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Ind. Eng. Chem. Res. 2009, 48, 4592–4602
Solid-Liquid Circulating Multistage Fluidized Bed: Hydrodynamic Study Prakash V. Chavan, Dinesh V. Kalaga, and Jyeshtharaj B. Joshi* Institute of Chemical Technology, UniVersity of Mumbai, Matunga, Mumbai 400 019, India
The solid-liquid circulating multistage fluidized bed (SLCMFB) was constructed with the principal components being the riser column and the multistage column. The riser column was made up of 50 mm i.d. and 2 m long glass pipe while the multistage column was made up of seven glass stages of 100 mm i.d. and 100 mm length. The ion-exchange resin was used as solid phase and water as fluidizing medium. The flow characteristics of SLCMFB were investigated for 0.365, 0.605, and 0.725 mm particle sizes (dry basis). The voidage in the riser and multistage column was measured using γ-ray tomography (GRT). In the riser column, the voidage was found to be maximum at the center and minimum near the wall. However, in the multistage column, voidage was found to be uniform over cross section of the column. The solid particle velocity was measured using ultrasonic velocity profiler (UVP) in the riser column. The particle velocity profiles show similar trend as the voidage, confirming the existence of the radial non-uniformity in the riser column. Further, the nonuniformity was analyzed using the drift flux model (DFM) and the effect of particle size and superficial liquid velocity on the non-uniformity was also investigated. 1. Introduction Conventional solid-liquid fluidization has been studied extensively since 1950.1,2 However, solid-liquid circulating fluidization is a relatively new field in the realm of fluidization. Solid-liquid circulating fluidized bed (SLCFB) consists of a riser column, main column, solid-liquid separator, and other auxiliary devices. The riser is usually operated at superficial liquid velocities higher than the terminal velocity of the particle, and the main column is operated at low superficial liquid velocities either in fixed or in expanded bed mode. The two liquid streams are supplied separately in the riser and the main column without intermixing. Continuous circulation of solid particles occurs with upward motion in the riser column and downward motion in the main column. SLCFBs have a number of attractive features over conventional solid-liquid fluidized beds (SLFB) such as an ability to accommodate continuous operation with respect to the solid phase which include both the steps of utilization (catalytic reaction, adsorption, etc.) and the regeneration. The main column is used for the adsorption/catalytic reaction and is usually in the form of multiple stages, as in the present case for reducing backmixing. It is possible to arrive at a combination of number of stages, liquid velocity, solid velocity, and particle size so as to get practically plug flow. The riser section may be sufficient for regeneration. However, if regeneration needs more residence time and/or many theoretical stages, the riser acts as a transport arm and another multistage column can be provided for regeneration. These unique features of SLCMFB make them suitable for various industrial processes such as production of linear alkylbenzene,3,4 continuous recovery of fermentation products,5-7 removal and recovery of cesium from liquid radioactive nuclear waste streams,8 wastewater treatment,9 and continuous enzymatic polymerization of phenol in biorefining process.10 The present work addresses the solid-liquid circulating multistage fluidized bed (SLCMFB) shown in Figure 1A. Though the SLCMFBs provide attractive features for applications like catalytic reactions and chromatographic separations, very scanty information is available regarding the rational * To whom all correspondence should be addressed. Phone: 00-9122-2414 5616. Fax: 00-91-22-2414 5614. E-mail:
[email protected].
design procedures. In particular, (1) we should be able to adjust the desired residence time in the riser and the downcomer columns depending upon the dynamics of adsorption (or catalytic reaction) and regeneration of the solid phase under consideration. (2) We should be able to get the flow behavior of solid and liquid phases as close to plug flow as possible. For this purpose, we need information regarding the extent of axial dispersion in solid and liquid phases with respect to particle size, liquid velocity, number of stages, and the other geometrical details of each stage. (3) We need the estimation procedure for solid-liquid mass transfer coefficient. The present work is concerned with the first aspect. An attempt has been made to measure hold-up and velocity profiles in the riser and downcomer sections over a wide range of particle size and liquid velocity. 2. Previous Work Liang et al.11-13 have found radial non-uniform distribution of solids hold-up and liquid velocity in SLCFB using electrical conductivity probes. Glass beads and silica gel beads were used as solid phases and tap water was used as the fluidizing liquid. It has been observed that the non-uniformity in the bed voidage profile decreases while the non-uniformity in the liquid velocity profile increases with an increase in superficial liquid velocity for a given solid circulation rate. However, the cross-sectionally averaged bed voidages at different bed heights were found to be the same, indicating uniform flow structure along the axial direction. Further, Liang and Zhu4 have studied the effect of non-uniform distributions of hold-up, liquid velocity, and solid particle (catalyst) velocity on the alkylation reaction of benzene with dodecane using solid catalyst. It has been observed that reaction conversion decreases significantly due to increase in reactant velocity and decrease in hold-up for a given catalyst circulation rate. At low reactant velocity (VL ) 51 mm s-1), the radial non-uniformity of the flow structure is less significant so that the effect of the radial non-uniformity on the reaction is small. With an increase of the reactant in the circulating fluidization regime (VL ) 100 mm s-1), the radial nonuniformity of the flow structure increases so that the effect of the radial non-uniformity on the reaction increases. Further, it
10.1021/ie8018627 CCC: $40.75 2009 American Chemical Society Published on Web 03/30/2009
Ind. Eng. Chem. Res., Vol. 48, No. 9, 2009 4593
Figure 1. (A) Schematic of experimental setup. (B) Schematic of stage configuration. Legend: (1) riser column, (2) top solid return pipe, (3) settler, (4) multistage column, (5) sieve plate, (6) calming section, (7) bottom solid return pipe, (8) adaptors, (9) mesh, (10) weir, and (11) downcomer.
