Holdup and solids circulation rate in liquid-solids ... - Semantic Scholar

Indian Journal of Chemical Technology Vol. 13, May 2006, pp. 247-254

Holdup and solids circulation rate in liquid-solids circulating fluidised bed P Natarajana*, R Velrajb & R V Seenirajc a

Department of Mechanical Engineering, Priyadarshini Engineering College (Anna University), Vaniyambadi 635 751, India b

Department of Mechanical Engineering, CEG, Anna University, Chennai 600 025, India

c

Department of Mechanical Engineering, CEG, Anna University, Chennai 600 025, India Email: [email protected] Received 25 May 2005; revised received 14 February 2006; accepted 9 March 2006

Experimental data, obtained using liquid-solids circulating fluidised bed, are presented to study the influence of liquid flow rate and the solids properties on the solids velocity and holdup in the riser. The influence of the auxiliary liquid flow facilitating the solids feed into the riser, and that of primary liquid flow providing the solids transport in the riser are clearly examined and correlations are presented for the holdup and the solids circulation rate based on the present data and the data reported in literature. Keywords: Liquid-solids circulating fluidised bed, Solids circulation velocity, Solids holdup, Stable operating range IPC Code: B01J8/00

The interest in the study of liquid-solids circulating fluidised bed in recent years arises from their potential applications in the fields of biochemical processing, petrochemical processing, food processing and metallurgical processing involving non-catalytic or catalytic liquid-solids reactions, and to physical processing. Specifically, they include continuous protein recovery from unclarified fermentation broth process through adsorption and desorption using anion-exchange resins1-4, synthesis of linear alkyl benzene from benzene and l-dodecene using zeolite catalysts5,6, manufacture of rutile6, binary solids mixing7 and removal of cesium using potassium titanium hexacyanoferrate from high radioactive liquid waste8. When liquid flows through a bed of solids, the solids remain stationary in the bed at low superficial velocity with liquid flowing through the interstices of the bed. When liquid flow rate exceeds minimum fluidisation velocity, the solids fluidise with a dense bed region at the bottom and a freeboard devoid of solids above. With an increase in liquid flow rate, the dense bed expands with consequent increase in bed porosity and some particles begin to entrain out of the bed. The character of fluidisation is particulate with no evidence of formation of solid aggregates unlike in the gas-solid fluidisation. With further increase in superficial velocity beyond the terminal velocity of the particle, the particle entrainment begins, resulting

in particle depletion in the bed, necessitating the feeding of fresh solids or recirculation of entrained solids to the bottom of the bed to maintain the solids inventory within the bed. This kind of operation in liquid-solids contacting is known as Liquid-Solids Circulating Fluidised Bed (LSCFB). If the liquid velocity is further increased beyond the transport velocity, the operation becomes hydraulic conveying. Thus, the liquid-solids contacting exhibits fixed bed, conventional fluidised bed, circulating fluidised bed and hydraulic conveying depending upon the liquid superficial liquid velocity. The radial fluid velocity and solids concentration profiles as well as the axial voidage distributions, differ from one contacting pattern to another leading to a difference in the performance. The bed voidage is higher near the wall region in a fixed bed, whereas the conventional particulate fluidised bed provides no radial or axial nonuniformities in the two phases. The circulating fluidised bed, though offers uniform axial solids concentration, and presents radial non-uniformities with lower voidage near the wall region, when compared to the voidage in the core. The radial nonuniformities however disappear in the transport regime. The earlier studies, covering the flow characteristics of LSCFB, are limited. Liang et al.9,10 used 140 mm internal diameter and 3 m high riser

