and returned to the bed, whereas theremaining (finest) fuel particles and unburned gas, in case com-

plete gaseous conversion is not attained, pass the cyclone intothe flue-gas duct and constitute a combustion loss. This is the

vertical scale-up problem, determined by the residence time of fuelcomponents in the riser as well as in the remaining circuit, wherecyclone efficiency and height of the furnace are essentialparameters.

Scaling between Plant I and Plant II requires that the residencetimes L/u of gas and particles in the risers of the two plants beidentical in order to allow the reactions to take place to the sameextent in both cases

uI LIuII=LII 12

This relationship is valid for the gas but also for the particlescarried by the gas, provided that the slip velocity, the differencein velocity between gas and particles, is proportional to the gasvelocity u (this may not be rigorously the case, but the influenceof variations of the slip is small compared to other factors in-volved, and this feature can be treated in a rather approximateway). The residence time is longer for most particles than for thegas because of recycling of particles through the cyclone loop.Therefore, their residence time has to be multiplied by the numberof times a particle circulates, and this depends on the efficiency ofseparation as will be further treated below. In order to fulfill Eq.(12) in scaling between plants of heights LI and LII, the fluidization

velocity has to be adjusted. Then the fluid-dynamic similarity isaffected.

3.2. The horizontal scaling problem

Leckner and Werther [15] applied the Damkhler criterion, Eq.(11), to a fuel particle with the equivalent diameter dp to expressthe significance of two important reactions occurring while thefuel particle is transported in the horizontal direction of the fur-nace: devolatilization and char combustion. The devolatilizationtime, including drying, for a fuel particle is usually written

sdev a1da2p 13

where the first constant a1

is related to the specific fuel and is about106 s=ma2 . The second constant a2 depends on the physical process.Theoretically, a2 approaches unity if the devolatilization is ther-mally limited by the external heat transfer. If the process is con-trolled by the kinetics, it becomes independent of particle sizeand approaches zero. For particles controlled by thermal conduc-tion, a2 approaches two. These numbers are approximate, becauseother factors also play a role. Empirically, for most fuels the con-stant a2 ends up in the region of 1.52 [16].

The burnout time of the relatively coarse char being dispersedin the bottom bed can be described roughly by the Nusseltsquare-law for external diffusion-controlled, shrinking particle,

schar qchard

2p;0

4McShDoxcox;114

where qchar is density of char with an initial size of dp,0, Mc molec-ular mass of carbon, Sh Sherwood number, Dox molecular diffusioncoefficient of oxygen in the vicinity of the particle, and cox is theaverage oxygen concentration (mole/m3) in the bed. Obviously,more refined expressions can easily be derived to estimate charburnout time under the present or other combustion regimes, ifnecessary.

The average dispersion time of the fuel particle can be esti-mated by using Einsteins classical expression [17]

st x2=2Dh 15

wherex is the average dispersion distance and Dh is an average hor-izontal dispersion coefficient in the bed.

With the reaction and dispersion times of Eqs. (13)(15)inserted into Eq. (11), information on the controlling processes

FUEL

FUEL

AIR

X

Fig. 5. The horizontal distribution of fuel at a fuel feed point.x is theaverage spreadof the fuel at a certain time. Air is introduced evenly over the cross section.


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(the slowest ones) can be obtained. This is illustrated graphically inFig. 6, showing the horizontal Damkhler number versus the aver-age dimensionless distance of dispersion in the horizontal direc-tion, x/dp. Somewhat arbitrarily, one can say that the fuel issufficiently evenly distributed over the cross section whenDah < 1, whereas the contrary is true when Dah > 1. In the lattercase, as shown by Eq. (11), the reaction is faster than the mixing.

MorespecificallyFig.6 shows thatdevolatilizationis much fasterthan char combustion; for fuels containing a high amount ofvolatiles the critical Dah is reached already at a distance of 0.1 mof cross-sectional width with mm-sized fuel particles, whereas for

char particles of the same size this takes place only at a width ofabout 1 m. This Da number obviously depends on thesize of thefuelparticle: larger particles are transported longer distances before re-actedand areless critical for mixing than smallones. The conclusionis clear: it is easier to obtain an even distribution of fuel and airacross thecrosssectionof anFBCfurnace with a low-volatile, coarsefuel than with high volatile or fine fuel. Consequently, fuel andoxygen tend to be better mixed in narrow laboratory-scale bedsthan in large beds. This conclusion is valid, although there is anincreasing impact of the walls on the fluid dynamics as the vesselbecomes small. In addition one has to be aware of the tendencyfor very small fuel particles to be carried away with the gas. Theintention is not to make an exact calculation but rather an estima-tion, and therefore certain approximations are acceptable.

