Mohanty

INDIAN CHEMICAL ENGINEER Copyright © 2007 Indian Institute of Chemical Engineers Vol. 49 No. 1 January-March 2007, pp. 1-10

Effect of Distributor Area on the Dynamics of Gas-Solid Fluidised Beds: A Statistical Approach Y.K. Mohanty,1* K.C. Biswal2 and G.K. Roy2 1 Department

of Chemical Engineering, G.I.E.T., Gunupur - 765 022, India of Chemical Engineering, National Institute of Technology Rourkela - 769 008, India

2Department

Abstract: Experiments have been carried out extensively to study the effectiveness of distributors in reducing bed fluctuation in gas-solid fluidised bed. The flow rate, bed height, particle size and four distributor plates of varying open area – 6, 8, 10 and 12% – of the column cross-sectional area have been used. Correlations for fluctuation ratio, expansion ratio and pressure drop at minimum fluidisation velocity have been developed by using statistical approach method. The values of fluctuation ratio, expansion ratio and pressure drop obtained from the developed correlations compare fairly well with the experimental values. It is observed that in case of distributor plates, cross-sectional area varies directly with expansion ratio and pressure drop, but inversely with fluctuation ratio. Keywords: Gas-solid fluidised bed, Distributor effect, Factorial design.

Nomenclature Ado Ac AA do dp Dc Gf Gmf GR Gt hs

Open area of distributor, m2 Area of column, m2 Distributor annular area, m2 Orifice diameter, m Particle diameter, m Column diameter, m Fluidisation mass velocity, kg/m2s Minimum fluidisation mass velocity, kg/m2s Mass velocity ratio, (Gf – Gmf )/(Gt – Gmf) Terminal mass velocity, kg/m2s Static bed height, m

*Author for Correspondence. E-mail: [email protected] Paper received: 01/04/2006; Revised paper accepted: 04/11/2006

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h1 h2 ∆Pmf r R Rep

AND

ROY

Minimum height occupied by the particles of the bed, m Maximum height occupied by the particles of the bed, m Pressure drop at minimum fluidisation velocity, N/m2 Fluctuation ratio Expansion ratio Particle Reynolds number, dimensionless

Greek Symbols ρS ρf

Density of solid, kg/m3 Density of fluid, kg/m3

Introduction Fluidisation is the operation by which fine solids are transformed into fluid-like state. It has extensive industrial applications, primarily, due to the enhancement of the rate of any transfer process. Under gas flow, more than minimum fluidisation velocity, the top of the fluidised bed may fluctuate considerably leading to instability in operation. Bed fluctuation and fluidisation quality are interrelated. The quality of fluidisation can largely be improved by introducing distributors of varying cross-sectional areas in a gas-solid fluidised bed. Out of the two methods viz. uniformity index and fluctuation ratio, the latter has widely been used to quantify fluidisation quality. The use of suitable distributor can improve fluidisation quality with better gas-solid contact through minimisation of channeling and slugging and limit the size of bubbles. A number of investigations have stressed the use of distributors to improve fluidisation quality and increase the range of applicability of gas-solid fluidised beds. This article attempts to bring the effect of distributors on the dynamics of gas-solid fluidised bed with reference to pressure drop at minimum fluidisation, expansion ratio and fluctuation ratio – which is a measure of fluidisation quality.

Literature Review Ghose and Saha [1] showed that quality of bubble formation is strongly influenced by the type of gas distributor used. Saxena et al. [2] studied the effect of distributors in a gassolid fluidised bed. Swain et al. [3] used distributors having 3 mm diameter orifices distributed in two zones – annular and central – with equal open area, varying from 2.28-6.36% of the column cross-section. They proposed the following correlation for bed fluctuation ratio

 Gf r = 3.316   Gmf 

   

0.60

 hs     Dc 

−0.35

 dp     Dc 

−0.43

 Ado     Ac 

0.24

 AA     Ac 

−0.11

 ρS   ρf 

   

−0.23

(1)

Although many studies have been reported on bed dynamics – improvement obtained in the homogeneity of the fluidised bed, bubble phenomenon, particle motion, fluid-solid mixing, pressure drop for different types of distributors – limited information is available on the improvement of fluidisation quality in terms of fluctuation ratio for such beds. Kumar and Roy [4] concluded that the quality of fluidisation can be improved through distributor parameter and proposed the following correlation for fluctuation ratio INDIAN CHEMICAL ENGINEER