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INDIAN J. CHEM. TECHNOL., MAY 2006

with silica gel and glass beads fluidised using water. The authors reported that the operation of LSCFB was characterised by non-uniform radial distribution of liquid velocity, particle velocity and solids holdup. They developed a core-annulus model11 to account for the radial non-uniformities and proposed a radial uniformity index for the flow structure. Zheng et al.12 experimentally investigated LSCFB using 76 mm internal diameter and 3 m high riser with steel shot, glass beads and plastic beads, and fluidised using water. The authors identified the initial circulating fluidisation zone, characterized by rapid increase in particle velocity with liquid velocity, and the fully developed circulating fluidisation zone characterised by negligible variation in particle velocity with the liquid velocity. Zheng and Zhu13 presented a pressure balance analysis and a dimensionless empirical correlation for the solids holdup in the riser and discussed the effects of liquid velocity, solids inventory and the unit geometry on the stable range of operation. They reported that the onset velocity depends only on the liquid and particle properties14. Kuramoto et al.15 investigated macroscopic flow structure of LSCFB using 93 µm and 182 µm glass beads fluidised with water and reported the formation of large scale aggregates at liquid velocities exceeding the particle terminal velocities. Roy et al.16 used radioactive isotopes to determine solids velocity and solids volume fraction distribution in a closed loop LSCFB. The experimental data, reported in the literature, is not extensive and so no correlations have been proposed to predict the important parameters such as solids circulation rate and solids holdup in the LSCFB. The present study aims at these factors based on extensive experimental data obtained in the study as well as the data reported in literature. Experimental Procedure The experimental setup, shown in Fig. 1, consists of Plexiglas riser column of 94 mm internal diameter and 2400 mm high, a liquid solids separator, a device for measuring the solids circulation rate, a storage vessel serving as solids reservoir and an inclined solid feed pipe connecting the storage vessel and the base of the riser. The base of the riser has two distributors, one for the primary liquid flow and the other for auxiliary liquid flow into the riser. The primary liquid flow distributor has 21 stainless steel tubes of 10 mm internal diameter, 12.8 mm outside diameter, and 172 mm long occupying 39.5 % of the total bed area and

extending 110 mm into the bed. The auxiliary liquid distributor has a brass plate with 2 mm openings to give 7.4% of free cross-sectional area. Liquid (tap water) from the reservoir is pumped into the riser as two streams, with one stream serving as the primary liquid, flows through the multi-tubular distributor and the second into the auxiliary distributor. The function of the auxiliary liquid flow is to fluidise the particles at the base of the riser; and to facilitate and regulate the solids flow from the storage vessel into the riser. In the absence of auxiliary liquid flow, particles do not flow into the riser and no particle circulation can be noticed. Once the fluidised particles reach the top of the primary liquid distributor using the auxiliary flow, if the combined flow rate of the primary and auxiliary flow rates, are higher than critical liquid velocity, it enables the particles to move co-currently to the top of the riser. The particles are separated from the liquid at the liquid solid separator and are returned to the particle storage vessel. The particle flow ratemeasuring device is located at the top of the storage vessel and is calibrated to give the weight of solids that are collected in a known time. During the operation, a ball valve provided at the bottom of the device, when closed, enables the solids to collect in the calibrated tube for a known time. The solids height in the tube and their weight are pre-calibrated for each fluid-solid system to give the weight of solids circulating per unit time. The primary and auxiliary liquid flows are metered through the calibrated orifice meters. The provision of the dual liquid flows into the distributor at the bottom of the riser enables the control of the liquid flow rate and the solid circulation

Fig. 1—Schematic diagram of experimental setup

NATARAJAN et al.: STUDY OF LIQUID-SOLIDS CIRCULATING FLUIDISED BED

rate independently by adjusting the auxiliary and primary liquid flows. Sand and cation exchange acrylic resin are used in the present study. The fractions are obtained by sieving and confirming to the standards. All the experiments are carried out at an ambient temperature of 28 ±1oC. The solids holdup is measured by noting the pressure gradient at different locations along the riser. Neglecting the effect of wall friction, the average solids holdup is determined for each measured section from the pressure gradient using the equation,

−

ΔP = (ρSε S +ρ l ε l )g ΔL

…(1)

(εS+εl) = 1 During the experiments, the auxiliary flow is maintained constant and the primary liquid flow is increased, to study the effect of the liquid flow rate on the solids circulation rate and solids holdup. Sufficient time is maintained to enable the system to attain steady state before the liquid flow rate, the solids circulation rate, and the pressure difference across the sections are recorded. For each set of experimental conditions, at least three readings are taken and are averaged to ensure the reproducibility and accuracy. The range of variables covered and physical properties of the solids used in the present study are given in Table 1. Minimum fluidisation velocity Umf and terminal velocity, Ut of the particles are estimated using the formulae17, 18:

Umf =

1 μ ⎡ 2 2 33.7 + 0.0408 Ar − 33.7⎤⎥ ( ) ⎢ dPρl ⎣ ⎦

…(2)

249

1

⎡ 4 gd P Δρ ⎤ 2 Ut = ⎢ ⎥ ⎣ 3Cd ρ l ⎦

…(3)

where Cd = (24/Rep) (1+.14Rep0.7) for 1 ≤ Rep ≤ 103 It is noted from Table 1 that the auxiliary liquid flow is maintained between Umf and Ut. Further, it is noticed that during the experiments the circulation of solids occurs when the true liquid velocity Vl is equal and higher than the terminal particle velocity, Ut. Results and Discussion Solids circulation rate

Figure 2 shows typical variation of the superficial solids velocity, Us in the riser with the primary liquid flow rate, Uf and the auxiliary liquid flow rate Ua. Us is estimated from the solids flux, Gs is based on the riser cross-section and the density of solids. Uf and Ua are the superficial liquid velocities that are based on the riser cross-sectional area.

Fig. 2—Variation in the solids circulation rate with primary and auxiliary liquid flow rates

Table 1—Range of experimental data considered in the development of correlations in the study Solids

dP (µm)

ρS (kg/m3)

Present study Sand −600 +500 Sand −500 +425 C-i resin −710 +600

2700 2700 1325

Literature data12 Glass beads 508 Steel shot 580

2490 7000

Umf (m/s)

Ut (m/s)

0.003 0.0893 0.00213 0.0744 0.00082 0.0341 0.00225 0.01095

0.075 0.216

Ua (m/s) Range

Uf (m/s) Range

Ul (m/s) Range

Us (m/s) Range

εS Range

0.0327-0.065 0.02 -0.164 0.08 - 0.207 4.8×10-5-1.3×10-3 0.010-0.07 0.024 -0.054 0.028-0.114 0.063-0.145 3.76×10-4-1.25×10-3 0.01 -0.06 0.010 -0.028 0.009-0.060 0.018-0.088 2.48×10-4-1.1×10-3 0.01 - 0.08 0.014-0.028 0.083-0.055

0.03-0.39 0.064-0.403 0.15-0.425 0.2-0.48

2.79×10-4-4.5×10-3 0.01-0.13 1×10-4-4.8×10-3 0.005-0.05

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It is observed from the figure that Us increases rapidly with Uf initially and approaches an asymptotic value at the high liquid velocities and are also observed that the variation of the solids circulation rate shows similar trends for all the range of auxiliary flow rates. Further, higher solids velocities are realised with an increase in the auxiliary liquid flow rate or a decrease in particle density and/or the size. The maximum in Us, i.e. Usm, depends on the auxiliary liquid velocity, Ua as well as the particle properties. Zheng et al.12 termed the initial rapid-rise in Us as ‘initial circulating fluidisation zone’ and the asymptotic region as ‘fully developed circulating fluidisation zone’. The authors also noted that Usm depends on Ua and the particle density. The data of the present study shows that the increase in solids velocity, Us with the primary liquid velocity, Uf is smooth and exponential with maximum in Us being dependent on the auxiliary liquid flow (as this alone controls the solids flow from the solids storage tank into the riser) and the physical properties of solids such as the density and the particle size. Noting that solids circulation begins when the true liquid velcoity Vl = [(Uf + Ua)/εl] equals the terminal velocity, Ut of the particle, Us is plotted against

Vl in Ut

Fig. 3 for the sand and resin particles. The data suggest that the transition from conventional fluidisation to circulating fluidisation occurs in liquidsolids fluidisation at the particle terminal velocity. This is as expected, since the character of liquidsolids fluidisation is particulate, with a minimum possibility of formation of solids aggregates; this is unlike gas-solids circulating fluidized beds wherein the transition velocities are usually higher than the particulate terminal velocity. The observation of Kuramoto et al.15 to the presence of solid aggregates could possible due to very fine particles used by the authors for the study. Based on the above observations, the data of the present study and that of Zheng et al.12 are correlated as (Fig. 4),

