Axial Solids Holdup Distribution in a Liquid–Solid ... - ACS Publications

Nov 6, 2012 - Department of Chemical Engineering, Visvesvaraya National Institute of Technology Nagpur (VNIT Nagpur), Nagpur-440010,. India. ‡...
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Axial Solids Holdup Distribution in a Liquid−Solid Circulating Fluidized Bed: Effect of the Liquid Distributor, Method of Operation, and Viscosity of the Fluidizing Media Vidyasagar Shilapuram† and P. S. T. Sai*,‡ †

Department of Chemical Engineering, Visvesvaraya National Institute of Technology Nagpur (VNIT Nagpur), Nagpur-440010, India ‡ Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai-600036, India ABSTRACT: While the choice of the location of the liquid distributor in a liquid−solid circulating fluidized bed is application dependent, three different methods exist for operating the riser in the circulating fluidization regime. Experiments were conducted to study the effect of the location of the liquid distributor, method of operation, liquid viscosity, and solids inventory on the axial solids holdup distribution in the circulating fluidized bed regime. The results show that the location of the liquid distributor has a significant effect on axial solids holdup, and the axial solids holdups obtained by the three methods of operation are different under identical conditions. The variation of the axial solids holdup distribution with liquid viscosity with a solid inventory of 0.15 m was different from that with both 0.25 and 0.35 m solid inventories. There is significant interaction of the solids inventory and liquid viscosity on the axial solids holdup distribution.

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INTRODUCTION

transitional liquid velocity to attain uniform axial solids holdup for heavier particles.12 The bed voidage was uniform along the length of the riser and nonuniform radially for the viscous solutions.13 Sand, silica gel, and resins showed uniform solids holdup along the length of the riser.16 A recent study for various particle shapes, densities, and sizes observed uniform axial solids holdup except at the lower location close to the distributor region.17 The effect of the solids inventory in the downcomer and viscosity of the fluidizing media on the pressure drop, critical transitional liquid velocity to the circulating fluidized bed regime, onset average solids holdup, average solids holdup, and solids circulation rate was reported.4 A critical analysis of the literature indicates that most of the investigations are restricted to studies with various particle shapes, sizes, and densities, and information on the effect of the liquid viscosity on the axial solids holdup distribution in the LSCFB is scanty. However, the only reported information is limited to one solid inventory with an LSCFB unit operated under variable inventory mode.13,14 The riser in the LSCFB can be operated by three different methods according to the introduction of the two liquid streams (primary and auxiliary). Of these three methods, the basis for the selection of a method to achieve a particular solids holdup and solids circulation rate in the riser to accomplish a desired product yield or separation is not available. Many of the investigators did not even mention the method of operation they followed. However, the onset of average solids holdup is greatly influenced by the method of operation,3 and the effect of the method of operation on the axial solids holdup has not been clearly known till now.

Liquid−solid circulating fluidized beds (LSCFBs) consist of a riser, a liquid−solid separator, and a downcomer, and the solids circulate continuously between the riser and the downcomer. In the LSCFB, two different streams can be applied in the riser and downcomer for two different operations or processes. The LSCFB finds applications in various physical, chemical, and biological processing in situations where conventional liquid− solid fluidized beds have disadvantages such as ineffective use of the column length for reaction, low product throughput because of low velocities, and inefficient contact between the viscous liquid and solids phases due to low operating velocities.1,2 On the basis of the structure of the solids feeding system and/or dependency of the solids holdup and solids circulation rate into the riser, the LSCFB can be classified as either a fixed or a variable inventory mode.3,4 A rather large number of publications have appeared on topics covering the hydrodynamics, and most of them concern the fixed inventory system.3−5 When radial variations in solids holdup do not affect the desired conversion/product yield, the axial solids holdup distribution provides useful information for the design of the equipment. The axial solids holdup distribution in liquid−solid and gas−liquid−solid circulating fluidized beds has been discussed by many investigators.6−17 The bed voidage was observed to be uniform along the length of the riser in the circulating fluidized bed regime for different primary and auxiliary liquid velocities.7−9 The axial solids holdup distribution becomes uniform once the riser enters the circulating fluidized bed regime for low-density particles (plastic beads) and for high-density particles (glass beads and steel shots); on the other hand, the axial solids holdup distribution is not uniform even after the riser enters the circulating fluidized bed regime.10 The liquid velocity must be larger than the critical © 2012 American Chemical Society