has also been observed that with an increase in catalyst circulation rate, the catalyst hold-up increases in the riser column. Consequently, the reaction conversion increases with the increase of catalyst circulation rate. Zheng et al.14 have investigated the radial distribution of solid hold-up in the riser column for glass beads and plastic beads using a fiber-optical probe to study the effect of particle density on the flow structure. The solid hold-up was found to be minimum at the center whereas maximum near the wall for all the operating conditions. Further, it has also been observed that the glass particles lead to a steeper radial profile of solid holdup and liquid velocity as compared to plastic bead particles. Zheng and Zhu15 have proposed new method of estimating an onset velocity for solid circulation (Ucf) in SLCFB. The method was based on the measurement of the time required for all the solids to leave the bed at various superficial liquid velocities when no fresh solids are fed into the riser column. Since Ucf was determined without the consideration of the solid inventory and the feeding of the solids to the riser column, it was found to be a function of liquid and solid properties only. This is in contrast to the findings of Liang et al.12 who have found that Ucf is a function of solid inventory and the solid feeding to the riser column. Singh et al.16 have studied hydrodynamics of solid-liquid multistage fluidized bed (SLMFB) using ionexchange resin as a solid phase and water as a fluidizing medium with a view to determine the operating range of water and resin
flow rates for smooth and stable operation. The empirical correlations were developed to estimate the bed voidage and pressure drop across the stage. This study, however, focuses on multistage solid-liquid fluidized bed rather than multistage circulating solid-liquid fluidized bed since solid particles were collected from the bottom and fed from the top using the conveyor belt. Lan et al.5-7 have developed and successfully applied the SLCFB for continuous protein recovery and the effect of operating variables on the hydrodynamics was investigated. When the total amount of solid particles was constant, the expansion of the bed in the main column at steady state was found to be dependent mainly on three factors: the superficial liquid velocities in the riser and main column, and the solid circulation rate. It has been observed that the bed expands with an increase in superficial liquid velocity and decreases with an increase in the solids circulation rate. In the riser column, it has been seen that the bed voidage decreases with an increase in solid circulation rate at a given superficial liquid velocity while for a given solid circulation rate the bed voidage increases with an increase in the superficial liquid velocity. Feng et al.8 have studied the effect of the system geometry on the hydrodynamic behavior of SLCFB for cesium removal. They have studied the optimum injection tap location (location of intersection of the riser column and the solid return pipe) in the riser column without auxiliary flow. It has been observed that solid
4594 Ind. Eng. Chem. Res., Vol. 48, No. 9, 2009
circulation rate increases steadily with an increase in superficial liquid velocity in the riser column when the injection tap was located at the middle of the intersection of the riser column and the solid return pipe. The effect of main column flow rate and auxiliary flow rate on solid circulation rate has also been studied. An increase in solid circulation rate has been observed with an increase in either main column flow rate or auxiliary flow rate. It has also been seen that for a given auxiliary flow rate, an increase in the main column flow rate also increases the solid circulation rate. This was attributed to the leakage of main flow rate to the riser column. Gaikwad et al.17 have studied adsorption of nickel ion on cation exchange resin in SLCFB wherein adsorption was accomplished in the main column and regeneration of the resin was carried out in the riser column. They have compared conventional fixed bed, expanded bed, and SLCFB in terms of height equivalent to theoretical plate (HETP) values. HETPs of the SLCFB, fixed bed, and expanded bed were found to be 50, 120, and 180 mm, respectively at 3.5 mm s-1 superficial liquid velocity. Table 1 shows details of the published work in the literature. It is clear that information available in the published literature on circulating solid-liquid fluidization is scarce unlike conventional solid-liquid fluidization. In particular, scanty information is available when multiple stages are used in the main column. Therefore, in the present investigation, it was thought desirable to undertake a systematic investigation in terms of bed expansions, hold-up and velocity profiles, and solid circulation rates. 3. Experimental Section 3.1. Characterization of Resin Particles. The weak base anion exchange resin (Indion 860) was used as a solid phase. The resin particles were classified by sieving into various sizes. The 0.365, 0.605, and 0.725 mm particle sizes were selected for the present work. 3.1.1. Swelling of the Resin. The ion-exchange resin usually swells when brought into contact with water. Therefore, it is necessary to estimate the equilibrium swelling of the resin since terminal settling velocity of the resin particle gets affected significantly on swelling of the resin.18 A known quantity of the resin (1 g) was taken and its volume was measured at a dry state and a wet state using calibrated glass tube and also by microscopic measurement. The swelling ratio (ratio of volume of swelled resin to the volume of the resin at a dry state) was found to be 1.3. This means that the diameter of the resin particle approximately increases by a factor of 1.09 upon swelling. 