quantitative estimation of solids holdups at dense and dilute regions of

8/11/2019 Quantitative Estimation of Solids Holdups at Dense and Dilute Regions Of

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.Powder Technology 101 1999 183190

Quantitative estimation of solids holdups at dense and dilute regions ofcirculating fluidized beds

D. Bai a,), K. Kato b

aNatural Gas Technologies Center,, 1350 Nobel Street, Boucherille, Quebec, J4B 5H3, Canada

bDepartment of Biological and Chemical Engineering, Gunma Uniersity, Kiryu, Gunma 376, Japan

Received 5 February 1995

Abstract

This paper focuses on developing correlations for better prediction of solids holdups at the dense and dilute regions of circulatingfluidized bed risers based on experimental data from the literature and our laboratory. Analysis of the experimental axial profile of solids

holdup and the data on and ) has identified a critical solid circulation rate: saturation carrying capacity of gas, G ), whichsd s s

distinguishes two different variations of and ) with solid circulation rate. In the case of G -G ), and ) increase withsd s s s sd s

increasing solid circulation rate and may vary with other system properties, whereas and )are only the functions of gas velocitysd s

and gas-solid properties and change little with the solid circulation rate, the riser diameter, the solids inventory as well as the solid feeding

system in the case of G G G ). Based on these facts, more generalized empirical correlations for estimation of and ) ares s sd s

obtained. Comparisons with experimental data and the existing literature correlations confirmed the validity of the present correlations.

q 1999 Elsevier Science S.A. All rights reserved.

Keywords:Solids holdup; Dense region; Dilute region; Circulating fluidized beds

1. Introduction

Understanding of the solids distribution and flow behav- .ior in circulating fluidized bed CFB risers is the key to

successful design and scale-up of CFB systems. The solids

distribution governs the pressure drop occurring along the

CFB riser and is directly related to the solids residence

time within the riser. It also determines the gas-solid

interfacial area per unit of the mixture, which directly

affects gas-solid contact efficiency, heat and mass transfer

rates, and chemical reaction performance. Furthermore,

better prediction of solids holdups at the dense and dilute

regions of CFB risers is often required in CFB modeling.

Considerable experimental investigations have demon-strated that the axial variation of cross-sectional average

solids holdup for simplicity this will be referred to as.solids holdup in this paper is dependent on many factors,

such as operating conditions, solid properties, solid inven-

tory, as well as the geometry and system design configura-

)

Corresponding author. Tel.: q1-450-641-8147; Fax: q1-450-449-

4994; E-mail: [email protected]

w xtion 1 4 . Although many correlations for estimating solidsdistributions in the CFB risers are available in the litera-

.ture see Tables 1 and 2 , many of them are limited to the

employed experimental conditions, and extrapolation of

these correlations to different operating conditions often

leads to considerable deviation. Therefore, the present

work focuses on developing general correlations for better

prediction of solids holdups at the dense and dilute regions

of CFBs, which should be applicable in a wide range of

operating conditions.

2. Experimental

2.1. Axial profile of solids holdup

Fig. 1 illustrates an ideal axial profile of solids holdup

in CFB risers. This is typical when the riser has a smooth

exit at its top and an entrance structure with weak restric- w x.tion e.g., 13,5,6,812,19 . At a very low solids rate

.G s G , solids move co-currently upward with the gass s1In this case, a uniform axial distribution of solids is

observed. This flow pattern has been well defined as dilute

0032-5910r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved.

.P II: S 0 0 3 2 -5 9 1 0 9 8 0 0 1 5 9 -4


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( )D. Bai, K. Kator Powder Technology 101 1999 183190 185

Fig. 1. Typical axial profiles of solid holdup in circulating fluidized bed risers.

from a pattern where all particles are traveling upwards

with no axial concentration profile of solids to a mode

where there is axial concentration profile of solids. The

solid holdups, and ), in this case increase as thesd s .solid circulation rate increases, as shown in Fig. 1 b .

