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A particle population balancing model for a circulating fluidized bed

combustion system

K. Redemann, E.-U. Hartge, Joachim Werther

Institute of Solids Process Engineering and Particle Technology, Hamburg University of Technology, Denickestr. 15, D-21071 Hamburg, Germany

a b s t r a c ta r t i c l e i n f o

Article history:

Received 4 September 2007

Received in revised form 15 August 2008

Accepted 23 September 2008

Available online 1 October 2008

Keywords:

Particle population balance

Circulating fluidized bed

Fluid dynamics

Refuse derived fuel

A dynamic simulation model of the particle population in a circulating fluidized bed combustor with external

heat exchanger has been developed. It considers the fluid dynamic processes in the various parts of the

system, as well as the particle attrition. To handle multiple solids types simultaneously and to fulfill the mass

balances, some of the fluid dynamic sub-models taken from the literature were modified. The model allows

to calculate the solids mass flows as well as the corresponding particle size distributions at any point inside

the combustion system.

The model has been applied to the combustion plant of Stadtwerke Neumnster in Germany, which operates

on refuse-derived fuel. The particle balancing model provides new insights into the operating behavior of

such a system. In particular, the calculation of the residence time of different particle classes in the system

reveals a very broad distribution of size dependent average residence times, ranging from several minutes to

a maximum of roughly 40 h. A size fraction exists between 100 and 300 m with a maximum average

residence time of about 40 h. The Preprint submitted to Elsevier Science 15 August 2008 simulation provides

a means for examining possibilities to control the particle size distribution in the combustion system. It is

shown how a recirculation of a fine ash fraction can be used to control the bed particle size distribution in the

combustion chamber.

2008 Elsevier B.V. All rights reserved.

1. Introduction

A key parameter for the proper operation of a circulating fluidized

bed combustor (CFBC) is the particle size distribution (PSD) of the bed

inventory.

It governs e.g. the solids circulation rate and with it the heat

transport from the combustion chamber into the external heat

exchanger. The particle population results from the PSDs and mass

flows of the solids fed into the system and reaction, classification,

transport and comminution processes occurring in the plant.

Improper operating conditions or imperfect plant components cancause serious problems in the plant operation.

For example, the separation behavior of the cyclone, which is

attached to the combustion chamber, is a major issue. A properly

designed cyclone should be able to keep a given mass of solids with a

predetermined particle size distribution in the cycle. If the loss of

material through the cyclone is too high and if the input of fresh ash

for example in the case of a coal with a low content of ash is too

small, it may be necessary to continuously add new bed material, in

order to keep the mass of solids in the inventory. Respective operating

experience exists with Rheinbraun [1].

It is thereforedesirable to have a properly designed cyclone,whose

design is considering the special operating conditions in CFB

operation, i.e. the high solids loading at the inlet. Comprehensive

work on the design of cyclones under these conditions, which was

mainly focused on the inlet design and the formation and flow of the

strand formed there, has been carried out by Muschelknautz and his

group at the University Stuttgart (e.g. [24]) and by Reh and his co-

workers at ETH Zrich (e.g. [5,6]). Their results have found a striking

confirmation by the experience made by Alstom in their Zeran project

[7]. The Zeran A boiler in Warsaw, Poland, a 450 t/h CFB steam

generator, was commissioned in 1995. At that time it was the largestCFB boiler in Poland and the first to operate on Polish hardcoal. Due to

the high debris rock content in the ash it turned out to be difficult to

achieve the proper particle size distribution of the circulating ash. The

cyclones were not able to prevent the loss offine inert material. When

the order for the boiler B of Zeran was placed in 1998, it was built

almost identical to boiler A, with the exception of the cyclone design.

In order to improve the separation efficiency the arrangement of the

cyclone's inlet ducts with respect to the furnace was optimized, the

inlet ducts were prolonged and inclined downward, the vertical

velocity in the cyclone was decreased and eccentric vortex finders

were installed.

The new design turned out to be extremely efficient: the 50% value

of the cumulative mass distribution of the circulating particles went

down from 180 m for boiler A to 75 m for boiler B. The increased

Powder Technology 191 (2009) 7890

Corresponding author. Tel.: +49 40 42878 3239; fax: +49 40 42878 2678.

0032-5910/$ see front matter 2008 Elsevier B.V. All rights reserved.

doi:10.1016/j.powtec.2008.09.009

Contents lists available at ScienceDirect

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cyclone efficiency and the thus realized finer inventory of the system

had several beneficial effects, including an increased overall heat

transfer coefficient, which allowed to reduce theinventoryand thus to

lower power consumption. Furthermore limestone utilization was

improved and even the NOx and CO emissions were reduced.

It is interesting to note in this context that the same experience

with regard to the significance of the cyclone design was made over10 years before in Germany [8]. Two 105 MWth CFB boilers were built

for Bayer AG on their Leverkusen site. Thefirst one was commissioned

in 1988, thesecond onein 1991. Duringoperation (both units operated

on the same coal) it turned out that in the second unit the combustion

efficiency was lower, the Ca/S ratio was twice as high, the dp,50 of the

recirculating ash was 170 m instead of 150 m and the fly ash had a

dp,50 of 80 m compared to 30 m in the first unit. A detailed analysis

brought the result that the cyclone design had been changed

unintentionally, i.e. the diameter of the vortex finder had been

increasedby 14% anda designchange of thevortexfinder's suspension

enabled a short-circuiting flow to take place.

The PSD of the bed inventory results from the fluid dynamic

processes in the different plant components, the ash formation

behavior of the fuel and additionally fed solids, e.g. additional inertsolids, limestone or recycled bed material. A mathematical simulation

tool considering these effects can be used to predict the PSDs in the

different parts of a circulating fluidized bed under various operating

conditions. It can also be used to survey and judge the impact of

changes in theoperation of a plant or in thecharacteristicsof theinput

fuel on the resulting particle size distributions.

In the present work a mathematical model based on particle

population balances is developed, which considers the circulating

fluidized bed combustion system as separate modules. Mathematical

descriptions were, as far as possible, taken from the literature.

However, in some cases available descriptions had to be modified in

order to fulfill the requirements of particle population balancing. The

resulting model represents a dynamical description of the system

behavior, which also allows conclusions about the residence time of

individual size fractions in the system to be drawn.

