solids back-mixing in cfb boilers

Chemical Engineering Science 62 (2007) 561–573www.elsevier.com/locate/ces

Solids back-mixing in CFB boilers

Andreas Johanssona,b, Filip Johnssona,∗, Bo Lecknera

aDepartment of Energy Conversion, Chalmers University of Technology, SE-412 96 Göteborg, SwedenbUniversity College of BorAAs, SE-501 90 BorAAs, Sweden

Available online 14 September 2006

Abstract

The furnaces of circulating fluidized bed (CFB) boilers have substantially lower height-to-width ratios than most of the laboratory CFBrisers from which experimental investigations on riser fluid dynamics are published. Therefore, it is uncertain whether literature expressionsfor prediction of the distribution of solids and the thickness of the wall layers, derived from investigations in laboratory units, are applicableto boilers. In this work, data from laboratory units are compared with boiler data, and the accuracy of literature expressions for prediction ofsolids distribution, solids flow and wall layer thickness is reviewed. It is found that the height-to-width ratio does have a significant impacton the flow properties. Correlations based on experiments in laboratory units show poor agreement when applied to boilers. Modifications ofliterature expressions for prediction of solids flow and solids distribution are proposed, and an improved expression is formulated for predictionof the thickness of the wall layer.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Circulating fluidized bed; Scale-up; Hydrodynamics; Modelling; Fluidization; Particle; Wall layers

1. Introduction

There are several favourable features of circulating fluidizedbed (CFB) combustion technology that motivate a continued in-terest in further development of this kind of boiler, for instancefuel flexibility (various types of solid fuels can be burned in thesame boiler) and environmental advantages. Detailed knowl-edge of the gas and solids flow pattern in CFB boilers is aprerequisite for design and optimization of CFB boilers. Thereare numerous published studies on CFB fluid dynamics, butmost of these have been carried out in small laboratory unitswith geometries and operational conditions that are differentfrom commercial CFB boilers. Considering the fluid dynamics,as pointed out by Werther (1993), Johnsson et al. (1995) andLeckner and Werther (2000), there is an important differencebetween these units in the height-to-width ratio (Ht/De) thatinfluences the development of the wall layers. For boilers thisratio is typically less than 10, whereas it generally exceeds 20for laboratory units (cf. Johnsson et al., 1995). As correlations

∗ Corresponding author. Tel.: +46 31772 1449; fax: +46 31772 3592.E-mail address: [email protected] (F. Johnsson).

0009-2509/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2006.09.021

and expressions in the literature mainly are based on resultsfrom laboratory units with large height-to-width ratio, it is notclear to what extent literature expressions are suitable for boilerapplications. In addition, only a few observations have beencarried out in boilers and then only in some locations wheremeasurements were possible. Comparisons made so far indi-cate differences between the two types of units (see Werther,1993; Johnsson et al., 1995) and hence there is a need to inves-tigate the accuracy of correlations concerning the solids flow inthese devices. This work therefore investigates the influence ofthe furnace height-to-width ratio and tests the applicability ofliterature expressions to boilers. Focus is on the vertical distri-bution of solids, the thickness of the wall layers and the solidsflow in the transport zone, i.e., the solids back-mixing process.

Previous studies on the vertical solids distribution in CFBfurnaces (e.g. Zhang and Johnsson, 1991; Johnsson et al., 1995)have divided the CFB furnace into three zones: a dense bed,a splash zone, and an upper dilute zone which is sometimesreferred to as the transport zone. The dense bed has spatiallya more or less uniform time-average solids concentration, al-though there are large fluctuations in time due to the bubbleflow. Above the dense bed (in the splash zone) there is a strongback-mixing causing a rapid decay in the solids concentration

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562 A. Johansson et al. / Chemical Engineering Science 62 (2007) 561–573

over a few metres, followed by a transport zone with less pro-nounced back-mixing occurring mainly at the furnace walls.As also described by Brereton and Grace (1993), two back-mixing flow mechanisms have been identified: a homogeneoussolids-clustering flow dominating the lower part of the riser,and a core/wall-layer flow in the upper part. The latter mecha-nism results in the development of solids wall layers, in whichthe solids move downwards. The wall layers have higher solidsconcentration than the core region. Wall layers prevent radiativeheat transfer from the core to the wall and may cause erosion ofthe walls. High downward fluxes in wall layers of considerablethickness have been observed by several authors, for instanceCouturier et al. (1991), Leckner et al. (1991), Werdermann(1992) and Zhang et al. (1993, 1995). It has also been foundthat the wall-layer thickness in boiler furnaces increase withthe distance from the top of the furnace (cf. Johnsson et al.,1995, Zhang et al. 1995).