3.1.2. Expansion Characteristics. Experiments were carried out in 50 mm i.d. and 1.2 m long acrylic column to estimate the (1) terminal settling velocity of a given particle size and (2) bed expansion characteristics. The voidage was estimated by measuring heights of dispersion and by pressure drop measurement.19 The Richardson and Zaki equation20 was used to analyze the bed expansion data. Table 2 shows terminal settling velocities of dry and swelled particles and the values of Richardson-Zaki index obtained for 0.365, 0.605, and 0.725 mm particle sizes. 3.2. SLCMFB. 3.2.1. Experimental Setup. A schematic diagram of the SLCMFB is shown in Figure 1A. The SLCMFB system mainly consists of a glass riser column (1), a liquid-solid separator (3), a top solids return pipe connecting the riser and the multistage column (2), a glass multistage column (4), calming section at the bottom of multistage column (6), and a bottom solids return pipe connecting the riser and the multistage column at the base (7). Two different liquid streams were
separately supplied in the multistage column and the riser column. The riser column was operated in the circulating fluidization regime and the multistage column was operated in the conventional fluidization regime. The solid phase and water contact countercurrently in the multistage column but cocurrently in the riser column. The superficial liquid velocity in the riser was maintained higher than the terminal velocity of the solid particles so that the solid particles were carried upward by the up flowing water. 3.2.1.1. Riser and Multistage Column. The riser was a 50 mm i.d. and 2 m long glass pipe, and the multistage column was of 100 mm i.d. and 950 mm in long. The riser column was connected to the multistage column at the upper part through the liquid-solid separator and solid return pipe. At the bottom, the riser and the multistage column were connected to each other through the bottom solid return pipe. The arrangement was made to measure pressure drop over a given length of the riser as well as multistage column using U-tube manometer wherein chlorobenzene (sp gr ) 1.11) was used as a manometric fluid. The configuration of the multistage column is similar to that of the sieve trays distillation column used for vapor-liquid contacts. The column essentially consists of seven stages assembled together with flange joints. A SS mesh with openings smaller than the particle size was fitted on both the sides of each sieve plate stage and sandwiched between pair of adjoining flanges. Holes of 2 mm were provided on each sieve plate distributor, providing 5% open area for water flow. The fluidized solid particles move across the stage to the next stage through a downcomer (10 mm i.d. and 50 mm long, SS tube), as water flows upward through the mesh openings. Figure 1B is the schematic of the single-stage configuration. A reciprocating pump of 150 × 10-6 m3 s-1 was used to feedwater to the riser column and the multistage column. A calming section of 150 mm length was provided underneath the last stage of multistage column to stabilize the flow of water. The water flow rate was adjusted by a ball valve and measured using rotameters. Necessary arrangements in the fittings and fixtures were made to ensure that no air bubbles intruded into the column during operation. 3.2.1.2. Distributors. An adapter of 25 mm o.d. was used as a distributor for the riser column. The calming section (150 mm) was used as a distributor for the multistage column. The calming section consisted of three layers of glass beads of different sizes. The bottom layer, intermediate layer, and top layer were composed of 4, 3, and 1 mm size glass beads, respectively. 3.2.1.3. Solid-Liquid Separator. The separator was a 130 mm i.d. and 850 mm long glass column having a convergent section of 150 mm at the bottom and 30 mm glass pipe of 25 mm i.d. to connect the upper stage of the multistage column. The solid particles settle in the separator column since upward liquid velocity was much lower than the terminal settling velocity. The convergent section provided at the bottom of the settler column allows solid particles to move to multistage column in orderly manner. 3.2.1.4. Top and Bottom Solid Return Pipes. The glass columns of 25 mm i.d. were used as a solid return pipes. Sufficient angle was provided so that the solid particles flow easily from the riser to the multistage column and vice versa. Since two liquid streams are to be supplied separately to the multistage and riser column, it is necessary to maintain the dynamic seal between these columns. The dynamic seal between the riser column and the multistage column was achieved by installing a butterfly valve in the solid return pipe. The presence
0.405 0.385
0.5081 0.526
0.526 0.508 1.00 0.58 0.55 0.65 0.925 0.8 1.2
Liang et al.12
Zheng et al.14
Zheng and Zhu.15
a
1100
1100 1485
1100 2490 2541 7000 1330
2490 1100
2460 1360
2475 1535
1080
FS (kg m-3)
SCR ) solid circulation rate.