An interesting experience was made by Alliston and Wu [18]with respect to horizontal distribution of fuel. They tested lime-stones in a smallpilot-scale CFB, burning bituminous coals as a sup-port for the design of full-scale boilers. Later, when the boilers werebuilt, the results from the test unit could be compared with thosefrom the boilers in cases with the same limestone, coal and opera-tion data. The conclusion from the comparison was that, despitethe similarities in operation conditions and materials used, the testsin the small-scale plant always showed better sulfur capture thanthose in the large boilers. An explanation can be derived from theirpublished oxygen and sulfur dioxide profiles, shown in Fig. 7.

The figure shows how the oxygen is completely consumed inthe vicinity of the fuel feed point of the 5 m wide boiler by thevolatiles released there. In that area also the SO2 concentration is

high because sulfur capture by limestone is inhibited under reduc-ing, oxygen-poor conditions [19]. In the smaller unit, mixing is less

critical; the airfuel mixture was more homogeneous, and thedeleterious effect of reducing zones is then less notable, resultingin better sulfur capture. The effect of mixing can be estimated

roughly from Fig. 6.

3.3. The vertical scaling problem riser

While the gas flows in the vertical direction in the lean sus-pension of the riser, mixing takes place with similar intensity asin a single-phase turbulent flow [5]. Additional mixing is pro-duced by the injection of secondary air. This provides the reac-tion environment for the gas and the particles, which aretransported upwards in the furnace by the vertical gas flow,leaving through the cyclone. If the mixing is sufficient, the gas-eous reactions are always fast enough to be completed beforethe gases leave the cyclone. Char combustion, however, is muchslower and some of the particles may have to be circulated sev-

eral times to be reacted. Then, a certain part (1 g) of the charparticles escapes the system because of the cyclone efficiencyg < 1, and the mass of recirculating char particles m of a given,constant size (independent of combustion) will be reduced eachtime L/up that they pass the cyclone

dm

dtm1 gL=up

yielding m m0 expt=st 16

where

st L=up

1 g17

is the time constant of the transport process, which is a measure ofthe time spent by the particles in the reactive environment, when

the number of passes through the cyclone is n 1=1 g and thevertical particle velocity is up = uo ut, the difference between theaverage superficial velocity in the riser and the terminal velocityof a single particle, neglecting clustering effects.

The cyclone efficiency is usually represented by an empiricalfunction

g 1

1 dp;50=dpm 18

where the coefficient m depends on the type of cyclone. It is be-tween 2 and 6 (here 2 is used) and dp,50 is the cut size, which canbe written as [20]

dp;50 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi9lDxvrCSqpv

2hCS

s 19

Fig. 6. Horizontal Damkhler number vs dimensionless dispersion distance,expressed as the average spread of a particle x [m] related to an average particlesize dp [m].

0

1

2

3

4

0 1 2 3 4 5

DISTANCE FROM FRONT WALL, m

SO2RELEASED/AVERAGE

0

2

4

6

8

O2CONC

ENTRATION,%

Overall O2

Top of primary zone, O2

SO2 Released/Average SO2

Fig. 7. Horizontal SO2 and O2 profiles in a large-scale CFB burning bituminous coal.The fuel is fed from the left-hand side. Adapted from [18].


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where Dx is the diameter of the vortex finder, vrCS and vhCS are theradial and the tangential gas velocities at the edge of the inner vor-tex, at a fictitious surface extending down from the vortex finder.With these data the efficiency can be described as in Fig. 8.

The mass of circulating char particles is reduced because ofreaction. According to the reactivity definition related to the exter-nal surface of the particle

dm

dt AexternalRchar AexternalMcKe;ocox 20

and Ke,o the effective combustion coefficient, including resistancesto reaction by external diffusion, diffusion through an ash layer,and kinetics

Ke;o 1

kdiffdpdp dc

2dcDox;ash

d2p

d2ckkin

!121

where kkin is the kinetic rate, Aexternal pd2

p the external surface of aspherical char particle, (dp dc)/2 the thickness of the ash layer, andkdiff is the external mass-transfer coefficient.

For the simplest case with external diffusion control and shrink-ing particle mode (as an example) we have

Rchar McKe;ocox;1 Mckdiffcox;1 McShDoxcox;1

dp22

Integrated over time, Eqs. (20) and (22) give Eq. (14), the burn-out time t= schar for the present conditions.

With the transport time from Eq. (17) the resulting verticalDamkhler number, Eq. (11), becomes.