The model is first applied to the simulation of the refuse-derived

fuel fired circulating fluidized bed combustor of Stadtwerke Neumn-

ster GmbH in Neumnster in north Germany. Its schematic layout is

shown in Fig. 1. Refuse-derived fuel (RDF) is fed into the combustion

chamber. Fly ash is leaving via the cyclone overflow and is collected in

the heat recovery boiler and the multi-cyclone. Finally small quantities

of ultra fine ash are passing into the flue gas treatment section.Since the ash particle size distribution which is produced by the

refuse-derived fuel cannot be easily predicted, the plant contains two

means for influencing the PSD of the bed inventory. The one is the

addition of sand, which was also used for starting the facility. The

second means is the recirculation offine ash, obtained after sieving of

the bottom ash offtake.

In the framework of a research project initiated by Stadtwerke

Neumnster, measurement campaigns were carried out where solids

mass flows and solids particle size distributions were measured at

different locations at the plant. Additional lab scale investigations

formed the basis for the development of the particle population

balances presented here. Since the experimental facts were decisive

for the design of the model, they will be presented below before the

description of the theory.

2. Experimental

2.1. Measurements at the Neumnster plant

In general measurements of solids mass flows and solids particle

size distributions in an industrial plant arequite difficult. Theaccess to

the various parts of such a complex system is not easy, safety

precautions have to be taken and above all, the refuse-derivedfuel is a

matter which is very difficult to characterize.

Solids mass flows were determined on larger time intervals by

counting the number and loading of trucks which transported the

ashes to a disposal site. This was done for the coarse bottom ash, the

fine bottom ash, the fly ash (sum of ashes taken from the radiation

boiler, convection boiler and the multi-cyclone). The sand supply was

Fig. 1. Flowsheet of a circulating fluidized bed combustion system (Neumnster plant).

79K. Redemann et al. / Powder Technology 191 (2009) 7890


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also measured. It is admitted that all flows necessarily contain sand

particles as well, so all ash streams are in reality mixtures of fuel ash

and sand. However, for simplicity these streams are still called ashhere. The mass flow of the ultra-fine ash was calculated from

information about the lime and activated coke fed to the flue gas

cleaning andabout the solidswithdrawn from theflue gas cleaning for

disposal. From these information the ash input with the refuse-

derived fuel could be calculated.

With regard to the solids particle size distributions samples were

taken of the coarse bottom ash, the fine bottom ash, the fly ash

(mixture offly ashes taken from the different sources) and from the

sand. The solids samples were analyzed by sieving and a laser

diffractometer (Beckman-Coulter LS 13 320). No sample could be

taken from the ultra-fine ash. For this latter material the correspond-

ing particle size distribution was estimated by calculating the

separation efficiency of the multi-cyclone for the given fly ash. Fig. 2

shows the particle size distributions of different samples and Table 1presents the measured solids mass flows.

2.2. Measurement of the attrition characteristics of the refuse-derived

fuel ash

The RDF which is used in the Neumnster plant is produced by

mechanical and biological processing of the municipal waste from

the north German region around Neumnster. The processing plant

has a total capacity of 210,000 t/h of household waste. It produces

103,000 t/h refuse-derived fuel. The processing results in an increase

of the calorific value of 9 MJ/kg for the original waste to 14.5 MJ/kg of

the RDF. The RDF itself is very difficult to characterize.

It contains pieces of wood and organic matter, as well as sheets of

paper and plastics. The

particles

have a maximum dimension ofroughly 10 cm. According to the concept of the primary ash particle

size distribution (PAPSD) suggested by Salatino and co-workers [9,10],

devolatilization and combustion of a solid fuel leads to an ash particle

size distribution, i.e. the PAPSD, which will during its further residence

time in the combustion chamber undergo fragmentation and attrition.

For population balancing purposes it is necessary to follow the

changes of particle sizes inside the combustion system. In previouswork on the modeling offluid bed catalytic reactors [11] and coal and

sludge combustion in the fluidized bed [12], the authors' group has

developed a tool for the description of attrition processes. In order to

apply the same tools to the RDF combustion problem, samples of the

original RDF were exposed for a short time to combustion conditions

in a fluidized bed in order to create an ash sample, which could then

be further used.

Fig. 3 gives an example of sucha distribution. Of course this is not a

real PAPSD in the sense of its definition, because it has already

undergone some stress in the fluidized bed due to the finite residence

time under combustion conditions. However, the material is well

suited for attrition experiments.

Following the distinction of the three attrition mechanisms [13]:

in-bed attrition by solids movement, induced by bubbles in-bed attrition, induced by distributor jet action

attrition during the passage through a cyclone

the attrition characteristicswere determinedin specialized testfacilities,

which have been described elsewhere [13].

Fig. 4 shows two sets of data for the bubble induced attrition. The

attrition rate r in kg of fines produced per kg of bed material and

second is plotted against the time. It is remarkable that contrary to

what was observed with catalyst and coal ashes [13] no constant

attrition rate is obtained after a certain time of operation. Obviously,

due to the structure of the RDF ash no steady-state attrition rate is

reached. On the contrary, the particles are continuously breaking

down and even after 1500 h of attrition no plateau is reached.

Fig. 2. Measured particle size distribution of ashes leaving the plant and of the feed

sand.

Table 1

Measured solids mass flows and calculated feed mass flow of attrited ash at the

Neumnster plant

Solids stream Mass flow

[kg/h]

Ultra fine ash 481

Fly ash 1778

Fine ash 1508

Coarse ash 1390Sand 373

Feed of attrited ash 4786

Fig. 3. Measured PAPSD originating from laboratory scale fluidized bed combustion.

Fig. 4. Results for bubble induced attrition experiments with two different ash samples,

operated at a superficial velocity of u =0.5 m/s, plotted against the operating time.

80 K. Redemann et al. / Powder Technology 191 (2009) 7890


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In Fig. 5 the attrition rate r is plotted against the relative material

loss matt/ mb0, where matt denotes the cumulative attrited mass and

mb0 is the initial bed solids mass. Both experiments can beapproximated by straight lines on the semi-logarithmic grid,

r a exp b mattmb0

& ': 1

The different slopes are probably due to the fact that both ashes

originate from different RDF samples.

Fig. 6 shows in its upper half the time-dependent attrition rate in

kg of attrited material produced per time unit for the jet attrition test,

as a function of time. Again, no steady state of attrition is reached. In

the lower half the attrition rate is plotted against the relative material

loss matt/mb0. Fig. 7 shows the results of the cyclone attrition test for

two different samples operated under different conditions. Here also,

no steady state attrition is reached.

