Ind. Eng. Chem. Res. 2008, 47, 8423–8429
8423
Analysis of the Acceleration Region in a Circulating Fluidized Bed Riser Operating above Fast Fluidization Velocities Esmail R. Monazam† and Lawrence J. Shadle*,‡ National Energy Technology Laboratory, U.S. Department of Energy, 3610 Collins Ferry Road, Morgantown, West Virginia 26507-0880, and REM Engineering SerVices, PLLC 3537 Collins Ferry Road, Morgantown, West Virginia 26505
In commercial circulating fluidized bed (CFB) processes the acceleration zone greatly contributes to solids mixing, gas and solids dispersion, and particle residence times. A new analysis was developed to describe the relative gas-solids concentration in the acceleration region of a transport system with air as the fluidizing agent for Geldart-type B particles. A theoretical expression was derived from a drag relationship and momentum and continuity equations to describe the evolution of the gas-solids profile along the axial direction. The acceleration zone was characterized using nondimensional analysis of the continuum equations (balances of masses and momenta) that described multiphase flows. In addition to acceleration length, the boundary condition for the solids fraction at the bottom of the riser and the fully developed regions were measured using an industrial scale CFB of 0.3 m diameter and 15 m tall. The operating factors affecting the flow development in the acceleration region were determined for three materials of various sizes and densities in core annular and dilute regimes of the riser. Performance data were taken from statistically designed experiments over a wide range of Fr (0.5-39), Re (8-600), Ar (29-3600), load ratio (0.2-28), riser to particle diameter ratio (375-5000), and gas to solids density ratio (138-1381). In this one-dimensional system of equations, velocities and solid fractions were assumed to be constant over any cross section. The model and engineering correlations were compared with literature expressions to assess their validity and range of applicability. These expressions can be used as tools for simulation and design of a CFB riser and can also be easily coupled to a kinetics model for process simulation. Introduction Circulating fluidized beds (CFBs) have been commercially utilized in the FCC process, coal combustion and gasification, and petrochemical industry. In general, a CFB consists of a riser, cyclones, standpipe, and solids returning system. Solid particles are accelerated in the bottom section of the riser where particles increase their velocity from the initial value (equal to zero or slightly higher) to a finite value, determined by the balance of forces acting on the solids. Conventionally the knowledge of the pressure drop, solid fraction, and velocity distribution along the riser of CFB is a prerequisite for the successful design of a CFB system. The distance where particles are accelerated is often neglected and this may lead to significant errors, especially in the case of a short riser. The most common approach to investigate the acceleration zone is based on the solution of a set of governing differential equations.1,2 Arastoopour and Gidaspow1 and Kmiec´ and Leschonski2 discuss the forms of solids momentum equation and the problems in obtaining good correlations for the drag coefficient and particle-wall friction factor. By virtue of these facts, different empirical and semiempirical methods have been developed to describe the hydrodynamic of the acceleration section of the riser of CFB. Many CFD techniques have been developed which qualitatively capture the acceleration region of the riser in a CFB; however, there is a lack of quantitative validation of these models in the literature. Pugsley and Berrutti3 developed a mathematical model to describe the acceleration region of the CFB assuming a core* To whom correspondence should be addressed. E-mail: lshadl@ netl.doe.gov. Tel.: 304-285-4647. Fax: -304-285-4403. † REM Engineering Services. ‡ U.S. Department of Energy.
