Particulate Science and Technology

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Novel multistage solid–liquid circulating fluidized

bed: liquid phase mixing characteristics

Manjusha A. Thombare, Dinesh V. Kalaga, Sandip B. Bankar, Rahul K.

Kulkarni, Satchidanand R. Satpute & Prakash V. Chavan

To cite this article: Manjusha A. Thombare, Dinesh V. Kalaga, Sandip B. Bankar, Rahul K.
Kulkarni, Satchidanand R. Satpute & Prakash V. Chavan (2019): Novel multistage solid–liquid
circulating fluidized bed: liquid phase mixing characteristics, Particulate Science and Technology,
DOI: 10.1080/02726351.2018.1522403

To link to this article: https://doi.org/10.1080/02726351.2018.1522403

Published online: 29 Jan 2019.

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PARTICULATE SCIENCE AND TECHNOLOGY
https://doi.org/10.1080/02726351.2018.1522403

Novel multistage solid–liquid circulating fluidized bed: liquid phase mixing

characteristics
Manjusha A. Thombarea, Dinesh V. Kalagab, Sandip B. Bankara,c, Rahul K. Kulkarnia, Satchidanand R. Satputed,
and Prakash V. Chavana
a
Department of Chemical Engineering, College of Engineering, Bharati Vidyapeeth (Deemed to be University), Pune, India; bDepartment of
Chemical Engineering, City College of New York, CUNY, New York, NY, USA; cDepartment of Bioproducts and Biosystems, Aalto University
School of Chemical Engineering, Aalto, Finland; dDepartment of Chemical Engineering, Vishwakarma Institute of Technology, Pune, India

ABSTRACT KEYWORDS
Liquid phase axial mixing studies have been carried out in the novel solid–liquid circulating fluid- Liquid mixing; dispersion
ized bed (SLCFB). The SLCFB primarily consists of a single multistage column (having an inner coefficient; solid–liquid
diameter of 100 mm i.d. and length of 1.40 m) which is divided into two sections wherein both fluidized bed; solid–liquid
circulating fluidized bed;
the steps of utilization, namely loading (e.g., adsorption and catalytic reaction) and regeneration axial dispersion model
of solid phase, can be carried out simultaneously in continuous mode. Weak base anion exchange
resin was used as the solid phase, whereas water as the fluidizing medium. The effects of physical
properties of solid phase, superficial liquid velocity, and solid circulation rate on liquid phase axial
dispersion coefficient were investigated. The dispersion coefficient increases monotonically with
an increase in the size of solid particle, superficial liquid velocity, and solid circulation rate. The
axial dispersion model (ADM) was used to model experimental residence time distribution (RTD)
data. A good agreement was found between ADM predictions and the experimental measure-
ments. A unified correlation has also been proposed to determine dispersion coefficient as a func-
tion of physical properties of solid and liquid phases, superficial liquid velocity, and solid
circulation rate based on all previous and present experimental data on multistage SLCFB.

1. Introduction main column, whereas regeneration operation in the riser

column. An integration of circulating and conventional flu-
Solid–liquid circulating fluidized beds (SLCFBs) are being
idization regimes in the existing SLCFBs eventually gives
consistently studied since last two decades owing to their
rise to certain limitations, such as (1) proper pressure bal-
unique eye-catching features over conventional solid–liquid ance requirement for a stable operation with no intermixing
fluidized beds (SLFBs) such as efficient liquid–solid contact, between the riser and main sections, (2) the expectation of
favorable mass and heat transfer, reduced backmixing of greater liquid phase mixing and solid phase mixing in the
phases, and integrated reactor and regenerator design. The riser column because it operates in circulation fluidization
applicability of SLCFBs is fairly investigated for the diversi- regime, and (3) probable failure when loading/regeneration
fied fields of industrial processes, such as production of lin- of solid phase is time intensive, demanding an enormous
ear alkyl benzene (Liang et al. 1995; Liang and Zhu 1997; height of the riser section. Moreover, it has also been
Han et al. 2003; Xu et al. 2004), continuous recovery of fer- reported in the literature that the flow structure of the riser
mentation products (Lan et al. 2000, 2002a, 2002b; column is non-uniform with respect to bed voidage and
Mazumder, Zhu, and Ray 2010; Prince et al. 2012), removal liquid velocity in the radial direction (Liang et al. 1996,
and recovery of cesium from liquid radioactive nuclear 1997; Roy and Dudukovic 2001; Zheng et al. 2002; Chavan,
waste streams (Feng et al. 2003), wastewater treatment (Cui Kalaga, and Joshi 2009; Kalaga et al. 2012; Sang and Zhu
et al. 2004; Islam et al. 2009; Chowdhury, Nakhla and Zhu 2012). The non-uniform flow structure adversely affects the
2008; Li, Nakhla, and Zhu 2012; Nirmala and driving force for transport processes and consequently
Muruganandam 2013), and continuous enzymatic polymer- reduces the overall performance of the SLCFB. Furthermore,
ization of phenol in bio-refining process (Trivedi, Bassi, and owing to non-uniform flow structure, the empirical correla-
Zhu 2006). tions developed on the basis of homogeneous fluidization
SLCFBs studied so far mainly consist of riser column that concept cannot be applied for practical design and scale-up
is operated in the circulation fluidization regime and main of SLCFB with sufficient degree of confidence. In view of
column that is operated in the conventional fluidization this, the present work proposes a novel multistage SLCFB to
regime. The loading operation is generally performed in the circumvent the limitations of existing SLCFBs. The proposed

CONTACT Prakash V. Chavan pvchavan@bvucoep.edu.in, pvcuict@gmail.com Department of Chemical Engineering, College of Engineering, Bharati
Vidyapeeth (Deemed to be University), Pune 411 043, India.
ß 2019 Taylor & Francis Group, LLC
2 M. A. THOMBARE ET AL.

