Ind. Eng. Chem. Res. 2002, 41, 4949-4956
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Pressure Balance Model for Circulating Fluidized Beds with a Loop-seal Sung Won Kim, Sang Done Kim,* and Dong Hyun Lee Department of Chemical and Biomolecular Engineering and Energy & Environment Research Center, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea
A pressure balance model is proposed to determine the flow dynamics around a circulating fluidized bed (CFB) loop. The model contains the effect of exit configuration on the axial pressure profile in a riser with an abrupt exit. In the model, the decay and the reflux constants have been correlated with the pertinent dimensionless numbers and geometry of the exit in the riser. The practical operating conditions in the solid recycle system with a loop-seal are considered for CFB combustor applications. The predicted pressure profile along the height from the proposed model exhibits a good agreement with the experimental data. Introduction Circulating fluidized beds (CFBs) have been commercially employed in numerous gas-solid contacting processes such as combustors, coal gasifiers, and catalytic reactors. In general, a CFB is composed of a riser, cyclone, downcomer, and solids feeding system. In a CFB, gas-solid flow behaviors in the riser and solid circulation rate are strongly dependent upon pressure drops of different sections. To obtain distribution of solids inventory, not only the mass balance but also the overall pressure balance is needed. Also, a pressure balance model with reasonable submodels for all parts of a CFB is required to analyze the flow behavior and to provide information for the design and operation principles.1 It has been known that the axial solids holdup in the riser is largely affected by operating conditions and the exit geometry.2-5 However, the reported models1,6-11 did not consider the exit effect in the riser as summarized in Table 1. Also, the models adopt nonmechanical valves in solids recycle systems for many applications in commercial CFBs. However, the models on CFB systems with loop-seals are comparatively sparse despite their wide application. Recently, Lim et al.11 proposed a pressure balance model for CFB with a loop-seal. They adopted the mechanical valve equation to predict pressure drop across the loop-seal. However, it is not proper to adopt such an equation because of the different operation principles between the mechanical and nonmechanical valves.12,13 Many previous models have considered a solids flow state in a downcomer simply as the moving bed or minimum fluidized state (Table 1). Nonmechanical valves in many CFB systems including CFB combustors are operated at a bubbling fluidizing state by a high aeration rate in a solids recycle system to prevent formation of clinkers and plugging by ash.14,15 Therefore, the hydrodynamic assumptions are restricted in the given operating ranges and may differ from reality in many applications of nonmechanical valves. In the present study, a pressure balance model for the entire loop of CFB with a loop-seal is proposed. In * To whom correspondence should be addressed. Tel: 8242-869-3913. Fax: 82-42-869-3910. E-mail:
[email protected].
the model, the effect of exit configuration on the axial pressure profile in the riser is considered at the practical operating conditions in a solids recycle system with a loop-seal for CFB combustor application. Experimental Section Experiments were carried out in a CFB with a Plexiglas riser (0.1 m i.d. by 7.6 m height) as shown in Figure 1. The solid particles used in this study were silica sand that is similar to recycling ash in CFB combustors,15 and their properties are shown in Table 2. The solid particles were supported on a perforated plate distributor located between the main column section and an air box into which air was fed through a pressure regulator, an oil filter, and a calibrated flowmeter. The top structure had an abrupt exit that is commonly used in CFB combustors. In the exit configuration, there