3. Theory

3.1. The particle population balancing model

Although Fig. 1 presents a special design of a circulating fluidized

bed combustion system the model, which is presented here, can be

applied to any other circulating fluidized bed combustor design. The

aim of the mathematical model is to track the particle population in

the bed inventory of a CFBC. The software tool calculates the physical

processes in a dynamic-sequential simulation with a pipe-and-filter

architecture [14].

The simulation model divides the CFB system into modules, each

representing an apparatus of the plant. The combustion chamber is

separated into two sub-modules, the dense bottom zone and the

upper dilute zone. The calculation of transport, classification and

comminution of the solids in the different parts of the plant isperformed in these modules. They are calculated sequentially in the

order the solids are passing them. An overview of the whole model

setup is given in Fig. 8.

Although a lot of more sophisticated models are available for the

description of the fluid mechanics of circulating fluidized beds (e.g.

[15]) a very simple approach is followed here, where the circulating

fluidized bed is modeled as a bubbling fluidized bed, operated at high

gas velocities with a correspondingly high solids elutriation. Therefore

above a dense bottom zone which contains the bubblingfluidized bed

and where the accumulation of solids is considered, we have a

freeboard section with solids transport and segregation with height.

In the cyclone the separation is considered and transport in the

return leg. The external heat exchanger is treated simply as a stirred

Fig. 5. Results for bubble induced attrition experiments for with different ash samples,

operatedat a superficial velocityofu =0.5 m/s, plotted against therelative mass loss due

to attrition.

Fig. 6. Resultsfor jetattritionexperiments, operated at a superficialvelocityofu=0.5 m/s,

jet velocity ofuj=50 m/s, nozzle diameter do=1 mm, ds=189 m plotted against time and

against the relative mass loss due to attrition.

Fig. 7. Results for cyclone attrition experiments for with different ash samples, operated

at different operating conditions (cyclone diameter: 90 mm, further details cf. [31]).



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tank with regard to the solids. Accumulation is taken into account, butno entrainment with the fluidizing gas. The entrainment may be

neglected, since entrained fines are fed again to the combustion

chamber together with the off-gas from the EHE.

The devolatilization and combustion times of the fuel particles are

in the order of seconds to minutes [16]. On the other hand the

residence times of ash particles in the system are of the order of

minutes to hours, as will be shown below. Therefore as a means of

simplification the combustion is placed outside the combustion

chamber and only ash with its primary ash particle size distribution

(PAPSD) is entering into the combustion chamber. The ash particles

are then undergoing bubble-induced attrition and jet attrition in both,

the dense bottomzone of the combustion chamber andin the external

heat exchanger. Furthermore attrition is occurring in the cyclone.

In CFBCs various solid types, e.g. fuel ash, sorbent material or

additional inert material, are present. These solids have different

physical properties, e.g. densities and particle sizes, which are

influencing the particle behavior in the fluidized bed system. Another

important parameter is the stress history of the particles (e.g. [11,12]).

In order to map all of these effects, the model treats particles of

different size, solid type andstress history separately. For that purpose

the bed inventory is discretized into a three dimensional matrix,

which contains classes of particles with the same combination of the

three characteristic properties, mentioned above. As proposed by

Scarlett [17], the matrix entries contain the masses in the respective

particle classes. All other characteristic values, e.g. the Sauter diameter

and the minimum fluidizing velocity are derived from that matrix.

3.1.1. Modeling of the combustion chamber

The combustion chamber module is divided into two sub-modules,the dense bottom zone and the upper dilute zone. The dense bottom

zone is modeled as a bubbling fluidized bed with an approach

according to Werther and Wein [18] and the upper dilute zone is

described according to Kunii and Levenspiel [19]. Both sub-modules

calculate the vertical solids volume profile. Solids are elutriated from

the dense bottom zone into the upper dilute zone, whereby the

masses of the particles classes in the upper dilute zone result from the

PSD in thedensebottom zone. Thetask of combustion chamber model

is to find the mass and PSD in the dense bottom zone with which the

mass balance in the total combustion chamber if fulfilled. This is

achieved in an iterative calculation process.

3.1.1.1. Modeling the dense bottom zone. The Werther and Wein

model [18] was used to calculate the vertical profile of the solidsvolume concentration in the dense bottom zone. To handle conical

shapes of the combustion chamber, thewideningof the cross-sectional

area with height is considered forthe calculation of themasses andthe

pressure drop in the dense bottom zone.

From the overall solids volume concentration cv at height h above

the gas distributor and the height of a suspension layer h, the solid

mass of the layer m can be calculated by

m A h s cv h h 2

where s is the solid and A(h) the cross-sectional area of the dense

bottom zone at the height h.

The pressure drop pb of the dense bottom zone can be calculated

from

pb sZhb

0

A h cv h dh 3

where hb denotes the height of the dense bottom zone.

3.1.1.2. Elutriation into the upper dilute zone. The mass elutriated

from the particle fraction i into the freeboard per time unit is given by

:mi

K4i

Q3;i

A

4

where Q3,i is the mass fraction in the dense bottom zone and A the

cross-sectional area of the combustion chamber at the height hb above

the distributor. The elutriation constant Ki is a key parameter for the

modeling of the upper dilute zone. A correlation for Ki was developed

by Colakyan and Levenspiel [20] for gas-particle systems at operating

conditions comparable to the conditions found in CFBCs. Unfortu-

nately, this elutriation model assumes that particles with a terminal

velocity ut exceeding the superficial velocity u cannot be elutriated.

The measurements taken in the Neumnster plant, which will be

described later on, have shown that this is not the case in a circulating

fluidized bed. We have found a considerable amountof particlesin the

external heat exchanger ash with sizes corresponding to terminal

velocities exceeding the operating gas velocity in the upper dilute

zone of the combustion chamber. Therefore a correction factor fKwithvalues between 0 and 1 was introduced into the Colakyan and

Levenspiel correlation,

K4i 0:011 s 1ut;i fK

u

2for ut;i fKb u

K4i 0 for ut;i fKz u5

where the solids density s is to be inserted in kg/m3. ut,i is the

terminal velocity of the particle class i. The effect of the factor fk is

shown in Fig. 9. The factor shifts the curve of the elutriation rate to the

right, towards higher terminal velocities. It follows for the solids

Fig. 8. General model layout.

Fig. 9. Elutriation rate calculated from the modified Colakyan and Levenspiel [20]

model, Eq. (5), for various values of fk (calculated with s=2350 kg/m3).