SLCFB primarily comprises a single multistage column and liquid viscosity on radial liquid phase dispersion coef-
which is divided into two sections wherein both the steps of ficient in the riser section of SLCFB using a salt-solution
utilization or loading (e.g., adsorption and catalytic reaction) tracer technique. The radial liquid phase dispersion coeffi-
and regeneration can be carried out simultaneously in con- cient decreased with an increase in superficial liquid vel-
ventional fluidization regime. The operation of both loading ocity and viscosity. However, it increased as the solid
and regeneration sections in the conventional fluidization circulation rate and solid particle size were increased. This
regime offers several advantages over existing SLCFBs, is due to the fact that the contact efficiency of solid and
such as efficient mass and heat transfer, reduced liquid phases decreases with an increase in superficial
back-mixing, and adjustment of the desired residence time liquid velocity and viscosity, whereas reverse is true with
for time-intensive loading/regeneration operations. To respect to solid circulation rate and solid particle size.
standardize the proposed SLCFB, however, it is essential to Singh et al. (2008) have carried out RTD experiments in
investigate hydrodynamic, mixing, heat transfer and mass multistage SLFB to investigate the extent of liquid phase
transfer characteristics as a function of system, operating, mixing on the stages using the step response technique. Tap
and geometrical parameters. The prime objective of the water was used as a fluidizing medium, whereas glass beads
work was to investigate the effect of physical properties of were used as solid phase. Experiments were conducted by
solid phase, superficial liquid velocity, and solid circulation varying solid flow rate and superficial liquid velocity. It was
rate on the liquid phase dispersion coefficient. The stable observed that the axial liquid phase dispersion coefficient
operating window was established for smooth and uniform increased with an increase in superficial liquid velocity and
fluidization of a given solid phase. The axial dispersion solid flow rate. Kalaga et al. (2012) have investigated axial
model (ADM) was employed to predict liquid phase disper- liquid phase mixing aspects of multistage SLCFB with prime
sion coefficients using experimental residence time distribu- emphasis on the development of empirical correlation to
tion (RTD) data. Furthermore, an attempt has also been predict liquid phase axial dispersion coefficient. Ion
made to propose a unified correlation to predict dispersion exchange resins and glass beads were used as a solid phase
coefficient using experimental data from the present and and water as a fluidizing medium. RTD experiments for
previous studies. both the riser column and the multistage column of SLCFB
have been conducted using pulse response technique. The
experimental findings showed that the liquid phase axial dis-
2. Previous work
persion coefficient increases with an increase in the liquid
Liquid phase mixing characteristics of conventional SLFB have velocity, particle diameter, and particle density for the multi-
been investigated extensively. Joshi (1983), Di Felice (1995), stage column. In contrast, for the riser column, the liquid
and Thombare et al. (2017) have presented excellent state-of- phase axial dispersion coefficient was found to decrease with
the-art reviews on the transport phenomena in solid–liquid an increase in the particle diameter and the particle density.
fluidization. However, scanty information is available in the lit- Based on the experimental data available in the literature,
erature on liquid phase mixing aspect of SLCFB. Few reports the empirical correlations have been proposed to predict
are available owing to Zheng (2001), Chen et al. (2001), Cho liquid phase axial dispersion coefficient in conventional
et al. (2005), Singh et al. (2008), and Kalaga et al. (2012). SLFB and multistage SLCFB.
Zheng (2001) has investigated the axial liquid phase It should be noted that most previous workers have
characteristics in the riser column of SLCFB using con- studied liquid phase mixing in the riser section of SLCFB,
ductivity measurement technique. Glass beads were used wherein superficial liquid velocity is maintained above the
as solid phase, and tap water was used as the fluidizing terminal settling velocity of solid particle, to investigate
liquid. The local axial dispersion coefficient was measured the effect of non-uniformity of flow structure on disper-
by traversing conductivity probe in a radial direction. The sion coefficient (Chen et al. 2001; Zheng 2001; Cho et al.
axial dispersion coefficients were higher at a center than 2005). Singh et al. (2008) and Kalaga et al. (2012) have
near the wall of the riser. This non-uniformity in axial dis- carried out liquid phase mixing study in multistage SLCFB
persion was due to the non-uniform distribution of super- with certain constraints. Singh et al. (2008) have used
ficial liquid velocity and bed voidage in radial direction of multistage SLFB rather than multistage SLCFB. They have
the riser column. Chen et al. (2001) have studied axial and collected solid particles at bottom of column and charged
radial mixing aspects of the liquid phase in the riser sec- them via conveyor belt at top of column. Kalaga et al.
tion of SLCFB using electrolyte tracer technique. Tap (2012) have conducted liquid phase mixing study separ-
water and glass beads were used as the liquid and solid ately in the riser and multistage columns due to practical
phases, respectively. The liquid phase mixing characteris- difficulty in maintaining dynamic seal between riser and
tics were adequately described using a two-dimensional multistage columns. Furthermore, their studies predomin-
diffusion model. It was found that the axial and radial antly reveal the effect of superficial liquid velocity and
Peclet numbers of liquid phase increased with an increase physical properties of solid phase on dispersion coefficient.
in the superficial liquid velocity. On the contrary, they In the present work, we have made an attempt to study
decreased with an increase in the solid circulation rate. the effect of solid circulation rate on dispersion coefficient
Cho et al. (2005) have investigated the effect of superficial along with the effect of superficial liquid velocity and
liquid velocity, solid particle size, solid circulation rate, physical properties of solid phase.
 PARTICULATE SCIENCE AND TECHNOLOGY 3