was a 90° takeoff of a connector (0.03 × 0.08 m) at 0.10 m below the top of the riser leading to the cyclone inlet. The details of the experimental facilities can be found elsewhere.16 Entrained particles from the riser were collected by primary and secondary cyclones. Solid particles from the cyclone were transferred into a loop-seal (0.10 m i.d.) through a downcomer (0.10 m i.d.) and were fed to the riser through a loopseal that regulates the solid circulation rate (Gs) by aeration.12 At steady state, Gs around the CFB loop was measured by diverting the entire solids flow from the two cyclones into a measuring column. The descending solid circulation rate was measured by timing the descending particles along a known distance in a transparent measuring column.6,12,17 The Gs was determined from the time and the bulk density measured previously in the measuring column. Pressure taps were mounted flush with the column wall and covered with a screen to prevent solid particle leakage from the bed. Pressure transducers (Valydine P306D) were connected to pressure taps along the column height to measure pressure drops between different locations. The pressure signals from the pressure transducer were amplified and sent via an A/D converter to a personal computer for recording. Solid holdup (s) was calculated from the measured pressure drop between the two locations.18
10.1021/ie0202571 CCC: $22.00 © 2002 American Chemical Society Published on Web 08/30/2002
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Table 1. Features of Previous Pressure Balance Models of CFBs riser author
exit structure
Rhodes and Geldart (1987)6 Yang (1988)7 Breault and Mathur (1989)8 Mori et al. (1991)9 Hannes et al. (1993)10 Lei and Horio (1998)1 Lim et al. (1999)11 this study
smooth smooth smooth abrupt abrupt abrupt abrupt abrupt
a
solid feeding system flow state
exit effecta
type
N N N N Y
mechanical valve (orifice) mechanical valve (orifice) pneumatic valveb J valve mechanical valve (orifice) L valve with orificea loop-seala loop-seal
downcomer solid flow state
moving bed flow moving bed flow moving bed flow minimum fluidized bed moving bed flow minimum fluidized bed moving bed flow fluidized bed
slow bed slow bed moving bed flow minimum fluidized bed slow bed minimum fluidized bed minimum fluidized bed fluidized bed
Y: considered. N: not considered. b Application of the mechanical valve equation.
(i) Riser Pressure Drop, ∆Pr. The riser is divided axially into the lower dense and upper dilute regions. In the lower dense region, a constant solid fraction is assumed, where the effects of particle acceleration, particle friction, and gas friction on the pressure drop can be neglected.1,19 In the upper dilute region, the axial solid holdup profile is assumed to decrease exponentially from the upper limit of the dense region to the exit region. From these assumptions, pressure drop of the riser (∆Pr) can be expressed as
∆Pr ) Fsg(sdzd +
∫zzs dz)
(2)
d
For the axial profile of the solid fraction in a CFB riser, several approaches have been proposed. In this study, the following simple expression is adopted:20
s - s∞ ) exp[-a(z - zd)] sd - s∞
(3)
Concerning the decay factor (a) in eq 3, the following correlation was recently proposed by Lei and Horio.1
aDr ) 0.019
Figure 1. Schematic diagram of the experimental apparatus: (1) riser, (2) cyclone, (3) downcomer, (4) loop-seal, (5) sampling bottle, (6) solid supply tank, (7) butterfly valve; (D) distributor, (P) pressure tap. Table 2. Physical Properties of Silica Sands and Fluidizing Gas particles mean diameter [µm] apparent density [kg/m3] gas gas density [kg/m3] Umf [m/s]
this study
Lim et al.11
silica sand 240 2582 air 1.185 0.048
mineral sand 130 4400 nitrogen 1.200 0.024
Results and Discussion 1. Pressure Balance Model. In a CFB, pressure in a loop should be balanced for stable operation. Pressure drop across the downcomer can be expressed as17
∆Pdc ) ∆Pls + ∆Pr + ∆Pc
(1)
where ∆Pdc ) PDB - PDT, ∆Pls ) PDB - PRB, ∆Pr ) PRB - PRT, and ∆Pc ) PRT - PDT (Figure 1).