Dav st=schar 23

3.4. Discussion

There are two approaches to the determination of the times in-volved in the Da numbers. One is detailed mathematical modelling,when the phenomena involved are described with some accuracy.The other approach is the more primitive one used here, lookingfor characteristic numbers only, which indicate the featuresinvolved. However, the scaling criteria must be relevant andcomparable. In the horizontal scaling case the total combustiontime of a diffusion-limited char particle was used because thedevolatilization was described by the total time. The transport,on the other hand, was described by a characteristic numberrepresenting an average dispersion of solids. The criterion is de-rived from the diffusion equation that was established for Brown-ian motion. The corresponding data available for fluidized beds,although sometimes called diffusion coefficients, are derived from

measurements, in most cases including convection mechanismstogether with diffusion. They should then be called dispersion

coefficients to emphasise the approximate nature of this quantity.In comparison to the estimate of the dispersion, the fuel conversiontimes have a reasonable accuracy, although the detailed mecha-nisms and their dependence on size were not treated here.

For the vertical process, the burnout time was derived for astrictly external surface-controlled reaction, expressed with theinitial particle diameter (Eq. (14)). The derivation can be developedfor any other relevant reaction mechanism, although it may bedifficult to find a closed form.

If combustion follows the shrinking core or the shrinking parti-cle model, the fuel particles change their size or their density,respectively. In both cases the separation efficiency according toEqs. (18), (19) is reduced, so the residence time is shorter com-pared to a fuel particle retaining its initial properties.

3.5. Application of the vertical scaling

In the vertical scaling case Dav should be greater than unity toensure that the particles, statistically seen, have had time to reactduring their flight, and the desired situation here is Dav > 1,whereas for the horizontal Damkhler number Dah < 1 is preferred.The situation for char particles carried through the vertical direc-tion of the riser can be illustrated by a simplified calculation. In thiscalculation we assume the particles to have constant sizes. Otherinput data are: particle and bed temperature 850 C, oxygen con-centration in the entire riser 5%, char density 1600 kg/m3, Sh = 2,and char combustion kinetics taken from Ref. [21].

The result is shown in Fig. 9a and b. Very small particles havesufficient time for reaction during their path through a riser andthe Damkhler number for these particles is larger than unity. Thisis also true for the larger, entrained particles, which are capturedby the cyclone and recirculated. However, for particles in betweenthese extremes there is a critical size range where unburned parti-cles may escape the cyclone. Fig. 9a shows that with a tall riser thisproblem becomes alleviated. This is, in essence, an illustration of

100

101

102

103

0

0.2

0.4

0.6

0.8

1

Particle size, m

Fractionalefficiency

Fig. 8. Cyclone efficiency for the particular case of a cut size of dp,50 = 27lm.

0 50 100 150 2000

0.5

1

1.5

2

2.5

dP, m

DaV

Parameter: Riser height, m

10


20


30


40

0 50 100 150 2000

0.5

1

1.5

2

2.5

dP, m

DaV

Parameter: dp,50

, m

20

Parameter: dp,50

, m

30

Parameter: dp,50

, m

40

(a)

(b)

Fig. 9. Vertical Damkhler number vs char particle size. Riser heightas a parameter

at a cyclone cut-size of dp,50 = 27lm (a). Cyclone cut-size as a parameter at a riserheight of 30 m (b).


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the vertical scaling problem: a low riser is less efficient than a tallone because the combustion efficiency is lower. However, the com-bustion efficiency may be affected in many other ways. One of themost important influencing factors, the cyclone efficiency,expressed in the form of its cut size dp,50, is shown to have a deci-sive impact on the char burnout in Fig. 9b. In addition to theparameters studied here, there is an influence from various factorssuch as: the reactivity of the char, the tendency to fragmentationand attrition, the oxygen concentration of the surrounding gas,the temperature, and so on.

3.6. The impact of the cyclone

With a constant contribution to the circulating flow from flyashes and small char particles entering into the circulation loopGin, a simple mass balance on the circulation loop yields the circu-lation flow

G Gin=1 g 24

It was shown how the cyclone efficiency plays a significant rolefor the burnout of char. At the same time as an increase in cycloneefficiency extends the residence time of char, the simple relation-ship, Eq. (24), shows how it enhances particle circulation in generaland consequently also vertical solids concentration and heattransfer.

