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Ind. Eng. Chem. Res. 1997, 36, 3898-3903
Analysis of the Overall Pressure Balance around a High-Density Circulating Fluidized Bed D. Bai, A. S. Issangya, J.-X. Zhu, and J. R. Grace* Department of Chemical Engineering, The University of British Columbia, 2216 Main Mall, Vancouver, Canada V6T 1Z4
A steady-state model is presented for predicting the flow behavior of a novel high-density circulating fluidized-bed coupled dual-loop system. The model allows the maximum achievable solids flux for given steady-state operating conditions to be predicted. The effects of superficial gas velocity, solids inventory, particle diameter and density, and the diameters of both risers and both downcomers as well as the position of the solids control valve are all predicted. Predictions are shown to be in good agreement with experimental values for solids circulation rates as high as 420 kg/m2 s for FCC particles in a dual-loop system. Parametric studies illustrate the usefulness of the approach for optimizing the operating conditions of complex gas-solid systems. Introduction Research in circulating fluidized beds (CFBs) continues to explore means of improving the gas-solids contacting efficiency and unit capacity. Almost all reported circulating fluidized-bed studies have been conducted with solids circulation fluxes below 200 kg/ m2 s and solids holdups less than 0.02 in the developed flow section (Zhu and Bi, 1995). However, high-density circulating fluidized-bed (HDCFB) systems are currently being used for some catalytic processes in the chemical and petrochemical industries. This has led to dual-loop systems to allow much higher solids holdups to be achieved in experimental risers (Bi and Zhu, 1993). A high-density circulating fluidized-bed system has recently been built and operated at The University of British Columbia (Issangya et al., 1997). As shown in Figure 1, the system consists of two risers (A and B), two downcomers (1 and 2), gas-solids separators, and solids flow control devices (gate valves 1 and 2). In such a system, the pressure drop characteristics of every component can affect the performance of the main riser. The solids circulation flux and the voidage distribution in the risers adjust themselves to satisfy the pressure balance. Theoretical analyses of the pressure balance around conventional, single-loop circulating fluidized beds (e.g., Weinstein et al., 1984; Kwauk et al., 1986; Rhodes and Geldart, 1987; Yang, 1988; Bi and Zhu, 1993) provide useful information on the proper design and operation of conventional CFB systems. In this study, the overall pressure balance around a dual-loop HDCFB system is analyzed, incorporating an overall solids material balance on the total solids inventory in the system. The analysis allows evaluation of the effect of operating conditions (e.g., superficial gas velocities) and design parameters (e.g., riser diameter and solids return leg configuration) on the steady-state hydrodynamics. Model Development The dual-loop CFB system consists of four major types of component: risers, downcomers, gas-solids separators, and solids flow control devices. Analysis of the CFB loop requires a balance of pressures around both loops: * To whom correspondence should be addressed. S0888-5885(97)00011-0 CCC: $14.00
1. Pressure Drop across Risers. The energy of gas entering the base of a riser is partially transferred to the solids through gas-solids interactions and partially dissipated due to friction. For most operating conditions, gravitational effects are much larger than frictional energy dissipation. However, friction effects may become significant, for example, at high gas velocities and high solids circulation rates. If the pressures at the outlets of the two secondary cyclones are assumed to be equal to the same reference pressure, Pref, then the pressure at the bottom of each riser can be expressed as
Pr ) Pref + FgjgH + Fpjs gH + ∆Pc,p + ∆Pc,s + ∆Pac + ∆Pfg + ∆Pfs (1) Here the pressure drop in the riser is assumed to be composed of the sum of components due to gas and solids heads, pressure drop across cyclones or other gas-solids separators, pressure drops due to solids acceleration, and friction from both gas and solids. In general, the pressure drop due to solids acceleration is insignificant at low solids circulation rates but needs to be considered at high Gs. As a first approximation, the particles can be considered to be accelerated from zero velocity at the riser bottom to Gs/Fpjs in the developed region within the riser, requiring a pressure drop of
∆Pac ) Gs2/Fpjs
(2)
For gas-wall friction, the Fanning equation is used.