Received: Revised: Accepted: Published: 16242

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The studies on the effect of the location of the primary distributor indicate that the primary liquid injection tap should be located at the middle of the intersection of the riser and solids feeding pipe.18 Thus, the solids circulation rate can simply be controlled by the primary liquid alone, i.e., even when the auxiliary velocity is zero. However, the system dimensions are too small (i.e., the riser is of 6 mm i.d. and 2.1 m height) to comment on the hydrodynamic parameters.18 On the other hand, in most of the situations with the riser as a reactor or desorption column and the downcomer as a regenerator or adsorption column, the location of the primary liquid distributor must be in such a way that there is a dynamic seal between the riser and downcomer.19 The influence of some hydrodynamic variables for two different locations of the primary liquid distributor with water as the fluidizing media is reported.20 The locations of the primary liquid distributors chosen were in such a way that no dynamic seal exists in one position and a complete dynamic seal exists in another position.20 Except for two investigations,18,20 there appears to be no published work discussing the effect of the location of the primary liquid distributor on the hydrodynamics in an LSCFB with the fixed inventory mode. Hence, in the present study, the effect of the location of the primary liquid distributor, experimental method of operation, solids inventory in the downcomer, and viscosity of the fluidizing media on the axial solids holdup distribution is investigated.

Figure 1. Location of the primary liquid distributor.

m solids inventories and water as the fluidizing media for various primary and auxiliary liquid velocities. Similarly, by method 3 of operation, experiments were repeated with the primary liquid distributor at position 2 for various viscosities of the liquids, i.e., 0.903, 1.17, 1.55, and 3.22 cP. These details are listed in Table 1.

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Table 1. Range of Variables Covered in the Present Study

EXPERIMENTAL SECTION The details concerning the experimental setup, experimental procedure employed and physical properties and range of liquid velocities used are described elsewhere.3,4,20 Glass beads with an average diameter of 1.36 mm and density of 2468 kg/m3 were used as the dispersed phase. Tap water and aqueous glycerol solutions were used as the continuous phase. At the steady state, the pressure drop along the length of the riser and solids circulation rate were recorded for various primary and auxiliary liquid velocities, solids inventories in the downcomer, and viscosities of the liquid. To study the effect of the method of operation on axial solids holdup distribution, the following methods were employed.3 In method 1, for a known solids inventory in the downcomer, the auxiliary liquid velocity was set to a constant value and the primary liquid velocity was varied from zero to a maximum value (limited by the pump capacity). In method 2, for a known solids inventory in the downcomer, the primary liquid velocity was set to a constant value and the auxiliary liquid velocity was varied from zero to a maximum value (limited by the flow meter). In method 3, for a known solids inventory in the downcomer, the primary liquid velocity was increased from zero until the solids in the riser were about to entrain. Once the solids in the riser started entraining, the auxiliary liquid flow was introduced and set to a particular value. The primary liquid velocity was then increased in small intervals to a maximum value (limited by the pump capacity). The locations of the primary liquid distributor chosen in the present study are shown in Figure 1. With the primary liquid distributor at position 2, experiments were conducted by methods 1 and 2 of operation with a 0.25 m solids inventory in the downcomer and water as the fluidizing media for a wide range of primary and auxiliary liquid velocities, whereas by method 3 of operation, experiments were conducted with the primary liquid distributor at position 1 with 0.15, 0.25, and 0.35

range variable primary liquid velocity, m/s auxiliary liquid velocity, m/s solids inventory, m viscosity of the liquid, Cp primary distributor location

