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Modeling circulating fluidized bed downers
Powder Technology 132 (2003) 85 – 100 www.elsevier.com/locate/powtec
Modeling circulating fluidized bed downers Yasemin Bolkan a,*, Franco Berruti b, Jesse Zhu b, Bruce Milne a a
Department of Chemical and Petroleum Engineering, The University of Calgary, 2500 University Drive, NW Calgary, Alberta, Canada AB T2N 1N4 b Department of Chemical and Biochemical Engineering, The University of Western Ontario, London, Ontario, Canada Received 5 April 2002; received in revised form 8 January 2003; accepted 8 January 2003
Abstract In this work, the hydrodynamic features of circulating fluidized beds (CFB) are integrated into a new computer simulation of a downer reactor. The mathematical model is based on fluid dynamic fundamentals and calculates the characteristic flow parameters (solids holdup, particle velocity and pressure gradient) along the downer axis. Cluster formation within the downer is expressed through the ‘‘Equivalent Agglomerate Diameter’’, which is calculated through an empirical correlation that relates the average size of agglomerates to operating conditions. Pressure loss due to particle – wall friction is usually difficult to determine and a new empirical correlation is developed to estimate its value. The impact of particle – wall interactions can be discerned for a given set of operating conditions using the derived relationship. A correlation for estimating the particle – wall friction factor has also been developed based on available downer data and is presented in this work. Comparison of simulation results with downer flow data demonstrates successful model matching. The simulator accurately describes the hydrodynamic behavior of the gas – solid suspension within the downer both in the developing-flow as well as in the fully developed flow regions. D 2003 Elsevier Science B.V. All rights reserved. Keywords: Circulating fluidized beds; Downer modeling; Clusters
1. Introduction Circulating fluidized beds (CFB) have been proven over the years to be highly effective reactors for fast gas –solid reaction systems. These types of reactors have been successfully employed for a wide range of applications, including catalytic cracking, calcination operations, polyethylene production and combustion of a variety of fuels, since they offer advantages such as high throughput rates and thorough gas – solid contact leading to excellent heat and mass transfer. Conventionally, CFBs have been designed with the entrance of the reactor located at the bottom end, where the gas and solid feeds meet and flow upward to the exit at the top of the reactor. In spite of their many advantages, such co-current up-flow CFB reactors, also called risers, suffer from significant solids backmixing that may result, in some applications, in reduced selectivity and irregular distribution of the desired product. In recent years, a new type of CFB reactor, the downer, has been developed. In a downer, the gas and solid phases enter the reactor at
* Corresponding author.
the top section, allowing for the gas– solid mix to flow co-currently downward along the direction of gravity. This set-up leads to desirable hydrodynamic qualities such as more uniform flow and better control of fluid – solid contact times. Reports on CFB downers point toward their benefit over risers [1– 4]. Due to the complexity of CFB hydrodynamics, however, this area of research requires further attention. Recently, data analysis conducted on a state-of-the-art riser/ downer pair [5] has made a comparative inquiry into risers and downers possible, since this CFB pair has important design parameters in common and experiments have been run under similar operating conditions. In this work, general trends of CFB hydrodynamics observed on this experimental unit are combined with fundamental fluid dynamic laws, and a downer model is presented that is applicable for both descriptive as well as predictive purposes.
2. Downer simulation While riser modeling has received wide-ranged attention [6], downer modeling is still quite scarce. Even though the
0032-5910/03/$ - see front matter D 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0032-5910(03)00059-7
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reactors themselves essentially share the same design, entering feed and catalysts from the top instead of the bottom of a CFB results in significant variations in hydrodynamic behavior, making it necessary to develop separate models for each of the reactors. Downer hydrodynamic studies have been conducted for over a decade [7,8]. Since the first downer model published in 1994 [9], a number of modeling efforts have been reported, all of which consistently point to some of the advantages of downers when employed to carry out specific chemical reactions [10 –12]. Limited work has been published in literature describing simulations where the riser and downer hydrodynamic characteristics are coupled with kinetics of fast reactions such as fluid catalytic cracking [9,13]. These simulations suggest that downers may provide improved conversion rates and product selectivity. The downer model presented in this study is built on fundamental equations derived from momentum balances and mass conservation laws, which were derived by BolkanKenny et al. [9]. Mass Conservation: Gs ¼ qp ð1 eÞup
ð1Þ
Momentum Balance (on single particle): qp Vp
u dup 1 u0 0 ¼ q g up up Ap CD þ ðqp qg ÞVp g 2 dt e e ð2Þ
Momentum Balance (on gas –solid suspension): dP ¼ dz
dP dz
dP dz head
dP dz friction accel
ð3Þ
where
dP dz dP dz
¼ qp ð1 eÞg þ qg eg
ð4Þ
head
¼ qp ð1 eÞup accel
dup u0 dðu0 =eÞ þ qg e dz dz e
ð5Þ
and
dP dz
¼
friction
dP dz
0:3164 Re0:25 g
þ gaswall
dP dz
ð6Þ particlewall
1 u2 qg 0 ¼ fg 2D e gaswall
ð8Þ
where Reg ¼
Du0 qg elg
ð9Þ
Similarly, pressure loss due to particle –wall friction can be formulated as follows: dP 1 q ð1 eÞu2p ¼ fp ð10Þ dz particlewall 2D p Due to the complex mechanics and difficulty to isolate frictional effects from other pressure losses, the particle – wall friction factor, fp, is hard to determine [15]. There are a number of empirical correlations available for fp, most of which have been developed for up-flow systems [16]. Further details on particle –wall friction are presented under Results and discussion. In the presented model, the downer volume is discretized, and the mentioned equations are solved simultaneously for average voidage and average particle velocity, along with the drag coefficient for each control volume. In order to minimize the impact of discretization, the height of the control volume is kept under 1 mm. Derivative functions at each step are approximated using the fourth-order Runge –Kutta method. The resulting computer program is written in the C++ language and solves for the key hydrodynamic parameters throughout the downer. Even though experimental observations indicate a small degree of local radial variation, it is clear that downers operate under conditions closely approximating the plug flow [17]. Based on this, the proposed model is one-dimensional, predicting average values across the radius. Once voidage and particle velocity are predicted, the change in pressure is computed by calculating the pressure gradient along the downer axis. When the drag coefficient is calculated, Stoke’s Law applies for low Particle Reynolds Numbers:
Pressure loss due to gas – wall friction can be expressed
dP dz
fg ¼
CD ¼
as
with fg being the gas friction factor. According to the empirical Blasius Formula [14]:
24 Rep
for Rep < 1
ð11Þ
where qg ue0 up dp Rep ¼ lg
ð12Þ
while Eq. (13) holds for high Rep values: ð7Þ
CD ¼ 0:44
for Rep > 1000
ð13Þ
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Various empirical correlations have been incorporated in the program for drag coefficient calculations in the intermediate range, which have been observed to cause relatively minor changes in results. Hence, the well-established correlation by Bird et al. [18] has been used as the default: CD ¼
18:5 Re0:6 p
for 1VRep V1000
ð14Þ
It has been experimentally observed that slip velocities in downers are generally significantly larger than the terminal settling velocity of a single particle [11,19]. Particle agglomeration appears to be the most reasonable explanation for this occurrence [10,20,21]. Therefore, agglomeration is incorporated in the downer model. Direct evidence of particle agglomeration has been documented for a downer experimental unit [22]. It is suspected that clusters start forming in the feeder region of the downer, which then collapse and reform throughout the entire downer length. This assumption is verified by Manyele et al. [23], whose experimental observations show that the number of clusters (cluster fre-
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quency) and their sizes (cluster existence time) vary throughout the downer length, their individual effects compensate each other. Therefore, the percentage of cluster formation (cluster time fraction) remains practically constant at all measured locations for any given set of operating conditions, as a result of a dynamic equilibrium that is established along the downer. In order to represent these experimental findings, a parameter named ‘‘Equivalent Agglomerate Diameter’’ is introduced in the downer model. Further information on this parameter is discussed in Results and discussion.
3. Experimental set-up and data collection Extensive data [17,19] have been gathered previously on a downer– riser unit, which is schematically presented in Fig. 1. The riser and downer both have an inner diameter of 0.1 m. FCC catalyst particles (67 Am diameter and 1500 kg/m3) enter the riser inlet from the storage tank and are fluidized by air with a relative humidity of 70 – 80% to minimize electrostatic effects. The gas – solid suspension travels upward
Fig. 1. Experimental set-up.