present work
Gaikwad et al.17
0.36 0.60 0.72
0.415 0.425
Feng et al.8
Singh et al.16
0.32
Lan et al.5
Investigator
dP (mm)
Solid phase
8.70 13.40
4.50
10 59 144 216 21.80 22.70 36.50 -
59 10
53 18
52 26
4.50
VS∞ (mm s-1)
1000
1000
1000
1000
1000
1000
1000
1000
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
µL (kg m-1 s-1)
Liquid phase FS (kg m-3)
Table 1. Summary of Experimental Work on SLCFB
D ) 120 H ) 2500 D ) 50 H ) 1550 D)H)D ) 200 H)D ) 200 H)D ) 100 H ) 500 D ) 30 H ) 1000 D ) 100 H ) 2000
H ) 3000 D)6 H ) 2100 D ) 140 H ) 3000 D ) 76.2 H ) 3000 D ) 76.2 H ) 2700 D)H)D ) 10 H ) 1000 D ) 50 H ) 2000
main col/ storage vessel (mm)
D ) 38
riser col (mm)
Dimensions
0.030
0.002 0.014 0.001 0.04 0.013
0.022 0.075 0.30 0.008 0.093 0.028 0.42 0.01 0.25
0.0011
Liquid velocity VL × 10-3 (mm s-1)
SCR: UVP and exptl method
voidage: GRT and press. drop method
voidage: press. drop method
voidage: press. drop method
-
voidage: optical fiber probe
voidage: electrical conductivity
SCR: slurry collection at riser outlet
voidage: press. drop method; SCR: sol accumuln rate
Measurement technique for voidage and SCRa
hydrodynamics of multistage circulating sol-liq fluidized bed was studied
modeling of SLCFB has been done
hydrodynamics of multistage col was studied
onset velocity for sol. circulation was estimated
effect of particledensity on flow structure was studied
non-uniformity in voidage and liq velocity was found
application: cesium recovery
application: protein recovery
Remark
Ind. Eng. Chem. Res., Vol. 48, No. 9, 2009 4595
4596 Ind. Eng. Chem. Res., Vol. 48, No. 9, 2009 Table 2. Richardson-Zaki Parameters for Different Particles Used in the Present Investigation Particle diameter, dp × 106 (m)
Experimental terminal settling velocity, VS∞ (mm s-1)
Richardson-Zaki index, n
dry basis
wet basis
single-stage column
multistage column
single-stage column
multistage column
725 605 362
798 665 398
13.00 9.00 4.7
13.00 9.20 5.00
3.37 3.40 3.52
3.37 3.39 3.48
of the valve prevents the flow of liquid from the multistage column to riser column. At the start of the operation, solid particles start accumulating in the solid return pipe and then the opening of the valve is adjusted in such a way that solid particles remains in the fixed bed mode. 3.3. Measurement Techniques. 3.3.1. γ-ray Tomography (GRT). 3.3.1.1. Methodology. The GRT system for the measurement of local voidage consists of 67.5 µCi 137Cs gamma source, sodium iodide (NaI) with thallium (Tl) activated scintillation detectors (BICRON), a photomultiplier tube, a preamplifier, a multichannel (5 channels) analyzer, data acquisition systems (Para Electronics Ltd.), and related hardware and software. In the multichannel counter, each channel was adjusted for 700-900 V. The source was collimated in a lead brick with a central slit of 35 × 8 × 30 mm which provides a fan beam subtending an angle of 30° in the horizontal plane. Detectors were collimated in SS bricks having central hole of 5 mm diameter and 40 mm length. Thus, the resultant emerging beam from the source detected by the detectors has the thickness of 5 mm, i.e., equal to the thickness of the vertical slit of the detector. The dwell time was optimized to 20 s for the given source of strength. These dimensions of the collimators were found to give the least sample variance in the number of photons detected by the detector for a given dwell time. The experimental methodology adopted for scanning measurements was fan beam scanning. In this method, the source was kept 5 mm away from the wall of the column wherein the central axis of the source and the column coincides. The detector was moved in an arc of radius 220 mm for multistage column and 120 mm for riser column. The detector was moved in an arc equal to the outer diameter of the column with angles equal to 0, 5, 10, 15, 20, 25, 30, 35° from the axis of the source. These angles cut the diameter at the radial (r/R) positions of 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.7, and 0.8, respectively. 3.3.1.2. Estimation of Voidage Profiles. The experimental chordal voidages were calculated using the following expression: Lchord )
ln(ITP /IL) ln(ISL /IL)
(1)
where ITP, IL, and ISL are γ-ray intensities in a two-phase, liquidfilled column, and column filled with solid and liquid, respectively. The method of estimation of voidage at a given radial location using eq 1 has been reported in detail by various investigators (Shollenberger et al.,21 Parasu Veera and Joshi,22 Thatte et al.23). 3.3.2. Ultrasonic Velocity Profiler (UVP). 3.3.2.1. Methodology. The axial velocity of the solid particle was measured using an ultra sound Doppler velocimeter aided by UVP METFLOW software. An ultrasound probe (15 mm in diameter and 200 mm in length) with a working frequency of 1 MHz was used for the measurement. One acrylic circular plate was fixed to the upper open end of the riser column. A slot of 48 mm × 20 mm was made on the circular plate. The ultrasound probe then inserted into the slot in such a way that its lower end dips into the water. Thus, the probe could be moved in the radial direction. The position of the probe was measured using the
scale attached on the circular plate. The measurement axis was parallel to the central axis of the riser column and probe was pointing downward. 3.3.2.2. Estimation of Velocity of the Solid Particle. When ultrasound (US) pulse hits a solid particle, part of the US energy scatters on the particle and echoes back. The echo reaches the transducer after a time delay t)