2. Theory

2.1. Vertical and lateral solids flow in the transport zone

Of the two back-mixing phenomena governing the decay inthe vertical solids concentration, the clustering flow has beensignificantly treated in the literature (see for example Kunii andLevenspiel, 1991, and references therein), but less has beenwritten about the separation of solids to the wall layers. For thatreason this section concerns the solids flow above the range ofthe ballistic movements in the splash zone, where the decay insolids concentration is dominated by back-mixing in the walllayers.

The continuity equation implies that the upward solids flowin the core of the transport zone is a function of solids concen-tration, mean velocity and cross-section area (Fc =�scv,cusA),which often is expressed per square metre as solids flux

Gc = cv,c�sus = �cus , (1)

where �s and cv,c are the particle density and the solids volumefraction in the core. A mass balance over a height element showsthat the difference between the net upward fluxes entering andleaving the element equals the net lateral flow out of the volume.Assuming that the net lateral solids transfer can be describedwith a constant lateral velocity, k (Bolton and Davidson, 1988),the lateral solids flow can be written as

dFl = �ck(U − 8�) dh. (2)

With the assumption of a wall-layer thickness � that is muchless than the furnace width (�>L) and applying the conceptof equivalent diameter, a mass balance over a height element(dFc + dFl = 0) yields after some rearrangement

−dFc

Fc

= 4k

Deus

dh. (3)

Here, it is assumed that the solids velocity in the core is inde-pendent of height in the furnace, and that the vertical variation

in the core area is negligible. Integration of Eq. (3) from anyheight h to h = Ht gives

Fc = �exit Aus,exit exp

(4k(Ht − h)

usDe

)= �exit Aus,exit exp(K(Ht − h)), (4)

where �exit and us,exit are the solids concentration and the solidsvelocity in the top of the furnace (at h=Ht). K=4k/usDe is thedecay coefficient in the transport zone. Kunii and Levenspiel(1991) derived the solids flow in the core in a similar way, butdescribed their decay coefficient, a, somewhat differently (cf.Eqs. (12) and (13)). Their model for prediction of the solidsflux yields

Gs = G∗s + (Gs0 − G∗

s ) exp[−a(Ht − h)], (5)

where G∗s and Gs0 are the solids flux in the top of the riser

and the solids flux just above the dense bed. The solids flowat the top of the furnace is approximately the same as the flowleaving the furnace into the cyclone—the external solids flux.There are several correlations for calculation of this flux (Biet al., 2000, and references therein), for example the correlationfrom Geldart (1986):

Gs = 23.7�gu0 exp(−5.4ut/u0). (6)

The downward flow in the wall layer can be described by sub-stituting the relationship between the core up-flow and the wall-layer down-flow,

Fw + Fc = Fw0 + Fc0 (7)

into Eq. (4), which gives the wall-layer solids flow as

Fw = Fw0 + Fc0(1 − exp(K(Ht − h))). (8)

Without exit effects, the initial values Fw0 and Fc0 are zero andFc at h=Ht is equal to the net solids flow, which at this heightis equal to the external recirculation flow. However, most CFBboilers have a more or less abrupt exit, and a fraction of solidsfails to leave the exit. Johnsson et al. (1995) therefore describedthe initial amount of solids down-flow Fw0 in proportion to thenet solids flow Gs as

Fw0 = −kbGsA, (9)

where kb is the back-flow ratio that represents the ratio of theinitial wall-layer flow to the solids flow through the furnaceexit. For large boilers this ratio is typically less than 0.1 (cf.Fig. 9). Combining Eqs. (7) and (9) results in

Fc0 = (1 + kb)GsA. (10)

Together with Eq. (4), the downward wall-layer solids flow cannow be expressed, in accordance with Nakamura and Capes(1973), as the solids recirculation ratio

Fw/(AGs) = 1 − (1 + kb) exp(K(Ht − h)). (11)

A. Johansson et al. / Chemical Engineering Science 62 (2007) 561–573 563

2.2. Vertical distribution of solids

Kunii and Levenspiel (1969, 1990) formulated a model todescribe the back-mixing in the freeboard above a bubblingbed, expressing the vertical distributions of solids as

� = x�∗ + (�0 − x�∗) exp[−a(hf )], (12)

where �0 and x�∗ are the solids concentration at the surface ofthe dense bed and in the top of the riser, and hf is the distancefrom the bed surface. This model was suggested to be valid forcirculating fluidized beds as well. Lewis et al. (1962) and Walshet al. (1984) found, for fine and coarse particles, respectively,that the decay coefficient a (cf. Eq. (12)) for bubbling beds canbe written as

au0 ≈ const., (13)

i.e., the decay in solids concentration above a bubbling bed isa direct function of the superficial velocity. This seems rea-sonable, since the decay above a bubbling bed is dominatedby back-mixing of solids and clustered solids thrown up intothe freeboard (due to high local gas velocities caused by thebubble eruptions). However, for circulating conditions there isan additional contribution from back-mixing in the wall layers,which must be included, as shown by Johnsson and Leckner(1995). Thus, based on previous models (cf. Kunii and Leven-spiel, 1969, 1990; Bolton and Davidson, 1988) Johnsson andLeckner derived an expression that included both of the above-mentioned back-mixing processes (clustering and wall-layerflows). They obtained