method 1

method 2

method 3

method 3

0−0.276

0−0.221

0−0.36

0−0.34

0−0.096

0−0.124

0−0.108

0−0.108

0.25 0.903

0.25 0.903

0.15−0.35 0.903

position 2

position 2

position 1

0.15−0.35 0.903− 3.22 position 2

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RESULTS AND DISCUSSION The total liquid superficial velocity (Ul) above the liquid distributor is the sum of the primary and auxiliary liquid velocities. Using the pressure drop measurements, the bed voidage and solids holdup at each measured section are obtained by combining the following equations, neglecting the effect of wall friction: ΔP − = (ρε + ρl εl,loc)g s s,loc (1) ΔH εs,loc + εl,loc = 1 (2) Eleven pressure taps were located along the length of the riser at regular intervals of 20 cm with the location of the auxiliary distributor plate as the datum level. All these pressure taps were connected to a multilimb manometer. Carbon tetrachloride was used as the manometric liquid. During the experimentation, the manometric liquid was static and fluctuations in the manometer readings were not noticed. H is defined as the axial distance from the auxiliary distributor plate. The axial solids holdup at H = 0.3 m is defined as the solids holdup obtained from the 16243

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pressure drop measured between 0.2 and 0.4 m from the auxiliary distributor plate. A similar definition holds for axial solids holdup from H = 0.5 m to H = 1.9 m. The first section is very near the primary liquid distributor (i.e., it lies in the distributor zone), and large fluctuations in the pressure drop are observed at high liquid velocities. Therefore, the axial solids holdup distribution measured at a sufficiently higher position (from H = 0.5 m to H = 1.9 m) from the solid recycle port to avoid the end effects is presented in the present study. The pressure drop between each section in the riser was obtained experimentally from the difference in manometer readings corresponding to that section, and it is equivalent to ΔP = (ρman − ρl)gh. Most of the experiments were conducted two to three times to ensure the reproducibility of the data. The average of all the runs was reported as axial solids holdup at each location. Furthermore, the variation noted in solids holdup was within ±5% for most of the experiments. Variation of the Average Solids Holdup and Bed Voidage with the Slip Velocity. The slip velocity is one of the important variables used to estimate the drag force acting on the particle in a multiphase system. Assuming homogeneous fluidization in the axial and radial directions, the following relation among the bed voidage, liquid velocity, and superficial solids velocity21 is used by extending the Richardson−Zaki (R− Z) equation:22 U εc Ul − s = εc n Ut Ut 1 − εc

Figure 2. Comparison of the experimental and predicted slip velocities.

(3)

Assuming homogeneous fluidization, the experimental and predicted slip velocities are as follows: Uslip,e =

Us Ul − εl 1 − εl

(4)

Uslip,c = Utεc n − 1

Figure 3. Comparison of the experimental and predicted bed voidages using the R−Z equation.

(5)

The exponent n can be calculated from the following relations: n = 4.65

Ret < 0.2

n = 4.45Ret−0.03

0.2 < Ret < 1

n = 4.45Ret−0.1

1 < Ret < 500

n = 2.39

Ul = Utεc n

(6)

As shown in the figure, the slip velocity is larger in the case of a circulating fluidized bed regime than in the conventional fluidized bed regime. However, at a higher solids circulation rate and higher total liquid velocity, the slip velocity exceeds the terminal velocity of a particle above a bed voidage of 0.93, even though the solids remain in the bed. This result once again confirms that the flow structure in the CFB regime is different from that in the conventional fluidization regime. Variation of the Relative Drag Coefficient with the Bed Voidage. In liquid−solid fluidized beds, the drag coefficient is a function of the physical properties of a falling or fluidized particle, the particle concentration, and the particle Reynolds number. The drag coefficient in liquid−solid fluidized beds is different from the standard drag coefficient CD,S, where the same particle moves in an infinite fluid in the absence of other particles. Hence, it is convenient to relate the relative drag coefficient CD/CD,S to the voidage. Assuming homogeneous fluidization, the experimental and predicted drag coefficients can be obtained by the following equations:21