2x c
(2)
where t is time delay between transmitted and received signals (s), x is the distance of scattering particle from transducer (m), and c is speed of sound (m s-1). If the scattering solid particle is moving, Doppler shift of echoed frequency takes place and the received signal frequency follows the Doppler effect. Thus, velocity component in the transducer axis is given by the following expression: VST )
cfd λ ) fd 2fo 2
(3)
where VST is a velocity component into transducer axis (m s-1), fd is the Doppler shift (Hz), fo is the transmitting frequency (Hz), and λ is the wavelength of ultrasound. The time delay and Doppler shift give the location and velocity of the particle, respectively. The details pertaining to the UVP technique can be found elsewhere (Takeda,24 Wang et al.25). 3.4. Experimental Procedure. A known quantity of the solid particles (1.2 kg) of a given size was loaded in the riser column. The water flow was started and subsequently controlled by the ball valves, and metered using the rotameters. For a given operating condition, the system was allowed to reach a steady state for 2 h. After the steady state was achieved, the pressure drop measurements were performed in the riser as well as in the multistage column. The solid particle velocity and voidage profiles were obtained using UVP and GRT, respectively. This procedure was repeated for a given size of particle for two different stage configurations (7 and 20 mm weir heights). 4. Results and Discussion In the riser column, different operating regimes were observed when the superficial liquid velocity was increased from zero. When the superficial liquid velocity is less than the minimum fluidization velocity, the bed stays in the fixed bed regime. When the superficial liquid velocity is higher than the minimum fluidization velocity but lower than terminal settling velocity of the solid particle, the bed is in the conventional fluidization regime, in which there is a uniform distribution of phase holdups both in the axial and radial directions, and there is no solid particle circulation as well. With the further increase in liquid velocity (just above the terminal settling velocity), the particles enter the circulating regime and a fraction of the solid particles get transported to the multistage column. Further, solid particles should be transported to the riser column from the multistage column through the bottom solid return pipe to maintain specific height of the solid inventory on each stage.
Ind. Eng. Chem. Res., Vol. 48, No. 9, 2009 4597
Figure 2. Operating window for a given particle size. Filled symbols: loading limit. Hollow symbols: flooding limit (]) 0.365 mm; (0) 0.605 mm; (4) 0.725 mm.
4.1. Operation of Multistage Column. The operating range has been determined for a given system and operating variables under steady-state conditions. The system variables include the size of the particles while operating variables include superficial liquid velocity in the riser (VL1) and multistage columns (VL2). In principle, the operating velocity of water in multistage column should be set between minimum fluidization velocity (Vmf) and terminal settling velocity (VS∞) of the particles. However, there are two additional operating limits, which need to be established a priori for smooth and stable operation of the multistage column. One is the minimum VL1 for a given VL2, below which the stage may be flooded with water, preventing solid particles from flowing down through the downcomer tube. The other is the maximum VL1, above which the stage may be loaded with excess solids. We describe below the operating range of VL1 and VL2 for the stable operation of the multistage column under the experimental conditions used in this work. Figure 2 shows the operating window for 0.365, 0.605, and 0.725 mm particle sizes. Figure 2 describes the VL1 as a function of VL2 corresponding to two limits of operation of the multistage column. The filled symbols represent the maximum VL1 at a given VL2, which may be used for stable and smooth operation of the column without loading of the stages with excess solids. Similarly, the hollows symbols represent the minimum VL1 at a given VL2, which may be used without flooding of the stage with water. Therefore, the difference between the two values of VL1 defines the operating range of fluidization without loading and flooding of the stages at a given VL2. For example, for 0.365 mm particle size, at a VL2 equal to 0.7 mm s-1 the operating range of VL1 is between 4.9 and 11.5 mm s-1 corresponding to flooding and loading in the multistage column. VL1 smaller than 4.9 mm s-1 gradually leads to the stage flooded, whereas that in excess of 11.5 mm s-1 causes loading of the stages. In the figure, the operating ranges for 0.365 mm are marked with vertical double-headed arrows for clarity. 4.2. Riser Column. 4.2.1. Radial Voidage Profiles. Experiments were carried by keeping superficial liquid velocity in the multistage column (VL2) constant and varying superficial liquid
Figure 3. Radial liquid fraction profiles for various particle sizes. (A) 0.365 mm: (])13 mm s-1, (0) 21 mm s-1, (4) 25 mm s-1, (O) 30 mm s-1. (B) 0.605 mm: (]) 13 mm s-1, (0) 21 mm s-1, (4) 25 mm s-1, (O) 30 mm s-1. (C) 0.725 mm: (]) 13 mm s-1, (0) 21 mm s-1, (4) 25 mm s-1, (O) 30 mm s-1.