[ ] [ ] ( ) Ug
-0.32
xgDr
Gs FgUg
-0.22
Fs - Fg Fg
0.41
(4)
For solids holdup in the dense phase of the riser, Bai and Kato’s21 equation was applied:
sd *s
) 1 + 0.00614
( ) ( )( )
(5)
s∞ ) 4.04*1.214 s
(6)
Ug Gs/Fs
-0.23
Fs - Fg Fg
1.21
Ug
xgDr
-0.383
where /s ) Gs/[Fs(Ug - Ut)]. Equation 3 in conjunction with eq 4 predicts well s distribution in the risers with the smooth exit. Recently, several studies2-4,22-24 have determined the effect of exit geometry of CFB risers on the axial s profile. If the exit has a sharp right angle to the vertical upflowing suspension, the top of the riser acts as a crude gassolid separator.2 The particles cannot negotiate the sharp turn, reflect off the top, and recirculate internally down along the walls of the riser. As a result, an area of densification is created around the exit and, depending on the operating conditions and the severity of the exit restriction, may extend a long way down the length of the riser. The deviation from the axial s distribution in the riser with a smooth exit is shown to be large in the case of an abrupt exit.3,5
Ind. Eng. Chem. Res., Vol. 41, No. 20, 2002 4951 Table 3. Summary of Experimental Studies on CFB Riser Exit Effects riser
particle properties dp [µm]
Fs [kg/m3]
resin
500
1400
5.20 6.24
4-32
0.10
sand
148
2650
3.7-9.2
9-89
0.32 0.10 0.20 0.055
catalyst sand sand sand
50 220 230 240
1420 2500 2600 2582
3-4.5 5.0-5.5
17-39 26-46
height [m]
project height [m]
diameter [m]
exit diameter [m]
Zheng and Zhang (1994)22
5.25
0.10
0.05 0.06 0.07
Brereton and Grace (1994)23
9.3
0.152
Schoenfelder et al. (1996)24 Pugsley et al. (1997)4
15.6 6.0 12.0 7.6
0 0.15 0.45 0.65 0 0.46 0.09 0 0.10 0.10
0.40 0.10 0.20 0.10
author
this study
operating variables
type
Ug [m/s]
4.5
Gs [kg/m2‚s]
5-46
Kunii and Levenspiel3 proposed the following equation to describe the deviation:
∆sr ) Cese exp[-ae(Hf - zf)]
(7)
where Ce is a reflux constant and ae is a decay constant affected by the exit geometry. In this study, the empirical correlations are proposed for ae and Ce in eq 7 based on previous4,22-24 and the present studies (Table 3).
aeDr )
[
][
(Ug - Ut)2 1.27 gDr
1/2
] () ( ) -1/2
Gs
Fs(Ug - Ut)
De Dr
-1/2
Fs - Fg Fg
-1
(8)
with a correlation coefficient of 0.90 and a standard error of estimate of 1.73.
Ce ) 0.046
[
(Ug - Ut) gDr
][
2 1/2
Gs
Fs(Ug - Ut)
] ()() -1/3
He dp
1/3
De Dr
Figure 2. Comparison between measured and calculated aeDr.
-3/4
(9)
with a correlation coefficient of 0.92 and a standard error of estimate of 0.012. The range of variables of eqs 8 and 9 covers 2 e [(Ug - Ut)2/gDr] e 45, 0.000 84 e Gs/[Fs/(Ug - Ut)] e 0.00740, 0.47 e De/Dr e 1.00, 50 e He/dp e 5800, and 1180 e (Fs - Fg)/Fg e 2235. The calculated aeDr and Ce values from eqs 8 and 9 predict well the experimental data of the present and previous4,22-24 studies as shown in Figures 2 and 3, respectively. To determine the axial s distribution in the riser with an abrupt exit, eqs 8 and 9 are employed in conjunction with eq 7, and s values from eq 3 are corrected by ∆sr from eq 7. The predicted axial s profiles from eq 3 in conjunction with eq 7 are shown in Figure 4. As can be seen in Figure 4a, Lei and Horio’s1 correlation evidently shows a serious deviation near the riser exit. The calculated values in the present study with the ∆ correction on the exit are well matched to the experimental data. Pugsley et al.4 proposed a model based on the coreannulus structure that is affected by the riser exit as shown in Figure 4b. However, the model prediction is not successful at the some axial location in the riser because of the assumptions of gas-solid flow as a fully developed flow and linear decrease of s by the exit effect at the region,4 whreas the present model predicts well s variation over the entire riser height. Finally, ∆Pr can
Figure 3. Comparison between measured and calculated Ce.