Ret > 500

Figure 2 compares the predicted slip velocity with the experimental value, and the experimental slip velocity is higher than the predicted value. As per homogeneous fluidization (eq 5), all the solids entrain out of the bed if the slip velocity is higher than the terminal velocity of a particle. However, the experimental results of the present study show that the solid particles remain in the bed and the bed can be operated in the circulating fluidized bed (CFB) regime with Uslip larger than Ut. This is because of the flow structure in the CFB regime where solids circulate continuously between the riser and downcomer, which is different from that in the conventional fluidization regime. Figure 3 shows the comparison of experimental and predicted bed voidages at different total liquid velocities plotted as a function of the slip velocity. The vertical bold line represents the terminal velocity of a particle, and the dashed line represents the bed voidage predicted by the R−Z equation:

C D,e = 16244

4 d p(Δρ)g 3 ρl (Uslip,e)2

(7)

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3 4 d p ρl (Δρ)g 3 μ2 Ret 2εc n − 2

with no intermix of riser and downcomer fluids. Hence, in the present study, the primary liquid distributor location at position 2 was chosen in such a way that the dynamic seal is maintained. Figure 5 shows that there is a significant difference in the axial solids holdup distribution at different locations of the

(8)

where Ret = (dpUtρl)/μ and CD,S = (4dp(Δρ)g)/(3ρlUt ). Uslip,e is the experimental slip velocity at a given Ul and Gs, and εc is the predicted bed voidage calculated using eq 3. Figure 4 shows the variation of the relative drag coefficient with the voidage. At a constant bed voidage, the experimental 2

Figure 5. Effect of the location of the liquid distributor on axial solids holdup. Figure 4. Comparison of the experimental and predicted relative drag coefficients.

primary liquid distributor. At any axial position, higher solids holdup can be obtained when the primary liquid distributor is at position 1. This means that more solids enter the riser from the solids return pipe (and also from the downcomer) when the location of the distributor is at position 1. Similar behavior was also observed when the solids inventory in the downcomer was at 0.15 and 0.25 m. If the primary liquid distributor is far below position 1, the primary liquid stream might enter the downcomer through the return leg, and this leads to further reduction in axial solids holdup compared to that of position 1. This phenomenon is similar to the injection tap location at taps 1 and 2 reported earlier.18 Therefore, the choice of the location of the primary liquid distributor depends on the application and plays a significant role in obtaining the desired solids circulation rate, axial and average solids holdup in the riser, and fluid dynamic stability/instability in the LSCFB unit. As reported earlier, the instabilities such as arch formation, liquid−solid separator blockage, and return pipe blockage were observed in both methods 1 and 2 of operation and not with method 3 of operation.3 Figure 6 shows the flow regime map obtained by the three methods of operation with the stable circulating fluidized bed regime. In Figure 6, points A, B, C, and D are selected from the common region of stable operation by the three methods. To understand the effect of the method of operation on the axial solids holdup distribution in the common region at the extremes of auxiliary and primary liquid velocities, the axial solids holdups obtained by the three methods of operation at these four points are plotted in Figure 7. These figures show the axial nonuniformity and indicate that the solids holdup obtained at any position is different in the three methods of operation. At any axial position, the solids holdup obtained by method 3 of operation is much less than that of either method 1 or method 2 of operation. However, this nonuniformity in axial solids holdup is not severe when compared to that in gas−solid circulating fluidized beds. Table 2 shows the comparison of average solids holdup at the four points A, B, C, and D. It can be observed that, irrespective of the method of operation, axial and average solids holdups

relative drag coefficient is lower than that predicted by assuming homogeneous fluidization. This is because the influence of a liquid on the solids is higher in homogeneous fluidization than in the CFB regime due to continuous circulation of the solids. It can be seen from Figures 2−4 that there is a significant deviation in the experimentally observed Uslip, CD, and ε from those predicted by assuming homogeneous fluidization. Figures 2−4 are with a static inventory of 0.15 m in the downcomer. Similar results (i.e., significant deviation between experimental and predicted flow characteristics) have been observed when the solids inventory in the downcomer is 0.25 and 0.35 m. Hence, correlations based on homogeneous fluidization may not be directly applicable to the circulating fluidization regime because of the difference in flow structure. These observations are similar to those reported in the literature.7−9 Axial Solids Holdup Distribution in the Circulating Fluidized Bed Regime. In the circulating fluidization regime, the axial solids holdup distribution varies with the primary liquid velocity, auxiliary liquid velocity, solids inventory in the downcomer, method of operation, and liquid viscosity. The effect of each of these variables on axial solids holdup is described below. The effect of the location of the primary liquid distributor on some of the hydrodynamic variables has been studied.20 When the location of the primary liquid distributor is at position 1, as shown in Figure 1, the flow of solids from the return leg into the riser is observed in the absence of auxiliary liquid flow at very high liquid velocities. This location (position 1), where there is no dynamic seal between the riser and downcomer, is advantageous to minimize the number of liquid streams in the LSCFB unit in nuclear radioactive waste treatment.18 On the other hand, as mentioned in the Introduction, the dynamic seal between the riser and downcomer must prevail when the LSCFB is used for other applications, especially while using the riser and downcomer for two different operations/processes 16245