annular flow structure such that the radius of the core is equal to that evaluated for the fully developed flow. Relationships provided by Werther4 and Patience and Chaouki5 were used for the thickness of the core in the fully developed region. Their model used a single particle force balance and was able to calculate the axial pressure drop across the acceleration region for relatively small diameter vessels over a wide range of gas and solids fluxes. On the other hand, Sabbaghan et al.6 described the development of solids flow in this acceleration region of a riser for clusters rather than individual particles. Their model is based upon the force balance of a single cluster as defined by Xu and Kato7 and was used to fit the same data.3 The frictional terms become more significant in such small diameter vessels. Knowlton et al.8 report that the influence of riser diameter becomes less important above 0.15 m. There are only a few empirical correlations available in the literature that predict the acceleration length of the CFB riser. Rose and Duckworth9 developed a correlation that relates the acceleration length to the Froude number, Stokes number, and the solids to the fluid loading ratio. They neglect the effect of gas and solid frictions in their analysis. Jotaki and Tomita10 developed a one-dimensional solids flow model for analyzing the acceleration region of pneumatic transport of granular solids in vertical pipes. On the basis of a solid force balance, they showed that the acceleration length was dependent on air velocity, particle terminal velocity, and solids friction coefficient. Yang and Keairns11 analyzed the length of acceleration zone on the basis of a force balance between drag forces, gravity forces, and solids friction. The resulting model is very sensitive to the value used for the solids friction factor. Enick et al.12 developed an empirical equation for predicting the acceleration length for horizontal and vertical pneumatic transport lines, using observed trends reported in the literature. Wong13 combined
10.1021/ie8009445 CCC: $40.75 2008 American Chemical Society Published on Web 10/02/2008
8424 Ind. Eng. Chem. Res., Vol. 47, No. 21, 2008 Table 1. Granulated Bed Material Characteristics solids Sauter packed bed mean, density, voidage, εb 3 bed material dp, µm Fs, kg/m cork coke glass beads
Figure 1. Schematic of NETL cold-flow circulating fluid bed depicting both the loop-seal and L-valve (insert) configurations
all the observed trends reported in the literature into one equation to predict the acceleration length by modifying Enick’s correlation. In this study a new analysis is presented describing the relative gas-solids concentration in the acceleration region for a set of experimental data generated for several different granular materials in a relatively large diameter riser of 0.3 m diameter. This analysis uses newly developed engineering expressions to define the boundary values for solids fraction at the riser inlet and fully developed regions. The relationships are used to predict the voidage distribution and acceleration length in a CFB riser operating above fast fluidization. A dense bed is a characteristic of the fast fluidization regime; however, the test data used in this study was limited to velocities above the fast fluidization as defined by Monazam et al.14 (i.e., superficial gas velocities higher than the upper transport velocity) and/or by Bi and Fan15 (VCA). While this analysis considers the axial dependence of the apparent solids hold-up in a CFB riser, it should be recognized that, especially in this acceleration region, and despite our focus on the more homogeneous transport flow conditions, there is considerable solids recirculation. This solids recirculation within the riser plays an important role in the design and use of CFB riser reactors. Experimental Section The test unit configuration is described by Monazam et al.16 and shown in Figure 1. The riser is constructed of flanged steel sections with one 1.22 m acrylic section installed 2.44 m above the solids feed location. The solids enter the riser from one of two nonmechanical valves (loop-seal, Figure 1; and L-valve, Figure 1 insert). The solids enter the riser at the same location for both valves such that the bottom of the inlet piping connects at a point about 0.155 m above the gas distributor. In the loopseal the solids flow down a 60° slope while in the L-valve the solids flow horizontally into the riser. Solids exit the riser through a 0.20-m port at 90° about 1.2 m below the top of the riser at a point 15.3 m above the solids entry location (centerline to centerline).