Table 1. The resin properties given by the manufacturer.

Property Weak base anion exchange resin, (Tulsion A-8X MP)
Particle size, mm 0.3–1.2
Particle density, kg.m
3 1100
Matrix structure Styrene-divinyl benzene copolymer
Functional group Ternary amine
Ionic form Free base
Moisture content, (% kg water.kg wet resin
1) 47
Exchange capacity, (mo.kg dry resin
1) 2.6

3. Experimental details multistage column at the base (3), a riser column (4),
liquid–solid separator (5), and a top solids return pipe
The weak base anion exchange resin (Tulsion A-8X MP) connecting liquid–solid separator and the multistage col-
was used as a solid phase, whereas tap water was used as a umn. The loading and regenerating sections mainly consist
liquid phase for experimentation. The resin particles were of five stages (each having an inner diameter of 100 mm
segregated into various sizes using standard SS sieves. The and height of 100 mm) assembled together with flange
0.60, 0.85, and 1.20 mm particle sizes were selected to study joints. The loading and regeneration sections were con-
liquid phase mixing characteristics. The physical properties nected to each other by SS pipe having an inner diameter
of the resin, supplied by the manufacturer are given in of 10 mm and length of 200 mm, giving total height of
Table 1. 1.40 m. A stainless steel (SS) mesh with openings smaller
than the solid particle size was fitted onto SS sieve plates
3.1. Experimental set-ups that were sandwiched between every pair of glass stages
using adjoining flanges. The holes of 2 mm were provided
3.1.1. Solid–liquid fluidized bed on each SS sieve plate, providing 5.0% open area for water
An acrylic column with an inner diameter of 100 mm and flow. The solid particles moved across on the stage to the
height of 1.20 m was used. A reciprocating pump of next stage through a downspout, as the liquid flows
250 mL.s
1 capacity was used to feed water to the column. upward through mesh openings. Two types of SS stages
To smoothen the liquid flow, a pulsation dampener was were arranged alternatively in multistage column using a
fitted to the pump. The dampener pressurizes the liquid pair of adjoining flanges. For one set of successive stages,
when the pump is at full flow and discharges to the system first stage consisted of a downspout which was fitted at
when the pump outflow falls. This significantly smoothes the center of the stage while the second stage comprised
the flow such that the outflow is practically uniform. The two downspouts located around periphery as circumferen-
water flow rate was measured using rotameter. A calming tial downspouts. The SS pipe having an inner diameter of
section packed with glass beads of 0.30 m height was pro- 10 mm with 75 mm length was used as downspout to
vided to homogenize the liquid flow before it reaches to encompass weir heights of 25 mm. The schematic of SS
the liquid distributor. The distributor was a perforated stage configuration is given in Figure 2(A).
plate containing 315 holes of 2 mm diameter on a triangu- The flow of solid particles from loading to regeneration
lar pitch, giving a free area ratio of 12.50%. A mesh of BSS section was controlled by a butterfly valve (V2) appended
100 was attached on top and bottom of the distributor on interconnecting SS pipe. There were two distributors at
plate to restrict the movement of particles across it. To the bottom of each section as (1) specially designed con-
ensure that no air bubbles intruded into the column dur- ical distributor, providing 17.30% open area for primary
ing operation, the necessary arrangements in the fittings liquid flow rate, and (2) secondary liquid distributor made
and fixtures were made. A septum was provided at the of a SS stage with 10.40% opening area for auxiliary liquid
bottom of the column below the liquid distributor for flow. Figure 2(B) shows the geometrical details of specially
injecting predetermined amount of the tracer using a syr- designed conical distributor for primary liquid inlet. The
inge (having 2 mm needle). The provisions were made for total liquid flow to the section is a summation of primary
online measurement of tracer concentration using con- and auxiliary flow rates. The auxiliary liquid flow rate
ductivity meter. The concentration of tracer was measured mobilizes the solid particles underneath primary distribu-
in terms of voltage with online data acquisition system at tor to ease solid particles flow from one section
a frequency of 10 Hz using a graphite electrode (probe), to another.
fixed at the bed surface. The solid particles moved via solid return pipe (having
an inner diameter of 25 mm and length of 500 mm) to the
riser column and subsequently carried to the solid–liquid
3.1.2. Multistage solid–liquid circulating fluidized bed separator. The separator (having an inner diameter of
A schematic diagram of the multistage SLCFB is shown in 300 mm and length of 500 mm) was used to charge solid
Figure 1. The multistage SLCFB assembly primarily con- particles to loading section through solid transport line
sists of a glass multistage column which was further div- wherein solid transport was controlled by valve V1. Solid
ided into loading section (1) and regenerating section (2), particles were kept in expanded state by liquid phase
a bottom solids return pipe connecting the riser and the charged from bottom of the separator via calming section of
4 M. A. THOMBARE ET AL.