Vol. 49 No. 1 January-March 2007

Effect of Distributor Area on the Dynamics of Gas-Solid Fluidised Beds

ρ r − 1 = 0.24GR0.85  s   ρf

0.63

   

0.21

 Ado     Ac 

 dp     do 

0.41

3

−0.36

 hs     Dc 

(2)

Murthy and Sekhar [5] used statistical approach method and found that due to stirring speed at minimum fluidisation velocity the pressure drop and power consumption decreases and increases, respectively, with increase in stirrer speed. Singh and Singh [6] predicted the expanded bed height and suggested the following equations for the lower and upper sections of the column, respectively Rlower = 4.7 × 10

−2

Rupper = 5.166 ×10

  Re p  

(

−3

dp     Dc 

)

  Re p  

(

1.25

.58 

)

.782

 dp     Dc 

ρ  s ρf  −1.407

   

−0.49 

  

 ρs   ρf 

   

(3)

0.39 

  

(4)

Davis [7] explained the statistical approach as one of the important methods for processing of experimental data due to its interaction effects among the variables and a less number of data are required for the development of model equations.

Experimental The experimental set-up consists of an air compressor of adequate capacity, air accumulator for storage of air at constant pressure and silica gel column after accumulator to arrest the moisture. Figure 1 shows the schematic representation of the experimental set-up. Rotameter is used to measure the airflow rate. The air distributor consists of cylindrical portion followed by conical bottom having cone angle 80-85°. The fluidiser is a transparent perspex column (9.9 cm internal diameter and 96 cm length) with one end fixed to a perspex 1: Compressor 2: Storage tank 3: Silica gel column 4: Rotameter 5: Fluidised column

6: Calming section 7: Manometer 8: Valve 9: Pressure gauge

5

4 9 1

8

9 2

3

7

4 6

Fig. 1. Schematic representation of the experimental set-up.

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flange. Two pressure tapings are provided for measuring the bed pressure drop through differential manometer in which carbon tetrachloride is used as the manometric fluid. Four distributors of varying open area of cross-section for air flow – 6, 8, 10 and 12% of column cross-sectional area – (Fig. 2) have been used. During fluidisation, the bed pressure drop, fluctuation and expansion data have been noted. The experimental runs are repeated with different bed heights and particle sizes for all four types of distributors. The scope of the experiment is given in Table 1.

Fig. 2. Schematic representation of the distributor plates of different open areas. Table 1. Scope of the experiment Properties of bed materials Materials Dolomite Bed parameter Initial static bed height Distributor parameters 6% open area 8% open area 10% open area 12% open area Flow property Mass velocity minimum, kg/m2s Gmf = 0.596 = 0.851 = 1.361

ρs × 10–3 kg/m3 2.817

dp × 103 m 0.55, 0.725, 1.29 hs × 102 m 8, 10, 12 Ado Ado Ado Ado

× × × ×

104 104 104 104

m2 m2 m2 m2

= = = =

4.618 6.158 7.697 9.237

Mass velocity maximum, kg/m2s Gf = 0.681 to 1.957 for particle size 0.0055 m = 0.935 to 1.957 for particle size 0.00725 m = 1.446 to 2.555 for particle size 0.0129 m

The variables affecting fluctuation ratio, expansion ratio and pressure drop are static bed height, particle size, mass velocity and free area of the distributor plate. Thus, the total number of experiments required at two levels for four variables are 16. Each experiment is repeated three times and the average of the three values is reported as response value. Development of Model Equations The fluctuation ratio r is defined as the ratio of highest to lowest bed heights of the fluidised bed in expansion, i.e. r = h2/h1. The expansion ratio R is defined as the ratio of average of highest and lowest bed height to the static bed height for a particular gas flow rate R = (h2 + h1)/2hs INDIAN CHEMICAL ENGINEER

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Effect of Distributor Area on the Dynamics of Gas-Solid Fluidised Beds

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In the present work, a mathematical model has been developed for the prediction of fluctuation ratio, expansion ratio and pressure drop. The model equations are assumed to be linear and they take the general form Y = a0 + a1A + a2B + a3C + a4D + …+ a12ABD + a13ACD + … + a15ABCD

(5)