∆Pfg )
2fgjFgU2 H Dr
with the friction coefficient, fg, estimated by
{
16 Re e 2300 Re fg ) 0.079 Re > 2300 Re0.313
(3)
Of several empirical correlations available in the literature for solids-wall friction (see Leung, 1980), the equation of Konno and Saito (1969) is utilized, giving © 1997 American Chemical Society
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3899
Figure 1. Schematic diagrams of high-density circulating fluidized-bed systems. Dotted and solid lines represent air and solids flows, respectively. a-c correspond to three different exit configurations.
∆Pfs )
2fsH Gs2 Dr Fpjs
(4)
with
fs )
0.0285 xgDr Gs Fpjs
( )
(5)
2. Pressure Drop across Cyclones. The pressure drop across a gas-solids separator depends on its design and operating conditions. Cyclones are usually employed to recover the solids carried beyond CFB risers. The pressure drop across a cyclone can be written (Perry et al., 1984) as
∆Pc ) kFgUcy2
(6)
where k is typically 1-20 depending on the design (Perry et al., 1984). Rhodes and Geldart (1987) proposed that this relationship be used for circulating fluidized-bed cyclones with Ucy taken as the superficial gas velocity in the riser and k ) 25. Given that the cyclone pressure drop is usually a relatively minor component in the pressure balance, we adopt this simple approach here. As mentioned above, the pressures at the outlets of the secondary cyclones are assumed to be equal to the same reference pressure, Pref. We further simplify the analysis by assuming that the pressure drops across the primary and secondary cyclones are the same. However, when a low-pressure quick gassolid separator is used as the primary cyclone, its pressure drop is neglected in this analysis. Different arrangements of cyclones have been found to influence the predictions only slightly. Clearly, the analysis can
be modified readily to provide more precise prediction of pressure drops across separators in cases where these are significant. 3. Pressure Drop across Downcomers. In CFB systems, the downcomer is commonly a fluidized bed operated under minimum fluidization conditions. For such a case, the solids acceleration and friction in the downcomer can reasonably be neglected. Thus, the pressure drop across the downcomer can be expressed by
Pd ≈ Pref + L(1 - mf)Fpg + ∆Pc,p + ∆Pc,s
(7)
Given that the downcomer is usually operated at minimum fluidization, the pressure drops across the primary and secondary cyclones connected to the top of the downcomer can be neglected because of extremely low gas velocity. However, when the gas flow is introduced into these cyclones from the riser (as in configuration c), these pressure drops are included. 4. Pressure Drop across Solids Flow Control Devices. The solids flow control devices used in circulating fluidized-bed systems can be mechanical or non-mechanical valves. In both cases, Yang and Knowlton (1993) found that the pressure drop can be characterized by the following equation due to Jones and Davidson (1965):
∆PV )
(
)
Ws 1 2Fp(1 - mf) CdAdisφ
2
(8)
The discharge coefficient, Cd, is about 0.7-0.8 for a variety of systems and control device configurations (Rudolph et al., 1991). Cd ) 0.75 is assumed in this analysis. 5. Conditions for Steady HDCFB Operation. For the HDCFB configurations shown in Figure 1, air
3900 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997
flows with superficial gas velocities, UA and UB, are introduced into risers A and B, respectively. The solids inventory in the whole system is Minv, and there is no solids addition to, and negligible removal from, the system. After adjusting the openings, φA2 and φB1, of the two gate valves, the system attains steady operation after a transient period where the solids fluxes through the two valves differ. When steady operation is achieved, the solids flux anywhere in the system (ignoring losses through the gas-solids separators) is designated as Ws. For simplicity, the solids inventories in parts of the system other than the downcomers and risers are ignored in the overall solids inventory balance. Under steady operation, the pressure and solids material balances around the HDCFB system can then be written:
∆PV1 ) Pd1 - PrB
(9)
∆PV2 ) Pd2 - PrA
(10)