Figure 1. Experimental set up. 1. Loading section, 2. Regenerating section, 3. Solid return pipe, 4. Riser column, 5. Solid–liquid separator, 6. SS stage with SS mesh,
7. Down-comer, 8. Overflow, 9. Tracer injection syringe, 10. Conductivity probe, 11. Data acquisition system, 12. Computer. V: valve; D: diffuser/solid distributor (All
dimensions are in mm).

150 mm. The separator was provided with top outlet for dis- 3.2. Methodology
charge of liquid via mesh to avoid loss of fine solid particles.
3.2.1. Expansion characteristics of solid particles
The solid particles moved from separator to multistage col-
umn in orderly manner via solid return pipe. The solid Expansion characteristics of solid particles of a given size
return pipe was provided with special type of valve to meas- were studied in SLFB. A known quantity of solid particles of
ure the mass flow rate of solid particles. Figure 2(C) shows a given size was charged in a column to encompass a prede-
dimensional detail of the specially designed valve. With the termined height of 0.20 m. The fluidizing medium, water,
valve open, the solid–liquid mixture was collected for a was charged to the column at a predetermined flow rate
known length of time. During the measurement, no solid–li- using calibrated rotameter. The system was allowed to attain
quid flow was permitted to flow to multistage column. a steady state for 1 h for a given superficial liquid velocity
Necessary arrangement was made to measure RTD of and solid particle size. The expanded bed height was then
liquid phase. A septum was provided at the bottom of the noted. The average voidage was determined by taking solid
loading column before the liquid distributor to inject prede- phase mass balance at initial and final fluidized states for a
termined the tracer using a syringe (having 2 mm needle). solid particle size under consideration at a given superficial
The concentration of the tracer was recorded in term of liquid velocity (Chavan and Joshi 2008).
conductivity of the solution at the outlet of the loading sec- p 2 p
D HO ð1
eLO Þ ¼ D2 H ð1
eL Þ (1)
tion as shown in Figure 1. 4 4
 PARTICULATE SCIENCE AND TECHNOLOGY 5

Figure 2. Geometrical detail of auxiliary devices. (A) SS stage, (B) Primary distributor, (C) Specially designed valve for solid circulation rate measurement: (a) open
position, (b) closed position (All dimensions are in mm).

where the subscript “O” denotes the initial fixed bed condi- liquid phases was in the counter-current direction. The similar
tions, H is bed height, D is diameter of column, and eL is flow pattern was achieved in the regenerating section when the
voidage. All experiments were carried out three times and valve V2 was gradually opened and solid particles were
average values were noted. allowed to enter into the section for given liquid flow rates in
the section. When solid particles reached to the bottom of the
regenerating section, valve V3 was gradually opened to trans-
3.2.2. Operating window of SLCFB
port solid particles to the top feed tank for continuous oper-
The solid transport from loading section to regenerating sec- ation. The system was allowed to attain steady state for 2 h
tion, and regenerating section to the riser was closed initially before all experimental measurements were carried out.
using valve V2 and valve V3, respectively. The primary and In the proposed system, the loading and regenerating sec-
auxiliary liquid streams were started in loading and regenerat- tions were interconnected by a solid transport line through
ing sections at a predetermined flow rate using calibrated rota- which solid particles flowed from one section to another. The
meters and subsequently the fresh solid particles were charged dynamic seal between these two sections is of critical import-
using valve V1 at the top of the loading section via diffuser in ance to avoid intermixing of two liquid streams of fairly dif-
order to distribute solid particles uniformly. The solid bed on ferent properties for successful operation. The dynamic seal
the stage was allowed to expand up to the weir height and was realized by maintaining a particle plug in the solid trans-
subsequently flowed to the next lower stage because solid par- port lines, allowing solid particles to flow in fixed bed mode.
ticles continued to pour from the adjacent upper stage through
downspout, creating difference between bed depths from the
center to the periphery of the stage or vice versa, depending 3.2.3. Liquid mixing study
upon the type of the downspout in that stage (center or cir- The pulse response technique was employed to investigate
cumferential). Thus, the state of fluidization on every stage the axial mixing characteristics of SLFB and multistage
was cross-current although the overall flow of the solid and SLCFB. A septum was provided at the bottom of the each
6 M. A. THOMBARE ET AL.