� = (�x − �2,Hx) exp(−a(h − Hx))

+ �exit exp(K(Hexit − h)), (14)

where a and K are decay coefficients corresponding to back-mixing from homogeneous clustering flow in the splash zoneand the core/wall-layer flow in the transport zone, respectively.Johnsson and Leckner (1995) showed that Eq. (13) is applicableto the decay in the splash zone (cf. Fig. 6c). They also suggesteda correlation for K, which was derived from experimental datayielding

K = 0.23/(u0 − ut ). (15)

A simpler expression is obtained if the flow balance of thesolids in the core region of the transport zone is considered.This balance consists essentially of three net flows of solids,one entering the core volume, the vertical solids flow (Fc,in),and two leaving the volume, the external solids flow (Fext) andthe lateral solids flow entering the wall layer (Fl). The densityof each flow depends basically on their masses of solids, as�s?�g . Then, the flow balance can be written

n1ms

VusA − n2ms

VusA − n3ms

VkUHtz = 0, (16)

where

Fc,in = n1ms

VusA, Fext = n2ms

VusA, Fl = n3ms

VkUHtz.

Here, ms represents the mass of an average-sized particle, U isthe circumference of the core region and Htz is the height ofthe transport zone. The amounts of solids in each flow (n1, n2and n3) are related, as the amount of solids entering the volumeequals the amount of solids leaving the volume, n1 = n2 + n3.Assuming a constant vertical solids velocity, us , the flow bal-ance expressed by Eq. (16) gives the net lateral solids velocity,

k = usA/UHtz = usDe/4Htz. (17)

A consequence, the lateral velocity of a particle reaching thewall layer increases with the width of the furnace. This sincean average particle can travel a longer distance in the lateraldirection before it leaves the core region in a wide furnacecompared to a narrow furnace (within a given residence time).According to the definition in Eq. (4), Eq. (17) yields the decaycoefficient

K = 1/Ht (18)

assuming that the height of the transport zone for tall boilers canbe approximated with the total height of the furnace, i.e., Ht ≈Htz. The decay coefficients a and K are further analysed below.

2.3. Wall-layer thickness

Based on previous observations (e.g. Johnsson et al., 1995)this work assumes the wall-layer thickness to increase withthe distance from the top of the furnace. Zhang et al. (1993)showed that the solids concentration of the wall layer is directlyproportional to the cross-sectional average solids concentration.Based on the experimental result in this work, it is found thatthe wall-layer thickness can be assumed to be proportional tothe solids concentration in the wall layer, i.e., the wall-layerthickness can be assumed to also be proportional to the cross-sectional solids concentration (see Fig. 10a) and that the solidsflow in the core nearly equals the external flow at the top ofthe furnace (GcAc ≈ GsA), the initial wall-layer cross-sectionarea Aw0 can be expressed from Eq. (9) as

Aw0 = kbA. (19)

With these assumptions the wall-layer area will, in pace withthe solids concentration, increase with the distance from thetop of the furnace. Consequently, the wall-layer area at eachheight is estimated by using the initial wall-layer area and theexponential expression corresponding to the decay in solidsconcentration in the transport zone (cf. Eq. (14)):

Aw = kbA exp(K(Ht − h)). (20)

With Aw ≈ �U the wall-layer thickness can then be written

�

De

= kb

4exp(K(Ht − h)), (21)

where De is the equivalent diameter of the furnace. It is likelythat the back-flow ratio kb depends on the exit geometry, pres-ence of internals, etc. However, derived from best fit to exper-imental data from boilers (see Fig. 9) the governing parameterseems to be the height-to-width ratio of the furnace/riser, as


expressed in the following fit to data:

kb = 0.0154(Ht/De). (22)

From data recorded both in boilers and in laboratory units,presented in Fig. 9, the back-flow ratio can be estimated as

kb = 0.0509 ln(Ht/De) − 0.015. (23)

Kim et al. (2004) summarized literature correlations for pre-diction of the wall-layer thickness. They also proposed anew correlation, which gives the best agreement with theirassembled data in the range 1.1�v∗ �11, 56�Frdp �312,0.028�(Us/Ug)�0.89, 15�(�p �s/�g �s)�373:

�

D0.85(u20/g)0.15

= 1.73(v∗)0.21(Frdp)−0.97

×(

�s cv

�g �

)0.16

: v∗ < 6.5, (24a)

�

D0.85(u20/g)0.15

= 0.53(v∗)0.32(

us

u0

)−0.55

×(

�s cv

�g �

)−0.70

: v∗ �6.5, (24b)

where

v∗ =[

�2g

g�g(�s − �g)

]1/3

×[u0 − Gs �

�s cv

].