Minv ) ArAFpjsAHA + ArBFpjsBHB + (Ad1L1 + Ad2L2)Fp(1 - int) (11) When known operating conditions and design variables are substituted into eqs 9-11, there are five unknowns: the riser voidages (jA and jB), solids circulation mass flowrate (Ws), and the heights of solids in the downcomers (L1 and L2). Two additional equations are necessary to solve for these five unknowns. For this purpose, the equation of Li and Kwauk (1980) was applied separately to each of the risers. This can be expressed by
- a ) e(z-zi)/z0 * -
(12)
The overall solids holdup can be obtained by integrating over the riser height, giving
(
)
j - a 1 + exp[(H - zi)/z0] z0 ) ln * - a H 1 + exp(-zi/z0)
(13)
For a tall riser with a smooth exit, the slip velocity between gas and solids approaches the terminal velocity of a single particle so that * ) 1 - Gs/Fp(U - vt). We approximate the limiting dense phase voidage as a ) mf. The voidages, d at the bottom (z ) 0) and e at the top exit (z ) H), are estimated from the empirical correlations of Bai and Kato (1996):
{
( ) (
1 - d UFp ) 1 + 6.14 × 10-3 1 - * Gs
( ) (
UFp 1 - d ) 1 + 0.103 1 - * Gs
1.13
) (x )
Fp - Fg Fg
-0.23
)
Fp - Fg Fg
1.21
U
U
gdp
1.85
(
Ar0.63
)
Fp - Fg Fg
-0.44
(16)
It now becomes possible to determine the parameters z0 and zi by substituting ) d at z ) 0 and ) e at z ) H into eq 12 for a given operating gas velocity and solids circulation mass flowrate. In such a manner, the overall solids holdup in each riser can be estimated based on eq 13. To solve the resulting set of equations, a numerical optimization (constrained variable metric) method was used. During the calculations, the average slip velocity between the gas and particles was not allowed to drop below the terminal mean settling velocity, i.e., the following constraint was incorporated:
vsi )
Ui Ws g vt (i ) A, B) ji AriFpjsi
(17)
By using different initial inputs, it was ensured that unique solutions could be obtained. Experimental Section Experimental data were measured in the HDCFB experimental system described in detail by Issangya et al. (1997) corresponding to configuration a in Figure 1, except that an inertial separator was used in place of the first cyclone. FCC particles were used with a mean diameter of 60 µm and a density of 1600 kg/m3. The diameters of the risers were 0.0765 m (A) and 0.102 m (B), while both downcomers had diameters of 0.304 m. The heights of risers A and B were 6.09 and 7.62 m, respectively. During each experiment, both gate valves were adjusted carefully until the whole system operated in a stable steady-state manner, with constant solids levels in both downcomers. The heights of solids in both downcomers were recorded under steady-state conditions for each experiment. Air flows were metered using orifice meters. The solids circulation rate was controlled by the gate valves and determined by measuring the accumulated solids for a known time in the top section of downcomer 2. The downcomer air flows were adjusted to maintain minimum fluidization conditions. Pressure drops over the various components were recorded using pressure transducers. The data were sampled with the aid of data acquisition software (LABTECH, Notebook) at 100 Hz for differential pressure measurements along both risers and at 5 Hz for absolute pressure measurements around both loops. In the following discussion, GsA ()Ws/ArA) refers to the solids circulation flux in riser A.
-0.383
gDr
Validation of the Model
for Gs > Gs*
-0.013
for Gs e Gs* (14)
and
1 - e ) 4.04(1 - *)0.214 1 - *
(x )
Gs*dp ) 0.125 µ
(15)
where the saturation carrying capacity of gas, Gs*, is given (Bai and Kato, 1996) by
Figure 2 shows the predictions of the model for all three configurations shown in Figure 1, with the column diameters and heights as in the experiments, a fixed solids inventory of 450 kg, both control valves wide open, and the ratio of superficial velocities UB/UA maintained at 1.2. In case a, there is one cyclone or other gassolid separator at the top of each riser and each downcomer. In case b there is a secondary cyclone for two of these primary separators. In case c the secondary cyclone for both risers also functions as the primary cyclone for the corresponding downcomer. Note that a gives the highest GsA, but the difference between the three configurations is not very significant, especially
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3901
Figure 2. Predicted solids circulation flux in riser A vs superficial gas velocity in riser A for the three configurations shown in Figure 1. Minv ) 450 kg, UB/UA ) 1.2, DrA ) 0.0765 m, DrB ) 0.102 m; Dd1 ) Dd2 ) 0.304 m, φA2 ) φB1 ) 1.0.