⎡ ⎛ U ⎞0.5 ⎛ U ⎞⎤ Us = 1.5 ⎢1 − ⎜ t ⎟ exp ⎜ − f ⎟ ⎥ U sm ⎢⎣ ⎝ U a ⎠ ⎝ U t ⎠ ⎥⎦

Fig. 3—Variation in the solids circulation rate with Ul/Ut and auxiliary liquid flow rates

Fig. 4a—Comparison of experimental data (present study) with predictions using Eq. (4)

…(4)

Table 2 gives Root Mean Square (RMS) deviation, σ defined as

Fig. 4b—Comparison of experimental data (12) with predictions using Eq. (4)


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Table 2—RMS deviation of experimental data with correlations used in the study Material Sand Sand C-i resin Glass beads Steel shot * Insufficient data

⎧ ⎪1 σ=⎨ N ⎩⎪

Size, (µm)

Eq. no.

σ

Eq. no.

σ

Eq. no.

σ

Eq. no.

σ

550 463 655 508 580

(4) (4) (4) (4) (4)

0.11 0.11 0.14 0.13 0.15

(7) (7) (7) * *

0.11 0.12 0.14 -----

(11) (11) (11) * *

0.147 0.152 0.15 -----

(8) (8) (8) (8) (8)

0.34 0.32 0.36 0.35 0.94

⎛ X exp − X pred ⎞ ⎟⎟ X exp N =1 ⎝ ⎠

N =N

∑ ⎜⎜

2

1

⎫2 ⎪ ⎬ ⎭⎪

…(5)

for the experimental data and the range listed in Table 1. It clearly shows that Eq. (4) predicts the experimental data with sufficient accuracy over a wide range in experimental conditions, particle properties and liquid rates. The maximum in solids velocity, Usm is related to the auxiliary liquid rate and the properties of solids for the present data as Usm = Ua Ar-0.5

…(6)

Solids holdup

Figure 5 shows the typical variation of average solids holdup, estimated using Eq. (1), with the primary and auxiliary liquid flow rates. εS decreases exponentially with an increase in Uf, and is higher for higher values of Ua. The data suggest that an increase in liquid flow rate or decrease in particle density and/or size, at a given Ua, increases particle velocity, thus decreasing the solids holdup with consequent shorter retention times for particles in the riser. Figures 6 and 7 show the variation of εS with Uf and Ul respectively for constant values of Us. An increase in Uf (or Ul) for a given solids superficial velocity decreases the solids holdup because of an increase in the slip velocity which is consistent with the observation due to Lapidus and Elgin19 for cocurrent countergravity system. The data of the present study are correlated as (Fig. 8),

⎛U ⎞ ⎛ U ⎞ ε S = 0.04 exp ⎜ a ⎟ exp ⎜ - f ⎟ ⎝ Ut ⎠ ⎝ Ut ⎠

…(7)

Fig. 5—Variation of solids holdup with primary and auxiliary liquid flow rates

Fig. 6—Variation of solids holdup with solids circulation rate and primary liquid flow rate


252

Fig. 7—Variation of solids holdup with solids circulation rate and total liquid flow rate

Fig. 9—Comparison of experimental solids holdup with the prediction using Eq. (11)

Considerable deviation (σ > 0.32) is noticed when the experimental data of the authors12 as well as of the present study, are compared with the predictions making use of Eq. (8). This is because Uf and Ua influence the solids holdup (and the solids circulation rate as well) differently and hence combining them into Ul to relate εS, is inappropriate. Solids holdup is also related to solids superficial velocity as (Fig. 9)

⎛U ⎞⎡ U ⎤ ε s = 0.09 ⎜ a ⎟ ⎢1 − 0.667 s ⎥ U sm ⎦ ⎝ Ut ⎠ ⎣

Fig. 8—Comparison of experimental solids holdup with the prediction using Eq. (7)

Zheng and Zhu13 empirically related solids holdup as

εs = Gs*0.8 / 0.25U l*1.9

…(8)

where the dimensionless solids circulation rate, Gs* and the dimensionless superficial liquid velocity, U l* are defined as

Gs* ≡ Gs /(μ l Δρgρ l )

1

U l* ≡ U l ( ρl2 /μ l gΔρ )

1

3

…(11)

The present analysis covering the solids circulation rate and solids holdup in the riser of liquid-solid circulating fluidised beds, considers the influence of solids size, their density, and the primary and auxiliary liquid rates on the aforementioned parameters. The amount of solids fed into the riser, is controlled by the auxiliary liquid flow rate, while their transport in the riser is essentially governed by the primary liquid rate. The experimental data of the present study and the data of Zheng et al.12 clearly delineate the influence of Uf and Ua. The properties of solids are adequately taken into account through Archimedes number.