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concentration above the transport disengaging height (TDH) which is

due to the particle class i

c4V;i K4i

s u ut;i fK : 6

The vertical solids volume profile in the upper dilute zone is

describedby the exponential decayapproach (Kunii and Levenspiel [19]),

cv h V c4v cvdc4v

eh V 7

where cvd isthe solidsvolume concentration at thesurfaceof thebed and

cv(h) the solids concentration at the height h above the dense bottom

zone. The decay constant is obtained from Kunii and Levenspiel [19],

u8

8

:

me;i cvi hf u ut;i fK s 9where hf is the distance between the surface of the dense bottom zone

and the middle of the inlet duct into the gas cyclone.

3.1.2. Modeling of the gas cyclone

For the calculation of the solids separation in the gas cyclone the

model of Muschelknautz [21], with themodifications by Muschelknautz

and Trefz [22] has been taken as a basis. In this model the separation

mechanismin the cyclone is divided into twoparts.At first, immediately

near the inlet that part of thesolids loadinge, which exceeds a limiting

valueg is forming a strand, whichflowsdirectly into theunderflow.The

remaining part of the solids is undergoing the separation in the vortex.

Both mechanisms are described by semi-empirical correlations, which

arebased on a large numberof measurements, including measurements

at large-scale industrial cyclones.Unfortunately,the Muschelknautz model doesnot fulfill the fractional

solidsmass balances forthe calculationof thestrand separation, which is

a crucial point fora particlepopulation balancingmodel. Also mixtures of

solids with different densities and particle size distributions have to be

considered in the present application. Therefore the Muschelknautz

model had to be modified.

3.1.2.1. Modeling the strand separation. Under the conditions prevail-

ing in circulating fluidized bed combustors the solids loading e at thecyclone inlet exceeds the loading limitg by far [6]. Therefore the strand

separation is responsible for most of the cyclone's separation efficiency.

Theparticleattribute which is decisive forthe separation in a gascyclone

isnot its sizebut rather its terminalvelocity. In order to beableto handle

mixtures of solids of different sizes and densities the terminal velocity is

chosen here as the quantity which unambiguously characterizes a given

particle with respect to its separation in the cyclone. The particle size

distributions of mixtures of solids of different densities are therefore

converted into a single distribution of terminal velocities ut.

Particles with a probability of 50% to be separated in the strand

have according to [21] a terminal velocity of

ws;50

0:5 0:9

:Ve

Aw 10

where Ve is the inlet gas volumeflowandAw is the sedimentation area

of the strand, defined in [21].

The loading limit g can by calculated from

g Kg4ffiffiffiffiffiffiffiffiffiffiffiffi

ws;50ut;50;e

s 10e k 11

The exponent k in Eq. (11) can be calculated by

k 0:15 0:66 exp e0:015

0:6 !12

ut,50,e is the50% valueof the terminalvelocity distributionof the solids

mixture entering the cyclone.In the original Muschelknautz model [21] the particle size

distribution of the solids going into the inner vortex is described by

Fig.10. Comparisonof theinner feedPSDs and separation efficiency curves calculated fromthe Muschelknautzand thenew model forthe strand separation in a laboratory cyclone(a,

b) and the large cyclone of the Neumnster plant (case c).


where u is to be inserted in [m/s]. The mass flow in the particle class

i (me,i) leaving the combustion chamber can be calculated with the

particle slip velocity


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a RRSB distribution. The assumption of this distribution leads to a

violation of the mass balance, because the RRSB distribution implies

the presence of particle sizes which need not exist in reality. To

circumvent this problem, the assumption of the RRSB distribution for

the inner feed material hasbeen replaced here by modeling the strand

separation with a separation efficiency function.

The mean terminal velocity of the particles entering the inner

vortex, ut,50,v is then in analogy to [22] calculated from

ut;50;v ut;50;e for e Vgut;50;v ffiffiffiffiffiffiffiffiffiffiffiffiut;50;ep ffiffiffiffiffiffiffiffiffiffiffiffiut;50;ep ffiffiffiffiffiffiffiffiffiffiffiws;50p 1g=e

0:75

2for g be V 4 g

ut;50;v ws;50 for e N 4 g

:

13

Using this terminal velocity the function for the strand separation

efficiency can be set up in analogy to the approach by Rogers [23],

T ut 1a T4 ut a 14

with

T4 ut

1

1 ffiffiffiffiffiffiffiffiffi

ut;50;vut

q exp 1

ffiffiffiffiffiffiffiffiffiut

ut;50;v

q3

!& ' ; 0 V T4 V 1 15where is the separation sharpness and a is an offset value.

The total solids mass flow m v into the vortex, the so-called inner

feed is prescribed by the solids loading limit g of the gas and its mass

flow. To comply with the loading limit, the inner feed is fitted by

means of the offset value a in Eq. (14). It adjusts the mass flow of the

solids going to the inner vortex, but leaves the PSD of this material

unchanged. It is calculated by

a i T4 ut;i :me;ig 0:9 :Ve s

i

T4 ut;i :me;i : 16

There are cases possible, where the total mass in the particleclasses with T(ut)b1 is too small to fulfill the required loading limit.

This will then lead to negative values of a with Eq. (16). For these

exceptional cases, the directive given in Eq. (13) is neglected and the

mean terminal velocity ut,50,v is raised until the loading limit is

fulfilled with an offset of a = 0.

The mass flow m v, i of a particle class i entering the inner vortex is

calculated from the massflow of theparticleclass entering thecyclone

m e,i, multiplied with the corresponding separation efficiency.

:mv;i 1T ut;i

:me;i: 17To estimate the impact of the changes made to the strand

separation model, three different cases were calculated with the

original model given in [21] and with the new model discussed above.

In Fig. 10 the results are compared.

In cases A and B laboratory cyclones were simulated with two

different feedparticle sizedistributions at the sameloadinglimite=0.05.

The geometry of the cyclone and the operating conditions are given

together with the calculation parameters values in Table 2. In case C a

large-scale cyclone with the dimensions and operating conditions of the

Neumnster plant has been chosen. Its dimensions and operating data

are also listed inTable 2. The most significant distinction between cases A

and B on the one side and case C on the other side is the high solidsloading ofg=8 in the latter case.

In addition to theinlet PSDs and thecalculated inner feed PSDs, the

separation efficiency curves according to the original model and the

new model are depicted in Fig. 10. The separation efficiency of the

original model [21] has been calculated from the ratio of the predicted

inner feed PSD to the corresponding mass fraction in the cyclone inlet.

In all cases the separation sharpness used in Eq. (15) was = 0.05. The

offset a has been calculated from Eq. (16).