Also the cyclone efficiency is affected by the scale. Assume twoplants, a small-scale plant (index I) and a large-scale plant (indexII) with geometrically similar cyclones. Usually, in combustioncomparisons the fluidizing velocity u (as well as other parametersmentioned above) is kept the same in both plants. Then, with thesame surface power (heat release per square meter cross-sectionalarea, proportional to gas velocity at constant air ratio) in both flu-idized-bed risers, the total power of the combustors Qis related tothe flow through the riser uoAr, and this, inturn, is equal to the flowthrough the cyclone

QI $ uoAr;I $ ucyclD2cycl;I

QII $ uoAr;II $ ucyclD2cycl;II

that is

QIQII

Ar;IAr;II

D2cycl;I

D2cycl;II25

Here Ar is the cross section of the riser and D2cycl that of the cyclone.

ucycl is a corresponding through-flow velocity in the cyclones re-lated to the cyclone diameter Dcycl, or it could even be the inletvelocity uin. Hoffmann and Stein [20] have treated cyclone scalingand pointed out that the great number of parameters influencingthe cyclone behavior can be reduced to a few dimensionless num-

bers, of which the Stokes number can be shown to be the mostimportant one, provided that the cyclone Reynolds number is suffi-ciently large and that the particle loading is small. For geometricallysimilar cyclones

gdp fStk 26

where

Stk d

2p50uinDq

18lDcycl27

where Dq is the difference between particle and gas density. Theefficiency condition Eq. (26) is not fulfilled in the CFB applicationwhere the particle loading is high. However, Muschelknauz and

coworkers have especially studied the separation conditions inhighly loaded cyclones. Summaries of their work can be found in

[22,20]. They found that the loading of particles above a certain lim-iting loading cp,L (the saltation condition) would always be sepa-rated, whereas the particles below this limiting value are separatedsimilar to a low-loaded cyclone. The efficiency can then be written(according to one of Muschelknauz approaches, quoted from [20]),

g 1 cp;Ldp;50

cp

cp;Ldp;50

cp

XN

i1

gimi 28

where mi is the ith mass fraction and gi is the corresponding effi-ciency according to Eq. (26).

Both constituents of the cyclone efficiency depend on Stokesnumber, and therefore, the efficiency of highly loaded cyclonesbecomes

gdp fStk; cp;L=cp 29

In geometrically similar cyclones with similar gas and particles,therefore, the Stokes number could serve as a characteristic num-ber both for the limiting value and for the fractional separationefficiency, although it is not exactly equal to the criteria definedby Muschelknauz. Therefore, assuming that Stokes number scalingcould be applied, the Stokes numbers should be the same forapproximate similarity

d2p50;IuinDq

18lDcycl;Id

2p50;IIuinDq

18lDcycl;II30

or

d2p50;I

d2p50;II

Dcycl;IDcycl;II

31

Combination of Eqs. (25) and (31) gives

dp50;Idp50;II

4

QIQII

32

The conclusion is that under the given conditions (geometricalsimilarity and constant entrance velocity) larger cyclones inevita-bly obtain higher cut size and, hence, lower efficiency than smallerones, as seen from expressions of the cut size, for instance Eq. (19).

To this problem we can add the effect of the residence times inthe cyclones. In the above presentation, the residence time in thecyclone was not included in the calculation of the gas residencetime for simplicity (although it could have been added to the res-idence time in the furnace). The cyclone works as an afterburnerthat contributes to the burnout of both gases and particles. It isclear that a small cyclone, having shorter gas residence time, is lessfavorable than a large one in this respect. An example in the formof a comparison of the residence times in three CFB combustors isgiven in Table 2. The combustors were of widely different sizes to

illustrate scale effects, although they are not geometrically similarand not scaled according to the above considerations. However,they were operated under similar combustion conditions.

It can be concluded from the table that the gas residence-timesin the furnaces were reasonably similar in the research rig, pilot

Table 2

Gas residence-times in three CFB combustors of different scale [23].

Name of plant TUHH CTH Flensburg

Thermal power (MW) 0.029 6 109Volume of the combustion chamber (m3) 0.13 31.4 590Volume of the cyclone, including entry duct (m3) 0.024 12.4 490Gas residence time in the combustion chamber

(s)2.6 2.2 3.8

Gas residence time in the cyclone (s) 0.5 0.9 3.2


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plant and the commercial boiler, except that the cyclone in thecommercial boiler was much greater than in the other equipment.