…(9) Stable operating range

3

…(10)

The experimental data and the correlations arrived at; using the data, show the existence of a maximum


253

in liquid-solid circulating fluidised beds. Us increases and εs decreases exponentially with the primary liquid rate, Uf. When Uf is increased, Us is increased but εs is decreased for a given Ua. The value of Usm and εs increases when Ua is increased and the density of the particle is decreased as well as its size is decreased. The solids circulation rate assumes a maximum value, Usm that depends upon Ua and the Archimedes number is defined for the fluid-particle system. Correlations are presented for Us and εs covering a wide range in the variables and operating conditions. The stable operating range in liquid rates is identified as

⎡ ⎛ U ⎞2 ⎤ U t ≤ U l ≤ U a ⎢1 + ⎜ t ⎟ ⎥ ⎢⎣ ⎝ U a ⎠ ⎥⎦ Fig. 10—Axial distribution of solids holdup in the riser

solids circulation rate, Usm (and a minimum solids holdup) dependent entirely on the auxiliary liquid flow rate and the properties of solids. Noting the total liquid flow rate corresponding to Usm as Ulm, the range of operation of LSCFB from Ul = Ut to Ul = Ulm represents the stable operation with the solids and the liquid input rates being equal to their respective output rates. If the liquid rate is increased beyond Ulm, the solids circulation rate decreases from Usm, necessitating a decrease in Uf to maintain Usm. The data of the present study and Zheng et al.12 suggest that the upper limit of stable operation should

The pressure differences measured along the length of the riser confirm uniform axial distribution of solids for the range of experimental conditions covered in the study. Acknowledgement Guidance received from Prof. Y. B. G. Varma (Retd.), Chemical Engineering, Indian Institute of Technology, Madras, India is gratefully acknowledged. Nomenclature

liquid rates, Ut ≤ Ul ≤ Ulm, the solids circulation rate increases and solids holdup decreases exponentially with Uf and increase with increase in Ua. It is observed in the present study that the axial distribution of solids is uniform for the aforementioned range in Ul (Fig. 10). The radial distribution is however non-uniform, with the visual observation of a few solids moving downward near the wall region, especially at low liquid flow rates.

Ar = Cd = dp = ΔP = Gs = Gs* = g= H= L= N= ReP = Ua = Uf = Ul = Umf = U1*= Us =

Conclusions The study, covering an experimental investigation, identifies the primary and auxiliary liquid flow rates, the solids size and their density as principal variables affecting the solids circulation rate and solids holdup

Usm= Ut = Vl = X= Xexp= Xpred=

approximately satisfy

⎡⎣U f U a / U t2 ⎤⎦ ≤ 1 . For the

…(12)

Archimedes number (dp3ρlΔρg/µl 2) drag coefficient mean particle size, m pressure drop at the test section, N/m2 solids circulation rate, kg/m2 s dimensionless solids circulation rate defined in Eq. (9) acceleration due to gravity, m/s2 riser height, m length of the test section in the riser, m number of data points particle Reynolds number, (ρlUldp/µl) auxiliary liquid velocity, m/s primary liquid velocity, m/s superficial total liquid velocity, (= Uf + Ua), m/s minimum fluidisation velocity, m/s dimensionless superficial liquid velocity defined in Eq. (10) solids circulation rate expressed as superficial solids velocity, m/s maximum solids circulation rate, m/s particle terminal velocity, m/s true liquid velocity m/s (Ul/ εl) axial distance of riser from the base, m parameter, experimental value parameter, predicted value

254


Greek letters εl = bed voidage (-) εs = solids holdup (-) σ = root Mean Square deviation as defined in Eq. (5) µ = viscosity of the liquid (kg/m s) ρl = liquid density (kg/m3) ρs = particle density (kg/m3) Δρ = (ρs −ρl)

10

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11 12

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