812 230 60
189 1250 2500
0.5 0.45 0.4
Ar 3593 608 29.6
Geldart Utr2, m/s type B/A B/A A/B
3.59 4.15 3.50
Riser velocities were corrected for temperature and pressure as measured at the base of the riser. The air’s relative humidity was maintained between 40 and 60% to minimize effects of static charge building up on the solids. Zero offsets in pressure measurements were corrected by subtracting a baseline pressure profile across the riser with gas flow prior to circulating solids. Flows utilized did not produce any significant pressure drop due to gas flow. Twenty incremental differential pressures were measured along the height of the riser using transmitters calibrated to within 0.1% of full scale or about 2 Pa/m. The primary response measurement was the overall riser pressure differential and it was calibrated within 0.45 Pa/m. Mass circulation rate was continuously recorded by measuring the rotational speed of a twisted spiral vane located in the packed region of the standpipe as described by Ludlow et al.17 This calibrated volumetric measurement was converted to a mass flux using the measured packed bed density presented in Table 1 and assuming that the packed bed void fraction at the point of measurement was constant (i.e., εb ) 0.45). Analysis of the standpipe pressure profile, estimated relative gas-solids velocities, and bed heights have indicated that this constant voidage estimate was reasonable over the range of operating conditions reported here. Operating conditions were varied by adjusting the riser flow or solids circulating rate while maintaining constant system outlet pressure at 1 atm. The solids circulation was varied by controlling the aeration flow at the bottom section of the standpipe and by adjusting the total system inventory to increase the standpipe height. Steady-state conditions were defined as holding a constant set of flow conditions and maintaining a constant response in the pressure differentials over a 5 min period. All steady-state test results represent an average over that 5 min period. Theory The analysis considers the acceleration zone that exists in a predominantly upward flowing gas-solid suspension. Weinstein and Lee18 developed the gas-solid mixture momentum balance including terms for the weight of the bed, acceleration, and the hydrostatic pressure. Assuming that the Fs . Fg they derived an expression for the changes in solids velocities along the acceleration zone of a vertical riser. They assumed that the drag force results in a solids velocity gradient that is proportional to the velocity difference between solids in the acceleration zone and those above the acceleration zone: dus ) k(us∞ - us) (1) dz The left-hand side of this equation represents the acceleration term in the force balance. The decay constant incorporates contributions of the gas and solids friction to the drag. The solids-wall and gas-wall friction were assumed to be insignificant as supported by the observation by Knowlton et al.8 that wall friction becomes small with larger diameter vessels. For one-dimensional flow, the continuity equation for the solid phase reduced to
Ind. Eng. Chem. Res., Vol. 47, No. 21, 2008 8425
d [F (1 - ε)us] ) 0 dz s Differentiating eq 2 yields
(2)
us d(1 - ε) dus )(3) dz 1 - ε dz Considering Gs ) Fs(1 - ε)us ) Fs(1 - ε∞)us∞, combining eq 1 and eq 3 yields dε k(1 - ε)(ε∞ - ε) ) dz (1 - ε∞)
(4)
The solution of eq 4 requires the knowledge of k, ε∞, and an initial voidage condition specified at any one location in the riser. Results and Discussion When the solid enters the riser of CFB, solid particles are accelerated in the bottom section and reach to a height where the axial voidage becomes relatively constant. In the acceleration section the pressure drop and consequently the apparent solid holdup decreases sharply with increasing bed height. The axial pressure profiles along the riser of CFB are displayed in Figure 2 for a gas velocity of 6.3 m/s and different solids flux for a cork particle. These measurements are conveniently used to infer axial voidage profile by assuming that the only contribution to the axial pressure drop is the hydrostatic head of solids. To distinguish the use of this assumption from that of a measured void fraction the term apparent voidage was adopted. To evaluate the axial apparent voidage, the axial pressure (Figure 2) was fitted to a polynomial in height (5th order) and then differentiated (dP/dz). The axial apparent voidage was related to the pressure drop through the following expression:19 dP ) Fs(1 - ε)g (5) dz The calculated axial apparent voidage profile along the riser is presented in Figure 3 for a different solids flux at a given gas velocity for cork particles. The voidage profiles exhibit distinct transitions between the acceleration zone at the bottom, the fully developed region in the midsection, and the deceleration zone at the top of the riser. These profiles represent typical examples of the C-shape voidage profile that is characteristic of the dilute regime when using an L-valve solids feed inlet and an abrupt Tee outlet. In this operating regime, the solids entered the bottom of the riser and were accelerated until they
Figure 2. Pressure along the CFB riser for a series of tests using cork bed material for Ug ) 6.3 m/s.
Figure 3. Axial voidage profile in the CFB riser for a series of tests using cork bed material for Ug ) 6.3 m/s.