column before the liquid distributor for injecting the tracer. Ð

1
tCdt
A pulse input of 2 mL NaCl solution (3.5 M) was injected
through a septum provided at the bottom of SLFB and load- tm ¼ 01
Ð (5)
ing section of multistage SLCFB using a syringe (having Cdt
0
2 mm needle). The time taken for the tracer injection in all
the experiments was less than one third of a second. The
provisions were made for online measurement of tracer con-
5. Result and discussion
centration using conductivity meter. To measure the con-
ductivity, graphite electrode (probe) was fixed at the outlet The physical properties of liquid and solid phases and
of the loading section of multistage SLCFB and bed surface superficial liquid velocity primarily affect the liquid phase
of SLFB. To record the online conductivity measurements, a mixing for a given geometrical parameters in conventional
conductivity meter was fabricated and the concentration in SLFB. Needless to mention that in conventional SLFB, solid
terms of voltage was measured at a frequency of 10 Hz using phase is in batch mode, whereas liquid phase in continuous
the online data acquisition system. The conductivity data mode. In SLCFB, however, the solid particles are maintained
was converted to salt concentration using calibration equa- in a circulation mode between the riser and main columns
tion based on separate experiments. in order to accommodate both the steps, namely loading
and regeneration, in a continuous mode. Therefore, it is
4. Mathematical model essential to consider solid particle circulation rate as one of
the operating parameters while discerning the liquid phase
In the present work, a one-dimensional ADM was applied mixing characteristics. In liquid fluidization, the factors that
to characterize axial liquid mixing. The key assumption in cause the axial mixing in the liquid phase are (1) the pres-
this model is that axial liquid dispersion coefficient is con- ence of particles, (2) the motion of particles, (3) the con-
stant along the bed length. Taking mass balance for a tracer tinuous formation and separation of particle wakes, and (4)
over a control volume, one can get the following unsteady the liquid phase radial velocity profile. The effect of these
state one-dimensional equation: factors on liquid phase axial mixing can be implicitly eluci-
@C @2C @C dated by ADM, wherein axial dispersion of the liquid is
¼ DL 2
U (2)
@t @z @z
with the boundary conditions
Cðz; 0Þ ¼ 0 for 0  z  H and t ¼ 0

DL @C
CO ¼ C
for z ¼ 0 and t  0
U @z

@C
¼ 0 for z ¼ H and t  0
@z
where DL is axial dispersion coefficient, C is concentration
of tracer at a given time (t) and position (z), CO is inlet con-
centration of tracer, and U is interstitial liquid velocity.
Equation (2) was numerically solved using “PDEPE” solver
in MATLAB (2016b). The axial dispersion coefficient was
estimated by calculating the mean squared error function
(Equation (3)) between experimental and predicted dimen-
sionless RTD curve.
1X
i i
m
EðhÞ exp
EðhÞ ADM
Error ¼ i (3)
m i¼m EðhÞ exp
Figure 3. Expansion characteristics of solid particles. Experimental: (䉫)
where E(H) is a dimensionless RTD function, defined as 0.60 mm, (~) 0.85 mm, (w) 1.20 mm; Richardson-Zaki equation: (––) 0.60 mm,
(- - -) 0.85 mm, (—) 1.20 mm.
follows:
EðHÞ ¼ tm EðtÞ Table 2. Expansion parameters of solid phase.
E(t) is a RTD function and tm is a mean residence time, Terminal
Particle settling Reynolds Galileo
estimated as follows: diameter, velocity, Richardson–Zaki number, number,
C dp (mm) VS1 (mm.s
1) parameter, n (–) Re (–) Ga (–)
Eðt Þ ¼ 1
Ð (4) 0.60 14.04 3.51 8.42 211.90
Cdt 0.85 17.93 3.34 15.24 613.15
0 1.20 21.32 3.24 25.58 1695.16
 PARTICULATE SCIENCE AND TECHNOLOGY 7

Figure 4. Effect of superficial liquid velocity on RTD of liquid phase for 0.85 mm
particle size in SLFB. Experimental: (w) 2.02 mm.s
1; (~) 3.50 mm.s
1; (䉫) Figure 5. Effect of the superficial liquid velocity on the dispersion coefficient in
5.50 mm.s
1; (o) 6.52 mm.s
1; ADM: (- - -) 2.02 mm.s
1; ( … ) 3.50 mm.s
1; (—) SLFB. Experimental: (䉫) 0.60 mm; (w) 0.85 mm; (~) 1.20 mm; ADM (—)
5.50 mm.s
1; (––) 6.52 mm.s
1. 0.60 mm; (- - -) 0.85 mm; (––) 1.20 mm.