Further increase in the solid circulation rate will result

in a steep axial distribution in solids holdup and a continu-

ously increase in the solids holdup at both the lower and .upper regions G s G . When the solids circulation rates s4

.is increased to a value termed as G ) in this paper ats

which much of the solids begins to accumulate at thebottom of the riser, a typical S-shaped solid holdup distri-

bution starts to form. Further increasing solid circulation

rate to go beyond this critical point will have negligible

effect on the solids holdup at the dense and dilute regions ..see Fig. 1 b , although the dense region continues to

.grow G sG , G . If sufficient driving force is avail-s s6 s7able to push the solids into the riser, the dense region may

eventually fill the whole riser.

It is clear that the variations of solids holdups, andsd ), are significantly different according to the solidscirculation rate. In the case of G -G ), solids holdupss s

increase with increasing G , while they change little withsG in the case of G G G ). This fact has to be taken intos s saccount when developing correlations for the prediction of

solids holdups at the dense and dilute regions of circulat-

ing fluidized bed risers.

2.2. Variation of solids holdup at dense region, s d

The solids holdup at the bottom of the riser, ,sdbasically denotes the solids holdup when z s y`. It is

however determined as the value at z s0 from the axial

profiles of solids holdup reported in the open literature and

obtained in our laboratory.

The solids holdups, , for three risers of differentsddiameters are plotted against the solid circulation rate in

Fig. 2. For a given operating gas velocity U s 2.5 mrs ing

Fig. 2. Variation of solids holdup at dense region with solid circulation .rate for different riser diameters L s1.7 m . Data are obtained fromd

w xNishino 8 .


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Fig. 5. Variation of solids holdup at dilute region with solid circulation .rate for different riser diameters L s1.7 m . Data are obtained fromd

w xNishino 8 .

in Table 3, the experimental data covers a wide range of

operating conditions with different riser configurations and

solids employed. The data points are 204 for and 147sdfor ), respectively.s

It is seen that all the literature correlations did not

distinguish different variations of and ) at lowersd sand higher solid circulation rates. These correlations gener-

ally give poor prediction of and ), especially whensd sthey are applied to high solid circulation rates where

unacceptable errors are derived. The root-mean standard . .deviation SD and the relative deviation RD between

experimental data in Table 3 and values calculated from

the literature correlations are provided in Tables 1 and 2. It

is seen that the relative deviation from the existing litera-

ture correlations is generally higher than 50%. Better

correlations are thus needed in order to give reliablepredictions of and ) in circulating fluidized bedsd srisers.

4. Development of new correlations for and )sd s

To get reliable correlations for solids holdups, andsd . . ), two cases, 1 G-G ) and 2 G G G ), ares s s s s

needed to be considered separately, because there are quite

different variation trends in and ) with solid circu-sd slation rate. The solids holdups and ) are indepen-sd sdent of the riser diameter, the solid inventory, the solid

feeding system as well as the solid circulation rate, but

vary only with gas velocity and solid properties in the case

of G G G ). On the basis of this consideration, the litera-s sture data have been catalogued into two groups in the light

of the solid circulation rate larger or lower than G ),sw xwhich has been correlated by the authors 13 as follows

y0.44G )d r y rs p p g1 .85 0 .63s0.125 Fr Ar 1 . /m rg

.The correlation coefficient for Eq. 1 is 0.94, and the

relative deviation for calculation of G )is within 30%. Ins .Eq. 1 , the Archimedes number defined by Ars

3 . 2 )d r g r y r rm ranged from 4.7 to 1019 and thep g p g .0.5Froude number defined by Fr s Ur gd ranged fromg p

)41 to 226. The ratio of densities r y r rr varied fromp g g607 to 3607 in the correlation.

In trying to find a reliable and more general correlationfor , we have attempted various dimensionless groupssdthat might give unified representation of the experimental

data. Since inevitable scatter exists between the data ob-

tained in different researchers under different experimental

apparatus, we ended up with the following empirical corre-

lations,

y0.23 1.21 U r y rsd g p gy3s 1 q 6.14=10X / / U rs d g

=

y0.383Ug

2 .

/'gD

for G -G ), ands s1.13 y0.013

U r y rsd g p gs 1 q 0.103 3 .X / / U rs d g

for G G G ), where X

represents the solids holdup fors s sthe ideal case of uniform flow with slip velocity equal to

the terminal velocity of the individual particle. X

can besexpressed as

GsX s 4 .s

r U y n .p g t

Except for a few points, most of the experimental data can . .be predicted by Eqs. 2 and 3 within a relative deviation

less than 30%, as shown in Fig. 6. The average relative

deviation for all the experimental data listed in Table 3 is

17%. The deviation of this magnitude can be considered

small in view of the essential divergence among the data

used for the correlation. Compared to the existing literature .correlations Table 1 , it is evident that the present correla-

. ..tions Eqs. 2 and 3 give much better predictions of sdin a wide range of operating conditions.