Figure 4. The apparent voidage in the fully developed region of the riser for each of the bed materials studied as a function of the riser gas velocity.
reached a height where the axial voidage became relatively constant. In the acceleration section the pressure drop, and consequently the solid fraction, decreased sharply with increasing bed height. Above the acceleration zone a fully developed region of the riser can be identified by the relatively constant incremental pressure differentials. The test data analyzed was taken from a broader range of experiments which included slugging and fast fluidized conditions. Those data sets were sorted on the basis of the analysis of Monazam et al.14 in which the highest velocity that could sustain a fast fluidized bed was determined on the basis of the emptying times recorded after abruptly halting the solids flow into the riser. This velocity is defined as the upper transport velocity, Utr2, and is similar to Bi and Fan’s15 VCA which represents the transition velocity between the fast fluid regime and core-annular flow. Transient solids cutoff tests were conducted for each of the three materials: cork, glass, and coke. All the steady-state tests conducted at velocities above Utr2 were included in the transport data set of interest. For this data set the apparent voidage in the fully developed midsection of the riser was determined using eq 5. These are plotted in Figure 4 against the superficial gas velocity in the riser. The breadth and range of operations in this data were demonstrated by the scatter in this plot. While the data included relatively dilute conditions with apparent voidages as high as 0.998, it also included more densely loaded data sets with a mean value of 0.97 and a lower quartile of 0.96. The minimum apparent voidage included in the data set was 0.87 using cork with the riser operating in a
8426 Ind. Eng. Chem. Res., Vol. 47, No. 21, 2008
dense transport regime. Selected on this basis not one of the observed riser pressure profiles display an S-shaped apparent voidage profile characteristic of fast fluidization. The very bottom of the riser was often observed to have an apparent voidage less than 80%, but this was a result of side entry and maldistribution of solids and gas at the inlet, and the apparent voidage was always found to increase exponentially along the riser to the level of that at fully developed flow. In this study, to solve eq 4 it is assumed the voidage at z ) 0 is the voidage at the base of the riser, εb, and ε∞ is the fully developed voidage, εFD. Thus, eq 4 can be integrated directly to (ε - εFD)(εb - 1) ) e-kz (εb - εFD)(ε - 1)
(6)
However, from experimental observation (Figure 3) it was apparent that the pressure gradient followed an exponential decay. To simplify eq 6 the ratio, (εb - 1)/(ε - 1), and the exponential factor, k, were combined to calculate a new effective exponential factor, Kdecay. Then eq 6 simplified to εapp - εFD ) e-Kdecayz εb - εFD
(7)
Where εapp is the apparent voidage along the acceleration zone, εb is the voidage at the bottom of the riser, εFD is the voidage for the fully developed region, and Kdecay is the rate constant. The new exponential constant, Kdecay is an apparent decay factor different from that in eq 6. In eq 7 the values for εapp approaches εFD for large z and dε/dz ) 0. The value for εb is the maximum voidage constraint at z ) 0, and when z > 0 the resulting values for εFD and Kdecay become greater than 0. The value for εFD is the voidage at its asymptotic limit. When z approaches 0 then εapp approaches εb. The experimentally determined apparent voidage profiles for the acceleration region were compared to those determined from eq 6 and eq 7 using the same boundary values. The variance explained was 96% using the more rigorous model (eq 6) and there was significant lack of fit, while the simpler model (eq 7) explained 99% of the variance. This may be a result of incorporating the uncertainty of the measured boundary values in the more rigorous model which have lower influence on the resulting profiles. Using the axial voidage profile (Figure 3) and eq 7, Kdecay and acceleration length can be obtained. Acceleration length is defined from the base of the riser to the point where fully developed flow has begun. The fully developed zone is the region of the riser where voidage remains constant. In this region the velocity and concentrations of the gas and solids were relatively constant with variations in riser height. A sample of comparison between the axial voidage profile using eq 5 and axial voidage profile obtained using eq 7 for the acceleration region is illustrated in Figure 5. Agreement is very good for all three materials over the entire acceleration region with variance explained at >96%. A series of steady state experiments was conducted to characterize the internal flow behavior of a riser above the upper transport velocity. The solid materials used for this study were cork, coke, and glass beads. The characteristics of each of the three bed materials tested are presented in Table 1. The cork was the lightest and the coarsest particle used, the glass beads were smallest and densest, and coke was intermediate in both respect. Over 75 steady state data sets were obtained spanning a range of gas velocities (3.5-13 m/s), pressures (1-3 atm), and solids recirculation rate (1-540 kg/m2 · s). The Froude
Figure 5. Comparison between the experimentally fitted axial voidage profile using eq 5 (dashed line) and the predicted axial voidage profile obtained using eqs 7-13 (solids line) for (a) cork, (b) glass beads, and (c) coke.