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along the 15.1-m-tall riser. At the riser exit, solids are separated from the air through cyclones. Just below the primary riser cyclone, solids enter the downer solids distributor where they are held at minimum fluidization (see insert in Fig. 1). Particles then fall through 31 vertical tubes of 0.36 m length and 12.7 mm OD. A gas distributor consisting of a plate with 31 holes of 16.7 mm ID is located 50.8 mm above the exit point of the vertical tubes. The downer air enters from above this plate and moves downward through the 2 mm gap between each tube and hole in order to interact with the particles exiting the tubes. The gas – solid suspension flows co-currently downward along the 9.3-m-long downer in the direction of gravity. At the downer exit, the solids are separated from the air in the fast separator and are moved to the storage tank. Further details of the experimental set-up are presented by Zhang et al. [17,19]. Local solids holdup and velocity along with axial pressure gradient were measured for each given set of superficial gas velocity and solids flux. The solids circulation rate was controlled by the solids control valve at the riser entrance and was measured by diverting the collected solids from the downer fast separator into the measuring vessel for a given period of time. The pressure drop along the downer was measured by pressure transducers. The local solids holdup was measured through an optical fiber solids concentration probe, the details of which are presented elsewhere [17]. The local particle velocity was measured using an optical fiber particle velocity probe [19]. The superficial gas velocity u0 ranged between 3.5 and 10.2 m/s, whereas the solid flux, Gs, varied between 49 and 208 kg/(m2s). Local solids holdup and particle velocity were measured in both the riser and the downer at 11 radial positions along eight axial locations, while pressure was measured at eight axial locations. Data gathered using the above-described unit are utilized for model verification. Radial averages of local downer data are determined at all measured axial positions and are then compared with model results that predict average values of flow parameters along the downer axis. Fully developed flow data is used to express the equivalent agglomerate diameter as a function of operating conditions. Pressure loss at the wall, which is a challenging parameter to determine experimentally, is also related to operating conditions. General trends of radial downer data are examined in order to ensure that no crucial information is lost in the averaging process. Additionally, radial profiles for a downer and riser based on data collected under similar operating conditions [7] are taken into account for a qualitative discernment of benefits and limitations of downers in comparison to risers.
4. Results and discussion 4.1. Comparison of model vs. data The predicted solids holdup, average particle velocity and pressure profiles have been compared with data collected on
the presented downer equipment. Figs. 2 –4 compare model predictions with downer data for a variety of operating conditions. At the top of the downer, the FCC particles are fluidized under minimum fluidization conditions at a solids holdup of approximately 0.40 [24,25]. When the catalyst particles enter the downer feeder tubes, they undergo a period of free-fall for roughly 0.5 m. The acceleration of particles in this section results in a considerable dilution of the solids concentration to less then 0.04 [24]. Average solids holdup at the downer inlet that are calculated in this manner match very well with available data. Once the solid phase enters the downer, further acceleration and consequent dilution of solids holdup occurs. The solids holdup eventually reaches a constant value, indicating that fully developed flow is established. Fig. 2 illustrates that at the fixed superficial gas velocity of 3.7 m/s, increasing solids flux from 49 to 101 kg/(m2s) and subsequently to 194 kg/(m2s) results in axial nonuniformity, causing steeper solids holdup profiles mainly in the entrance zone of Zd = 0– 2 m. Higher solids flux also extends the developing flow region. Since solids concentration is a direct function of the solids throughput, average solids holdup at any location is higher for increased solids flux scenarios. It is evident from Fig. 2 that the model matching of data is accurate. Figs. 3 and 4 illustrate axial solids holdup profiles for superficial gas velocities of u0 = 7.2 and 10.2 m/s, respectively. For a similar range of solids fluxes as for u0 = 3.7 m/ s, at roughly 50, 100 and 200 kg/(m2s), the higher superficial gas velocity scenarios result in similar trends for axial solids holdup profiles. At a closer look, however, it is evident that increasing gas velocity causes a consistent decrease in solids holdup at any axial position. For example, when solids flux is approximately 200 kg/(m2s), averaged solids holdup data near the exit (Zd = 9.2 m) drops 17.5% or 34.9%, as u0 increases from 3.7 to 7.3 m/s or to 10.1 m/s, respectively. The axial profiles for average particle velocity are illustrated in Figs. 5– 7. Contrary to solids holdup, particle velocity is found to be more sensitive to variations in gas velocity than solids flux. For a better overview, the nine sets of operating conditions at which data has been collected are gathered in each figure such that gas velocities are varied at constant flux. Initially, as the particles are leaving the top solids distributor fluidized bed, the velocity of particles is in accordance with the minimum fluidization voidage and is calculated from the mass conservation equation (Eq. (1)). Within the feeder tubes, particles undergo a period of freefall. The amount of resulting acceleration is calculated based on the length of these feeder tubes. The calculated particle velocities at the downer inlet are in good agreement with measured values near the entrance. Particles continue accelerating once they enter the downer, until reaching a constant velocity. The value of this fully developed particle velocity exceeds the actual gas velocity due to gravity effects.
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Fig. 2. Model predictions vs. data for solids holdup along the downer, u0 = 3.7 m/s.
Even though all of the presented average particle velocity profiles in Figs. 5 – 7 share the same trend, particle velocity at any axial location increases at higher superficial gas
velocities. Increasing gas velocity at a constant solids flux is also found to shorten flow development. Increasing solids flux on the other hand indicates extended flow develop-
Fig. 3. Model predictions vs. data for solids holdup along the downer, u0 = 7.2 m/s.
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Fig. 4. Model predictions vs. data for solids holdup along the downer, u0 = 10.2 m/s.
Fig. 5. Model predictions vs. data for particle velocity along the downer, Gs = 49 kg/(m2s).
Y. Bolkan et al. / Powder Technology 132 (2003) 85–100
Fig. 6. Model predictions vs. data for particle velocity along the downer, Gs = 101 kg/(m2s).
Fig. 7. Model predictions vs. data for particle velocity along the downer, Gs = 202 kg/(m2s).
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ment. For all flow scenarios, at constant superficial gas velocity, the particle velocity at the exit is higher for increased solids flux. At u0 = 3.7 m/s, for example, increasing Gs from 49 to 101 kg/(m2s) or to 194 kg/(m2s) has quite an impact on particle velocity, resulting in an increase in the exit up from 6.5 to 7.6 m/s (16.9%) or to 8.3 m/s (27.7%), respectively. Worth noting is that the presented radial solids holdup and particle velocity data are the result of multiple local readings at a given radial location at any axial position. These local readings are averaged to determine data at a particular radial location. Since this process introduces a variation from actual readings, using the resulting solids holdup and particle velocity data to calculate solids flux causes a minor discrepancy in mass conservation. Solids flux calculated in this manner is found to vary up to 11% from the inlet solids flux. Hence, it is inevitable that the downer simulator, which incorporates conservation of mass, produces slightly different results than radial averages of these values that are averaged at each radial location. Nonetheless, in the overall trend of the downer fluid dynamics, it is clearly observed that data and model predictions match very well. As described by Eq. (3), the pressure gradient is made up of three components. Static head causes the pressure to increase along the downer, whereas acceleration and frictional effects result in pressure loss. The pressure gradient in the downer is illustrated in Fig. 8 for a variety of operating conditions. For all operating conditions, at
constant solids flux, an increase in superficial gas velocity results in a decrease in the pressure gradient, which has also been observed by Aubert [2]. On the other hand, at a fixed superficial gas velocity, increasing the solids flux results in increased pressure gradients showing the strong effect that static head has on the pressure gradient profile. Frictional losses include gas – wall and particle – wall interactions. While the gas – wall friction factor is wellestablished, a reliable method for calculating the particle – wall friction factor for downers is not available. Eq. (10) presents the relationship of frictional losses to particle concentration and velocity. Solids holdup data has quite low values for all operating conditions, while particle velocity is lowest for the gas velocity of u0 = 3.7 m/s. Hence, particle – wall effects would be least dominant for this low gas velocity. In order to determine the quality of model prediction prior to introducing an empirical correlation for the particle –wall friction term, the model is run for the stated operating conditions excluding any particle – wall interaction. The pressure gradient data, which is measured at eight axial locations along the downer, is compared to model predictions for all there solids fluxes ( Gs = 49, 101 and 194 kg/(m2s)) at the fixed gas superficial velocity of u0 = 3.7 m/s in Fig. 9. The pressure gradient starts out negative, mainly due to pressure losses during particle acceleration. Once acceleration effects lessen, the static head starts dominating the changes in pressure while frictional losses counter-
Fig. 8. Pressure gradient profiles along the downer.