3.7. The vertical scaling problembubbling bed

In some cases the vertical processes in the bubbling bottom-beddominate the combustion performance of the boiler. Then it is a

common approach to represent the fluid dynamics by the fluidiza-tion velocity and by various transport coefficients. The startingpoint for modelling, as well as for the derivation of scaling criteria,is the vertical (one-dimensional) mass-transport equation. Theone-dimensional version of Eq. (9) for oxygen in the vertical direc-tion Z=z/L without dispersion is,

UdC

dZ Dav 33

where C= c/cin is the dimensionless concentration of oxygen alongthe reactor, expressed in volume fractions, transported with theconstant fluidization velocity U= u/uo and reacted by Dav = Rz0/cinu0. In dimensional form Eq. (33) becomes

udc

dz

R 34

This equation is applied to the flow of oxygen in the bubble andparticle (emulsion) phases of a fluidized bed (details can be foundin a recent review[24]). The usual assumptions are that the volatilegases (gg) only react in the bubble phase, whereas the gassolidreactions (gs) take place in the emulsion phase, where the char isfound most of the time. Expressed for the two phases, Eq. (34)takes the form of Eqs. (35) and (36) whose last term representsthe gas transported from one phase to the other through the spe-cific surface of the bubbles ab = 6eb/db for spherical bubbles ofdiameter db with the exchange coefficient kbe,

ebu0 umfdcbdz

ebRgg ebabkbecb ce 35

eeumfdcedz

1 ee1 ebrcRgs ebabkbecb ce 36

The dimensionless parameters are C= c/cin, Z=z/L,b = (uo umf)/uo. The reaction terms are first order (for simplicityonly) (information on the reactions contained in K is given in[24]) and may represent drying, devolatilization, char combustionas well as homogeneous reactions,

Rgg Kggcb

Rgs Kgsce37

Eqs. (35) and (36) in dimensionless form are

ebbdCbdZ

ebDagg NTUCb Ce 38

ee1 bdCedZ

1 ee1 ebrcDags NTUCb Ce 39

The dimensionless criteria characterizing the process are:Damkhler numbers Da, often called Number of Reaction Units,and the Number of Transfer Units NTU, together with the velocityratio b, defined as follows:

Dagg KggCbL

u0; Dags

KgsCeL

u0; NTU

ebabkbeLu0

; b u0 umf

u0

40

Solutions of the equations are often presented in analytic form.Especially for catalytic fluidized-bed reactors several examples

have been shown in reviews [25,26], where common simplifyingassumptions, also used in combustion applications, are sorted up

and their effects are analysed. Similar, but more complex solutionsare available for combustors and gasifiers. Common boundary andother conditions are seen in Fig. 10, where the emulsion phase hasbeen assumed to be well stirred with constant concentration ce,supplied from the bubbles with oxygen, which is gradually re-moved by reaction.

The catalytic beds differ from the fuel conversion beds in twoways: (1) there is no volatile release and (2) the reacting bed par-ticles are not affected (unless poisoned), whereas in the fuel bed,additional knowledge on the size distribution and degree of con-version of the fuel particles is needed for a solution. The parameterrc = 1 in a catalytic bed, since all bed particles are supposed to beactive, whereas in a fuel bed rc < 1 and has to be determined.

The simplest possible solution of Eqs. (35) and (36) for a cata-lytic bed with no flow through the particle phase of constant voi-dage has been shown [25] to be

CzL exp DagsNTU

Dags NTU

41

The reactions are first order for simplicity, rc = 1, b = 1 and thevoidages are included in Dags. NTU describes the transfer of gasfrom the bubbles to the particles, and the rate of reaction in thepresence of gas in the reactor is given by Dags. An early scaling ofcatalytic reactors by means of this reaction was carried out byWerther [27] who used empirical information on the impact ofthe reactor scale (width) on the NTU (the width of the vessel influ-ences the bubbles). It was then possible to determine the reactorheight necessary for a given conversion (Cz=L) in reactors of variouswidths. Afterwards similar models have been applied to severaltypes of catalytic scaling problems and, in an extended form, alsoto combustor modelling.

There are limitations in applying the criteria just mentioned toscale-up of combustors, principally because of the much highervelocities employed in combustors compared to many chemicalreactors. Available scientific information on high velocity fluidiza-tion has normally been obtained in narrow test rigs (typically0.1 m, and in most cases less than 0.5 m in diameter) without con-sidering scaling, and where the wall effects can be suspected to belarge. The data available are therefore uncertain to use for scalingof combustors, especially the bubble properties bb, ab and kbe.

3.8. Concluding remark

Simplified approaches have been used in the absence of detailedfluid-dynamic and mixing information. Gaseous reactions in com-bustor scaling depend on mixing of fuel and air, and hence, mostlyon the horizontal dispersion of fuel. The vertical transport time is

always much longer than the combustion time for gas reactionsand is not a problem, provided that fuel and air are mixed. For char

ce

Cin

Cb,out

Height

C

oncentration

Emulsion

Bubblephase

Fig. 10. Concentrations in the bubble and particle phases of a fluidized bed.