They excluded data from large boilers and declared that out-side the investigated range of data, the correlation should beused with caution. The correlation proposed by Werther (1993),which gave the second best result in the survey of Kim et al.,is also included here for comparison:

�

De

= 0.55 Re−0.22t (Ht/De)

0.21((Ht − h)/Ht)0.73. (25)

In addition, Werther (2005) recently modified Eq. (25) for boilerapplication exclusively, yielding

�

De

= 1.1 Re−0.33t (Ht/De)

0.68((Ht − h)/Ht)0.92. (26)

3. Results and discussion

3.1. CFB furnaces versus laboratory risers

Table 1 summarizes the main characteristics of the in-vestigations compared. It is based on the data reviewed byJohnsson et al. (1995) and is updated with data from investi-gations in a 125 MWe boiler (Lafanechere and Jestin, 1995),a 250 MWe boiler (Wiesendorf et al., 1999) and a 235 MWe

boiler (Johansson, 2005). In Fig. 1, furnaces and risers are di-vided into two groups, showing that furnaces (upper part ofFig. 1) have height-to-width ratios of less than 10 and that lab-oratory risers typically have height-to-width ratios above 20.The first group is characterized by net solids fluxes of 1 to45 kg/m2 s and, as pointed out by Johnsson et al. (1995), byflat horizontal solids flux profiles surrounded by pronouncedsolids wall layers (Zhang and Johnsson, 1991). The secondgroup shows parabolic solids flux profiles as well as parabolicgas velocity profiles (van Breugel et al., 1969), and the netsolids flux ranges from 8 to 400 kg/m2 s under various flu-idization conditions. If fluid-dynamic scaling were applied, itwould, of course, be possible to operate a narrow unit underconditions that may resemble those of boilers, but this is usu-ally not done. It should be pointed out that the above differencein solids profiles is for the upper part of the riser/furnace abovethe splash zone or any dense region. In the group of boilerfurnaces there is a continuous decrease in solids concentrationwith height along the transport zone (see, for instance, data inFig. 5), which, together with the insignificant downward flux inthe core, indicates a continuous separation of solids along thefurnace walls. The flat flow profile and the continuous decayin solids concentration in the furnace of a CFB boiler implythat the profile is developing. Hence, the narrow and tall unitsappear then to be characterized by developed flow sufficientlyfar from the bottom.

In Fig. 2, wall-layer fluxes are plotted versus level of mea-surement position, expressed as the ratio of height of measure-ment position to width of riser/furnace. The wall-layer flux isnormalized by the net solids flux in an attempt to make the plotindependent of operating conditions. The wall-layer flux de-creases with increasing height until the measurement positionapproaches 10 times the equivalent diameter. At higher posi-tions in the risers, the flux becomes more or less independentof height. All boilers (open symbols) are within the region withan obvious height dependence, whereas laboratory units (filledsymbols) have little or no dependence on height. A similar dis-tinction between the two groups is seen in Fig. 3, which plotsthe wall-layer thicknesses of the units. Again, measurement po-sitions corresponding to h/De > 10, which are found only inthe laboratory units, show little or no dependence on height,whereas there is a clear height dependence when h/De < 10.From Figs. 2 and 3 it can be concluded that there is a distinctdifference between typical CFB furnaces and laboratory risers,and that the height-to-width ratio is a significant parameter,which needs to be considered when describing the flow patternin a CFB unit.

3.2. Vertical solids flow in upper dilute zone

Fig. 4 compares measured and calculated values of upwardsolids flow in the core (Eq. (4), Fig. 4a) and solids flow in thewall layers (Eq. (8), Fig. 4b), for the boilers investigated byapplying the decay coefficient K from Eq. (18) and the back-flow ratio kb from Eq. (22). The calculations are thus madefrom semi-empirical expressions. The plots include measure-ments from various heights, but only from the transport zone


Table 1Main characteristics of investigations compared

Boilers/investigations Ht Ht/De Solids �s dp T u Gs Axial solids profile(m) (dimensionless) (kg/m3) (mm) (◦C) (m/s) (kg/m s2)

12 MWth 13.5 8.7 Ash 2600 0.22 850 3.4–5.9 1–45 DecreasingJohnsson et al. (1995) 0.3372 MWth Couturier et al. (1991) 23.8 6.0 Ash 2500a – 850 6.4 36 Decreasing109 MWth Werdermann (1992) 28 5.5 Ash 2500 0.21 860 6.3 15 Decreasing165 MWth Zhang et al. (1995) 33.5 4.9 Ash 2600 0.28 830 4.6 < 5 Decreasing226 MWth Werdermann (1992) 32 4.0 Ash 2500 0.18 860 5.3 10 Decreasing125 MWe Lafanechere and Jestin (1995) 35 3.6 – – – – – – Decreasing235 MWe Johansson (2005) 44 3.3 Ash 2600 0.24 950 4.5 ∼ 7 Decreasing250 MWth Wiesendorf et al. (1999) 45 3.4 – 2780 0.26 – – –