be obtained from eq 2 in conjunction with eq 5 and the correction of s values. (ii) Pressure Drop between the Riser Exit and the Cyclone Outlet. The pressure drop between the riser exit and the cyclone outlet is composed of pressure drops across the horizontal section from the riser exit to the cyclone inlet and cyclone.
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Figure 4. Prediction of solid holdup in risers.
(1) Pressure Drop in the Horizontal Section between the Riser and Cyclone. On the basis of the study of Patience et al.,25 the pressure drop in a horizontal section between the riser and cyclone is taken to be 2
∆Ph ) Gsh(2.84 + 0.0108Ugh )
(10)
where Gsh and Ugh are the solid circulation flux and gas velocity in the horizontal section, respectively. (2) Cyclone Pressure Drop, ∆Pc. The pressure drop across a cyclone is assumed to be dependent only on the gas velocity1,7
∆Pc ) Ccy(Ar/Ac)2Fg
Ug2 2
(11)
where Ar and Ac are respectively the riser area and the inlet area of a cyclone. The empirical coefficient (Ccy) is chosen as 10.0.1,7 (iii) Downcomer Pressure Drop, ∆Pdc. Because the downcomer is operated in a bubbling fluidized state,15 the pressure drop is that required to support the particle weight in the bed
∆Pdc ) Fs(1 - dc)gHdc
(12)
where Hdc is obtained from a mass balance as in eq 19. Loop-seal Pressure Drop, ∆Pls. A loop-seal consists of weir and vertical aeration sections.12,13 ∆Pls can be expressed as
∆Pls ) ∆Pw + ∆Pva
(13)
In the weir section, solid flow is in a fluidizing state so that (∆P/L)w can be expressed as
(∆PL)
w
) Fs(1 - )g
(14)
In a commercial CFB combustor, a loop-seal is operated at higher aeration rates. Thus, the solid in the loop-
seal and downcomer is in a highly expanded state.15 To obtain voidage () in the bed, Grewal and Saxena’s correlation26 is adopted, i.e.
)
{ {[
µFgUo 1 0.4 + 4 2 2.1 dp [Fg(Fs - Fg)]φs2g
] }} 0.43 1/3
(15)
The obtained from eq 15 is used in eqs 12 and 14. The obtained ∆Pva values in the present and previous studies12,13,27 have been correlated with Gs, particle properties, and the loop-seal diameter as
(∆PL)
va
) 0.0056Gsd0.51Fbulk2.01dp-0.97Dls-0.76 (16)
with a correlation coefficient of 0.94 and a standard error of estimate of 623 Pa m-1. The range of variables in eq 16 covers 0 e Gsd e 70 kg/m2‚s, 877 e Fbulk e 1824 kg/m3, 65 e dp e 240 µm, and 0.08 e Dls e 0.10 m. ∆Pls can be calculated from eq 13 in conjunction with eqs 14-16. A comparison of the measured and calculated values, ∆Pls, from eq 13 is shown in Figure 5 at different bottom aeration rates. As can be seen, eq 13 describes well the effect of the solid circulation rate on ∆Pls at different bottom aeration rates. 2. Material Balance. The total amount of solids in the whole system, Mt, is expressed as
Mt ) Mr + Mdc + Mls
(17)
where Mr, Mdc, and Mls are mass of the solid in the riser, downcomer, and loop-seal, respectively, that can be calculated by the equations
Mt ) ∆PrAr ) Fsg(sdzd +
∫zzs dz)Ar d
(18)
Mdc ) Fs(1 - dc)gHdcAdc
(19)
Mls ) Fs(1 - ls)gLlsAls
(20)
where dc and ls can be obtained from eq 15.