It can be taken from Fig. 10 that the separation efficiency curves

calculated with the present model are practically identical with those

derived from the Muschelknautz model. The advantage of the present

model is that it does not violate the fractional mass balances and

therefore can be used for population balancing.

3.1.2.2. The separation in the inner vortex. The particle diameter dv

with force equilibrium on the radius with the maximum vortex

velocity can be calculated according to [21]

d4v ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

18L0:9:Ve

sg

u2i 2hi

vuut 18

where Ve is the volumetric gas flow entering the cyclone, L the

dynamic viscosity of the gas, g and s the densities of gas and solids,

respectively, hi is the distance between the vortex finder and the apex

and ui the maximum tangential gas velocity. According to Eq. (18)

Table 2

Cyclone dimensions, suspension and model parameters and intermediate results of the

strand separation calculation for three different cyclone arrangements, carried out with

the Muschelknautz [21] and the present model

Parameter Unit Cases

A B C

Cyclonedimensions

Inlet width [mm] 13 13 1890Inlet height [mm] 37 37 4240

Outer diameter [mm] 90 90 6020

Total height [mm] 140 140 14710

Cylinder height [mm] 42 42 6464

Vortex finder dia. [mm] 28 28 1325

Vortex finder height [mm] 41 41 1065

Apex diameter [mm] 34 34 1010

Suspension Solids density [kg/m3] 2500 2500 2500

Gas density [kg/m3] 1.2 1.2 0.3

Dynamic gas viscosit y [Pa s] 18.2E6 18.2E6 46.8E6

Inlet velocity [m/s] 16.6 16.6 15.6

Solid loading [] 0.1 0.1 8

Wall friction coefficient 0 [] 0.005 0.005 0.005

Factor in Eq. (11) Kg [] 0.025 0.025 0.025

Intermediate

results

Mean inlet terminal vel. ws,50 [m/s] 0.151 0.151 0.301

Mean inlet particle dia. de [m] 19 76 76

Exponent for loading limit k [] 0.179 0.179 0.150

Loading limit g [] 1.69E3 4.22E4 1.96E2

Strand separation sharpness [] 0.05 0.05 0.05

Offset value a [] 0.632 0.323 0.991

Fig. 11. Simplified model layout, using the attrited ash particle size distribution as the

fuel ash PSD entering the system.



9/14


solids with different densities have different vortex separation cut

sizes dv. These cut sizes are used to calculate the vortex separation

efficiency F according to [21],

F dp 0:5 1 cos 1 log

dpd4v logD

2logD

0@ 1A24 350@ 1A: 19The parameter D is discussed in [21] and can be used for the fitting

of the separation efficiency curve of a given cyclone. In cases where

solids with different densities are present in the cyclone, different

separation efficiencies for the same particle size apply due to the

different separation cut sizes. F is then a function of both dp and s.

The mass flow of a particle class (same size, same density) going

into the cyclone overflow m Ov,i results from

:mOv;i F dp;s

:mv;i 20where m

v,idenotes the solids mass flow of particle class i entering the

inner vortex.

3.1.3. Modeling of return leg and bed material bunker

Both, the return leg and the bed material bunker are modeled as

pipes with plug flow behavior and have a constant total mass. The

solids leaving the bed material bunker are fed into the bottom zone of

the combustion chamber. The solids leaving the return leg are split

into two material streams, one going directly back to the combustion

chamber and one going to the external heat exchanger.

3.1.4. Modeling of the external heat exchanger

The external heat exchanger (EHE) is modeled as a stirred tank.

Particles in the EHE are exposed to jet and bubble induced attrition,

when comminution processes are considered. As a simplification the

existence of the freeboard with its entrainment and classification

effects is neglected.

3.1.5. Modeling of the solids recycle loop

Part of the bottom ash can be recycled after removing the coarseparticles on a sieve. In the simulation the total solids mass in the bed

material silo is kept constant. The solids mass needed to be drained

fromthe combustion chamber to generatethe recyclemassflowoffine

ash can be calculated from the PSD in the dense bottom zone and the

separation efficiency curve of the sieve which is modeled according to

Rogers [23]. The model parameters arederived form the split between

the fine and coarse ash measured at the technical plant.

3.2. Modeling the attrition

The comminution processes of ashes in CFBCs can be divided into

fragmentation and attrition. Fragmentation is the breakage of a

mother particle into two or more pieces, which leads to a broader and

finer PSD. Attrition is the abrasion of small particles from a much

larger mother particle, making the mother particle shrinks slowly [13].

Abrasion is the dominant mechanism for catalysts in fluidized bed

chemical reactors [13]. As a first approximation it is assumed that the

same mechanism generally holds also for the ash particles in fluidized

bed combustion.

For the population balance expressions are required for the fines

production, on the one hand per unit time for in-bed attrition induced

by bubbles and grid jets, respectively, and on the other hand per pass

in the case of attrition in the cyclone.

The experiments described in Section 2.2 above have shown that

the rate of bubble induced attrition rb(t) is described by Eq. (1). rb is

defined as the ratio offines produced due to attrition matt to the

product of the bed mass at the time t, mb(t) and the time interval t.

rb t mattmb t t: 21

Among the factors influencing the bubble induced attrition are the

most important ones theexcess gas velocity (uumf) and the diameter

of the particle size fraction under consideration. Since no systematic

investigation of these parameters has been carried out in the present

work it is assumed according to Merrick and Highley [24], Arena et al.

[25] and Pis et al. [26],

rb~ uumf : 22

Furthermore, according to Ray et al. [27], Donsi et al. [28] and

Chirone et al. [29] it holds

rb~1

dp: 23

Fig. 12. Overview of the solids streams entering and leaving the circulating fluidized bed combustion plant.

Fig.13. Measured particle size distributions of ashes leaving the plant, the sand and the

calculated AAPSD.



10/14


Since the dependence of the attrition rate on time twas found to

be described by Eq. (1), as a first assumption it is now assumed that

the attrition rate rb(t) is given by

rb t Kb uumf

dp exp bb

matt t mb0

& '24

where Kb and bb are material specific constants.

For grid jet attrition we are in the same situation: The influencing

parameters particle size dp, orifice diameter dor and jet velocity uorhave not been systematically varied in the present work. Therefore we

adopt the findings by Werther and Xi [30], who found that

rj~dp g d2or u3or: 25

Although the description of the time-dependence with an

exponential function is not as good as in the case of bubble-induced

attrition, we formulate

rj t Kj dp g d2or u3or exp bj matt t

mb0

& ': 26

The attrition in the cyclone occurs during the passage of the solids.