considered to be composed of the molecular diffusion, the demonstrates good agreement between the experimental
turbulent diffusion, and the convective diffusion. RTD curves with those predicted by ADM. The similar
experimental dimensionless curves have been seen for 0.60
and 1.20 mm solid particle sizes. Figure 5 demonstrates the
5.1. Solid–liquid fluidized bed effect of superficial liquid velocity on axial dispersion coeffi-
5.1.1. Expansion characteristics cient for a given solid particle size. Figure 5 also depicts the
The velocity–voidage relationships were established by fluidiz- comparison between experimental data and ADM simula-
ing solid particles at different superficial liquid velocities in tions where the agreement was found to be within a stand-
the range of 1–15 mm s
1 for a given solid particle size in ard deviation of 10%. The superficial liquid velocity strongly
SLFB. The solid mass balance method was used to estimate influences the axial liquid phase dispersion coefficient. The
average voidage of a bed at given superficial liquid velocity. dispersion coefficient increases fairly linearly with an
Figure 3 shows experimental expansion data for three different increase in superficial liquid velocity. With an increase in
particle sizes (0.60, 0.85, and 1.20 mm). The terminal settling superficial liquid velocity, the movement of solid particles
velocity of solid particles was determined by fitting the increases and thus the liquid is subjected to a vigorous tur-
Richardson–Zaki equation to the experimental data. bulence. The similar observation has been put forth by pre-
vious researchers while investigating the liquid phase mixing
VL characteristics of SLFB. Most of these studies report that
¼ eL n (6)
VS1 liquid phase axial dispersion coefficient increases with an
where VL is superficial liquid velocity, VS1 is terminal set- increase in superficial liquid velocity. A maximum value of
tling velocity of solid particle, eL is bed voidage, and n is the axial dispersion coefficient was reported at a superficial
Richardson–Zaki parameter. The solid lines in Figure 3 liquid velocity corresponding to bed voidage of about 0.70
show the fitting of Richardson–Zaki equation to experimen- (Cairns and Prausnitz 1960; Mehta and Shemilt 1976; Kim
tal data with maximum deviation of 1.60%. The and Kim 1983; Tan and Krishnaswamy 1989). On the con-
Richardson–Zaki parameters for a given particle size are trary, in the present investigation, it has been observed that
reported in Table 2. the axial dispersion coefficient monotonically increases with
an increase in superficial liquid velocity. Similar results have
been obtained by Asif, Kalogerakis, and Behie (1992) and
5.1.2. Liquid mixing Kalaga et al. (2012).
Figure 4 shows the typical dimensionless RTD curves meas- The effect of particle size on the axial dispersion coeffi-
ured experimentally and those derived from the ADM at cient is also depicted in Figure 5. It is clear that axial disper-
different superficial liquid velocities for 0.85 mm solid par- sion coefficient increases with an increase in solid particle
ticle size. All the symbols in this figure represent experimen- size. For example, the values of dispersion coefficient were
tal values of the dimensionless tracer concentration and the found to be 5.21, 6.60, and 7.68  10
5 m2.s
1 for 0.60, 0.85,
solid lines represent curves predicted from ADM. Figure 4 and 1.20 mm solid particle sizes, respectively at superficial
8 M. A. THOMBARE ET AL.

liquid velocity of 3.50 mm.s
1. All previous researchers have

reported the similar finding with respect to the effect of
solid particle size on the axial dispersion coefficient (Cairns
and Prausnitz 1960; Chung and Wen 1968; Tang and Fan
1990; Asif, Kalogerakis, and Behie 1992; Kalaga et al. 2012).
The terminal settling velocity of solid particle increases with
an increase in solid particle size. Therefore, to maintain a
desired voidage for particles of higher terminal settling
velocity, higher relative liquid velocity is required.
Consequently, the power consumption per unit volume
increases which results into higher intensity of turbulence,
leading to higher extent of mixing.