(i) Coefficients are calculated by Yate’s technique

ai = Σ αi yi N

(6)

where ai is the coefficient, yi the response, αi the level of variables and N the total number of treatments. (ii) Calculation of the levels of variables A: Level of distributor = [distributor area, m2: 0.08]/0.02 B: Level of static bed height = [bed height, m: 1.01]/0.202 C: Level of particle size = [particle size, m: 0.00725]/0.0018 D: Level of mass velocity = [mass velocity, kg/m2s: 1.098]/0.036

(7)

The experimental data based on factorial design and analysis, as well as nature of the effects are presented for fluctuation ratio, expansion ratio and pressure drop in Tables 2 and 3, respectively. The following equations have been developed for fluctuation ratio, expansion ratio and pressure drop, respectively r = 1.083 – 0.00743A + 0.0033B – 0.0053C + 0.0145D – 0.00518AB – 0.00406AC – 0.00168AD + 0.00893BC + 0.00931BD + 0.00318CD – 0.00381ABC + 0.001ABD + 0.00168ACD – 0.00056BCD + 0.00243ABCD

(8)

R = 1.706 – 0.0214A – 0.0451B – 0.019C + 0.209D – 0.072AB + 0.034AC – 0.069AD + 0.039BC – 0.026BD – 0.0164CD – 0.0813ABC + 0.0343ABD – 0.03ACD + 0.0266BCD – 0.0734ABCD

(9)

∆P mf = 2.712 + 0.2437A – 0.0562B + 0.4625C + 1.525D + 0.1625AB + 0.1187AC + 0.1812AD + 0.1312BC – 0.0562BD + 0.65CD – 0.025ABC + 0.1625ABD + 0.1812ACD + 0.1312BCD – 0.025ABCD

(10)

Table 2. Factorial design analysis Variable name

Variable general symbol

Factorial design symbol

Minimum level (– 1)

Distributor area Static bed height Particle size Mass velocity

Ado/Dc hs /Dc dp /Dc Gf /Gmf

A B C D

0.06 0.808 0.0055 1.062

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Maximum level (+ 1) 0.12 1.212 0.0129 3.283

Magnitude of variables

0.06, 0.08, 0.10, 0.12 0.808, 1.01, 1.212 0.0055, 0.00725, 0.0129 1.062 to 3.283

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Table 3. Analysis of fluctuation ratio, expansion ratio and pressure drop data S. No.

A

B

C

D

D

r

Experimental 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

0.06 0.12 0.06 0.12 0.06 0.12 0.06 0.12 0.06 0.12 0.06 0.12 0.06 0.12 0.06 0.12

0.08 0.08 1.212 1.212 0.08 0.08 1.212 1.212 0.08 0.08 1.212 1.212 0.08 0.08 1.212 1.212

0.0055 0.0055 0.0055 0.0055 0.0129 0.0129 0.0129 0.0129 0.0055 0.0055 0.0055 0.0055 0.0129 0.0129 0.0129 0.0129

1.142 1.142 1.142 1.142 1.062 1.062 1.062 1.062 3.283 3.283 3.283 3.283 1.877 1.877 1.877 1.877

1.093 1.093 1.062 1.062 1.056 1.058 1.088 1.04 1.1 1.092 1.114 1.095 1.081 1.069 1.134 1.1

R

Experimental 1.427 1.427 1.427 1.427 1.188 1.188 1.188 1.188 3.015 3.015 3.015 3.015 1.689 1.689 1.689 1.689

1.25 1.312 1.208 1.229 1.25 1.25 1.291 1.187 2.5 2.531 2.166 2.312 2.156 2.468 2.0 1.895

D

∆Pmf

Experimental 0.713 0.713 0.713 0.713 0.312 0.312 0.312 0.312 0.857 0.857 0.857 0.857 0.937 0.937 0.937 0.937

1.25 1.5 1.25 1.5 1 1 1 1 3.75 3.25 2.25 3.25 4.75 5.65 4.5 6.5

Columns A, B and C are common for all set of calculations.