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combustion, on the other hand, the vertical transport time is a lim-iting factor, directly related to scaling. In that environment at highgas velocities, the impact of bubbles is degenerated into an infinitecontact surface for exchange between particle and bubble phase(NTU?1) and Eq. (41) now represents a situation close to plugflow with some back mixing. In its simplest form, we are interestedin the efficiency of combustion in a L m high reactor with a giventemperature and oxygen concentration, usually disregarding thefeatures of a bubbling bed. This leads to the considerations pre-sented in the previous sections.

4. Boiler design scaling

Fluidized-bed boilers have undergone a gradual scale-up in sizeduring the last 30 years, as shown in Fig. 11 from statistics on CFBboilers in the world except China and China alone where also agreat number of CFB boilers are in operation.

During the last 10 years the interest has been focused on utility-size CFB boilers. This means, sizes of at least 600800 MWe (thenumber in thermal MW is more than twice as large) to competeeconomically with pulverized coal (PC) boilers. Other applications,

such as biomass boilers, are limited in size by the supply of fuel,because transportation of biomass fuel sets a limit, and the indus-trial boilers are limited on the demand side and have alreadyreached their maximum sizes. Non-circulating (bubbling) fluidizedbeds can be treated by the methods described above, but they areless interesting for scale-up to electric utility size.

This development can be illustrated by the layout of a furnace,as seen in Fig. 12, showing the horizontal cross section of CFBfurnaces with cyclones of Foster Wheelers design from 1994 andonwards (Similar data have been shown by other boiler makers).

During the process of gradual scale-up, the elements of designfrom smaller boilers are used in larger boilers with a rather smallindividual increase in size, instead increasing the number of re-peated elements. The cyclone is such an element whose efficiencytends to decrease with increasing size, although, as seen in the par-ticular case of Fig. 12, both number and size can be considered.Therefore, the number of cyclones is increased instead of exces-sively changing their size. This, on the other hand, leads to thequestion of whether all parallel cyclones will perform in the sameway, especially when applying an uneven number of cyclones [31],an issue that also motivated the research shown in Fig. 4 regardingcold model testing of parallel cyclones.

There are a few relationships concerning the shape of the com-bustion chamber that are worth mentioning: again, the cross-sectional size and the height are important scaling parameters,now also from a heat transfer point of view.

The cross-section surface-power qc [MWfuel/m2crosssection] is a di-rect measure of the foot-print of the furnace. At a given amountof excess air, the mass flow of gas upwards through the furnaceuoqgas divided by the specific mass flow of gas per kg fuel, yv,including fuel moisture, and multiplied by the lower heating valueHu, gives the fuel power released per square meter cross-sectionalarea

qc uoqgasHu=yv 42

It is known that the quantity Hu/yv is surprisingly constant,independent of type of fuel, and the density qgas is constant for acombustor at a given bed temperature and pressure (atmosphericor pressurized). For this reason the surface power is basically pro-portional to the fluidization velocity.

The impact of surface power according to Eq. (42) on furnacesize is as important today for scale-up as it was in the beginning

of the development of fluidized-bed combustion. The developmentstarted with bubbling beds, where elutriation of particles from thebed was seen as an inconvenience that should be avoided, as is re-flected from publications in the early International Fluidized BedCombustion Conferences, for instance. To do so, but to retain highsurface power (high fluidization velocity), large-particle beds wereproposed to allow high fluidization velocity without elutriation,and, among other topics, work was carried out on heat transferto immersed heat exchangers in large-particle beds. It soon be-came evident that immersed boiler tubes in fluidized beds oper-ated at high velocity were not a viable solution because of severeerosion on the tubes. It appears that tubes in dense fluidized bedscan only withstand erosion to some extent at low fluidizationvelocity but then the surface power is also low, and this results

0

200

400

600

800

1 000

1 200

1 400

1 600

1 800

2 000

1980 1985 1990 1995 2000 2005 2010 2015

Year

CFBBoilerLoad,

MWth

World except China

China

Fig. 11. Development of the capacities of Circulating Fluidized Bed boilers up to2010 expressed in MW thermal power. (Sources: [28] World except China; [29]China; recalculated from MWe data).

Fig. 12. Scale-up of CFBmodular approach [30]. Cross sections of the furnace with connected cyclones.


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in a wide furnace. Then a creative, but in retrospect quite natural,thought was presented proposing to remove the boiler tubes fromthe bed, increase the fluidization velocity, reduce the size of thebed particles to allow the particles to be carried away by the gas,and employ the tubes covering the furnace walls for heat exchangeby convection and radiation. Of course, particles serving as a heattransport medium were then carried away with the gas; a particleseparator and a system for recirculation of particles to the bedwere needed. This lead to the introduction of circulating fluidizedbed, CFB in boilers (CFB had been invented already in 19401950[32] with application in the petroleum industry). At the same timeas the fluidization velocity was increased, so was the surface powerand, therefore, the combustion chamber became more reasonablein size, a fact that formed the basis for further advantageousscale-up.