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Table 2. Comparison of the Average Solids Holdup at Four Points of the Common Operating Region of the Three Methods of Operation (Figure 6) point point point point

A B C D

method 1

method 2

method 3

0.091 0.11 0.099 0.084

0.087 0.106 0.092 0.069

0.047 0.075 0.057 0.029

Table 3. Correlations Proposed in the Present Study for Predicting the Average Solids Holdup method 1 2 3 3

Figure 6. Flow regime map by different experimental methods of operation.

correlation εs εs εs εs

= = = =

−0.60

0.22

0.07Ul1 Ul2 0.06Ul1−0.62Ul20.20 0.02Ul1−0.99Ul20.31L00.51μl−0.19 0.22(Ul1/Ut)−0.99(Ul2/Ut)0.31L00.51(μl/μw)0.055

rms error (%) 13 8 29 29

true if one requires lesser axial and average solids holdups in the riser. Since the average solids holdup profiles obtained are different for the three methods of operation as well as for different operating conditions (i.e., primary and auxiliary liquid velocities, solids inventory, and viscosity of the liquid), it is not possible to present a unified empirical correlation for average solids holdup for the three methods of operation. Hence, different correlations are proposed for the three methods of operation for predicting the average solids holdup in terms of

decrease with an increase in the primary liquid velocity and increase with an increase in the auxiliary liquid velocity. This dependence can also be noticed from the empirical correlation developed for prediction of average solids holdup by the three methods of operation as presented in Table 3. Hence, one should select a larger auxiliary liquid velocity and a smaller primary liquid velocity to achieve higher axial and average solids holdups in the circulating fluidized bed regime. The converse is

Figure 7. Effect of the method of operation on axial solids holdup at points (a) A, (b) B, (c) C, and (d) D of Figure 6. 16246

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input operating variables as shown in Table 3. For method 3 of operation, empirical correlation has also been proposed in terms of solids inventory and dimensionless velocities and liquid viscosity. The effect of the primary liquid velocity on the axial solids holdup distribution is shown in Figure 8 for a 1.17 cP solution

Figure 10. Effect of the solids inventory on axial solids holdup.