Ind. Eng. Chem. Res., Vol. 41, No. 20, 2002 4953
Figure 5. Effect of the solid circulation rate on the pressure drop across a loop-seal.
Figure 7. Comparison of the predicted pressure loop profile with experimental results.
Figure 8. Prediction of the pressure loop profiles with variation of the solid circulation rate.
Figure 6. Computational algorithm of the CFB pressure balance.
3. Model Validation. For solid distributions in the riser and pressure balance around the CFB loop, the proposed model is applied using the computation procedure, as shown in Figure 6. For pressure distribution around the CFB loop with different Gs at the given Mt and Ug, the calculated results are compared with the experimental data in Figure 7. As can be seen, the height of the solid bed in
the downcomer, Hdc, decreases and s and ∆P in the riser increase with increasing Gs at the given Ug and Mt. The predicted pressure profile describes well the experimental data and shows especially good agreement in the upper region of the riser that affected by the exit configuration. In a CFB with a loop-seal as a nonmechanical valve, Gs varies with the aeration rate in the loop-seal.12 As can be seen in Figure 8, Gs increases with an increase in the vertical aeration rate (UA) at the given bottom aeration rate (UBA) in the loop-seal, system inventory, and gas velocity in the riser. At the same time, ∆Pr increases with increasing solid holdup in the riser because of the enlarged exit effect. The pressure drop across the loop-seal, ∆Pls, increases with the increment of ∆Pva (eq 16) because of an increase of Gs. The solid height in the downcomer increases with increasing bed
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Figure 9. Prediction of the pressure loop profiles with variation of the solid inventory.
(Mt) in a CFB because of the increment of the total pressure drop in a downcomer.12 The effect of the system inventory on the pressure balance at the given Ug and aeration rate is shown in Figure 9. As can be seen, ∆Pr, ∆Pls, and ∆Pdc increase with an increase in Mt at the given UBA and UA due to the increment of Gs. The model predicts well the variation of Mt in a CFB system. With a CFB system having an abrupt exit (T bend) in a riser (0.04 m i.d. and 1.9 m height) with a loopseal, Lim et al.11 proposed a model to predict the pressure profile in the loop, as shown in Table 4. As can be seen, they adopted the pressure drop equation by changing the flow direction at the riser exit to accommodate the exit effect. However, their equation cannot describe well the solid holdup distribution in the riser with the abrupt exit. Also, the simple mechanical valve equation for ∆Pls in the model produced a high error bound of (30%11 because the loop-seal cannot be considered as a mechanical valve that is composed of one component (orifice). Comparisons of pressure profiles in the loop predicted from the present model and previous studies11 are shown in Figure 10. As can be seen, the correlation of Lim et al.11 overestimates ∆Pls and exhibits irregular profiles near the riser exit region, whereas the proposed model of this study describes well the pressure profiles in the CFB loop at the given Ug and Gs.
Table 4. Key Pressure Drop Equations (Lim et al.11) equation exit effect in the riser downcomer loop-seal cyclone
∆P ) fbendFs(1 - )Ug with fbend ) 0.375 2
dP/dz ) Fs(1 - mf)g ∆Pls ) (GsAsp)2/(CDoAls)22Fs(1 - mf) with CDoAls ) 11 × 10-6 m2 ∆P ) Ccy Fg Ug2/2 with Ccy ) 50
voidage. The proposed model predicts well the pressure profiles around the CFB loop, as shown in Figure 8. When the aeration rate through a loop-seal is high, Gs exhibits a maximum value, which means that Gs has a constant value irrespective of the variation of UA. The maximum Gs increases with increasing solid inventory
Conclusions A pressure balance model is proposed to describe the flow dynamics around a CFB loop. The model accounts for the effect of the exit configuration on the axial pressure profile in a riser with an abrupt exit. Also, in the model, the decay constant and the reflux constant have been correlated with the pertinent dimensionless numbers and exit geometry to describe the exit effect in the riser. Practical operating conditions in a solid recycle system with a loop-seal are considered for CFB combustor applications. The predicted results from the present model exhibit good agreement with the experimental data.