Y. Bolkan et al. / Powder Technology 132 (2003) 85–100
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Fig. 9. Model predictions vs. data for pressure gradient along the downer, u0 = 3.7 m/s.
act to a lesser degree. This causes the pressure gradient to become positive, which eventually reaches a constant value indicating that flow development is complete. Increasing the solids flux causes larger static heads, which in turn leads to higher pressure gradient profiles. The results of the simulation are in good agreement with the data and confirm that at low gas velocity, particle – wall friction is negligible. For higher gas velocities, however, particle –wall frictional losses are found to be more significant. 4.2. Particle – wall friction Isolating the component of pressure drop that refers to frictional losses at the wall is difficult due to the complex mechanics involved [17]. In this work, the magnitude of frictional loss due to the interaction between the solid phase and the wall is determined using a unique feature of the downer model. Unlike solids holdup and velocity, the pressure function in the downer model calculates the pressure gradient at a given axial location independent of pressure at any other location, i.e. the pressure gradient solely depends on the flow condition at any specific axial location. This makes it possible to determine a pseudopressure gradient that excludes particle – wall friction for fully developed flow conditions. When this output is compared to fully developed flow data, the difference between model prediction and data represents the frictional losses caused by particle – wall interaction for each operating
condition. Resulting particle – wall friction values are shown graphically in Fig. 10. As expected, particle – wall friction becomes more dominant with an increase in gas velocity as well as solids flux. An empirical correlation is proposed to calculate the particle –wall friction term as a function of operating conditions:
dP dz
¼ 0:028u0:876 G1:177 0 s
ð15Þ
particlewall
This empirical correlation, graphically represented in Fig. 10, can be used to discern whether the particle – wall friction term is significant for a given set of operating conditions. The particle –wall friction factor, fp, can be calculated for individual operating conditions along with known particle concentration and velocity by equating Eqs. (10) and (15). Capes and Nakamura [16] developed an empirical correlation based on data gathered in a riser in order to relate the particle –wall friction term to particle velocity. fp ¼ 0:206u1:22 p
ð16Þ
Since the hydrodynamics of up-flow and down-flow systems vary quite drastically near the wall, and experimental data used for their correlation involved relatively large particles, the coefficients in the correlation are not expected
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Fig. 10. Effect of operating conditions on particle – wall friction. Symbols: calculated particle – wall friction. Lines: particle – wall friction as a function of operating conditions (Eq. (15)).
to be suitable for downers. Nonetheless, the relationship between the friction term and particle velocity is expected to be similar for risers and downers, and the following correlation is determined for down-flow CFBs based on the available downer data with FCC catalysts. This friction factor expression can be improved further once new downer data is produced.
This slip velocity is equal to the terminal free-fall velocity of a particle of size dp falling through a fluid. Based on fluid mechanics [25]:
fp ¼ 0:003u0:426 p
where CD is a function of Particle Reynolds Number which in turn is a function of particle diameter and terminal free-fall velocity (Eq. (12)). Through an iterative process, a particle diameter is determined that is consistent with each calculated slip velocity. Using this approach, the equivalent agglomerate diameter, da, the diameter that represents the size of agglomerates (clusters) in the fully developed flow region of the downer, can be determined. To do so, superficial gas velocity data along with averages for particle velocity and voidage of fully developed flow data gathered on the presented downer equipment are introduced into Eq. (18). The equivalent agglomerate diameters thus determined are presented by the symbols in Fig. 11. The extent of clustering within the downer is strongly affected by operating conditions, so that it is beneficial to describe this parameter in terms of the operating conditions in order to make it a fully predictable feature within the downer simulator. The data points show that as the solids flux increases da increases due to particles having more
ð17Þ
4.3. Equivalent agglomerate diameter The ‘‘Equivalent Agglomerate Diameter’’ is determined for the solid phase, based on the fluid mechanic relationship between a particle and its terminal settling velocity. For a particle that has a terminal velocity, ut, a particle diameter, dp, can be calculated, representing an equivalent particle of spherical shape. In case of the solids moving in a downer in fully developed flow, the terminal velocity of the solid phase is represented by the slip velocity. For a given set of operating conditions, the superficial gas velocity along with voidage and particle velocity in fully developed flow are used to calculate the slip velocity: us ¼
u0 up e
ð18Þ
"
4dp ðqp qg Þg u s ¼ ut ¼ 3qg CD
#1=2 ð19Þ
Y. Bolkan et al. / Powder Technology 132 (2003) 85–100
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Fig. 11. Effect of operating conditions on equivalent agglomerate diameter. Symbols: calculated values based on data [5]. Lines: calculated values based on Eq. (20).
opportunity to interact and cluster, and as gas velocity increases da decreases, caused by the reduced suspension density and stability within the suspension. For data gathered on the presented downer unit, the dependence of the equivalent agglomerate diameter on operating conditions, Gs and u0, can be expressed by a consistent linear relationship through the following empirical correlation (represented by the lines in Fig. 11): da ¼ 0:7173 þ 0:0015Gs 0:0672u0
ð20Þ
Krol et al. [22] report that the solid phase starts out as single particles that gradually agglomerate to average cluster sizes of two to six single particle diameters and estimate that 28 – 29 ms are required for a cluster of four particles to be formed. The model incorporates single particles at the entrance of the downer which start clustering within the agglomeration formation time, gradually growing into clusters that have a particular equivalent agglomerate diameter in accordance with current fully developed flow conditions. Considering that experimental observations by Krol et al. are based on FCC particles in a downer of 2.5 cm diameter operating at very low solids fluxes (3 –7 kg/m2 s) and low gas velocities (0.5 – 4 m/s), it is highly possible that the reported values could vary with operating conditions. In accordance with more recent observations [26], agglomeration formation times up to 100 ms have been taken into account in the proposed model. However, such changes in this parameter are found
to be insignificant, and the agglomeration formation time is kept at the default value of 30 ms for all reported results. 4.4. Radial profiles All data used for model verification so far, as presented in Figs. 2 – 11, are based on radial average values of flow parameters. In this section, the source data that is used to determine these values at any given axial position is examined to ensure that this radial averaging process results in a reasonable approximation. The general trends of radial solids holdup profiles in the downer are illustrated on the right-hand side in Fig. 12. In the downer, the solids holdup in the core region of r/ R = 0.0 – 0.4 stabilizes quite quickly, with es varying minimally along the downer axis. The trend in the middle region of r/R = 0.4 – 0.8 seems to also settle relatively quickly, with its initial upward drift flattening out as the solids move through the downer. The most distinct variation in es values is observed throughout the downer in the annular region, r/R = 0.8 – 1.0. In the entrance zone, a significant densification is evident near the wall. Further down the column, the solids holdup at the wall drops considerably, resulting in a maximum accumulation of solids at about r/R = 0.9, which has also been reported in other experimental units [1]. Near the downer exit, the solids holdup profile is essentially flat, with a slight drop in es at the wall for most operating conditions.
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Fig. 12. Radial solids holdup profiles along the riser and the downer (data from Ref. [5]).
Even though some degree of radial non-uniformity is observed, in particular in the wall region of the downer, the significance of this phenomenon is put in proportion when compared with observations in the riser. The general trends of radial solids holdup profiles in the riser are presented on the left-hand side of Fig. 12. These profiles are based on data collected on a riser/downer pair that has important design parameters in common [5]. Presenting solids holdup profiles for the riser and downer on the same scale at similar operating conditions demonstrates the distinct variation in hydrodynamic behavior between
these two types of CFBs. Fig. 12 illustrates that the solids holdup profile in the riser is most elevated in the annular region of r/R = 0.8– 1.0. This profile undergoes a transition within r/R 0.4 –0.8, becoming practically flat in the core region (r/R 0.0 – 0.4). This flow structure within CFB risers, presenting the same solids holdup profile of a dense radial suspension near the wall with low density in the core region throughout the reactor, has also been reported elsewhere [6]. Even though the solids holdup profile flattens out toward the riser exit for all presented operating conditions, the core-annular flow structure
Y. Bolkan et al. / Powder Technology 132 (2003) 85–100
remains evident for most operating conditions throughout the riser. On the other hand, in view of riser profiles, downer profiles are practically flat. Hence, the average values predicted by the simulator may be a close approximation of local values at most radial locations for any given axial position. Another issue to consider is whether the point at which flow becomes fully developed according to the axial profiles is in agreement with local observations across the radius. Variations in local solids holdup occur most significantly in the vicinity of the wall (Fig. 12). Hence, the behavior of local solids holdup near the wall (r/ R = 0.975) is examined to determine when fully developed flow is reached in the downer. Fig. 13 illustrates that in spite of considerable fluctuations near the downer entrance, solids holdup near the wall reaches a constant value at around 4 m for all flow scenarios except for the operating condition with the lowest gas velocity (3.7 m/s) and highest solids flux (194 kg/m2s), in which case the axial solids holdup profile flattens out at roughly 6 m. Overall, the accumulation of solids near the wall appears to be more sensitive to variations in gas velocity than to changes in solids flux. The fact that this hydrodynamic parameter reaches a constant value indicates that flow conditions have become fully developed. These observations overlap with characteristics of axial profiles, and hence verify that even the hydrodynamic behavior in the most turbulent radial section of the downer is in agreement with averaged axial profiles.