5.2. Novel multistage solid–liquid circulating

fluidized bed
Before we embark on liquid phase characteristics of the pro-
posed model, it is essential to establish the stable operating
window of the operation for the proposed SLCFB. The oper-
ating window determines the limiting values of superficial
Figure 6. Operating window for multistage SLCFB. Filled symbols: loading limit.
liquid velocity and solid circulation rate for stable and Hollow symbols: flooding limit. (w) 0.60 mm; (~) 0.85 mm; (䉫) 1.20 mm.
smooth operation of the SLCFBs. Therefore, the present sec-
tion is divided into two parts: (1) establishment of operating
window and (2) study of liquid phase mixing characteristics
of proposed SLCFB. Figure 6 shows the operating window for 0.60, 080, and
1.20 mm particle sizes. The filled symbols represent the max-
imum solid flow rate at a given superficial liquid velocity,
5.2.1. Operating window
which may be used for stable and smooth operation of the
In SLCFB, solid circulation rate is an important operating
column without loading of the stages with excess solids.
parameter which determines the operating window of oper-
Similarly, the hollows symbols represent the solid flow rate
ation together with superficial liquid velocity. It has been at a given superficial liquid velocity, which may be used
well established that the smooth and stable operation of the without flooding of the stage with water. Therefore, the dif-
column is not solely dependent on the superficial liquid vel- ference between the two values of superficial liquid velocity
ocity but equivalently dependent on solid circulation rate. defines the operating range of fluidization without loading
The ratio of solid circulation rate to superficial liquid vel- and flooding of the stages at a given superficial liquid vel-
ocity implicitly sets the criterion of stable and smooth oper- ocity. For example, for 0.85 mm particle size, at a superficial
ation of SLCFBs (Singh et al. 2008; Chavan, Kalaga and liquid velocity equal to 3.66 mm.s
1 the operating range of
Joshi 2009; Chavan et al. 2018). Therefore, the operating solid circulation rate is between 1.45 and 2.40 g.s
1 corre-
window has been established for the smooth and stable sponding to flooding and loading in the multistage column.
operation of the multistage column. The superficial liquid The solid circulation rate smaller than 1.45 g.s
1 gradually
velocity was varied for a given solid circulation rate to deter- leads to the stage flooded, whereas that in excess of
mine two extremes conditions, namely loading and flooding. 2.40 g.s
1 causes loading of the stages. In Figure 6, the oper-
Although the multistage column operates in conventional ating range is marked with vertical double-headed arrows
fluidization regime wherein superficial liquid velocity ranges for clarity for a given size of solid particle.
between minimum fluidization velocity and terminal settling
velocity, it is essential to determine flooding and loading
states for stable operation of the system for given physical 5.2.2. Liquid phase mixing
properties of liquid and solid phases. There is a minimum RTD experiments were carried out in the multistage column
solid flow rate for a given superficial liquid velocity below within an operating window by varying superficial liquid
which the column is considered to be flooded. At the flood- velocity and solid circulation rate to ascertain the extent of
ing state, the fluidizing medium (water in the present study) liquid phase mixing for a given solid particle size. For
prevents the flow of solid particles from one stage to example, superficial liquid velocity was varied in the range
another through the downcomer. There is another extreme of 0.50–3.0 mm.s
1 and solid circulation rate was kept con-
state, called as loading state, wherein solid particles get stant at 1.40 g.s
1 for 0.85 mm solid particle size to study
excessively loaded on the stage for a given superficial liquid the effect of superficial liquid velocity on liquid phase axial
velocity at a certain solid flow rate. At the loading condition, mixing. Similarly, the effect of solid circulation rate was
the solid particles chock the downcomer, preventing the investigated by varying solid circulation rate in the range of
flow from one stage to another. 1.0–2.0 g.s
1 at superficial liquid velocity equal to
 PARTICULATE SCIENCE AND TECHNOLOGY 9

Figure 7. Effect of superficial liquid velocity on RTD of liquid phase for 0.85 mm Figure 8. Effect of the superficial liquid velocity on the dispersion coefficient in
particle size in multistage SLCFB. Experimental: (w) 0.50 mm.s
1; (~) SLCFB. Experimental: (䉫) 0.60 mm; (w) 0.85 mm; (~) 1.20 mm; ADM: (—)
1.50 mm.s
1; (䉫) 2.17 mm.s
1; (o) 3.0 mm.s
1; ADM: (—) 0.50 mm.s
1; ( … ) 0.60 mm; (- - -) 0.85 mm; (––) 1.20 mm.
1.50 mm.s
1; (- - -) 2.17 mm.s
1; (––) 3.0 mm.s
1.

2.17 mm.s
1. Correspondingly, the effect of superficial liquid mixing in the liquid phase by eliminating any cross-flow
velocity and solid circulation rate on liquid phase axial mix- across the sieve plates. This, in turn, reduces the axial
ing was studied for other solid particle sizes under consider- liquid mixing, which is very desirable for any separ-
ation. It may be noted that tracer concentration was ation technique.
measured at the outlet of the multistage column which com- Figure 9 shows the RTD curves as a function of solid
prises five stages. The multistage column was operated in circulation rate for a given superficial liquid velocity for
conventional fluidization regime wherein superficial liquid 0.85 mm solid particle size. Figure 10 demonstrates the
velocity varies from minimum fluidization velocity to ter- effect of solid circulation rate on axial dispersion coeffi-
minal settling velocity of the solid particle. Consequently, cient for solid particle sizes under consideration. It can be
each stage comprises SLFB at the bottom and solid particle seen that axial dispersion coefficient increases with an
free liquid at the top under steady state operation of multi- increase in solid circulation rate. Although solid and liquid
stage column. The measured RTD at the outlet is overall phases contact counter-currently in multistage column,
effect of such five stages. solid particles meet cross-currently with liquid phase on
Figure 7 shows typical dimensionless RTD curves meas- each stage contact. An increase in solid circulation rate
ured experimentally and those derived from ADM as a tends to enhance cross-current flow solid particles which
function of superficial liquid velocity within an operating in turn intensify radial movement of liquid phase.
window for 0.85 mm particle size. All the symbols repre- Consequently, RTD curve spread increases which result
sent the experimental values while solid lines represent into increase in axial dispersion coefficient with solid cir-
curves predicted from ADM. As mentioned earlier, on culation rate. Similar result has been demonstrated by
each stage (sieve plate) of the multistage column a conven- Singh et al. (2008) while investigating the effect of solid
tional fluidization regime was attained. Figure 8 shows the circulation rate on axial dispersion coefficient. It is also
comparison between experimental and ADM predicted val- clear from Figures 9 and 10 that the dispersion coefficient
ues of dispersion coefficients as a function superficial values predicted by ADM are in good agreement with
liquid velocity for a given solid particle size within a experimental values.
standard deviation of 10%. A similar trend has been
observed in multistage column as in the conventional
5.3. Correlation for dispersion coefficient in
SLFB. However, the values of dispersion coefficient are
multistage SLCFB
lower for a given solid particle size when compared to the
corresponding dispersion coefficient values obtained in Voluminous reports are available in the literature wherein
conventional SLFB. The presence of the sieve trays empirical correlation has been proposed to estimate axial
decreases the axial mixing in the multistage column of the dispersion coefficient as a function of physical properties
SLCFB as compared to that in the conventional SLFB. The of solid and liquid phases, and superficial liquid velocity
presence of the sieve trays tends to render the velocity for a given geometrical parameters (Chung and Wen 1968;
profile more uniform and physically reduces the back- Krishnaswamy and Shemilt 1972; Krishnaswamy,
10 M. A. THOMBARE ET AL.