solids flux enters into the riser and leads to a higher solids holdup distribution. Figure 11 shows the effect of the liquid viscosity on the axial solids holdup distribution as a function of the viscosity of the fluidizing media at a constant set of primary and auxiliary liquid velocities for different solids inventories in the downcomer. There appears to be no reported information dealing with the combined effect of the solids inventory and viscosity of the liquid on axial solids holdup. Axial solids holdup is more or less uniform along the length of the riser. At any constant set of primary and auxiliary liquid velocities, as mentioned in Figure 11, the solids holdup at every axial position increases with increasing liquid viscosity and decreases with a further increase in the liquid viscosity. This shift in behavior depends on the solids inventory and can be observed on comparing part a to part c of Figure 11. The reason can be explained as follows. At any constant set of primary and auxiliary liquid velocities, when the solids inventory in the downcomer is 0.25 and 0.35 m (Figure 11b,c), solids holdup increases with an increase in the liquid viscosity from 0.9 to 1.55 cP at every axial position. With a further increase in the liquid viscosity to 3.22 cP, the solids holdup is less than the solids holdup corresponding to the 0.9 cP solution. The critical transitional liquid velocity to the CFB regime is very small for the 3.22 cP solution compared to other viscous solutions.4 For example, at Ul1 = 0.15 m/s and Ul2 = 0.063 m/s (Figure 11), the normalized primary liquid velocity (normalized with respect to the critical transitional liquid velocity) is around 1 for 0.9, 1.17, and 1.55 cP solutions, whereas for the 3.22 cP solution, it is far away from 1. This indicates that the CFB regime starts much earlier for the 3.22 cP solution {(Ul1/Ucr)3.22 cP = 1.64, whereas (Ul1/Ucr)0.9 cP = 0.91, (Ul1/Ucr)1.17 cP = 0.98, and (Ul1/Ucr)1.55 cP = 1.13}. Hence, the primary liquid effect is dominant in more viscous solutions (3.22 cP), and more solids are thrown out of the riser, hence resulting in a lesser solids holdup, while the viscosity effect is dominant in liquid media with a viscosity up to 1.55 cP for a given constant set of auxiliary and primary liquid velocities. When the solids inventory is 0.15 m, as shown in Figure 11a, the axial solids holdup distribution is different from that obtained for other solids inventories, i.e., 0.25 and 0.35 m. At a constant set of primary and auxiliary liquid velocities, solid holdup increases when the viscosity is increased from 0.9 to 1.17 cP. With a further increase in the viscosity from 1.55 to 3.22 cP, the solids holdup distribution is less than that corresponding to the 0.9 cP solution.

Figure 8. Effect of the primary liquid velocity on axial solids holdup.

at a fixed solids inventory and auxiliary liquid velocity. It can be seen from the figure that, for a given set of conditions, the axial solids holdup decreases with increasing primary liquid velocity and the axial solids holdup is more or less uniform along the length of the riser. The effect of the auxiliary liquid velocity on the axial solids holdup distribution is shown in Figure 9 for a 1.17 cP solution

Figure 9. Effect of the auxiliary liquid velocity on axial solids holdup.

at a fixed solids inventory and primary liquid velocity. It can be observed from the figure that, at every axial position, solids holdup increases with an increase in the auxiliary liquid velocity. For a constant total liquid velocity (at various combinations of auxiliary and primary liquid velocities), solids holdup at every axial position increases with an increase in the auxiliary liquid velocity. Figure 10 shows the effect of the solids inventory on the axial solids holdup distribution at a fixed auxiliary liquid velocity, primary liquid velocity, and viscosity of the liquid. As shown in this figure, at the same total liquid velocity, the solids holdup increases with an increase in the solids inventory at any axial position. This is because, at a higher solids inventory, more 16247

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Figure 11. Effect of the liquid viscosity on axial solids holdup at (a) L0 = 0.15 m, (b) L0 = 0.25 m, and (c) L0 = 0.35 m.

Figure 12. Effect of normalized primary and auxiliary liquid velocities on axial solids holdup at (a) L0 = 0.15 m, (b) L0 = 0.25 m, and (c) L0 = 0.35 m.

The critical transitional velocity and development of circulating fluidization are different for the four types of viscous liquids of the present study.4 The variation of the axial solids holdup distribution with the liquid viscosity is plotted in Figure 11. To facilitate direct comparison, the auxiliary liquid velocity and primary liquid velocity are normalized by their respective critical transitional velocity to the circulating fluidized bed regime (Ucr) for the four viscous solutions. Figure 12 shows the effect of the liquid viscosity on the axial solids holdup distribution at the same normalized primary (Ul1/ Ucr) and auxiliary (Ul2/Ucr) liquid velocities at different solids inventories. These figures show that no particular trend is observed in axial solids holdup with an increase in the liquid viscosity, while the range of the initial zone of the circulating fluidized bed regime observed earlier10 is the same, in terms of

the solids circulation rate, for different particle densities when the total liquid velocity is normalized by respective particle terminal velocities. The axial solids holdup distribution is not unique, which indicates that there is a significant interaction effect of the solids inventory and liquid viscosity on the axial solids holdup distribution. Upon comparison of Figures 7−12, it is noted that, under some chosen experimental conditions, the corresponding change in axial solids holdup is insignificant with changes in one of the operating variables. For example, with an increase in the solids inventory from 0.25 to 0.35 m, the change in the axial solids distribution is small (Figure 10). In addition to the particle properties (density, size, terminal settling velocity), 16248