velocity in the riser column (VL1) from 10 to 30 mm s-1. The local voidage was measured using GRT over the different radial locations. Figure 3 shows radial distribution of voidage, measured at different VL1 for three different particle sizes. The voidage was found to be maximum at the center while minimum near the wall for all particle sizes, confirming the existence of non-uniformity in the radial distance. The particle size and VL1 also affect the radial voidage profile. The voidage profile of 0.365 mm particle size was found to be more uniform as compared to other particle sizes at a given VL1. Further, it has
4598 Ind. Eng. Chem. Res., Vol. 48, No. 9, 2009
) (1 - )(F ( dP dZ )
-
L
z
S
- FL)g
(6)
The bed voidage profiles were obtained at various radial locations at two axial locations (1 m and 1.5 m from the bottom of the riser column) using GRT. Figure 5 shows the variation of the axial bed voidage at VL1 equal to 13 and 30 mm s-1 for 0.365 mm particle size. It can be seen that the voidage profiles remain practically constant at different axial locations, confirming axial uniformity in the bed voidage. The average voidage over cross sectional area can be estimated using voidage profile obtained by GRT as follows: L )
Figure 4. Comparison of radial voidage profile of 0.725 mm particle with Liang et al.11 (line 1) and proposed correlation (line 2): (4) 30 mm s-1, (0) 13 mm s-1.
also been observed that the voidage profile becomes uniform with an increase in VL1 for a given particle size. This means that the voidage profile moves to become uniform with an increase in VL1 and decrease in particle size. Experimental results of Liang et al.11 have shown that radial voidage profiles are nearly the same under the same average bed voidage but with different combinations of superficial liquid velocity and particle circulation rate, although variations in either superficial liquid velocity or particle circulation rate can significantly affect the radial voidage profile. It indicates that the average bed voidage determines the radial profile of the bed voidage. Therefore, the radial distribution of the bed voidage is a function of only the average bed voidage and the radial position. They have proposed the following empirical equation based on their experimental results: L ) L[0.75
+ 0.40(r/R)0.90]
(4)
∫
1 A
R
0
2πrL dr
(7)
Figure 6 compares the average voidage estimated by pressure drop measurement and GRT. A very good agreement was found using these two methods. 4.2.3. Radial Profiles of Particle Velocity. Since resistance to solid upflow is minimum at the center of the riser column than near the wall, solid velocity was expected to be maximum at the center of the riser column than near the wall. The solid particle velocity measured by UVP technique shows that particle velocity is, indeed, maximum at the center. Figure 7 shows the particle velocity profiles for three particle sizes for a given VL1. It is clear that the solid particle velocity profiles are relatively uniform for 0.365 mm particle size as compared to 0.605 and 0.725 mm particle sizes for a given superficial liquid velocity. The volumetric flow rate of particles at any section in the riser column can be estimated if the solid velocity ensemble in any section of the riser column as well as the volume fraction of solids in that section is known. Thus, if QS represents volumetric flow rate of solid particles, VST is the solid velocity, S the solids volume fraction, and A the cross-sectional area of flow in that section, then QS is given by following equation: QS )
∫V A
dA
STS
(8)
In general, the flow rate of solids could be fluctuating in various zones of the riser column, and a representative estimate of solid circulation rate should be based on a time-averaged measurement. Thus, time ensemble averaging of eq 8 and recognizing that the time average of the fluctuations in either VST or S is zero yields the following equation: jS ) Q
∫ Vj A
STS
dA +
∫ V' A
ST′S
dA
(9)
14
When eq 4 is applied to the experimental data of Zheng et al., it has been found that eq 4 underpredicts the values of local voidage. Therefore, based on the experimental data of Liang et al.,11 Zheng et al.,14 and present investigation, the following correlation has been proposed: L ) L
[0.95 + 0.75(r/R)2.65]
(5)
Figure 4 shows comparison between eq 4 and the proposed correlation (eq 5) using experimental data of 0.725 mm particle at VL1 equal to 13 and 30 mm s-1. A fairly good agreement was found between the experimental and predicted values (eq 5). 4.2.2. Axial Bed Voidage. The average axial bed voidage was estimated by measuring the pressure drop over a bed length, assuming wall friction and acceleration effects to be negligible, using the following equation:
Assuming the fluctuations in both the solids velocity (V′ST) and the solids volume fraction (′S) are negligibly small, the solids flow rate in terms of the cross-sectional average solids hold-up and velocity can be written as follows: j STSA jS ) V Q
(10)
j ST can be estimated similarly as eq 7 for average voidage The V wherein L can be replaced by VST at a given radial location in the riser column. The volumetric flow rate of solid particles of a given size was also estimated by measuring the flow rate of solid particles at the top solid return pipe to check the applicability of eq 10. A special type of valve was fabricated which permits solid-liquid mixture to come out for a known length of time. During the measurement, no solid-liquid flow was permitted to flow to the multistage column. The mass of solid particles was then
Ind. Eng. Chem. Res., Vol. 48, No. 9, 2009 4599
Figure 5. Axial voidage profile for 0.365 mm particle: (4) 30 mm s-1, (]) 13 mm s-1. Filled symbols: 1 m above distributor. Hollow symbols: 1.5 m above distributor.