number Ug2/(gD) varied from 0.5-39, load ratio Gs/(FgUg) varied from 0.2-28, density ratio (Fs - Fg)/Fg varied from 138-1381, Reynold number FgUgdp/µg varied from 8-600, and the Archimedes number (Ar) varied from 29-3600. These parameter ranges extend those reported by Bai and Kato20 in their literature review (Fr, 41-226; density ratio, 607-3607; and Ar, 4.7-1019); however, they did not report ranges for load ratio or Re. The limiting velocity to maintain the operating conditions above fast fluidization was measured using the methods described by Monazam et al.14 Using this wide pool of experimental data, empirical expressions for the voidage at the base of the riser, length of the acceleration zone, and the voidage for the fully developed region were developed. A systematic approach was used to determine which of the dimensionless parameters were relevant to the development of the acceleration zone: including the solids fraction at the bottom, the decay rate of that solids concentration, and the overall length of the acceleration zone. The voidage at the bottom of the riser was determined as the values at z ) 0 from the axial voidage profile (Figure 3). In trying to find a reliable and more general correlation for εb, various dimensionless groups that might give unified representation of the experimental data were tested. The most important experimental quantities measured were superficial gas velocity, solids mass flow rate, pressure drop across the riser, solid inventory in the riser, and particle properties. A series of dimensionless parameters are known to ensure hydrodynamic similitude when scaling circulating fluid beds.21-23 These scaling parameters represent a nondimensionalization of the continuum equations (balances of masses and momenta) that describe multiphase flows as derived by Anderson and Jackson.24 Dimensionless parameters included in this analyses were load, velocity, diameter, and density ratios, as well as Re, Fr, and Ar. Multiple regression analyses were conducted using a stepwise approach to maximize the variance explained. Those parameters which did not contribute significantly to the variance explained were discarded. The following empirical correlation for predicting the voidage at the base of the riser was obtained:
( ) () ( )
εb ) 1.0 - 0.005
Us Ug
1.045
D dp
0.541
FgUgdp µg
0.915
(8)
The coefficients were taken as the average of the upper and lower limits for the 95% confidence limits. The coefficients are 0.005 ( 0.005, 1.045 ( 0.1195, 0.541 ( 0.121, and 0.915 ( 0.149 for each term, respectively. As a result, eq 8 could be simplified within the statistical significance of the data such that the exponent on the first and third term could be considered unity and for the dimensionless length it could be assumed 1/2.
Ind. Eng. Chem. Res., Vol. 47, No. 21, 2008 8427
Figure 6. Comparison of the experimentally measured apparent voidages at the base of the riser with those estimated from eq 8.
However, if this is done, then care must be taken to evaluate whether the terms yield consistent units when the dimensionless groups are broken down, and the variability of each of the terms should be comparable or the result could generate a bias not found in the original data. The comparison between the experimental data on the bottom voidage (εb) and the predicted of eq 8 is illustrated in Figure 6. Agreement is good with variance explained (R2) of 86%. The apparent voidage at the base of the riser had a nearly linear dependence upon both the solids and gas velocity ratio and Re and a square root dependence on the reactor and particle diameter ratio. It was not surprising that the apparent voidage was most strongly related to the solids particle velocity or circulation rate, but the lack of overall dependence on the superficial gas velocity was unexpected. By contrast, King25 found that the apparent voidage for the dense bed at the bottom of a CFB riser operating in the fast fluidization regime is solely dependent upon gas velocity. Certainly, the implication is that the extended dense region in the lower part of a fast fluidized riser was not dominated by the same acceleration effects observed at the very base of a transport riser. The very bottom of a riser operated in a fast fluidized regime was observed to have a very short acceleration zone not readily detected, because of the high apparent solids fraction in the dense bed immediately above it. By contrast, the acceleration zone in a riser operated in the more dilute transport regimes exhibited a distinct acceleration zone not easily missed. Moreover, the solids circulation rates that can be achieved in the transport regimes can be varied over a much wider range permitting its detection. In this study, the following correlation was developed to predict the acceleration length in the dilute regime:
( ) ( ) (
Ug2 Lacc ) 0.805 D gD
-0.446
Gs FgUg
0.145
Fs - Fg Fg
)
-1.297
() D dp
Figure 7. Comparison of the estimated Lacc/D using eq 9 and the model by Wong (1991) with experimentally measured values.