Unfortunately, because of the decreasing surface to volume ra-tio of a furnace at increasing volume (size of the boiler), the wallsurfaces are not sufficient for heat absorption in large boilers.Now, the scale-up problem became a problem of finding heat ex-changer surface area in addition to that on the walls of the com-bustion chamber. The problem is most easily understood bystudying a cube with side length L. The wall area available forthe corresponding furnace (volume) is proportional to 1/L andthe available relative surface area decreases with increasing sizeL of the furnace. As a result, there is ample space for heat transfersurface in small devices, while there is a deficit of space for wallsurface area in large boilers. It is well known that in laboratory de-vices, the walls are so efficient for cooling that even insulation isnot sufficient to compensate for the heat loss, and usually electricalheating is required to maintain a desired bed temperature. As thecombustion chambers grew in size, more wall surface area canbe covered by heat transfer surfaces, but already at about 50100 MWth all available wall area is occupied, and additional typesof surface are needed. This becomes especially critical for scale-upto utility sizes.

Fig. 13 displays some types of heat transfer surface in contact

with the bed material. Surface (a) is the furnace wall covered bytubes, protected by refractory in the most exposed places. Thenumbers indicate examples of different type of inserted heat trans-fer surfaces: (1) wing walls the most common type, tube bundlesprotruding from the walls like wings, (2) platen tube bundles forsuperheaters, (3) omega tubes expensive, flat surfaces with anomega-shaped void for steam-water flow, extended inside the fur-nace space and protected against erosion (4) additional insidetube-walls in very large boilers. Often the particle separator ismade up of heat transfer tubes (Surface b), but they are protectedby refractory and their heat transfer capacity is limited. Surface (5)is a heat exchanger in the return leg from the cyclone, utilizing the

return flow of particles from the separator. There are severalarrangements, as seen in Fig. 14.

It should be noted that the heat transfer surfaces related to thescale-up problem are those within the recirculation loop, requiredto achieve a desired bed temperature. In this context, the tube bun-

dles of the back pass are not of interest, as they serve for coolingthe flue gases downstream of the circulation loop. They belong toconventional boiler equipment. However, the organization of thebottom part of the furnace, the returnsystemfor bed material fromthe separator, and the related bed material handling are of partic-ular interest, as they create possibilities for cooling the bed mate-rial and for allocation of superheaters. This is illustrated in Fig. 14where the designs of thee major boiler manufacturers arecompared.

The tube bundle in the INTREX cooler receives hot bed materialfrom the particle separator (external circulation) but also fromthe internal bed material falling down along the furnace walls

1

2

3

4

a

b

5

Fig. 13. Heat transfer surfaces in the bed loop of a CFB boiler. Adapted from [33].

Fig. 14. Details of the bottom zone of various designs of large-scale CFB (not drawn in the same scale). The left-hand design is a pant-leg bottom part with external heatexchangers from an Alstom boiler [34]. In the central figure, an INTREX cooler from Foster Wheeler [35], and to the right, shown for comparison, the lower part of a Metso

boiler with an integrated ash cooler fromthe 160 MWth Manitowoc plant. The seemingly empty part (the loop seal, supplied with particles fromthe cyclone) contains a heatexchanger.


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(internal recirculation). As a comparison, the arrangement fromthe Metso boiler on the right-hand side of the figure, a heatexchanger in the loop seal also utilises the returning bed materialfor heating, but no details are presented. The other large boiler ma-ker, Alstom, whose boiler is seen on the left-hand figure, employs amore extensive arrangement of heat absorption in the form of sep-arate external heat-exchangers with greater capacity (if needed). Inrecent designs the external heat exchangers are moved in closercontact with the furnace. Additional surfaces inside the combus-tion chamber are used for middle-sized boilers when such surfacesare more convenient than the external ones that are more usefulfor the largest boilers. The flow from the loop seal to the externalheat exchanger can be controlled by a hot valve (cone valve).

In Europe, mostly old power stations use coal. A decade ago gasbecame the dominant fuel and very few coal-fired plants werebuilt. A certain amount of coal power plants are planned, and thereis a recent trend towards diversification with the purpose of reduc-ing the dependence on gas and also because of rising prices on gascompared to coal. In countries like India and China coal-firing ismore important, and CFB with increasing size is now introducedto a large extent. Modern coal-fired power stations employ effi-cient and well developed PC boilers, whose size is about 20003000 MWth, with high steam data to achieve high efficiency in

power production. The only CFB boilers included in this group ofpower-producing units are those having the advantage of burningcoals that are less suitable for PC boilers. Both size and efficiency ofCFB boiler power-plants have to increase in order to be competi-tive. A development with this aim is presently going on.