Figure 6. Parity plot for average voidage estimated using pressure drop measurement and GRT. Filled symbols: riser column. Hollow symbols: multistage column.
measured to estimate the volumetric flow rate of the particles. Figure 8 shows parity plot for solid circulation rate (mass flow rate measured by eq 10 and experimental mass flow rate). The experimental mass flow rate of solid was found to be greater than the mass flow rate estimated by eq 4. The mean deviation was found to be 14% with a maximum deviation of 25%. This may be attributed to the accumulation of solid particles in the vicinity of the valve.
Figure 7. Radial solid velocity profiles for various particle sizes. (A) 0.365 mm: (]) 13 mm s-1, (0) 21 mm s-1, (4) 25 mm s-1, (O) 30 mm s-1. (B) 0.605 mm: (]) 13 mm s-1, (0) 21 mm s-1, (4) 25 mm s-1, (O) 30 mm s-1. (C) 0.725 mm: (]) 13 mm s-1, (0) 21 mm s-1, (4) 25 mm s-1, (O) 30 mm s-1.
4.3. The Multistage Column. 4.3.1. Voidage. The expansion characteristics of three solid particles of different sizes were studied using two stage configurations. The bed voidage was measured by using pressure the drop method and GRT. Experiments were carried out by varying VL2 and keeping VL1 constant. In the case of 7 mm weir height of the stage, the bed remains in the fixed mode for all the particle sizes covered in this work. The cross flow of solids with respect to water was observed on
4600 Ind. Eng. Chem. Res., Vol. 48, No. 9, 2009
VL ) L3.4 VS∞
(14)
The experimental expansion data has been fitted to eqs 11 and 14. A good agreement has been found between the experimental values and those predicted using eqs 11 and 14. Figure 11 shows the comparison of the estimations of eqs 11 and 14 to the expansion data of 0.365 mm particle size. The Richardson-Zaki
Figure 8. Parity plot for solid circulation rate.
each stage. At the start of the operation, the resin particles fill up the bed to a certain fraction of the weir height. As the operation progresses, the bed height reaches to the upper edge of the weir and further the resin particles start flowing to the next stage. The difference in the heights gets developed across the stage from left to right, resulting in the cross flow of the fluidized resin particles on the stage. In the case of 20 mm weir height of the stage, in contrast to the 7 mm weir height, the bed was in the expanded state. The bed expands with an increase in liquid velocity. Figure 9 shows that the voidage remains uniform over the cross section of the column for all the resin particles of different sizes unlike to the voidage in the riser column. For a given VL2, expansion of 0.365 mm resin particles was observed to be maximum followed by 0.605 mm and least for 0.725 mm resin particles. It has been observed visually that the incoming and outgoing flow rates of resin particle and bed height remain practically constant on each stage. Figure 10 shows the variation of voidage with liquid velocity for resin particles of different sizes for 20 mm weir height. The expansion data can be represented by Richardson-Zaki and Joshi equations, respectively, as follows: VL ) Ln VS∞
( )
VS CD∞ ) VS∞ CD
(11)
1/2
(12)
where CD∞ is the drag coefficient acting on a particle in an infinite medium. The drag force acting on a particle in the presence of other particles is given as follows (Pandit and Joshi26): CD ) CD∞L-4.8
(13)
Substituting eq 13 into eq 12, the following velocity-voidage relationship can be obtained:
Figure 9. Radial voidage profile for various particle sizes in multistage column. (A) 0.365 mm: (]) 0.70 mm s-1, (0) 1.00 mm s-1, (4) 1.40 mm s-1, (O) 1.75 mm s-1, (×) 2.10 mm s-1. (B) 0.605 mm: (] 1.00 mm s-1, (0) 1.75 mm s-1, (4) 2.50 mm s-1, (O) 2.80 mm s-1, (×) 3.50 mm s-1. (C) 0.725 mm: (]) 1.00 mm s-1, (0) 1.75 mm s-1, (4) 2.50 mm s-1, (O) 3.10 mm s-1-, (×) 4.20 mm s-1.