Laboratory unitsvan Breugel et al. (1969) – – Al. 2700 0.040 Amb. 6 390 –Gajdos and Bierl (1978) 5.8 76 FCC 1600 0.061 Amb. 3 104 S-shapedMonceaux et al. (1985) 8 56 FCC 900 0.059 Amb. 2–7 22–44 Nearly const.Bader et al. (1988) 12.2 40 FCC 1714 0.076 Amb. 4.6 147 S-shapedRhodes (1990) 6.1 40 Al. 1800 0.064 Amb. 2.8, 4.0 42, 63 Nearly const.Werther et al. (1991) 8.5 21 Sand 2600 0.13 Amb. 3.6, 5.4 30, 75 –Werdermann (1992) 9.0 23 Sand 2600 0.12 Amb. 4.2 50 DecreasingZhang and Johnsson (1991) 8.5 43 Sand 2600 0.15 Amb. 3.0 8.5 Decreasing

aassumed value, –not given, Al. = alumina, Amb. = ambient conditions.

Fig. 1. Vertical measurement position and total riser/furnace height, both related to the equivalent cross-section diameter. The height-to-width ratio of the250 MWe boiler is the assumed value.

(i.e., above the splash zone) as the expressions only accountfor solids flow in this region. The solids flows are normalizedby the net solids flux to make the plots as independent of op-erating conditions as possible. Still, the plots can only serve asa basis for rough estimates, because of measurement inaccu-racies and effects of internals and exit configuration that havebeen neglected. It can be seen that Eqs. (4) and (8) give reason-

able results, except for the position in the top of the 235 MWeboiler. This position is situated on the wall opposite to thecyclone inlet, and this may explain why the predicted solidsflow is significantly higher than the measured flow. An obvi-ous disadvantage of Eqs. (4) and (8) is that the density of thegas–solids mixture in the top of the furnace, �exit, is needed asinput.


Fig. 2. Solids flow in the wall layer as a function of measurement position related to the equivalent diameter of the furnace/riser. The wall-layer flow is madedimensionless by division with the external flow. In the upper right corner the data is shown using logarithmic scale.

Fig. 3. Wall-layer thickness as a function of measurement position related to the equivalent diameter of the furnace/riser. In the upper right corner the data isshown using logarithmic scale.

Fig. 4. (a) Dimensionless upward flow in the core region. Comparison of measurements and predictions by Eq. (4). (b) Dimensionless downward flow in thewall layer. Comparison of measurements and predictions by Eq. (8).


Table 2Deviation between measured and predicted wall-layer thickness, using the expressions applied in this work

Investigation Equation Data from Average absolute deviation, �1 (%) Root-mean-square deviation, �2 (%)

This work (21)a Boilers 12 15This work (21)b Boilers 20 27This work (21)c Boilers and laboratory units 33 45This work (27) Boilers 25 43Kim et al. (2004) (24) Boilers 47 52Kim et al. (2004) (24) Laboratory unitsd 29 38Werther (1993) (25) Boilers 35 42Werther (2005) (26) Boilers 22 27Werther (1993) (25) Laboratory unitsd 93 146

�1 = 100N

N∑i=1

∣∣∣ prediction−experimentalexperimental

∣∣∣ , �2 = 100

√1N

N∑i=1

(prediction−experimental

experimental

)2.

akb obtained through measurement.bkb from Eq. (22).ckb from Eq. (23), laboratory units included.dData taken from Kim et al. (2004).

The estimation of the solids flow in the core suggested byKunii and Levenspiel (1991), Eq. (5), proved to be difficultto apply to boilers, since it requires the solids fluxes at theonset of the dilute region and in the top of the furnace asinput. Because of lack of densely spaced pressure taps (seeJohansson, 2005), this information was only found for the235 MWe boiler and the 12 MW boiler. Furthermore, Eq. (5)by Kunii and Levenspiel (1991) agrees rather poorly with theavailable data; the average deviation became 45% (the aver-age deviation from the measured data is calculated as sug-gested by Kim et al., 2004; see also Table 2). For compari-son, it can be mentioned that the average deviation in Fig. 4ais 19%, and that the correlation for estimates of the externalflux (Eq. (6)) resulted in an average deviation from measure-ment data at the top of the furnaces of 31%. It is suggestedthat Eqs. (4) and (8) be used when possible, and that Eq. (6)can be useful when determining the solid flow in the top ofthe furnace.