The cyclone attrition rate is therefore defined as the ratio of the mass

offines matt(n) produced during the nth passage to the mass of the

solids passing through the cyclone in this passage. According to the

experimental results in Section 2.2, rc is also described by an

exponential function. The governing parameters according to Reppen-

hagen and Werther [13] for cyclone attrition are the solids loading at

the cyclone entry e, the inlet velocity uc,in and the particle size dp.

With the same reasoning that was used above in the derivation of

Eqs. (24) and (26) the relationship determined by Reppenhagen and

Werther [13] is adapted here, which leads to

rc t Kc dp u2c;in

ffiffiffiffiffie

p exp bc matt t mc0;in

& '27

where mc0,in is the mass of the solids batch at the beginning of the setof experiments.

With the population balances the unsteady state changes in the

various parts of the fluidized bed system are monitored. For the

description of what happens during a given time interval in a given

part of the system with regard to attrition an information about the

stress history which the particle have previously undergone is

required. How far is a given particle fraction already attrited?

In previous work (Klett et al. [11]) on the time-dependence of ash

particle attrition in fluidized bed systems a stress history parameter

was used. This latter parameter basically indicates how far a given

particle is away fromthe steady stateof attrition.Unfortunately, for the

present RDFash such a steadystate is notreached, as hasbeenfoundin

the experiments described above. Therefore another description has to

be found. It is suggested now to characterize the state of the stresshistory by calculating the ratio of the mass offines matt produced

from the beginning of the attrition process, to the initial mass of the

same particle fraction m0. is taken as an indication of the amount of

stress the particle has already experienced,

mattm0

: 28

The mass offines matt can either result from the time-dependent

attrition induced by bubbles and grid jets, or from the attrition in the

cyclone, which is dependent on the number of passes or a successive

mixture of these mechanisms.

The particle population balancing calculation proceeds sequen-

tially from one module of the system to another. At the beginning of

each time-interval in a given module, the particle class i indicates itsstatus of the stress history by the mass of attrited fines matt,i, which

have originated from this particle class since its introduction into the

system, divided by the original mass m0,i. For this value ofthe actual

amountof attrition, which is occurring in the givenmodule duringthe

time-intervalt, can then be calculated as the product of attrition rate

and time-interval t, with the attrition rate being given either by

Eq. (24), (26) or (27), respectively.

3.3. The AAPSD concept

Upon entering the combustion chamber the fuel particles will be

heated and dried. Then they will devolatilize until finally the

Fig.14. Development with time of the mean particle diameter in the dense bottom zone

of the combustion chamber, the external heat exchanger and the cyclone overflow.

Fig.15. Comparison of the measured values of the pressure profile and the profile of the solids volume concentration with steadystate calculation results for the 100% load operating

conditions at the Neumnster plant.



11/14


carbonaceous matrix is burnt out leaving the primary ash behind. Thisprimary ash will then undergo fragmentation and attrition. The

determination of the primary ash particle size distribution (PAPSD)

and of its attrition characteristics is quite difficult. The question is

whether it is absolutely necessary to consider the ash fragmentation

and attrition processes inside the combustion system, when aiming at

the population balancing of the CFB system as a whole. In this respect

a comparison of the mean residence time of the ash particles in the

combustion system with the burnout time of coal particles in a

fluidized bed combustor can be helpful.

If we take the conditions of the Neumnster plant, we have an solids

inventory in the combustion chamber of 43 t, in the external heat

exchanger of 23 t and in the return line of 6 t, whichyields a total solids

inventory of 72t. Considering thetotal ash inputof 4.8 t/hand of sand of

0.8 t/h we obtain a total solids flux of 5.6 t/h, which leads a to mean

residence time of the solids in the system of roughly 13 h. On the other

hand the burnout time of coal particles with 13 mm in afluidized bed

combustoris between 1 and10 minaccordingto La Nauze [16].Ifwetake

into account that most of thefragmentation andattritionoccurs with the

fresh ash particles, this may be taken as a justification to neglect in a

first approximation ash formation, fragmentation and attrition influ-

ences in the calculation of the particle population balances for the

fluidized bed system. This simplified model of the fluidized bed

combustor is shown in Fig. 11, which now shifts the ash formation,

fragmentation and attrition effects out of the combustion chamber such

that attrited ash only is entering the combustor. This simplified model

canonlybe used forcases as theone treated here, wherethe ashparticles

do not or onlynegligibly changethere size for most of the time theystay

in the system. In cases where larger primary ash particles shrink over a

long period and are carried out as fines only, this concept would fail.From Fig.12 it follows that thefollowing mass balance holds for the

integral mass flow

:mAA :muf

:mfly

:mcoarse :mfine

:msand: 29

However, the analogous balance also holds for the particle size

class i

:mAA;i

:muf;i

:mfly;i

:mcoarse;i

:mfine;i

:msand;i: 30

4. Results and discussion

4.1. Determination of the attrited ash particle size distribution (AAPSD)

In the first step the measurements of the solids mass flows and

corresponding particle size distributions, which have been described

in Section 2.1 in detail were used to calculate the attrited ash particle

size distribution. For this purpose both, the fractional and the integral

mass balances Eqs. (29) and (30) were solved. Fig.13 shows the result

in comparison with the measured particle size distribution of the

various flows. The attrited ash particle size distribution is a very wide

distribution. It contains all particle sizes occurring in the system, from

the coarse ash particles, which end up in the bottom ash, to the veryfine particles in the micron range, which result from attrition

processes. The thus determined AAPSD is the starting point for the

population balance modeling of the CFB system.

4.2. Particle balance modeling with the AAPSD

Tofit the calculation results to measured values some adjustments

of the models had to be done. In the cyclone model the wall friction

coefficient of the brick-lined gas cyclone in the Neumnster plant was

set to 0=0.0075.

In order to consider the entrainment of large particles into the

external heat exchanger, theelutriationparameter in Eq. (5) was set to

fK=0.4.

The population balance modeling gives a dynamic description ofthe system behavior. In the present case the calculation was started

with only sand as the solid material in the system and ash with the

AAPSD was added. Fig.14 shows the developmentof themean particle

diameter in the dense bottom zone, in the external heat exchanger

(EHE) and in the cyclone overflow. We see that the bed material in the

dense bottom zone is getting coarser, while the inventory of the EHE

becomesfiner and there is practically no change in themean diameter

at the cyclone overflow. It takes of the order of 100 h to reach a steady

state.