Figure 5. Predicted effect of solids inventory and gas velocity in riser A on solids circulation flux. UB ) 8 m/s and φA2 ) φB1 ) 1.0.
Figure 6. Predicted effect of superficial gas velocities on solids circulation flux. Minv ) 300 kg and φA2 ) φB1 ) 1.0. Figure 3. Comparison of predicted and experimental average solids holdup for riser A for UA ) 4-8 m/s and GsA ) 15-420 kg/ m2 s.
experimental equipment, eqs 9-11 were solved by adjusting the openings of the solids flow control valves (i.e., setting φA2 and φB1) to match the solids circulation flux for the given superficial gas velocities and solids inventory. The calculations lead to predictions of L1 and L2 as well as φA2 and φB1. The model predictions are seen to be within (15% of the experimental results for the operating conditions employed in this study. Discussion
Figure 4. Comparison of predicted and experimental solids heights in downcomers for UA ) 4-8 m/s, UB ) 4-16.5 m/s, and Minv ) 360-550 kg.
at low gas velocities where the gas-solids separators contribute little to the overall pressure balance. The overall solids holdups obtained experimentally in riser A for superficial gas velocities from 4 to 8 m/s and various solids circulation fluxes up to more than 400 kg/m2 s are compared in Figure 3 with the predictions from the model outlined above. Some of the experimental data were reported previously (Issangya et al., 1997). Both the magnitude of the predictions and the trends with UA and UB are seen to be in good agreement with the experimental data, with almost all data within (15% of the predictions. Further validation of the model is given in Figure 4 for UA ) 4-8 m/s, UB ) 4-16.5 m/s, GsA ) 25-450 kg/ m2 s, and Minv ) 360-550 kg. As in operation of the
Some additional sample calculations were carried out using the model in order to improve the understanding of the operation performance of this specific dual-loop high-density CFB system, as well as to demonstrate the ability of models of this type to predict multiphase flow in complex systems in general. The predictions provide useful information about how to operate and control such systems for a range of conditions not readily verifiable experimentally. Figures 5 and 6 show that increasing the solids inventory as well as the superficial velocities in both risers is helpful in achieving high solids fluxes in riser A. For each inventory in Figure 5, GsA increases quickly with increasing UA at low UA, whereas little change is predicted at high UA. This may result from the limitations of the second riser, since a fixed gas velocity UB results in a limited capacity to carry particles. GsA is predicted to increase with increasing UB for any gas velocity UA (Figure 6). This is because the overall solids holdup, and hence the pressure drop in the second riser, decreases as UB increases, increasing the available pressure head in the downcomer to push solids into riser A. The increase of solids circulation flux with increasing
3902 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997
Figure 7. Predicted effect of DrB/DrA on the solids circulation flux. Minv ) 300 kg, UB/UA ) 1.2, DrA ) 0.0765 m, Dd1 ) Dd2 ) 0.304 m, and φA2 ) φB1 ) 1.0.
Figure 9. Predicted effect of particle diameter and density on the solids circulation flux under (a) constant solids inventory (Minv ) 450 kg) and (b) constant volume of solids. UA ) 8 m/s, UB ) 9.6 m/s, DrA ) 0.0765 m, DrB ) 0.102 m, Dd1 ) Dd2 ) 0.304 m, and φA2 ) φB1 ) 1.0.
Figure 8. Predicted effect of fractional openings of solids flow control valves on the solids circulation flux. Minv ) 300 kg, UB/UA ) 1.2, DrA ) 0.0765 m, and DrB ) 0.102 m, and Dd1 ) Dd2 ) 0.304 m.