3.3. Vertical distribution of solids

Fig. 5a shows the vertical solids concentration in severalunits versus height in furnace, whereas Figs. 5b and c comparedata from two of the furnaces with various representations. Theconcentration profiles are similar in all units, and there is anobvious dependence on height. The solids concentration de-creases strongly within the first metres before it levels out after5–10 m height. The strong decay within the first metres is dueto the clustering flow in the splash zone, and the weak decay inthe transport zone is due to solids back-mixing in the wall lay-ers. The black line shows the predicted solids concentration forthe 235 MWe boiler, using Eqs. (14) and (18). The parametersgoverning the decay due to the clustering flow and the down-ward flow in the wall layers are further investigated in Figs. 6and 7. Figs. 5b and c compare the vertical solids concentra-tion, predicted by both Eqs. (12) and (14), with the measuredsolids concentrations in the 235 MWe boiler and in the 12 MWboiler. These units cover the range of height-to-width ratios of

the investigated boilers: they are the largest and the smallest ofthe boilers.

Fig. 5b shows that Eq. (12) underestimates the solids con-centration in the transport zone and predicts the same solidsconcentration at all heights above 10 m. The latter is due to thesingle exponential in Eq. (12), which does not capture the decayof concentration in the upper part of the riser. Eq. (14) overesti-mates the solids concentration in the freeboard when the decaycoefficient, K, is calculated according to Eq. (15), whereas theagreement with measurement data is rather good when K iscalculated according to Eq. (18). Fig. 5c shows a similar com-parison between measured solids concentrations in the 12 MWboiler and Eqs. (12) and (14). Eq. (14) agrees well, with K cal-culated either way (Eqs. (15) or (18)). Eq. (12) gives reasonableresults as well, but again, it predicts a constant solids con-centration throughout the transport zone. Both models requireinformation on the solids concentration above the dense bedand in the top of the furnace as inputs. This explains the goodagreement between predicted and measured values in positionscorresponding to these levels. In Fig. 5(a–c) the decay coeffi-cient a is obtained from Eq. (13) with the constant in Eq. (13)calculated as suggested by Johnsson and Leckner (1995), i.e.,as 4ut .

To clarify the relation between the decay coefficient a andthe vertical decrease in solids concentration above a dense bed,Eq. (13) is compared with literature data from various beds.Fig. 6(a–c) therefore gives measured values of the decay coef-ficient a, plotted against predicted values from Eq. (13). Thedata are taken from Walsh et al. (1984), Kunii and Leven-spiel (1991) and Johnsson and Leckner (1995), and the coef-ficient in Eq. (13) is obtained from a best fit to data. Fig. 6agives an example of the good agreement between Eq. (13) andthe decay in the freeboard above a bubbling, non-circulatingbed using data from Walsh et al. (1984). Kunii and Levenspiel(1991) suggested that this equation is applicable to the free-board of a circulating bed as well, but the agreement betweentheir assembled data from laboratory-scale risers (Fig. 6b) andEq. (13) is poor and not at all as clear as for bubbling beds.


Fig. 5. (a) Solids concentration versus height for various boilers. The black line indicates the predicted result for the 235 MWe boiler using Eqs. (13), (14)and (18). (b) Comparison of different models and data from the 235 MWe boiler. (c) Comparison of different models and data from the 12 MW boiler.

The reason is most likely that the vertical solids concentrationdepends on back-mixing effects in both the splash and trans-port zones. As mentioned above, the model of Johnsson andLeckner (1995) only devotes the decay coefficient, a, to thedescription of one of these effects, the decay due to cluster-ing flow (ballistic movement of solids in splash zone), whichin circulating beds is most important for back-mixing in thesplash zone. As a consequence, good agreement is reached forcirculating conditions as well with Eq. (13) compared to datafrom the splash zone, as shown in Fig. 6c, where the com-parison is done with data from Johnsson and Leckner (1995).In conclusion, Eq. (13) seems to be applicable only when theclustering flow is the dominant flow, as in the freeboard of bub-bling, non-circulating beds and in the splash zone of circulatingbeds.

The measured data on decay in solids concentration in thetransport zone provide less clear support for the correlation ofoperational parameters. Application of Eq. (15) with the decaycoefficient K as a function of gas velocity gives a rather poorfit to experimental data (average deviation of 66%) as shown inFig. 7a. As can be seen in Fig. 7b, a better prediction (averagedeviation of 34%) is obtained if K is calculated using Eq. (18),which implies that the decay in the freeboard only depends onthe furnace height. In two of the boilers investigated, the 12 and226 MW boilers, the cyclone inlet is situated in a relatively lowposition compared to the total height of the furnace. In thesecases the calculated decay coefficient is based on the heightof the cyclone inlet instead of the total height of the furnace.Eq. (18) agrees well with data from boilers, where verticalconcentration profiles depend on height, but it should obviously


Fig. 6. Comparison of the velocity dependence of the decay constant a (Eq. (13)) as reported in literature. (a) The decay above a bubbling bed (data fromWalsh et al., 1984). (b) The decay above the bed during circulating conditions for various CFB risers (data from Kunii and Levenspiel, 1991). (c) The decayin the splash zone during circulating conditions as obtained in the Chalmers boiler (data from Johnsson and Leckner, 1995).