97
Finally, the effect of changing operating conditions is considered for axial and radial downer data. Higher gas velocities that were found to cause more uniform flow axially (Figs. 2 – 4) are also found to improve radial uniformity (Fig. 12). Figs. 2 –4 in relation with Fig. 12 also reveal that increasing solids flux results in axial as well as radial non-uniformity throughout the downer. No radial observation is found that counteracts the assumption that radial average values present a realistic approximation of the downer hydrodynamics. 4.5. Downer vs. riser usage In order to determine benefits and limitations of downers, general trends of hydrodynamics of downers are compared to risers. Fig. 14 illustrates that fluctuations observed near the wall in the downer are not as evident as that in the riser. However, the solids holdup profile continues changing until the exit for all measured flow conditions for the riser. For the case of u0 = 3.5 m/s and Gs = 100 kg/m2s, the local solids holdup variation at r/ R = 0.975 is as high as 20% within the last 2 m of the riser, decreasing from 0.094 to 0.071 between 12.3 and 14 m, respectively. Some similarities in riser and downer hydrodynamics exist, such as higher gas velocities and lower solids flux causing more uniform flow in both reactors, as shown in Fig. 12. The dependence on gas velocity is much stronger in the riser, however, since it is the gas phase that pushes
Fig. 13. Variation in solids holdup near the wall along the downer (data from Ref. [5]).
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Fig. 14. Variation in solids holdup near the wall along the riser (data from Ref. [5]).
the suspension against gravity. In the riser, the effect of increased solids flux is more noticeable as the accumulation of solids occurs mainly in the annulus, increasing the steepness of the upward curve in this zone. In the downer, changes in solids flux affects solids holdup more evenly across the radius. Comparing Fig. 14 with Fig. 13 reveals one of the most significant benefits of downers regarding the length of flow development: the flow development length is much longer for the riser. Another undesirable characteristic of CFB risers is known to be backmixing. This is usually observed near the wall where a substantial amount of solids flow down, backwards with respect to the entrance zone. The resulting non-uniformity in residence time could affect reaction performance adversely. This occurrence is alleviated in the downer since gas and solids flow in the direction of gravity. On the other hand, a potential drawback of the downer is low solids holdup throughout the reactor. Under similar operating conditions, the riser contains more solids relative to the downer (Fig. 12). For example, the radial average of solids holdup for the riser at 10 m is 0.04 under operating conditions of u0 = 3.5 m/s and Gs = 100 kg/m2s, whereas in the downer at 9.2 m for u0 = 3.7 m/s and Gs = 101 kg/m2s, it is 0.01, merely a quarter of its counterpart in the riser. While enabling more uniform flow is one of the most significant benefits of downers, facilitating higher solids concentrations is a strong hydrodynamic feature of risers. Therefore, advantages of downers may
be most evident for reaction systems that operate in dilute solids suspension. Comparison of riser and downer data obtained from the presented test unit [5,27] indicates that downers have an excellent potential for applications in industry that require high fluid– solid contact efficiency and product selectivity within short reaction times. Nevertheless, it would be beneficial to determine how sensitive the reaction system is to the time in which fully develop flow is reached, and to the degree of backmixing, as well as to the attainable suspension density within the reactor, before discerning whether a riser or downer reactor would be more appropriate for a particular chemical reaction.
5. Conclusions A downer simulator is presented which accurately describes the hydrodynamic behavior of the gas – solid suspension within the reactor both in the developing-flow and fully developed flow regions. The computer program is based on fluid dynamic fundamentals and calculates average flow parameters along the downer axis. A comparison between simulation results and flow data demonstrates successful model matching regardless of the state of flowdevelopment. An empirical formula is developed to relate the particle– wall friction term to a given set of operating con-
Y. Bolkan et al. / Powder Technology 132 (2003) 85–100
ditions. While it is found that particle – wall friction is insignificant for low gas velocity, this correlation can be used to estimate the impact of the particle – wall friction term on the pressure gradient profile for operating conditions corresponding to higher gas velocities and solids fluxes. Furthermore, based on available data, a preliminary correlation has been proposed for the particle –wall friction factor in downers. The downer model is enhanced by the introduction of an empirical correlation to estimate the average size of agglomerates that form within the downer. The ‘‘Equivalent Agglomerate Diameter’’ is expressed as a function of operating conditions, and enables the downer model to be applicable for predictive purposes, such as modeling data under developing flow conditions or simulating operating conditions of interest to industry. Examining trends of radial profiles in comparison with radially averaged data verifies that averaging flow parameters in this manner causes no crucial loss of information within the downer. Hence, the downer model, which matches radially averaged data very well, constitutes a realistic representation of the downer hydrodynamics. Additionally, a qualitative discernment of benefits and limitations of downers in comparison to risers is determined using general trends of radial profiles in a downer and riser pair that was run under similar operating conditions. Downers may offer improved performance in comparison to the riser, especially for dilute reaction systems. However, before discerning whether a riser or downer reactor would be more appropriate for a particular chemical reaction, it is found to be beneficial to determine how sensitive the reaction system is to the time in which fully develop flow is reached, and to the degree of backmixing, as well as to the attainable suspension density within the reactor. Nomenclature Ap cross-sectional area of particle (m2) CD drag coefficient (dimensionless) D column diameter (m) da equivalent agglomerate diameter (mm) dp particle diameter (mm) fg gas friction factor (dimensionless) fp particle –wall friction factor (dimensionless) g gravitational constant (m2/s) Gs solids flux (kg/(m2s)) P pressure (Pa) r/R normalized radial distance from center of reactor (dimensionless) Reg gas Reynolds number (dimensionless) Rep particle Reynolds Number (dimensionless) t time (s) u0 superficial gas velocity (m/s) up particle velocity (m/s) us slip velocity (m/s) ut terminal settling velocity (m/s)
Vp Z Zd Zr
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volume of particle (m3) distance (m) distance from downer entrance (m) distance from riser entrance (m)
Greek symbols e voidage (dimensionless) es solids holdup (dimensionless) lg gas viscosity (kg/(m2s)) qg gas density (kg/m3) qp solid density (kg/m3)
Acknowledgements The authors would like to acknowledge the financial support of NSERC and the following persons for taking the experimental data: H. Zhang, W. Huang, P.S. Johnston, and J.S. Ball. In addition, the assistance of Mr. Siva Ariyapadi in the preparation of the figures is gratefully acknowledged.
References [1] D.R. Bai, Y. Jin, Z. Yu, N. Gan, Radial profiles of local solid concentration and velocity in a concurrent downflow fast fluidized bed, in: P. Basu, M. Horio, M. Hasatani (Eds.), Circulating Fluidized Bed Technology, vol. III, Pergamon, Toronto, 1991, pp. 157 – 162. [2] E. Aubert, Pressure profiles and slip velocities in a co-current downflow fluidized reactor, in: A.A. Avidan (Ed.), Circulating Fluidized Bed Technology, vol. IV, AIChE, New York, USA, 1993, pp. 403 – 405. [3] J.-X. Zhu, Z.-Q. Yu, Y. Jin, J.R. Grace, A. Issangya, Co-current downflow circulating fluidized bed (downer) reactors—a state of the art review, Can. J. Chem. Eng. 73 (1995) 662 – 677. [4] P. Lehner, K.-E. Wirth, Characterization of the flow pattern in a downer reactor, Chem. Eng. Sci. 54 (1991) 5471 – 5483. [5] H. Zhang, W.-X. Huang, J.-X. Zhu, Gas – solid flow behavior: CFB riser vs. downer, AIChE J. 47 (2000) 2000 – 2011. [6] F. Berruti, J. Chaouki, L. Godfroy, T. Pugsley, G. Patience, Hydrodynamics of circulating fluidized risers: a review, Can. J. Chem. Eng. 73 (1995) 579 – 602. [7] Z. Wang, D. Bai, Y. Jin, Hydrodynamics of concurrent downflow circulating fluidized bed (CDCFB), Powder Technol. 70 (1992) 271 – 275. [8] Y.L. Yang, Y. Jin, Z.Q. Yu, Z.W. Wang, Investigation on slip velocity distribution in the riser of dilute circulating fluidized bed, Powder Technol. 73 (1992) 67 – 73. [9] Y.G. Bolkan-Kenny, T.S. Pugsley, F. Berruti, Computer simulation of the performance of fluid catalytic cracking risers and downers, I&EC Res. 33 (1994) 3043 – 3052. [10] Y.-L. Yang, J.-X. Zhu, Y. Jin, Z.-Q. Yu, Investigating and modeling of cocurrent downflow circulating fluidized bed (downer), Chem. Eng. Commun. 170 (1998) 133 – 157. [11] P.M. Herbert, T.A. Gauthier, C.L. Briens, M.A. Bergougnou, Flow study of a 0.05 m diameter circulating fluidized bed, Powder Technol. 96 (1998) 255 – 261. [12] S.-Y. Jiao, J.-X. Zhu, M.A. Bergougnou, M. Ikura, M. Stanciulescu, Investigation and modelling of the thermal cracking of waste plastics derived oil in a downer reactor, Chem. Eng. Res. Dev. (Process. Saf. Environ.) 76 (1998) 319 – 331. [13] W. Fei, R. Xing, Z. Rujin, G. Luo, Y. Jin, A dispersion model for fluid
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[17]
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Y. Bolkan et al. / Powder Technology 132 (2003) 85–100 catalytic cracking riser and downer reactors, Ind. Eng. Chem. Res. 36 (1997) 5049 – 5053. H. Schlichting, Boundary Layer Theory, 4th ed., McGraw Hill, New York, USA, 1960, pp. 502 – 533. W. Yang, Estimating the solid particle velocity in vertical pneumatic conveying lines, Ind. Eng. Chem. Fundam. 12 (1973) 349 – 352. C.E. Capes, K. Nakamura, Vertical pneumatic conveying: an experimental study with particles in the intermediate and turbulent flow regimes, Can. J. Chem. Eng. 51 (1973) 31 – 38. H. Zhang, J.-X. Zhu, M.A. Bergougnou, Hydrodynamics in downflow fluidized beds: (1). Solids concentration profiles and pressure gradient distributions, Chem. Eng. Sci. 54 (1999) 5461 – 5470. R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, Wiley, New York, USA, 1960. H. Zhang, J-X. Zhu, Hydrodynamics in downflow fluidized beds: (2). Particle velocity and solids flux profiles, Chem. Eng. Sci. 55 (2000) 4367 – 4377. C. Cao, Y. Jin, Z. Yu, Z. Wang, The gas – solid velocity profiles and slip phenomenon in a concurrent downflow circulating fluidized bed, in: A.A. Avidan (Ed.), Circulating Fluidized Bed Technology, vol. IV, AIChE, New York, USA, 1993, pp. 406 – 413.