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Fig. 6. Correlation of solids holdup at dense region under the cases of

G -G )and G GG ).s s s s

To estimate the solids holdup ), earlier studies usu-sally assumed the dilute region as fully developed flow,

X w x.giving )r s1 e.g., Ref. 14 . Recently, Ouyang ands sw xPotter 15 studied the consistency of circulating fluidized

bed experimental data on solids holdup available in the

literature, and found that the average of )rX

is 2.6s swith a standard deviation of 0.9. Given the fact that a

uniform dispersion of particles in a gas is always unstable

and can lead to formation of clusters of particles in aw xgassolid concurrent upflow 6,16 , which results in higher

slip velocity and thus a higher solids holdup X. Althoughs

Ouyang and Potters approach, as a first approximation, is

a better way for estimation of X, its accuracy, however,s

should be improved further from point of view of optimaldesign and operation of CFB reactors. As described above,

a more general correlation with relatively high accuracy

could be obtained by taking the different variation trends

of X

with G into consideration. Therefore, the collecteds sexperimental data including ours were catalogued accord-

ing to the solid saturation carrying capacity G ). As asresult, the following empirical correlations are proposed.

)s X0.214s 4.04 5 .X s

s

for G -G ), ands s

0. 5 y0.082 ) U r y rs g p g

s 1 q0.208 6 .X / / U rs d gfor G GG ).s s

The comparisons between the experimental data on

. .solids holdup ) and the calculations of Eqs. 5 and 6s . .are shown in Fig. 7 a for G -G ) and Fig. 7 b fors s

G G G ), respectively. It is found that for all 147 experi-s smental data points from seventeen literature publications,

. .the average relative deviations for Eqs. 5 and 6 are 12%

and 15%, respectively. The relative deviations are greater

than 30% for only a few points. 75% of the experimental . .data is predicted within 10% by Eqs. 5 and 6 . This

error should be considered acceptable considering the in-

evitable divergence among the data used for the correla-tion. Compared to the existing literature correlations Ta-

. . ..ble 2 , the present correlations Eqs. 5 and 6 are

recommended for the prediction of X

in a wide range ofsoperating conditions.

Fig. 7. Correlation of solids holdup at dilute region under the cases of

G -G )and G GG ).s s s s


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( )D. Bai, K. Kator Powder Technology 101 1999 183190190

5. Conclusions

The variation of the solid distribution in CFB risers is

analyzed. It is found that for the given operating condi-

tions, the solids holdups at the bottom dense and the upper

dilute regions increase with increasing solid circulation

rate at lower G values. Once the solid circulation rate issgreater than G ) where the S-shaped profile is formed, thes

solids holdups and ) appear to be independent ofsd sthe riser geometry parameters, the solid circulation rate, as

well as the solid inventory. In the light of these facts, more

general empirical correlations for estimation of andsd ) are developed. Comparisons with experimental datasand the existing literature correlations confirmed the valid-

ity of the present correlations.

6. List of symbols

3 . 2 ..Ar Archimedes number Ars d r g r y r rmp g p g

.D Riser diameter m .d Particle diameter mp

)0.5 .Fr Froude number Fr s Ur gdg p 2 ..G Solids circulation rate kgr m ss

2 ..G ) Saturation carrying capacity of gas kgr m ss .H Riser height m

.L Static bed height in slow bed or downcomer md . .U Superficial solid velocity U sG rr mrsd d s p

.U Superficial gas velocity mrsg .n Terminal velocity of a single particle mrst

.z Axial coordinate of the riser m

Greek letters

Average solids holdupsX

Solids holdup at uniform flow with slip velocitysequal to t

) Average solids holdup at dilute regions Average solids holdup at dense regionsdm Gas viscosity, Pa s

r Gas density, kgrm3gr Particle density, kgrm3p

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quantitative estimation of solids holdups at dense and dilute regions of

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