UA slows down for high UB, an indication that the solids circulation begins to be restricted by the solids control valve. In addition, pressure losses due to particle-wall friction in both risers reduce the pressure head available for particle circulation. The model can also be used to predict the influence of changes in system geometry. For example, Figure 7 shows the predicted influence of changing the diameter of riser B for a riser A diameter of 0.0765 m and a fixed solids inventory. Note that increasing DrB is predicted to increase the solids circulation flux for the complete range of UA considered. This occurs because of the reduced fractional holdup of solids, and hence the lower pressure drop, in riser B, increasing the available pressure head on the downcomer side to push solids into riser A. Similar to the practical operation of the experimental equipment, the fractional openings of the solids flow control valves were next adjusted to obtain different solids circulation fluxes. This makes it possible to adjust the superficial gas velocity and the solids circulation flux independently. The predicted solids circulation fluxes are plotted for different values of φA2 and φB1 in Figure 8 as a function of UA. It is seen that GsA increases significantly with increasing valve opening for φA2 ) φB1 < 0.6, but further increases in φA2 and φB1 influence the solids circulation flux much less because the valves then have relatively low pressure losses. These trends have been confirmed in the experimental equipment. Previous extensive operating experience with circulating fluidized beds has indicated that high solids
fluxes are only achievable for relatively fine particles (e.g., FCC riser reactors), while coarser particle circulating fluidized beds (e.g., CFB combustors) are usually operated at low solids circulation fluxes. This is consistent with the model, as shown in Figure 9 where the superficial gas velocities and solids inventory are held constant. For a given particle density, GsA is predicted to decrease with increasing mean particle diameter, due mainly to the decreased solids carrying capacity of the gas (see Figure 9a). For particles of the same mean diameter, an increase in particle density results in not only a decrease in solids carrying capacity, but also a decrease in the heights of solids in the two downcomers for a constant solids inventory. Hence, the solids circulation fluxes are predicted to decrease significantly with increasing particle density. When the total volume (rather than mass) of solids is kept constant, an increase in particle density leads to increases in solids circulation flux, as shown in Figure 9b. Further experiments are needed with a range of particulate materials to verify these trends. Conclusion Pressure and solids material balances around a highdensity circulating fluidized-bed system lead to a simple steady-state model which is in good agreement with experimental data obtained in a novel dual-loop circulating fluidized-bed system. The model shows how the solids circulation fluxes are affected by the operating conditions (superficial gas velocities, particle diameter and density, solids inventory, and fractional opening of the solids flow control valves) as well as by the system geometry (riser diameters, downcomer diameters, etc.). It is demonstrated that the model offers guidance for design and operation of dual-loop high-density circulating fluidized-bed systems, and the approach can clearly be adapted to other complex gas-solids flow systems.
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3903
Acknowledgment Financial support from the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged. Notation A ) cross-sectional area, m2 Ar ) Archimedes number ()dp3Fgg(Fp - Fg)/µ2) Cd ) solids discharge coefficient, (-) D ) diameter, m dp ) mean particle diameter, m fg ) gas-wall Fanning friction coefficient fs ) solids-wall friction coefficient g ) acceleration due to gravity, m2/s Gs ) net solids circulation flux in riser, kg/m2 s H ) riser height, m k ) constant in eq 6 L ) height of solids in downcomer, m L0 ) static bed height when all particles are stored in downcomer, m Minv ) total solids inventory, kg Pd ) pressure at the