This might be expected since the larger and denser particles exhibit greater slip than the smaller or lighter particles and thus travel a shorter length before the drag force offsets the gravitational force. In Figure 7 the experimental acceleration length is compared with the predicted acceleration length based on eq 9. The coefficient of multiple variations is 0.7 indicating that 70% of the variance explained by the regression data is described by eq 9. For the sake of comparison to literature results, the correlation developed by Wong13 is also depicted in Figure 7 for glass beads and coke materials tested. The data sets used to develop Wong’s correlation were from bed materials with densities above 2500 kg/m3 except in one case. As a result the Wong13 correlation overpredicts the acceleration length for coke and cork, but the glass beads were within the experimental data of the test cases used in this study. The cork is not displayed in Figure 7, because it was off-scale to the right and was an order of magnitude in overpredicting the acceleration length. In Table 2 the literature values for the acceleration length,26-28 Lacc, are listed along with those calculated using eq 9. These literature data were taken from tests conducted on risers larger than 0.3 m diameter. Agreement was very good with variance explained, R2, as greater than 93%. Therefore, eq 9 was demonstrated to provide an easy procedure for evaluating the effect of acceleration zone on the hydrodynamic of the riser for a variety of bed materials with larger diameter risers. The smaller diameter literature data13 did not display as good a match with eq 9. This was thought to be a result of the greater wall effects affecting the acceleration region in those tests, which could not be captured in the relationships developed here. The decay constant, Kdecay, in eq 7 was related to the acceleration length using the following equation:
× 1.352
Kdecay ) 0.415
(Reg)
(9)
Like in eq 8, the coefficients were taken as the average of the upper and lower limits for the 95% confidence limits. The coefficients are 0.805 ( 2.686, -0.446 ( 0.173, 0.145 ( 0.062, -1.297 ( 0.227, 1.352 ( 0.421, and 0.415 ( 0.349 for each term, respectively. The length of the acceleration zone was dependent on the load ratio, particle and diameter ratios, Fr, and Re. The density and diameter ratios were the strongest factors determining the length of the acceleration zone. The acceleration length was inversely related to both solids density and size; the larger the particle density and diameter the shorter the acceleration zone.
π Lacc
(10)
The coefficient for this expression was empirically found to be 3.14 and the value of π was used to express this value. This is consistent with Figure 8 which displays the curvature typically found in a circular shape. Figure 8 shows a comparison between experimentally determined, Kdecay and that calculated using eq 10. Agreement was very good with variance explained, R2 > 95%. The fully developed zone is the region of the riser where the voidage remains constant. In this region the velocity of the gas and solids are relatively constant with variations in riser height. There are a few correlations in open literature for the prediction of the voidage in the fully developed region.20,29-31 In this study,
8428 Ind. Eng. Chem. Res., Vol. 47, No. 21, 2008 Table 2. Comparison of Predicted (eq 9) and Experimental Acceleration Length for Literature Results from a Larger Diameter Riser26-28 data source
Gs (kg/m2s)
Ug (m/s)
Fs (kg/m3)
dp (µm)
D (m)
Lacc, exptl (m)
Lacc, (eq 9) (m)
Arena et al. 1990 Bader et al. 1988 Harge et al. 1986
215 147 65
5 9.1 5
2543 1714 2500
90 76 56
0.4 0.305 0.4
4.0 3.2 3.5
4.0 3.3 3.7
This form of the relationship was adopted from earlier work because the value for solids voidage approaches unity in the limit of high gas superficial velocity.29 The only parameters found to be significant for the wide sample set were Fr, Re, and the density ratio. In terms of primary control parameters, the slip in this fully developed regime was linearly related to gas velocity and even more strongly related to solids density and particle size. More analysis of the detailed data in the fully developed regime is under investigation.