Fig. 7. Values of the decay constant K , as given by Johnsson et al. (1995) and Johansson (2005), compared with the values predicted by (a) Eq. (15), averagedeviation 66%, (b) Eq. (18), average deviation 35%.

give poorer agreement with data from units where there is azero net flow of solids into the wall layers. The reason for thisis that no further decay then occurs in the solids concentration.The boilers investigated were all operated under typical boilerconditions, which may contribute to the accuracy of Eq. (18).

In summary, to predict the decay in the solids concentra-tion in a CFB unit, back-mixing phenomena in the splash andtransport zones need to be considered separately. These phe-nomena have different governing mechanisms. The clusteringflow, which produces the back-mixing in the splash zone, de-pends on the gas velocity. The downward solids flow in thewall layers, which causes the back-mixing in the upper dilutezone, seems to depend on the furnace height in the range ofdata investigated, rather than on the slip velocity.

3.4. Wall-layer thickness

Fig. 8a shows the agreement between boiler data on wall-layer thickness and Eq. (24). As mentioned above, Eq. (24)agrees well with data from laboratory units, which are the data

used as a basis for the correlation; but the result becomes poorerwhen compared with boiler data, as in Fig. 8a (see also Table 2),which are partly outside of the suggested range of applicationof Eq. (24). However, even within the range of validity thisequation is difficult to apply in boiler modelling and scale-up, since the solids concentration is needed as an input at allheights where the wall-layer thickness is to be estimated; thecorrelation requires measured or estimated solids concentrationas input (and consequently data from boilers where the solidsconcentration was not given are not included in Fig. 8).

Eq. (26) is suggested to be suitable for boiler conditions,and was correlated using data from boilers exclusively. Apply-ing this correlation to present data gives satisfactory agreementexcept for the 235 MWe boiler (open plus signs), as shown inFig. 8b. The reason could be that this boiler has a very lowheight-to-width ratio, in combination with the fact that Eq. (26)includes the Reynolds number with the equivalent cross-sectiondiameter as a characteristic length. The Reynolds number maywell be unsuitable in boilers where gas and solids profiles aredeveloping. In Fig. 8c, the data in Fig. 8b are plotted against the


Fig. 8. Dimensionless wall-layer thickness. Comparison of measurements and predicted values. (a) Predicted values using Eq. (24). (b) Values predicted byEq. (25). (c) Values predicted by Eq. (21) and the approximation of the back-flow ratio (Eq. (22)). (d) Values predicted by Eq. (21) and applying measuredvalues of the back-flow ratio (Eq. (22)).

Fig. 9. The back-flow ratio, kb , as a function of the height-to-width ratio. The fit of Eqs. (22) and (23) are shown.

expression given in this work (Eq. (21)). There is slightly bet-ter agreement, but what is more important is that Eq. (21) givesa rather satisfactory result also for the 235 MWe boiler. Theback-flow ratio, kb, and the decay coefficient, K , in Eq. (21)are obtained from Eqs. (22) and (18). If kb is instead obtainedfrom integration of measured solids flux profiles in the top ofthe furnaces, as in Fig. 8d, the agreement can be further im-proved (cf. Table 2). However, this method requires measure-ments in the furnace, which makes the method ineffective for

design purposes, even though it demonstrates that high accu-racy can be achieved. The back-flow ratio depends on the fur-nace geometry (design of the exit region, presence of internals,etc.) and will thus be rather unique for each furnace. Still, anattempt was made to describe this parameter by using only theheight-to-width ratio of the furnace. The agreement is shownin Fig. 9. Here, the back-flow ratios were obtained from bestfit to the measured wall-layer thicknesses, as empirical valuesare lacking. Since data were taken from several positions, the


Fig. 10. (a) Dimensionless wall-layer thickness versus the cross-sectionalsolids concentration. (b) Wall-layer thickness versus reduced distance fromtop of furnace.

plotted back-flow ratios show the average value for each fur-nace (low variations were found). Fig. 9 includes also the fit ofEqs. (22) and (23).