[21] K. Tuzla, A.K. Sharma, J.C. Chen, T. Sciewe, K.E. Wirth, O. Molerus, Transient dynamics of solid concentration in downer fluidized bed, Powder Technol. 100 (1998) 166 – 172. [22] S. Krol, A. Pekediz, H.I. de Lasa, Particle clustering in down flow reactors, Powder Technol. 108 (2000) 6 – 20. [23] S.V. Manyele, J.-X. Zhu, H. Zhang, Characterizing cluster dynamics in a co-current downflow CFB using an optical fiber probe, Chem. Eng. Commun. (2001) (accepted for publication). [24] P.M. Johnston, H.I. de Lasa, J. Zhu, Axial flow structure in the entrance region of a downer fluidized bed—effects of the distributor design, Chem. Eng. Sci. 54 (1999) 2161. [25] D. Kunii, O. Levenspiel, Fluidization Engineering, 2nd ed., Butterworth-Heinemann, New York, 1991. [26] S. Krol, H. de Lasa, Particle interaction in down flow reactors, Proceedings of the Tenth Engineering Foundation Conference on Fluidization, United Engineering Foundation, New York, USA, 2001, pp. 189 – 196. [27] J.S. Ball, J.-X. Zhu, A comparison of solids fluxes in a pair of downer and riser reactors, Chem. Eng. Technol. 23 (2000) 701 – 705.
Modeling circulating fluidized bed downers Yasemin Bolkan a,*, Franco Berruti b, Jesse Zhu b, Bruce Milne a a
Department of Chemical and Petroleum Engineering, The University of Calgary, 2500 University Drive, NW Calgary, Alberta, Canada AB T2N 1N4 b Department of Chemical and Biochemical Engineering, The University of Western Ontario, London, Ontario, Canada Received 5 April 2002; received in revised form 8 January 2003; accepted 8 January 2003
Abstract In this work, the hydrodynamic features of circulating fluidized beds (CFB) are integrated into a new computer simulation of a downer reactor. The mathematical model is based on fluid dynamic fundamentals and calculates the characteristic flow parameters (solids holdup, particle velocity and pressure gradient) along the downer axis. Cluster formation within the downer is expressed through the ‘‘Equivalent Agglomerate Diameter’’, which is calculated through an empirical correlation that relates the average size of agglomerates to operating conditions. Pressure loss due to particle – wall friction is usually difficult to determine and a new empirical correlation is developed to estimate its value. The impact of particle – wall interactions can be discerned for a given set of operating conditions using the derived relationship. A correlation for estimating the particle – wall friction factor has also been developed based on available downer data and is presented in this work. Comparison of simulation results with downer flow data demonstrates successful model matching. The simulator accurately describes the hydrodynamic behavior of the gas – solid suspension within the downer both in the developing-flow as well as in the fully developed flow regions. D 2003 Elsevier Science B.V. All rights reserved. Keywords: Circulating fluidized beds; Downer modeling; Clusters
1. Introduction Circulating fluidized beds (CFB) have been proven over the years to be highly effective reactors for fast gas –solid reaction systems. These types of reactors have been successfully employed for a wide range of applications, including catalytic cracking, calcination operations, polyethylene production and combustion of a variety of fuels, since they offer advantages such as high throughput rates and thorough gas – solid contact leading to excellent heat and mass transfer. Conventionally, CFBs have been designed with the entrance of the reactor located at the bottom end, where the gas and solid feeds meet and flow upward to the exit at the top of the reactor. In spite of their many advantages, such co-current up-flow CFB reactors, also called risers, suffer from significant solids backmixing that may result, in some applications, in reduced selectivity and irregular distribution of the desired product. In recent years, a new type of CFB reactor, the downer, has been developed. In a downer, the gas and solid phases enter the reactor at
* Corresponding author.
the top section, allowing for the gas– solid mix to flow co-currently downward along the direction of gravity. This set-up leads to desirable hydrodynamic qualities such as more uniform flow and better control of fluid – solid contact times. Reports on CFB downers point toward their benefit over risers [1– 4]. Due to the complexity of CFB hydrodynamics, however, this area of research requires further attention. Recently, data analysis conducted on a state-of-the-art riser/ downer pair [5] has made a comparative inquiry into risers and downers possible, since this CFB pair has important design parameters in common and experiments have been run under similar operating conditions. In this work, general trends of CFB hydrodynamics observed on this experimental unit are combined with fundamental fluid dynamic laws, and a downer model is presented that is applicable for both descriptive as well as predictive purposes.
2. Downer simulation While riser modeling has received wide-ranged attention [6], downer modeling is still quite scarce. Even though the
0032-5910/03/$ - see front matter D 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0032-5910(03)00059-7
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Y. Bolkan et al. / Powder Technology 132 (2003) 85–100
reactors themselves essentially share the same design, entering feed and catalysts from the top instead of the bottom of a CFB results in significant variations in hydrodynamic behavior, making it necessary to develop separate models for each of the reactors. Downer hydrodynamic studies have been conducted for over a decade [7,8]. Since the first downer model published in 1994 [9], a number of modeling efforts have been reported, all of which consistently point to some of the advantages of downers when employed to carry out specific chemical reactions [10 –12]. Limited work has been published in literature describing simulations where the riser and downer hydrodynamic characteristics are coupled with kinetics of fast reactions such as fluid catalytic cracking [9,13]. These simulations suggest that downers may provide improved conversion rates and product selectivity. The downer model presented in this study is built on fundamental equations derived from momentum balances and mass conservation laws, which were derived by BolkanKenny et al. [9]. Mass Conservation: Gs ¼ qp ð1 eÞup
ð1Þ
Momentum Balance (on single particle): qp Vp
u dup 1 u0 0 ¼ q g up up Ap CD þ ðqp qg ÞVp g 2 dt e e ð2Þ
Momentum Balance (on gas –solid suspension): dP ¼ dz
dP dz
dP dz head
dP dz friction accel
ð3Þ
where
dP dz dP dz
¼ qp ð1 eÞg þ qg eg
ð4Þ
head
¼ qp ð1 eÞup accel
dup u0 dðu0 =eÞ þ qg e dz dz e
ð5Þ
and
dP dz
¼
friction
dP dz
0:3164 Re0:25 g
þ gaswall
dP dz
ð6Þ particlewall
1 u2 qg 0 ¼ fg 2D e gaswall
ð8Þ
where Reg ¼
Du0 qg elg
ð9Þ
Similarly, pressure loss due to particle –wall friction can be formulated as follows: dP 1 q ð1 eÞu2p ¼ fp ð10Þ dz particlewall 2D p Due to the complex mechanics and difficulty to isolate frictional effects from other pressure losses, the particle – wall friction factor, fp, is hard to determine [15]. There are a number of empirical correlations available for fp, most of which have been developed for up-flow systems [16]. Further details on particle –wall friction are presented under Results and discussion. In the presented model, the downer volume is discretized, and the mentioned equations are solved simultaneously for average voidage and average particle velocity, along with the drag coefficient for each control volume. In order to minimize the impact of discretization, the height of the control volume is kept under 1 mm. Derivative functions at each step are approximated using the fourth-order Runge –Kutta method. The resulting computer program is written in the C++ language and solves for the key hydrodynamic parameters throughout the downer. Even though experimental observations indicate a small degree of local radial variation, it is clear that downers operate under conditions closely approximating the plug flow [17]. Based on this, the proposed model is one-dimensional, predicting average values across the radius. Once voidage and particle velocity are predicted, the change in pressure is computed by calculating the pressure gradient along the downer axis. When the drag coefficient is calculated, Stoke’s Law applies for low Particle Reynolds Numbers:
Pressure loss due to gas – wall friction can be expressed
dP dz
fg ¼
CD ¼
as
with fg being the gas friction factor. According to the empirical Blasius Formula [14]:
24 Rep
for Rep < 1
ð11Þ
where qg ue0 up dp Rep ¼ lg
ð12Þ
while Eq. (13) holds for high Rep values: ð7Þ
CD ¼ 0:44
for Rep > 1000
ð13Þ
Y. Bolkan et al. / Powder Technology 132 (2003) 85–100
Various empirical correlations have been incorporated in the program for drag coefficient calculations in the intermediate range, which have been observed to cause relatively minor changes in results. Hence, the well-established correlation by Bird et al. [18] has been used as the default: CD ¼
18:5 Re0:6 p
for 1VRep V1000
ð14Þ
It has been experimentally observed that slip velocities in downers are generally significantly larger than the terminal settling velocity of a single particle [11,19]. Particle agglomeration appears to be the most reasonable explanation for this occurrence [10,20,21]. Therefore, agglomeration is incorporated in the downer model. Direct evidence of particle agglomeration has been documented for a downer experimental unit [22]. It is suspected that clusters start forming in the feeder region of the downer, which then collapse and reform throughout the entire downer length. This assumption is verified by Manyele et al. [23], whose experimental observations show that the number of clusters (cluster fre-
87
quency) and their sizes (cluster existence time) vary throughout the downer length, their individual effects compensate each other. Therefore, the percentage of cluster formation (cluster time fraction) remains practically constant at all measured locations for any given set of operating conditions, as a result of a dynamic equilibrium that is established along the downer. In order to represent these experimental findings, a parameter named ‘‘Equivalent Agglomerate Diameter’’ is introduced in the downer model. Further information on this parameter is discussed in Results and discussion.