The on-going development effort aims at increasing steam datain a CFB from conventional 540/540 C, 170 bar to supercritical600/620 C and 270 bar and even higher if new tube materials be-come available. This would require a Benson-type of boiler (once-through). CFB appears to be suitable for such an application, sincethe heat load on the furnace walls is quite even and highest in thebottom part, which is in a position of boiling heat transfer on thewater side far away from the critical point.

The two largest manufacturers of CFB, Alstom and Foster

Wheeler, have both made conceptual designs of fluidized-bed boil-ers for sizes between 450 to 800 MWe. Some features are summa-rized in Table 3. In addition, the very ambitious work on scale-upby Electricit de France [36,37] should be mentioned.

The shape of the combustion chambers cross section tends tobe rectangular (see Fig. 12). The length of penetration of secondaryair jets determines the maximum width to about 10 m. The heightis determined by allocation of heat transfer surface, but with vari-ous additional heat transfer surfaces, as shown above, excessiveheights can be avoided, and 4050 m seems to be the ideal maxi-mum height. The third dimension is determined by the gas flowthat has to pass the combustion chamber to burn the given amountof fuel at a given excess air and fluidization velocity (that is, thepower of the boiler). The gas velocity should be high to limit the

size of the combustion chamber. On the other hand, erosion onwalls and heat transfer surfaces increases with velocity, so the

velocity may be chosen as the result of a compromise, to be inthe order of 45 m/s, yielding a heat release of 2.54 MWth/m

2

cross-sectional area. This determines the length of the combustionchamber, given that particle separators, fuel feed devices and sec-ondary air nozzles have space enough to be located on the sidewalls.

5. Conclusions and discussion

Strict scaling of all simultaneous processes in a combustiondevice can be formulated theoretically, but it can hardly be car-ried out in practice. Therefore, combustion scaling with applica-tion to fluidized bed combustors has to be focused on aparticular aspect of the scaling problem after an analysis of thesystem to identify the limiting processes. Here three aspectshave been treated according to their particular possibilities andconditions: fluid-dynamic scaling, scaling of combustion pro-cesses, and scale-up related to boiler design. Heat transfer isonly implicitly involved in the scaling by the assumption of abed temperature.

Fluid-dynamic scaling, based on scaling criteria derived fromthe fundamental fluid-dynamic equations, describes the move-

ment of the two-phase medium in a fluidized-bed reactor. It canbe performed with relatively good success, transferring resultsform a small-scale, cold test-rig to a large boiler operated in its nor-mal conditions. The most difficult part in this process is to find bedparticles of correct size, shape, and density for the cold scale-model.

Combustion scaling could include scale-up of the chemistry,such as studied in a small laboratory bench-scale reactor and thenapplied to the large-scale boiler. It also means the scale-up of data,obtained in a laboratory combustion-plant, to a boiler or from asmall boiler to a larger one, both employing about the same oper-ation data. In scaling-up from a laboratory plant, complete fluid-dynamic similarity can never be attained, because a laboratoryplant by definition must be limited in size, at least in the horizontal

direction, whereas the residence times required to represent com-bustion conditions can be approached in the vertical direction. De-spite this limitation, several aspects of combustion-relatedreactions can be studied in such devices if one is aware of the con-sequences of the restrictions. In combustion scaling from boiler toboiler, provided the operation conditions are about the same as inthe target plant, the fluid dynamics play a subordinate role. Thescaling can focus on the vertical or horizontal transport or reactionphenomena depending on the purpose of the study, using theDamkhler number as a scaling criterion.

In boiler-design scaling the main problem is the scale-up ofknown features to very large size. Then, scaling can use design ele-ments already developed, similar in size but multiplied in number,to reach the large size. Examples of such multiplied items are feed

systems, cyclones, return loops etc. The new problems consist infinding place for cooling surfaces and to obtain an even distribu-

Table 3

Comparison between conceptual designs.

Item Foster Wheeler [33] Alstom [34]

Size MWe 800 450600Steam pressure bara 315 (design pressure) 270 (header outlet)Steam temperature (C) 604/621 600/620Separators 8 6Bed cooling except walls Internal walls + INTREX (1020 MWth each), eight consisting of two in series External heat exchangers (no size limitation)

Size Ten meter wide to allow penetration of secondary air, pant-leg in Alstom. Less than 50m high, and as wide as needed for the power of 2.54 MWth/m

2 cross-section area

a Actually, the pressures are equal but expressed for different locations.


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tion of the performance of design elements introduced in parallelduring scale-up to very large size.

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