A general picture of the parameters governing the thicknessof the solids wall layer is given in Fig. 10. Here, the wall-layer thicknesses are plotted against the corresponding solidsconcentration (Fig. 10a) and the distance from the top of thefurnace (Fig. 10b). The wall-layer thicknesses show an obvi-ous increase with increasing values of these parameters. Theseperformances support the assumption made behind Eq. (21).In fact, the connection between wall-layer thickness and solidsvolume concentration in Fig. 10a is clear enough to formulatea simple correlation, which can be applied with reasonable ac-curacy in cases where the vertical solids distribution is known.Thus, the wall-layer thickness can be correlated to the corre-sponding solids concentration (Fig. 10a), keeping in mind thatfor a given set of operating conditions the solids concentra-tion depends on height in the furnace which is reflected in the

height dependency of the wall-layer thickness (Fig. 10b). Thecorrelation yields (see also Table 2)

�

De

= 4.516 cv + 0.008. (27)

The absolute average and the root-mean-square deviation be-tween measured and calculated values of the wall-layer thick-ness, using the expressions for calculation dealt with in thiswork, are given in Table 2. The deviations between predictedvalues (using Eqs. (24) and (25)) and data from laboratory unitsin Table 2 are taken from Kim et al. (2004). There exist manyways to calculate the wall-layer thickness in a boiler with rea-sonable accuracy, for example Eqs. (25)–(27). These equations,however, are developed from correlations with the same datawhich they are compared to. A new method (Eq. (21)) was sug-gested in this work, giving the highest accuracy with knownvalues of the back-flow ratio. If this ratio has to be calculated,using the suggested correlations, the accuracy becomes similarto those of Eqs. (25)–(27). Yet in contrast to these equations,Eq. (21) seems to be able to also predict the wall-layer thick-ness in large power boilers such as the 235 MWe boiler withreasonable accuracy.

4. Conclusions

The low height-to-width ratio of the furnace in a typical CFBboiler results in a significant height dependence on fluid dy-namic parameters throughout the furnace, which is not seen tothe same extent in central and upper parts of a typical laboratoryunit. Consequently, it may be misleading for boiler applicationsto use empirical correlations based on experiments in labora-tory units. It was found that the decay in solids concentrationcan be described as a function of velocity in the splash zone,but that the decay due to separation of solids to the wall layer,for the conditions studied, is a function of height, as suggestedin Eq. (18), rather than of gas velocity. Literature expressionsfor prediction of the solids flow in the core (Eq. (4)), the solidsflow in the wall layers (Eq. (11)), and the vertical solids con-centration (Eq. (14)) showed better agreement with boiler dataafter modification leading to Eq. (18). Previous expressions forwall-layer thickness, which were derived from best fits to datafrom laboratory units, give rather poor results when comparedto boiler data. Here, a new expression is suggested (Eq. (21))that predicts the wall-layer thickness in boilers with reasonableaccuracy.

Notation

a decay coefficient, 1/mA cross-section area, m2

Ac core cross-section area, m2

Aw wall-layer cross-section area, m2

cv solids volume fraction, dimensionlesscv cross-sectional average solids holdup, dimension-

less


cv,c core solids volume fraction, dimensionlesscv,w wall-layer solids volume fraction, dimensionlessdp particle diameter, mDe equivalent diameter, mFc, Fw vertical solids flow in the core and wall layer, kg/sFc,in, Fext vertical core solids flow in and out of the transport

zone, kg/sFc0, Fw0 initial values at h = Ht , kg/sFl lateral solids flow, kg/sg acceleration due to gravity, m/s2

Gs solids flux, kg/m2 sGs0 solids flux above the dense–dilute interface,

kg/m2 sG∗

s saturated solids flux, kg/m2 sGc core solids flux, kg/m2 sGw wall-layer solids flux, kg/m2 sh height above air distributor, mhf height above dense bed, mHexit height (above air distributor) of centre of gas outlet,

mHtz height of the transport zone, mHt total height of furnace, mHx height of bottom bed, mk net solids transfer coefficient, m/skb back-flow ratio, dimensionlessK decay coefficient, 1/mms mass of an average-sized particle, kgn1, n2, n3 amount of solids in Fc,in, Fext and Fl , dimension-

lessu0 superficial gas velocity, m/sus solids velocity, m/sut terminal velocity, m/sU circumference of the furnace, mv∗ dimensionless slip velocity, dimensionlessV volume, m3

Greek letters

� wall-layer thickness, m� voidage, dimensionless�s cross-sectional average voidage, dimensionless�g gas viscosity, kg/m s�exit solids concentration at gas exit, kg/m3

�g gas density, kg/m3

�s solids density, kg/m3

�x solids concentration in bottom bed, kg/m3

�2,Hx solids concentration due to dispersed phase at upperposition of bottom bed, kg/m3

�c solids concentration in the core, kg/m3

�0 solids concentration at the surface of the dense bed,kg/m3

Acknowledgement

This work is financed in part by the Swedish Energy Agencyand the European Commission within the fifth Framework Pro-gramme, under Contract ENK5-1999-00005. The assistance of

Elektrownia Turow and Foster Wheeler Energia OY is greatlyappreciated.

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