3. Experimental set-up and data collection Extensive data [17,19] have been gathered previously on a downer– riser unit, which is schematically presented in Fig. 1. The riser and downer both have an inner diameter of 0.1 m. FCC catalyst particles (67 Am diameter and 1500 kg/m3) enter the riser inlet from the storage tank and are fluidized by air with a relative humidity of 70 – 80% to minimize electrostatic effects. The gas – solid suspension travels upward
Fig. 1. Experimental set-up.
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along the 15.1-m-tall riser. At the riser exit, solids are separated from the air through cyclones. Just below the primary riser cyclone, solids enter the downer solids distributor where they are held at minimum fluidization (see insert in Fig. 1). Particles then fall through 31 vertical tubes of 0.36 m length and 12.7 mm OD. A gas distributor consisting of a plate with 31 holes of 16.7 mm ID is located 50.8 mm above the exit point of the vertical tubes. The downer air enters from above this plate and moves downward through the 2 mm gap between each tube and hole in order to interact with the particles exiting the tubes. The gas – solid suspension flows co-currently downward along the 9.3-m-long downer in the direction of gravity. At the downer exit, the solids are separated from the air in the fast separator and are moved to the storage tank. Further details of the experimental set-up are presented by Zhang et al. [17,19]. Local solids holdup and velocity along with axial pressure gradient were measured for each given set of superficial gas velocity and solids flux. The solids circulation rate was controlled by the solids control valve at the riser entrance and was measured by diverting the collected solids from the downer fast separator into the measuring vessel for a given period of time. The pressure drop along the downer was measured by pressure transducers. The local solids holdup was measured through an optical fiber solids concentration probe, the details of which are presented elsewhere [17]. The local particle velocity was measured using an optical fiber particle velocity probe [19]. The superficial gas velocity u0 ranged between 3.5 and 10.2 m/s, whereas the solid flux, Gs, varied between 49 and 208 kg/(m2s). Local solids holdup and particle velocity were measured in both the riser and the downer at 11 radial positions along eight axial locations, while pressure was measured at eight axial locations. Data gathered using the above-described unit are utilized for model verification. Radial averages of local downer data are determined at all measured axial positions and are then compared with model results that predict average values of flow parameters along the downer axis. Fully developed flow data is used to express the equivalent agglomerate diameter as a function of operating conditions. Pressure loss at the wall, which is a challenging parameter to determine experimentally, is also related to operating conditions. General trends of radial downer data are examined in order to ensure that no crucial information is lost in the averaging process. Additionally, radial profiles for a downer and riser based on data collected under similar operating conditions [7] are taken into account for a qualitative discernment of benefits and limitations of downers in comparison to risers.
4. Results and discussion 4.1. Comparison of model vs. data The predicted solids holdup, average particle velocity and pressure profiles have been compared with data collected on
the presented downer equipment. Figs. 2 –4 compare model predictions with downer data for a variety of operating conditions. At the top of the downer, the FCC particles are fluidized under minimum fluidization conditions at a solids holdup of approximately 0.40 [24,25]. When the catalyst particles enter the downer feeder tubes, they undergo a period of free-fall for roughly 0.5 m. The acceleration of particles in this section results in a considerable dilution of the solids concentration to less then 0.04 [24]. Average solids holdup at the downer inlet that are calculated in this manner match very well with available data. Once the solid phase enters the downer, further acceleration and consequent dilution of solids holdup occurs. The solids holdup eventually reaches a constant value, indicating that fully developed flow is established. Fig. 2 illustrates that at the fixed superficial gas velocity of 3.7 m/s, increasing solids flux from 49 to 101 kg/(m2s) and subsequently to 194 kg/(m2s) results in axial nonuniformity, causing steeper solids holdup profiles mainly in the entrance zone of Zd = 0– 2 m. Higher solids flux also extends the developing flow region. Since solids concentration is a direct function of the solids throughput, average solids holdup at any location is higher for increased solids flux scenarios. It is evident from Fig. 2 that the model matching of data is accurate. Figs. 3 and 4 illustrate axial solids holdup profiles for superficial gas velocities of u0 = 7.2 and 10.2 m/s, respectively. For a similar range of solids fluxes as for u0 = 3.7 m/ s, at roughly 50, 100 and 200 kg/(m2s), the higher superficial gas velocity scenarios result in similar trends for axial solids holdup profiles. At a closer look, however, it is evident that increasing gas velocity causes a consistent decrease in solids holdup at any axial position. For example, when solids flux is approximately 200 kg/(m2s), averaged solids holdup data near the exit (Zd = 9.2 m) drops 17.5% or 34.9%, as u0 increases from 3.7 to 7.3 m/s or to 10.1 m/s, respectively. The axial profiles for average particle velocity are illustrated in Figs. 5– 7. Contrary to solids holdup, particle velocity is found to be more sensitive to variations in gas velocity than solids flux. For a better overview, the nine sets of operating conditions at which data has been collected are gathered in each figure such that gas velocities are varied at constant flux. Initially, as the particles are leaving the top solids distributor fluidized bed, the velocity of particles is in accordance with the minimum fluidization voidage and is calculated from the mass conservation equation (Eq. (1)). Within the feeder tubes, particles undergo a period of freefall. The amount of resulting acceleration is calculated based on the length of these feeder tubes. The calculated particle velocities at the downer inlet are in good agreement with measured values near the entrance. Particles continue accelerating once they enter the downer, until reaching a constant velocity. The value of this fully developed particle velocity exceeds the actual gas velocity due to gravity effects.
Y. Bolkan et al. / Powder Technology 132 (2003) 85–100
89
Fig. 2. Model predictions vs. data for solids holdup along the downer, u0 = 3.7 m/s.
Even though all of the presented average particle velocity profiles in Figs. 5 – 7 share the same trend, particle velocity at any axial location increases at higher superficial gas
velocities. Increasing gas velocity at a constant solids flux is also found to shorten flow development. Increasing solids flux on the other hand indicates extended flow develop-
Fig. 3. Model predictions vs. data for solids holdup along the downer, u0 = 7.2 m/s.
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Y. Bolkan et al. / Powder Technology 132 (2003) 85–100
Fig. 4. Model predictions vs. data for solids holdup along the downer, u0 = 10.2 m/s.
Fig. 5. Model predictions vs. data for particle velocity along the downer, Gs = 49 kg/(m2s).
Y. Bolkan et al. / Powder Technology 132 (2003) 85–100
Fig. 6. Model predictions vs. data for particle velocity along the downer, Gs = 101 kg/(m2s).
Fig. 7. Model predictions vs. data for particle velocity along the downer, Gs = 202 kg/(m2s).