bottom of downcomer, Pa Pr ) pressure at the bottom of riser, Pa Pref ) reference pressure at the outlet of both secondary cyclones, Pa Re ) Reynolds number ()DrUFg/µ) U ) superficial gas velocity, m/s Ucy ) gas velocity in cyclone inlet, m/s vs ) slip velocity between gas and solids, m/s vt ) terminal velocity of a single particle, m/s Ws ) solids flux, kg/s z ) vertical coordinate measured from the bottom of riser, m z0 ) characteristic length in eq 12, m zi ) height of the inflection point in eq 12, m Greek Symbols ∆Pac ) pressure drop due to solids acceleration, Pa ∆Pc,p ) pressure drop across primary cyclone, Pa ∆Pc,s ) pressure drop across secondary cyclone, Pa ∆Pd ) pressure drop across downcomer, Pa ∆Pfg ) pressure drop due to gas-wall friction, Pa ∆Pfs ) pressure drop due to particle-wall friction, Pa ∆PV ) pressure drop across the solids flow control valve, Pa ∆z ) distance between two adjacent taps ()0.3 m in this work), m Fg ) gas density, kg/m3 Fp ) particle density, kg/m3 ) voidage in riser at height z j ) overall average voidage in the riser a ) limiting dense phase voidage d ) voidage in riser at z ) 0 e ) voidage in riser at z ) H * ) asymptotic voidage in riser as z approaches ∞ mf ) voidage at minimum fluidization s ) overall average solids holdup in riser µ ) gas viscosity, Pa‚s φ ) fractional opening of solids flow control valve Subscripts
1 ) downcomer 1 or valve at exit from downcomer 1 2 ) downcomer 2 or valve at exit from downcomer 2 A ) riser A B ) riser B d ) downcomer dis ) solids discharge pipe i ) in riser i (i ) A or B) r ) riser
Literature Cited Bai, D.; Kato, K. Estimation of solids holdups at bottom dense and upper dilute regions of circulating fluidized beds. Powder Technol. 1996, in press. Bi, H. T.; Zhu, J. Static instability analysis of circulating fluidized bed and the concept of high density risers. AIChE J. 1993, 39, 1272-1280. Bi, H.-T.; Grace, J. R.; Zhu, J.-X. On types of choking in vertical pneumatic systems. Int. J. Multiphase Flow 1993, 19, 10771092. Issangya, A.; Bai, D.; Bi, H.-T.; Lim, K. S.; Zhu, J.-X.; Grace, J. R. Axial solids holdup profiles in a high density circulating fluidized bed riser. In Circulating Fluidized Bed Technology V; Li, J., Kwauk, M., Eds.; Science Press: Beijing, 1997; in press. Jones, D. R. M.; Davidson, J. F. The flow of particles from a fluidized bed through an orifice. Rheol. Acta 1965, 4, 180-192. Konno, H.; Saito, S. Pneumatic conveying of solids through straight pipes. J. Chem. Eng. Jpn. 1969, 2, 211-217. Kwauk, M.; Wang, N.-D.; Li, Y.; Chen, B.-Y.; Shen, Z.-Y. Fast fluidization at ICM. In Circulating Fluidized Bed Technology; Basu, P., Ed.; Pergamon Press: Toronto, 1986; pp 33-62. Leung, L. S. The ups and downs of gas-solid flowsa review. In Fluidization; Grace, J. R., Matsen, J. M., Eds.; Plenum Press: New York, 1980; pp 25-68. Li, Y.; Kwauk, M. The dynamics of fast fluidization. In Fluidization; Grace, J. R., Matsen, J. M., Eds.; Plenum Press: New York, 1980; pp 537-544. Perry, R. H.; Green, D. W.; Maloney, J. O. Perry’s Chemical Engineer’s Handbook, 6th ed.; McGraw-Hill: New York, 1984. Rhodes, M. J.; Geldart, D. A model for the circulating fluidized bed. Powder Technol. 1987, 53, 155-162. Rudolph, V.; Chong, Y. O.; Nicklin, D. J. Standpipe modeling for circulating fluidized beds. In Circulating Fluidized Bed Technology III; Basu, P., Horio, M., Hasatani, M., Eds.; Pergamon Press: Oxford, 1991; pp 49-64. Weinstein, H.; Graff, R. A.; Meller, M.; Shao, M.-J. The influence of the imposed pressure drop across a fast fluidized bed. In Fluidization IV; Kunii, D., Toei, R., Eds.; Engineering Foundation: New York, 1984; pp 299-306. Yang, W. C. A model for the dynamics of a circulating fluidized bed loop. In Circulating Fluidized Bed Technology II; Basu, P., Large, J. F., Eds.; Pergamon Press: New York, 1988; pp 181191. Yang, W. C.; Knowlton, T. M. L-valve equations. Powder Technol. 1993, 77, 49-54. Zhu, J.-X.; Bi, H. T. Distinctions between low density and high density circulating fluidized beds. Can. J. Chem. Eng. 1995, 73, 644-649.
Received for review January 3, 1997 Revised manuscript received May 30, 1997 Accepted June 2, 1997X IE970011+
X Abstract published in Advance ACS Abstracts, August 1, 1997.