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h = manometer reading (m) H = axial distance from the auxiliary distributor plate (m) L0 = solids inventory in the downcomer (m) n = exponent in the Richardson−Zaki equation Ret = terminal Reynolds number, Ret = utdpρl/μl Umf = minimum fluidization velocity (m/s) Ul = total superficial liquid velocity (m/s) Us = particle circulation rate expressed in particle superficial velocity (m/s), Us = Gs/ρs Ul1 = primary or main liquid velocity (m/s) Ul2 = secondary or auxiliary liquid velocity (m/s) Uslip,e = experimental slip velocity (m/s) Uslip,c = predicted slip velocity (m/s) Ucr = critical transition velocity from the conventional to circulating fluidization regime (m/s) Ut = particle terminal velocity (m/s)

each variable studied in the present study (primary liquid velocity, auxiliary liquid velocity, solids inventory, experimental method of operation, and viscosity of the fluidizing media) has an influence on the axial solids holdup distribution. In the present study, the auxiliary liquid velocity, solids inventory, and viscosity of the fluidizing media showed a positive effect on axial solids holdup individually. On the other hand, the primary liquid velocity showed a negative effect on the axial solids holdup distribution individually. When all these parameters act together, each acting with different contributions, the interaction effect may be in such a way that in some cases axial solids holdup may be insignificant depending on the experimental conditions chosen. The significant effect of all the above parameters on average solids holdup is reported elsewhere.4 This can also be noticed from the correlations proposed for average solids holdup and the corresponding exponent of these parameters (Table 3). The nonmechanical valve configuration (lift pot, riser and return pipe dimensions, angle made by the return leg with the riser) also plays a key role in obtaining the solids holdup in addition to the above-mentioned operating parameters.20,23 Since all these variables influence the solids holdup, under some chosen experimental conditions, the corresponding change in axial solids holdup would be insignificant with changes in one of the operating variables.

Greek Letters

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CONCLUSIONS The axial solids holdup distribution in the circulating fluidization regime varies with the primary liquid velocity, auxiliary liquid velocity, solids inventory in the downcomer, method of operation, and liquid viscosity. Correlations based on homogeneous fluidization may not be readily applicable to the circulating fluidization regime. At any axial position higher solids holdup can be obtained when there is no dynamic seal (i.e., at position 1) compared to when there is a dynamic seal (i.e., at position 2). The axial solids holdup obtained is different for the three methods of operation. At any axial position, axial solids holdup decreases with an increase in the primary liquid velocity and increases with an increase in the auxiliary liquid velocity irrespective of the method of operation and fluidizing media. The behavior of the axial solids holdup distribution with the viscosity of the liquid is different when the solid inventory in the downcomer is 0.15 m from that when the solids inventory is 0.25 and 0.35 m. Significant interaction effects of the solids inventory and liquid viscosity on the axial solids holdup distribution are observed.

■

■

ρs = particle density, kg/m3 ρl = liquid density, kg/m3 εS,loc = experimental sectional solids holdup εl,loc = experimental sectional bed voidage holdup ε = voidage εl = average bed voidage in the riser or liquid holdup εs = average solids holdup in the riser εc = predicted bed voidage (defined in eq 3) Δρ = density difference(kg/m3), Δρ = ρs − ρl ΔP/ΔH = static pressure gradient (Pa/m) μ = liquid viscosity (cP) μl = viscosity of the liquid (cP)

REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +91-44-2257 4163. Fax: +91-442257 4152. Notes

The authors declare no competing financial interest.

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NOMENCLATURE CD,c = predicted drag coefficient CD,e = experimental effective drag coefficient CD,S = drag coefficient of a single particle dp = particle diameter (m) Gs = solids circulation rate (kg/(m2·s)) g = acceleration due to gravity (m/s2) 16249

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Industrial & Engineering Chemistry Research

Article

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