Ind. Eng. Chem. Res., Vol. 48, No. 9, 2009 4601 Table 3. Drift Flux Model Constants Particle diameter, dp × 106 (m)
C1 (mm s-1)
Co (-)
dry basis
wet basis
using eq 15
using eq 16
using eq 15
using experimental liquid velocity and solid velocity
725 605 362
798 665 398
0.97 0.93 0.87
0.96 0.92 0.86
10.00 7.00 3.60
11.00 7.80 4.00
solid phases. These non-uniformities in the riser column can be analyzed by using the drift flux model. The drift flux model of Zuber and Findlay27 is given by the following equation: jS V S
j + C1 ) C0V
(15)
The distribution constant (Co) and C1 are the drift flux constants and are given as follows:
Figure 10. Average voidage against superficial liquid velocity (VL2) in the multistage column: (]) 0.365 mm, (0) 0.605 mm, (4) 0.725 mm.
SV ) Co ) j 1 SV A
[
∫ V dA ∫ V dA][ A1 ∫ 1 A
parameters obtained by using eq 11 for various particle sizes are reported in Table 2. The values of terminal settling velocities obtained from the experimental expansion data in the multistage column are comparable to those obtained in the single-stage column. This means that there is no leakage of feedwater from multistage column to the riser column. 5. Drift Flux Model Section 4.1 showed that there is a significant non-uniformity in the velocity and hold-up in the riser column for liquid and
A S
A
C1 )
Figure 11. Comparison of expansion data of 0.365 mm particle size with Richardson-Zaki20 and Joshi1 corelation: line 1, Richardson-Zaki;20 line 2, Joshi.1
A S
SLVR S
]
(16)
dA
(17)
All the experimental data presented in this work were analyzed using eq 15. Table 3 shows the values of Co and C1. The constant Co takes into account the extent of the non-uniformity and concentration of solid particles across the column cross section while C1 gives the relative velocity between the solid and liquid phases. When solid hold-up is uniform across the column diameter, Co is equal to 1 which is the case in conventional particulate fluidized bed. The constant Co is greater than unity when the concentration at the center is more than the concentration near the wall which is the case in bubble column. However, in the present work, the values of Co were found to be less than unity, confirming the higher voidage at the center and lower near the wall. The values reported in Table 3 also indicate that the non-uniformity in the case of 0.365 mm solid particle is minimum as compared to 0.605 and 0.725 mm solid particle since the value of Co obtained for 0.365 mm is close to unity for a given operating condition. The values of Co obtained by using eqs 15 and 16 are also reported in the Table 3. The values of relative velocities obtained for a given particle size are lower than those actual values (local experimental values of liquid velocity and solid velocity). Table 3 shows the comparison between the relative velocities obtained from eq 15 and the actual values. 6. Conclusions The following conclusions can be drawn based on the present investigation: 1. The radial non-uniform distributions of bed voidage and solid particle velocity have been found in the riser column. 2. The radial variation of voidage in the riser column can be correlated by the following empirical correlation: L ) L[0.95
+ 0.75(r/R)2.65]
4602 Ind. Eng. Chem. Res., Vol. 48, No. 9, 2009
3. The radial voidage and solid velocity distribution profiles are nearly the same along the height of the bed under given operating conditions. The cross-sectionally averaged bed voidages and solid velocities at different bed levels were also found to be the same, indicating uniform flow structure along the axial direction. 4. The radial non-uniformity reduces with an increase in superficial liquid velocity and decrease in solid particle diameter. 5. The radially uniform distribution of bed voidage has been observed in the multistage column in contrast to the riser column. Further, the increase in weir height of the stage increases the expansion of the bed for a given VL2 in the multistage column. Nomenclature A ) cross-sectional area, m2 C ) speed of sound, m s-1 CD ) drag coefficient Co ) distribution coefficient defined by eq 16 C1 ) constant defined by eq 17, m s-1 fd ) Doppler shift, Hz fo ) transmitting frequency, Hz g ) acceleration due to gravity, m s-2 I ) γ-ray intensity m ) mass flow rate of a given particle size, kg s-1 n ) Richardson-Zaki index QS ) volumetric flow rate of solid, m3 s-1 r ) any radial distance, m R ) radius of the column, m t ) time delay between transmitted and received signal, s V ) mixture velocity, m s-1 VL ) superficial liquid velocity, m s-1 VLT ) true liquid velocity, m s-1 VR ) slip velocity, m s-1 VS ) superficial solid velocity, m s-1 VST ) true solid velocity, m s-1 x ) distance of scattering particle from transducer, m Z ) column height, m Greek Letters L ) voidage of the bed at any radial distance S ) solid volume fraction at any radial distance FL ) liquid density, kg m-3 FS ) solid density, kg m-3 λ¨ ) wavelength of ultrasound, m Subscripts 1 ) corresponds to riser column 2 ) corresponds to multistage column ∞ ) infinite medium L ) liquid phase SL ) solid-liquid at fixed bed condition TP ) two phase
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ReceiVed for reView December 5, 2008 ReVised manuscript receiVed February 16, 2009 Accepted February 23, 2009 IE8018627