conducted to map the entire operating regime for each bed material. Tests which produced uniform axial pressure profiles or in which a fully developed uniform region could be identified were selected for analysis of the gas-solids hydrodynamics. Over 75 steady state data sets were available spanning a range of gas velocities (3.5-13 m/s), pressures (1-3 atm), and solids recirculation rate (1-450 kg/m2 · s). A new analysis approach was developed. The theoretical expression was derived from a drag relationship and momentum and continuity equations to describe the evolution of the gas-solids profile along the axial direction. The results were obtained by introducing values for the boundary conditions from the experimental tests. The acceleration zone was characterized using nondimensional analysis of the continuum equations (balances of masses and momenta) that described multiphase flows. A series of engineering correlations were developed for the voidage at the riser inlet and in the fully developed regions. In addition the test data was analyzed to evaluate the acceleration length and, in turn, the decay constant. The decay constant is directly related to the solids flux and the relative density of the gas and solids and indirectly related to the particle density and gas velocity. In this operating regime the apparent voidage at the base of the riser had a nearly linear dependence upon both the solids and gas velocity ratio and Re and a square-root dependence on the reactor and particle diameter ratio. The particle-gas slip ratio in the fully developed regime was linearly related to gas velocity and even more strongly related to solids density and particle size. These engineering expressions can be used as a tool for simulation and design of the riser of CFB and also can be easily coupled to kinetics model for process simulation.
Summary
Acknowledgment
The riser pressure profile was analyzed for a series of tests conducted in the regimes above fast fluidization using bed materials of different size and density. The solid materials used for this study were cork, coke, and glass beads. The cork was the lightest (Fs ) 189 kg/m3) and the coarsest particle (dp ) 812 µm) used, the glass beads were smallest (dp ) 60 µm) and densest (Fs ) 2500 kg/m3), and coke was intermediate in both respects (230 µm and 1250 kg/m3). Extensive testing was
The authors acknowledge the Department of Energy for funding the research through the Fossil Energy’s Gasification Technology and Advanced Research funding programs.
the following correlation was developed to predict the slip ratio, Ψ, in the fully developed region of the riser using the same data set and the same dimensionless parameters discussed above:
( ) (
ψ ) 1 + 2.25 × 10-6
Ug2 gD
-1.18
Fs - Fg Fg
)( ) 1.6
FgUgdp µg
1.5
(11)
Again the coefficients were taken as the average of the upper and lower limits for the 95% confidence limits. The coefficients are 2.25 × 10-6 ( 5.48 × 10-6, -1.18 ( 0.22, 1.60 ( 0.23, and 1.50 ( 0.3 for each term, respectively. Experimentally the slip value was determined from the superficial gas and solids velocities in the fully developed region of the riser. The slip value is defined as ψ)
Ug ⁄ ε Gs ⁄ Fs(1 - ε)
(12)
The void fraction in the fully developed region was obtained using eq 12 as εFD )
UgFs UgFs + Gsψ
(13)
Figure 8. The measured decay constant, Kdecay, compared to that estimated from eq 10 for different measured acceleration lengths, Lacc.
Appendix Notation Ar ) Archimedes number, g(Fs - Fg) Fg dp3/µg 2 D ) riser diameter (m) dp ) mean particle diameter (m) g ) acceleration due to gravity (m2/s) Gs ) solids flux (kg/m2 s) k ) rate constant (m-1) Kdecay ) effective decay constant (m-1) Lacc ) acceleration length (m) Re ) Reynolds number P ) pressure (kPa) Ug ) superficial gas velocity (m/s) us ) solid velocity (m/s) us∞ ) solid velocity at the end of acceleration zone (m/s) Us ) superficial solid velocity (m/s) Utr2 ) upper transport velocity (m/s) VCA ) A choking velocity (m/s) z ) vertical coordinate (m) Greek Symbols
Ind. Eng. Chem. Res., Vol. 47, No. 21, 2008 8429 εapp ) apparent voidage εb ) voidage at the base of the riser εFD ) fully developed voidage ε∞ ) voidage at the end of acceleration zone φ ) inner diameter (m) µg ) gas viscosity (g/cm-s) Fg ) gas density (g/cm3) Fs ) solid density (g/cm3) Ψ ) slip ratio
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ReceiVed for reView June 16, 2008 ReVised manuscript receiVed August 6, 2008 Accepted August 12, 2008 IE8009445