91
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Y. Bolkan et al. / Powder Technology 132 (2003) 85–100
ment. For all flow scenarios, at constant superficial gas velocity, the particle velocity at the exit is higher for increased solids flux. At u0 = 3.7 m/s, for example, increasing Gs from 49 to 101 kg/(m2s) or to 194 kg/(m2s) has quite an impact on particle velocity, resulting in an increase in the exit up from 6.5 to 7.6 m/s (16.9%) or to 8.3 m/s (27.7%), respectively. Worth noting is that the presented radial solids holdup and particle velocity data are the result of multiple local readings at a given radial location at any axial position. These local readings are averaged to determine data at a particular radial location. Since this process introduces a variation from actual readings, using the resulting solids holdup and particle velocity data to calculate solids flux causes a minor discrepancy in mass conservation. Solids flux calculated in this manner is found to vary up to 11% from the inlet solids flux. Hence, it is inevitable that the downer simulator, which incorporates conservation of mass, produces slightly different results than radial averages of these values that are averaged at each radial location. Nonetheless, in the overall trend of the downer fluid dynamics, it is clearly observed that data and model predictions match very well. As described by Eq. (3), the pressure gradient is made up of three components. Static head causes the pressure to increase along the downer, whereas acceleration and frictional effects result in pressure loss. The pressure gradient in the downer is illustrated in Fig. 8 for a variety of operating conditions. For all operating conditions, at
constant solids flux, an increase in superficial gas velocity results in a decrease in the pressure gradient, which has also been observed by Aubert [2]. On the other hand, at a fixed superficial gas velocity, increasing the solids flux results in increased pressure gradients showing the strong effect that static head has on the pressure gradient profile. Frictional losses include gas – wall and particle – wall interactions. While the gas – wall friction factor is wellestablished, a reliable method for calculating the particle – wall friction factor for downers is not available. Eq. (10) presents the relationship of frictional losses to particle concentration and velocity. Solids holdup data has quite low values for all operating conditions, while particle velocity is lowest for the gas velocity of u0 = 3.7 m/s. Hence, particle – wall effects would be least dominant for this low gas velocity. In order to determine the quality of model prediction prior to introducing an empirical correlation for the particle –wall friction term, the model is run for the stated operating conditions excluding any particle – wall interaction. The pressure gradient data, which is measured at eight axial locations along the downer, is compared to model predictions for all there solids fluxes ( Gs = 49, 101 and 194 kg/(m2s)) at the fixed gas superficial velocity of u0 = 3.7 m/s in Fig. 9. The pressure gradient starts out negative, mainly due to pressure losses during particle acceleration. Once acceleration effects lessen, the static head starts dominating the changes in pressure while frictional losses counter-
Fig. 8. Pressure gradient profiles along the downer.
Y. Bolkan et al. / Powder Technology 132 (2003) 85–100
93
Fig. 9. Model predictions vs. data for pressure gradient along the downer, u0 = 3.7 m/s.
act to a lesser degree. This causes the pressure gradient to become positive, which eventually reaches a constant value indicating that flow development is complete. Increasing the solids flux causes larger static heads, which in turn leads to higher pressure gradient profiles. The results of the simulation are in good agreement with the data and confirm that at low gas velocity, particle – wall friction is negligible. For higher gas velocities, however, particle –wall frictional losses are found to be more significant. 4.2. Particle – wall friction Isolating the component of pressure drop that refers to frictional losses at the wall is difficult due to the complex mechanics involved [17]. In this work, the magnitude of frictional loss due to the interaction between the solid phase and the wall is determined using a unique feature of the downer model. Unlike solids holdup and velocity, the pressure function in the downer model calculates the pressure gradient at a given axial location independent of pressure at any other location, i.e. the pressure gradient solely depends on the flow condition at any specific axial location. This makes it possible to determine a pseudopressure gradient that excludes particle – wall friction for fully developed flow conditions. When this output is compared to fully developed flow data, the difference between model prediction and data represents the frictional losses caused by particle – wall interaction for each operating
condition. Resulting particle – wall friction values are shown graphically in Fig. 10. As expected, particle – wall friction becomes more dominant with an increase in gas velocity as well as solids flux. An empirical correlation is proposed to calculate the particle –wall friction term as a function of operating conditions:
dP dz
¼ 0:028u0:876 G1:177 0 s
ð15Þ
particlewall
This empirical correlation, graphically represented in Fig. 10, can be used to discern whether the particle – wall friction term is significant for a given set of operating conditions. The particle –wall friction factor, fp, can be calculated for individual operating conditions along with known particle concentration and velocity by equating Eqs. (10) and (15). Capes and Nakamura [16] developed an empirical correlation based on data gathered in a riser in order to relate the particle –wall friction term to particle velocity. fp ¼ 0:206u1:22 p
ð16Þ
Since the hydrodynamics of up-flow and down-flow systems vary quite drastically near the wall, and experimental data used for their correlation involved relatively large particles, the coefficients in the correlation are not expected
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Y. Bolkan et al. / Powder Technology 132 (2003) 85–100
Fig. 10. Effect of operating conditions on particle – wall friction. Symbols: calculated particle – wall friction. Lines: particle – wall friction as a function of operating conditions (Eq. (15)).
to be suitable for downers. Nonetheless, the relationship between the friction term and particle velocity is expected to be similar for risers and downers, and the following correlation is determined for down-flow CFBs based on the available downer data with FCC catalysts. This friction factor expression can be improved further once new downer data is produced.
This slip velocity is equal to the terminal free-fall velocity of a particle of size dp falling through a fluid. Based on fluid mechanics [25]:
fp ¼ 0:003u0:426 p
where CD is a function of Particle Reynolds Number which in turn is a function of particle diameter and terminal free-fall velocity (Eq. (12)). Through an iterative process, a particle diameter is determined that is consistent with each calculated slip velocity. Using this approach, the equivalent agglomerate diameter, da, the diameter that represents the size of agglomerates (clusters) in the fully developed flow region of the downer, can be determined. To do so, superficial gas velocity data along with averages for particle velocity and voidage of fully developed flow data gathered on the presented downer equipment are introduced into Eq. (18). The equivalent agglomerate diameters thus determined are presented by the symbols in Fig. 11. The extent of clustering within the downer is strongly affected by operating conditions, so that it is beneficial to describe this parameter in terms of the operating conditions in order to make it a fully predictable feature within the downer simulator. The data points show that as the solids flux increases da increases due to particles having more
ð17Þ
4.3. Equivalent agglomerate diameter The ‘‘Equivalent Agglomerate Diameter’’ is determined for the solid phase, based on the fluid mechanic relationship between a particle and its terminal settling velocity. For a particle that has a terminal velocity, ut, a particle diameter, dp, can be calculated, representing an equivalent particle of spherical shape. In case of the solids moving in a downer in fully developed flow, the terminal velocity of the solid phase is represented by the slip velocity. For a given set of operating conditions, the superficial gas velocity along with voidage and particle velocity in fully developed flow are used to calculate the slip velocity: us ¼
u0 up e
ð18Þ
"
4dp ðqp qg Þg u s ¼ ut ¼ 3qg CD
#1=2 ð19Þ
Y. Bolkan et al. / Powder Technology 132 (2003) 85–100
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Fig. 11. Effect of operating conditions on equivalent agglomerate diameter. Symbols: calculated values based on data [5]. Lines: calculated values based on Eq. (20).
opportunity to interact and cluster, and as gas velocity increases da decreases, caused by the reduced suspension density and stability within the suspension. For data gathered on the presented downer unit, the dependence of the equivalent agglomerate diameter on operating conditions, Gs and u0, can be expressed by a consistent linear relationship through the following empirical correlation (represented by the lines in Fig. 11): da ¼ 0:7173 þ 0:0015Gs 0:0672u0
ð20Þ
Krol et al. [22] report that the solid phase starts out as single particles that gradually agglomerate to average cluster sizes of two to six single particle diameters and estimate that 28 – 29 ms are required for a cluster of four particles to be formed. The model incorporates single particles at the entrance of the downer which start clustering within the agglomeration formation time, gradually growing into clusters that have a particular equivalent agglomerate diameter in accordance with current fully developed flow conditions. Considering that experimental observations by Krol et al. are based on FCC particles in a downer of 2.5 cm diameter operating at very low solids fluxes (3 –7 kg/m2 s) and low gas velocities (0.5 – 4 m/s), it is highly possible that the reported values could vary with operating conditions. In accordance with more recent observations [26], agglomeration formation times up to 100 ms have been taken into account in the proposed model. However, such changes in this parameter are found
to be insignificant, and the agglomeration formation time is kept at the default value of 30 ms for all reported results. 4.4. Radial profiles All data used for model verification so far, as presented in Figs. 2 – 11, are based on radial average values of flow parameters. In this section, the source data that is used to determine these values at any given axial position is examined to ensure that this radial averaging process results in a reasonable approximation. The general trends of radial solids holdup profiles in the downer are illustrated on the right-hand side in Fig. 12. In the downer, the solids holdup in the core region of r/ R = 0.0 – 0.4 stabilizes quite quickly, with es varying minimally along the downer axis. The trend in the middle region of r/R = 0.4 – 0.8 seems to also settle relatively quickly, with its initial upward drift flattening out as the solids move through the downer. The most distinct variation in es values is observed throughout the downer in the annular region, r/R = 0.8 – 1.0. In the entrance zone, a significant densification is evident near the wall. Further down the column, the solids holdup at the wall drops considerably, resulting in a maximum accumulation of solids at about r/R = 0.9, which has also been reported in other experimental units [1]. Near the downer exit, the solids holdup profile is essentially flat, with a slight drop in es at the wall for most operating conditions.