Figure 10. Comparison of the pressure loop profiles predicted from the present and previous studies of Lim et al.11
Ind. Eng. Chem. Res., Vol. 41, No. 20, 2002 4955
Acknowledgment We acknowledge a grant-in-aid for research to S.D.K. from the Ministry of Commerce, Industry and Energy, Korea. Notation A ) area, m2 a ) decay constant in eq 4, m-1 ae ) decay constant affected by the exit geometry of the riser, m-1 Ccy ) cyclone coefficient CDo ) valve coefficient Ce ) reflux constant D ) diameter, m De ) diameter of the riser exit (Figure 3), m dP ) pressure difference, Pa dP/dz ) pressure gradient, Pa/m dz ) height difference, m dp ) particle diameter, µm g ) gravitational acceleration, m/s2 fbend ) friction factor in the bend Gs ) solid circulation rate, kg/m2‚s Gsd ) solid mass flux based on the loop-seal area, kg/m2‚s Gsh ) solid mass flux based on the horizontal section area, kg/m2‚s Hdc ) height of the solid bed in a downcomer, m He ) projected height of the riser exit (Figure 3), m Hf ) height of the freeboard, m Hr ) height of the riser, m L ) length, m M ) mass, kg P ) pressure, Pa ∆P ) pressure drop, Pa UA ) aeration rate in the vertical aeration section of a loopseal (Figure 1), m/s UBA ) bottom aeration rate in a loop-seal (Figure 1), m/s Ug ) gas velocity in the riser, m/s Ugh ) gas velocity in the horizontal section, m/s Umf ) gas velocity at the minimum fluidizing state, m/s Uo ) gas velocity, m/s Ut ) terminal velocity of a particle, m/s z ) height, m zd ) height of the dense bed in the riser, m zf ) height in the freeboard, m Greek Letters ) voidage dc ) voidage of a solid bed in a downcomer mf ) voidage at the minimum fluidization state s ) solid holdup /s ) Gs/[Fs(Ug - Ut)] sd ) solid holdup in the dense bed of the riser se ) solid holdup at the exit ∆sr ) with reflux - without reflux s∞ ) solid holdup at uniform flow with the slip velocity ) Ut µ ) gas viscosity, kg/m‚s φs ) shape factor of the particle Fbulk ) bulk density, kg/m3 Fg ) gas density, kg/m3 Fs ) particle density, kg/m3 Subscripts c ) cyclone dc ) downcomer DB ) downcomer bottom DT ) downcomer top e ) exit h ) horizontal section
ls ) loop-seal r ) riser RB ) riser bottom RT ) riser top sp ) standpipe t ) total va ) vertical aeration section w ) weir section
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(21) Bai, D.; Kato, K. Quantitative Estimation of Solids Holdups at Dense and Dilute Region of Circulating Fluidized Beds. Powder Technol. 1999, 101, 183. (22) Zheng, Q. Y.; Zhang, H. Experimental Study of the Effect of Exit (End Effect) Geometric Configuration on Internal Recycling of Bed Material in CFB Combustor. In Circulating Fluidized Bed Technology IV; Avidan, A. A., Ed.; AIChE: New York, 1994; p 145. (23) Brereton, C. M. H.; Grace, J. R. End Effects in Circulating Fluidized Bed Hydrodynamics. In Circulating Fluidized Bed Technology IV; Avidan, A. A., Ed.; AIChE: New York, 1994; p 137. (24) Schoenfelder, H.; Kruse, M.; Werther, J. Two-Dimensional Model for Circulating Fluidized Bed Reactors. AIChE J. 1996, 42, 1875.
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Received for review April 8, 2002 Revised manuscript received July 9, 2002 Accepted July 9, 2002 IE0202571