Fig. 15 shows the pressure profile and the profile of the solids

volume concentration under conditions of steady state. The compar-

ison with the measurements shows that the calculated steady state is

in quite good agreement with the actual situation in the Neumnster

plant.

The particle balancing model allows us now to calculate solids

particle size distributions and mass flows at any point inside the

fluidized bed system. As an example Fig. 16 shows the comparison

between measured and calculated particle size distributions in the

bottom zone of the combustion chamber, in the EHE and in the

overflow of the cyclone. The matching between measurement and

calculation is excellent. Thesame is true forthe ashmassflows leaving

theplant, which arecompared in Table 3. An interesting information is

the solids mass flow into the cyclone. We see that for an input of fresh

ash of 4.8 t/h a circulating mass flow of 1343 t/h is achieved. This

enormous solids circulation rate, which corresponds to a mass flow

rate of 11.7 kg/m2/s in the upper part of the combustion chamber, is

one of the characteristic advantages of circulating fluidized bed

combustion systems, because it is responsible for the temperature

homogeneity.Another interesting feature of population balancing modeling is

that it allows to follow the fate of individual particle classes. As a result

it is possible to calculate the average residence times of different size

classes, as it is shown in Fig. 17. We see that particle sizes below 80 m

have an average residence time of a few minutes only, whereas

particles between roughly 100 and 1000 m have residence times

Fig. 16. Measured (symbols) and calculated (lines) particle size distributions in the

combustion chamber, the external heat exchanger and in the cyclone overflow for the

Neumnster plant, together with measured and calculated solids mass flows.

Table 3

Comparison of the measured and calculated ash mass flows at the Neumnster plant

Ash stream Measured Calculated

[kg/h] [kg/h]

Cyclone overflow 2259 2259Fine ash 1508 1535

Coarse ash 1390 1361



12/14


between 2040 h. Larger particles have residence times below 5 h,

because they are accumulating in the bottom dense bed and are

withdrawnwiththe bottom ash. As a practical conclusion onecan take

from Fig. 17 that, if supporting bed material is to be fed, one shouldchoose a size fraction between 200300 m because such a material

will be kept for a maximum time in the system.

4.3. Particle balancing modeling with consideration of attrition effects

When the attrition behavior of the bed material is known, the

PAPSDof thefuel ashcan be calculated by utilizingthe simulation tool.

The calculation is carried out with consideration of the particle

attrition, while the PSD of fuel ash fed is varied until the PSDs of the

solids discharged from the plant are identical to the measured PSDs.

The ash particle size distribution in the fuel feed is the identical with

the PAPSD.

The characteristic attrition parameters used for the calculation

were distinguished by fitting the correlations discussed in Section 3.2to the attrition rate measurements, shown in Figs. 57. The derived

attrition parameters are summarized in Table 4.

The PAPSD calculated by this procedure is depicted in Fig. 18. One

can see clearly that differences between the AAPSD and the PAPSD are

only observed for particle sizes below 200 m. Larger particles have a

limited entrainment rate from the combustion chamber and therefore

do not experience the cyclone attrition, which is the governing

attrition source here. The limited attrition the large particles are

facing, in combination with their comparatively short residence time

causes no distinct change to their particle size and thus they leave the

system almost unchanged. As it should be, the AAPSD contains more

finesthan thePAPSD, since theformer distributioncontainsthe effects

of fragmentation and attrition.

Further calculations were carried out for an alternative operating

point with a recycled ash mass flow of 3360 kg/h instead of 840 kg/h.

Both conditions were simulated using either the AAPSD, not

considering the particle attrition in the plant, or the PAPSD under

consideration of the particle attrition. Fig. 19 shows the results of the

four simulation runs. First of all, it is obvious that the particle size

distributions in the cyclone overflow and in the EHE vary to a minor

extent only, although the recycle feed rate was drastically changed.

In contrast, the particle size distribution in the dense bottom zone

of the combustion chamber becomes significantly finer with the

higher recirculation rate. One can further see that the symbols,

representing the results of the calculations using the PAPSD are

concurrent with the lines, representing the results using the AAPSD.

This can be taken as a justification for simulating the plant behavior

under various operating conditions by using the AAPSD without

consideration of the ash comminution effects inside the plant.

5. Summary and conclusions

A dynamic simulation tool to model the particle population of a

circulating fluidized bed combustor with external heat exchanger and a

recycling of a fine fraction of the bottom drain material into the

combustionchamberhas been developed. It considersthefluid dynamic

processes in the combustion chamber and in the gas cyclone, as well as

the particle attrition. Tohandle multiple solidstypes simultaneouslyand

to fulfill the massbalances, some of the fluid dynamic sub-models taken

from the literature were modified. The model allows to calculate the

solids massflowsas well as the corresponding particle size distributions

at any point inside the combustion system.

Upon entering the combustion chamber the solid fuel particles are

heated and dried. The devolatilization follows and finally the char is

burning out, leaving the primary ash behind. The particle size

Fig. 17. Residence time of particles in the Neumnster plant.

Table 4

Attrition parameters of the refuse-derived fuel ash

Attrition source Kb/c/j bb/c/j

Bubble induced attrition 3.10E13 [] 54.9

Cyclone attrition8:46E2

s2

m3

! 14.5

Jet attrition2:58E2

s2

m3

! 37.7

Fig.18. Measured ash particle size distributions and the AAPSD in comparison with the

PAPSD.

Fig. 19. Calculated PSDs for the operation with different ash recycle feed rates, carried

out using the AAPSD and the PAPSD, respectively, as feed PSDs.



13/14


distribution of the primary ash, i.e. the primary ash particle size

distribution, is then undergoing fragmentation and attrited. These

processes have been considered in the model such that the population

balances canbe calculated if the PAPSD is known. However, in the case

of a given industrial plant for RDF combustion it is very difficult to

determine the PAPSD with sufficient accuracy.

The measurements at the Neumnster plant have shown that theaverage particle residence time in the system is of the order of 13 h,

while on the other hand, coal particles burn-out times influidized bed

combustor are in the range of several minutes. Taking into account

that most of the fragmentation and attrition occurs with the fresh

particles and this also happens in a comparatively short time, ash

formation, fragmentation and attrition influences are neglected in the

calculation of the particle population balances for the fluidized bed

system. Instead a model is suggested, were the fuel enters with the

attrited ash particle size distribution (AAPSD) into the combustion

chamber. The AAPSD concept shift ash formation, fragmentation and

attrition effects out of the fluidized bed system. For a given plant the

AAPSD can be calculated from the ash flows and their particle size

distributions leaving the plant.