Figure 9. Effect of solid circulation rates on RTD of liquid phase for 0.85 mm par- Figure 10. Effect of the solid circulation rate on the dispersion coefficient in
ticle size in SLCFB. Experimental: (䉫) 1.0 g.s
1; (w) 1.40 g.s
1; (~) 1.75 g.s
1; (o) SLCFB. Experimental: (䉫) 0.60 mm; (w) 0.85 mm; (~) 1.20 mm; ADM: (—)
2.0 g.s
1 ADM: (––) 1.0 g.s
1; (- - -) 1.40 g.s
1; (—) 1.75 g.s
1; ( … ) 2.0 g.s
1. 0.60 mm; (- - -) 0.85 mm;(––) 1.20 mm.

dP 3 qL ðqS
qL Þg
Ganapathy, and Shemilt 1978; Kikuchi et al.1984; Tan and Ga ¼
Krishnaswamy 1989; Tang and Fan 1990; Kalaga et al. lL 2
2012). However, there is no correlation available in the lit-
erature to predict axial dispersion coefficient in multistage Equation (9) can be extended to multistage SLCFB with fol-
column with due consideration of solid circulation rate. lowing modification to take into an account the solid circu-
Kalaga et al. (2012) have made an attempt to propose a lation rate:
correlation in multistage column. However, their correl-  ½ð3cþ2f Þ=3
ation does not elucidate the effect of solid circulation rate DL ð
c
2f Þ qL
¼ K ðReÞ ðGaÞf ðM S Þh (10)
on axial dispersion coefficient since RTD measurements dP VL qS
qL
were carried out as a function of superficial liquid velocity
by keeping the solid circulation rate constant for all solid where MS is a normalized mass flow rate of solid particles,
particle sizes under investigation. Therefore, there is need defined as follows:
to propose a unified correlation in order to account the
effect of solid circulation rate on axial dispersion GS
MS ¼
coefficient. VL AqL
Literature indicates that the liquid phase dispersion coef-
ficient is a strong function of physical properties of solid where GS is a solid circulation rate and A is a cross-sectional
and liquid phases and superficial liquid velocity. Therefore, area of column.
following equations can be written: To the best of authors knowledge, Singh et al. (2008) and
  Kalaga et al. (2012) have carried out RTD measurements in
DL ¼ f VL ; dP ; lL ; qL ; ðqS
qL Þ; g (7)
multistage SLCFB and reported liquid phase dispersion coef-
and ficients with due consideration of solid circulation rate.
b Therefore, the correlation constants in Equation (10) have
DL ¼ K ðVL Þa ðdP Þ ðlL Þc ðqL Þd ðqS
qL Þe ðg Þf (8)
been obtained by using their experimental data sets and pre-
Equation (8) can be written in terms of dimensionless sent experimental data by least square regression analysis.
numbers by using Rayleigh’s method of dimensional analysis The following expression has been obtained:
as follows:
 
1:60
 ½ð3cþ2f Þ=3 DL 0:64
0:46 qL
DL ð
c
2f Þ qL ¼ 6:52  104 ðReÞ ðGaÞ ðMS Þ0:62
¼ K ðReÞ ðGaÞf (9) dP VL qS
qL
dP VL qS
qL
(11)
where
Figure 11 shows that values of DL predicted using
dP VL qL
Re ¼ Equation (11) match satisfactorily with experimental values
lL with a maximum deviation of 17.21%.
 PARTICULATE SCIENCE AND TECHNOLOGY 11

Re Reynolds number based on superficial liquid velocity, (–)

t time, (s)
tm mean time, (s)
U interstitial liquid velocity, (m.s
1)
VL superficial liquid velocity, (m.s
1)
VS1 terminal settling velocity of solid particle, (m.s
1)
z bed height, (m)

Greek letters
eL voidage of the bed, (–)
lL viscosity of liquid, (kg m
1 s
1)
qL liquid density, (kg m
3)
qS solid density, (kg m
3)

Subscripts
O initial condition

Funding
The authors acknowledge the financial support from the Department
Figure 11. Parity plot. (w) Singh et al. (2008); (䉫) Kalaga et al. (2012); (~)
of Science and Technology (DST), New Delhi, India (DST No.: SB/S3/
Present work. CE/025/2014/SERB).

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