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Fig. 12. Radial solids holdup profiles along the riser and the downer (data from Ref. [5]).
Even though some degree of radial non-uniformity is observed, in particular in the wall region of the downer, the significance of this phenomenon is put in proportion when compared with observations in the riser. The general trends of radial solids holdup profiles in the riser are presented on the left-hand side of Fig. 12. These profiles are based on data collected on a riser/downer pair that has important design parameters in common [5]. Presenting solids holdup profiles for the riser and downer on the same scale at similar operating conditions demonstrates the distinct variation in hydrodynamic behavior between
these two types of CFBs. Fig. 12 illustrates that the solids holdup profile in the riser is most elevated in the annular region of r/R = 0.8– 1.0. This profile undergoes a transition within r/R 0.4 –0.8, becoming practically flat in the core region (r/R 0.0 – 0.4). This flow structure within CFB risers, presenting the same solids holdup profile of a dense radial suspension near the wall with low density in the core region throughout the reactor, has also been reported elsewhere [6]. Even though the solids holdup profile flattens out toward the riser exit for all presented operating conditions, the core-annular flow structure
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remains evident for most operating conditions throughout the riser. On the other hand, in view of riser profiles, downer profiles are practically flat. Hence, the average values predicted by the simulator may be a close approximation of local values at most radial locations for any given axial position. Another issue to consider is whether the point at which flow becomes fully developed according to the axial profiles is in agreement with local observations across the radius. Variations in local solids holdup occur most significantly in the vicinity of the wall (Fig. 12). Hence, the behavior of local solids holdup near the wall (r/ R = 0.975) is examined to determine when fully developed flow is reached in the downer. Fig. 13 illustrates that in spite of considerable fluctuations near the downer entrance, solids holdup near the wall reaches a constant value at around 4 m for all flow scenarios except for the operating condition with the lowest gas velocity (3.7 m/s) and highest solids flux (194 kg/m2s), in which case the axial solids holdup profile flattens out at roughly 6 m. Overall, the accumulation of solids near the wall appears to be more sensitive to variations in gas velocity than to changes in solids flux. The fact that this hydrodynamic parameter reaches a constant value indicates that flow conditions have become fully developed. These observations overlap with characteristics of axial profiles, and hence verify that even the hydrodynamic behavior in the most turbulent radial section of the downer is in agreement with averaged axial profiles.
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Finally, the effect of changing operating conditions is considered for axial and radial downer data. Higher gas velocities that were found to cause more uniform flow axially (Figs. 2 – 4) are also found to improve radial uniformity (Fig. 12). Figs. 2 –4 in relation with Fig. 12 also reveal that increasing solids flux results in axial as well as radial non-uniformity throughout the downer. No radial observation is found that counteracts the assumption that radial average values present a realistic approximation of the downer hydrodynamics. 4.5. Downer vs. riser usage In order to determine benefits and limitations of downers, general trends of hydrodynamics of downers are compared to risers. Fig. 14 illustrates that fluctuations observed near the wall in the downer are not as evident as that in the riser. However, the solids holdup profile continues changing until the exit for all measured flow conditions for the riser. For the case of u0 = 3.5 m/s and Gs = 100 kg/m2s, the local solids holdup variation at r/ R = 0.975 is as high as 20% within the last 2 m of the riser, decreasing from 0.094 to 0.071 between 12.3 and 14 m, respectively. Some similarities in riser and downer hydrodynamics exist, such as higher gas velocities and lower solids flux causing more uniform flow in both reactors, as shown in Fig. 12. The dependence on gas velocity is much stronger in the riser, however, since it is the gas phase that pushes
Fig. 13. Variation in solids holdup near the wall along the downer (data from Ref. [5]).
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Fig. 14. Variation in solids holdup near the wall along the riser (data from Ref. [5]).
the suspension against gravity. In the riser, the effect of increased solids flux is more noticeable as the accumulation of solids occurs mainly in the annulus, increasing the steepness of the upward curve in this zone. In the downer, changes in solids flux affects solids holdup more evenly across the radius. Comparing Fig. 14 with Fig. 13 reveals one of the most significant benefits of downers regarding the length of flow development: the flow development length is much longer for the riser. Another undesirable characteristic of CFB risers is known to be backmixing. This is usually observed near the wall where a substantial amount of solids flow down, backwards with respect to the entrance zone. The resulting non-uniformity in residence time could affect reaction performance adversely. This occurrence is alleviated in the downer since gas and solids flow in the direction of gravity. On the other hand, a potential drawback of the downer is low solids holdup throughout the reactor. Under similar operating conditions, the riser contains more solids relative to the downer (Fig. 12). For example, the radial average of solids holdup for the riser at 10 m is 0.04 under operating conditions of u0 = 3.5 m/s and Gs = 100 kg/m2s, whereas in the downer at 9.2 m for u0 = 3.7 m/s and Gs = 101 kg/m2s, it is 0.01, merely a quarter of its counterpart in the riser. While enabling more uniform flow is one of the most significant benefits of downers, facilitating higher solids concentrations is a strong hydrodynamic feature of risers. Therefore, advantages of downers may
be most evident for reaction systems that operate in dilute solids suspension. Comparison of riser and downer data obtained from the presented test unit [5,27] indicates that downers have an excellent potential for applications in industry that require high fluid– solid contact efficiency and product selectivity within short reaction times. Nevertheless, it would be beneficial to determine how sensitive the reaction system is to the time in which fully develop flow is reached, and to the degree of backmixing, as well as to the attainable suspension density within the reactor, before discerning whether a riser or downer reactor would be more appropriate for a particular chemical reaction.
5. Conclusions A downer simulator is presented which accurately describes the hydrodynamic behavior of the gas – solid suspension within the reactor both in the developing-flow and fully developed flow regions. The computer program is based on fluid dynamic fundamentals and calculates average flow parameters along the downer axis. A comparison between simulation results and flow data demonstrates successful model matching regardless of the state of flowdevelopment. An empirical formula is developed to relate the particle– wall friction term to a given set of operating con-
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ditions. While it is found that particle – wall friction is insignificant for low gas velocity, this correlation can be used to estimate the impact of the particle – wall friction term on the pressure gradient profile for operating conditions corresponding to higher gas velocities and solids fluxes. Furthermore, based on available data, a preliminary correlation has been proposed for the particle –wall friction factor in downers. The downer model is enhanced by the introduction of an empirical correlation to estimate the average size of agglomerates that form within the downer. The ‘‘Equivalent Agglomerate Diameter’’ is expressed as a function of operating conditions, and enables the downer model to be applicable for predictive purposes, such as modeling data under developing flow conditions or simulating operating conditions of interest to industry. Examining trends of radial profiles in comparison with radially averaged data verifies that averaging flow parameters in this manner causes no crucial loss of information within the downer. Hence, the downer model, which matches radially averaged data very well, constitutes a realistic representation of the downer hydrodynamics. Additionally, a qualitative discernment of benefits and limitations of downers in comparison to risers is determined using general trends of radial profiles in a downer and riser pair that was run under similar operating conditions. Downers may offer improved performance in comparison to the riser, especially for dilute reaction systems. However, before discerning whether a riser or downer reactor would be more appropriate for a particular chemical reaction, it is found to be beneficial to determine how sensitive the reaction system is to the time in which fully develop flow is reached, and to the degree of backmixing, as well as to the attainable suspension density within the reactor. Nomenclature Ap cross-sectional area of particle (m2) CD drag coefficient (dimensionless) D column diameter (m) da equivalent agglomerate diameter (mm) dp particle diameter (mm) fg gas friction factor (dimensionless) fp particle –wall friction factor (dimensionless) g gravitational constant (m2/s) Gs solids flux (kg/(m2s)) P pressure (Pa) r/R normalized radial distance from center of reactor (dimensionless) Reg gas Reynolds number (dimensionless) Rep particle Reynolds Number (dimensionless) t time (s) u0 superficial gas velocity (m/s) up particle velocity (m/s) us slip velocity (m/s) ut terminal settling velocity (m/s)
Vp Z Zd Zr
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volume of particle (m3) distance (m) distance from downer entrance (m) distance from riser entrance (m)
Greek symbols e voidage (dimensionless) es solids holdup (dimensionless) lg gas viscosity (kg/(m2s)) qg gas density (kg/m3) qp solid density (kg/m3)
Acknowledgements The authors would like to acknowledge the financial support of NSERC and the following persons for taking the experimental data: H. Zhang, W. Huang, P.S. Johnston, and J.S. Ball. In addition, the assistance of Mr. Siva Ariyapadi in the preparation of the figures is gratefully acknowledged.
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