The model has been applied to a refuse-derived fuelfi

red plant ofStadtwerke Neumnster. The results of the measured and calculated

mass flows and particle size distributions are in good agreement. It is

shown that the AAPSD concept is sufficient to simulate the operating

behavior of the plant. The particle balancing model provides new

insides into the operating behavior. In particular the calculations of

the residence time of different particle classes in the system reveal a

very broad residence time distribution, ranging from several minutes

to a maximum of roughly 40 h. A size fraction exists between 100 and

300 m with a maximum residence time of about 40 h.

The simulation provides a means for examining possibilities to

control the particle size distribution in the combustion system. It is

shown howrecirculation of a fine ash fraction can be used to achieve a

finer bed particle size distribution in the combustion chamber.

Acknowledgments

The help of the staff of the Neumnster plant during the mea-

surement campaigns and with supplying operating data is gratefully

acknowledged. One of the authors (K. Redemann) would like to thank

Stadtwerke Neumnster GmbH for financial support.

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[3] U. Muschelknautz, E. Muschelknautz, Special design of inserts and short entranceducts to recirculating cyclones, in: M. Kwauk, J. Li (Eds.), Proc. 5th Int. Conf.Circulating Fluidized Beds, Beijing, P. R. China, 1996, pp. 597602.

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[12] E.U. Hartge,C. Klett, J. Werther,Dynamicsimulation of theparticlesize distributionin a circulating fluidized bed combustor, Chem. Eng. Sci. 62 (12) (2007) 281293.

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[14] M. Shaw, D. Garlan, SoftwareArchitecture: Perspectives on an EmergingDiscipline,

Prentice Hall, Upper Saddle River, New Jersey, 1996.[15] J.R. Grace, H. Bi, M. Golriz, Circulatingfluidized beds, in:W.-C.Yang(Ed.),Handbookof Fluidization and Fluid-Particle Systems, Marcel Dekker Inc., Pittsburgh,Pennsylvania, U.S.A., 2003, pp. 485546.

[16] R.D. La Nauze, Fundamentals of coal combustion influidised beds, Chem. Eng. Res.Des. 63 (1985) 333.

[17] B. Scarlett, Particle populations tobalance ornot tobalance, that is thequestion!Powder Technol. 125 (1) (2002) 14.

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[19] D. Kunii, O. Levenspiel, Fluidization Engineering, Ch. High-Velocity Fluidization,2nd Edition, Butterworth-Heinemann, London, 1991, pp. 201206.

[20] M. Colakyan, O. Levenspiel, Elutriation from fluidized beds, Powder Technol. 38(1984) 223232.

[21] VDI Heat Atlas, vol. 10, Springer-Verlag, Berlin, 2006.[22] E. Muschelknautz, M. Trefz, Secondary flow and short circuit flow at the dust

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[23] R.S.C.Rogers,A classification functionfor vibratingscreens, Powder Technol. 31(1)

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thecombustion ofa char ina circulatingfluidized bed,Combust. Sci.Technol. 73(1)(1990) 383394.

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Glossary

: Sharpness of the separation efficiency function of the cyclone strand, m e: Mass flowof solids entrained fromthe combustion chamber, enteringthe

gas cyclone, kg/sm v: Mass flow of solids going to the inner vortex of the gas cyclone, kg/sm AA: Mass flow of attrited ash fed into the combustion chamber, kg/sm coarse: Mass flow of the coarse ash fraction of the bottom drain material, kg/sm fine: Mass flow of the fine ash fraction of the bottom drain material, kg/sm fly: Mass flow offly ash, separated in the boiler and the multi-cyclone, kg/sm Ov: Mass flow in the cyclone overflow, kg/sm sand: Mass flow of sand fed into the combustion chamber, kg/sm uf: Mass flow of ultra fine ash, separated in the flue gas cleaning plant, kg/sVe: Cyclone inlet gas volume flow, m

3/sF: Separation efficiency function of the inner vortex of the gas cyclone, L: Dynamic gas viscosity, Pa s: Exponent for the calculation of exponential decay of the solids volume

concentration in the upper dilute zone, e: Gas loading in the cyclone inlet, g: Loading limit of the gas going to the inner vortex, g: Gas density, kg/m

3

s: Solid density, kg/m3

: Attrition history parameter, a: Offset value for the separation efficiency function of the cyclone strand,

Aw: Sedimentation area of the cyclone strand, defined in [21], m2

bb/j/c: Exponent for calculation of the bubble-induced, grid jet and cycloneattrition rate (aterial property),

cv: Solid volume concentration, cv: Solids volume concentration above the transport disengaging height, cvd: Solids volume concentration at the surface of the dense bottom zone, D: Modeling parameter for the separation efficiency function of the inner

vortex of the gas cyclone, dp: Particle diameter, mdv*: Particle size with force equilibrium on the radius with the maximum

cyclone vortex velocity, mdor: Orifice diameter of the grid jets, m

fK: Elutriation correction factor, h: Height above surface of dense bottom zone, m



14/14


hf: Total height of the upper dilute zone, mhi: Distance between the vortexfinder and the apex in the gas cyclone, mk: Exponent for the calculation of the loading limit in the gas cyclone, Kb: Parameter for the calculation of the bubble-induced attrition rate

(material property), Kg: Model parameter for the calculation of the loading limit in the gas

cyclone, Ki: Elutriation rate, kg/m

2/s

Kj/c: Parameter for the grid jet and cyclone attrition rate (material property),s2/m3

m0: Solid mass before any attrition occurred, kgmatt: Total attrited mass, kgnor: Total number of orifices of the grid jets, rb: Bubble-induced attrition rate, kg/kg/s

rc: Cyclone attrition rate, kg/kgrj: Grid jet attrition rate, kg/sT: Total separation efficiency function of the cyclone strand, T: Reduced separation efficiency function of the cyclone strand, u: Superficial gas velocity, m/sui: Maximum tangential gas velocity in the inner vortex of the gas cyclone,

m/sut: Terminal velocity, m/s

umf: Minimum fluidizing velocity, m/sut,50,e: Mean terminal velocity of the particles in the cyclone inlet, m/sut,50,v: Mean terminal velocity of the particles going to the inner vortex, m/sws,50: Terminal velocityof a particleshavinga probability of 50% to be separated

in the cyclone strand, m/s


redemann et al powdertechnol 2009

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