Results and Discussion The method of experimentation is based on statistical design of experiments (factorial design and analysis) in order to bring out the interaction effect of variables, which would not be found otherwise by conventional experimentation and to explicitly find out the effect of all the four variables quantitatively on the response. In addition, the number of experiments required is far less as compared to the conventional experimentation. When a bed of particles is fluidised by an upward flow of air, the surface of the bed is forced upward to a higher level than the level prior to fluidisation. The expansion beyond the point of incipient fluidisation is primarily due to gas bubbles, which increase the bed volume. It is observed that there is a reduction in fluctuation ratio for the distributor having a large free area of cross-section, i.e. for 12% at lower velocity, maybe owing to the reduction of channeling and slugging effects, and 10% for higher velocity ranges as gas bubbles break up at greater heights (Fig. 3) while the fluctuation ratio increases with increase in particle size and static bed height (Fig. 4). There is a gradual increase in expansion ratio for distributor having cross-sectional area ranging from 6-12% for all velocity ranges, which may be attributed to the formation of small length spouts (at the origin) in case of small diameter orifices. On the other hand, lower expansion is observed for 10% distributor for lower velocity ranges (Fig. 5). Further, it is also observed that expansion ratio is large for small particle sizes (Fig. 6). The pressure drop increases with increase in particle size for the distributor having large area of cross-section, i.e. for 12% except for 10%, where the pressure drop is less (Fig. 7) and remains constant for different static bed height. INDIAN CHEMICAL ENGINEER

Vol. 49 No. 1 January-March 2007

Fluctuation ratio

Effect of Distributor Area on the Dynamics of Gas-Solid Fluidised Beds 1.22 1.20 1.18 1.16 1.14 1.12 1.10 1.08 1.06 1.04 1.02 1.00

7

6% distributor 8% distributor 10% distributor 12% distributor

0

0.5

1 1.5 Mass velocity

2

Fluctuation ratio

Fig. 3. Effect of distributor on fluctuation ratio for 0.00055 m particle size. 1.17 1.16 1.15 1.14 1.13 1.12 1.11 1.10 1.09 1.08 1.07 1.06

0.08 m bed height 0.10 m bed height 0.12 m bed height

0

1 2 Mass velocity

3

Fig. 4. Effect of bed height on fluctuation ratio. 3.5 Expansion ratio

3.0 6% distributor 8% distributor 10% distributor 12% distributor

2.5 2.0 1.5 1.0 0.5 0 0

0.5

1 1.5 Mass velocity

2

Fig. 5. Effect of distributor on expansion ratio.

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Expansion ratio

8

4 3.5 3 2.5 2 1.5 1 0.5 0

AND

ROY

0.00055 m particle size 0.00073 m particle size 0.00129 m particle size

0

0.5

1 1.5 2 Mass velocity

2.5

Fig. 6. Effect of particle size on expansion ratio.

Pressure drop

450 400 350 300 250 200 150 100 50 0

6% distributor 8% distributor 10% distributor 12% distributor

0

0.5

1 1.5 Mass velocity

2

Fig. 7. Effect of distributor on pressure drop for 0.00129 m particle size.

The comparison of fluctuation ratio, expansion ratio and pressure drop are shown in Figs. 8, 9 and 10, respectively. The values obtained from the developed equations are compared with experimental data taken at conditions other than those used for development 1.2

Calculated

1.0 0.8 0.6 0.4 0.2 0 0

0.5

1

1.5

Experimental Fig. 8. Comparison of fluctuation ratio.

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Effect of Distributor Area on the Dynamics of Gas-Solid Fluidised Beds

9

3.0

Calculated

2.5 2.0 1.5 1.0 0.5 0

0

0.5

1

1.5 Experimental

2

2.5

3

Fig. 9. Comparison of expansion ratio. 6

Calculated

5 4 3 2 1 0

0

1

2 3 Experimental

4

5

Fig. 10. Comparison of pressure drop.

of correlations and they are found to agree within a standard deviation of ± 5% for fluctuation ratio, ± 12.6% for expansion ratio and ± 15% for pressure drop. The deviation is more in case of pressure drop and expansion ratio due to varying particle sizes and distributor areas of cross-section. It is evident from Eqs. (8) and (9) that mass velocity and distributor parameters have a larger effect on fluctuation ratio and expansion ratio as compared to that of static bed height and particle size. But Eq. (10) gives a different picture, i.e. mass velocity and particle size have a larger effect on pressure drop as compared to that of the other two variables.

Conclusion It is apparent that the quality of fluidisation can be improved by lowering the bed height, particle size and using a distributor of optimum cross-section area. But a 10% distributor plate, in particular, offers the best fluidisation quality as is evident from the experimental findings. The developed equations can be successfully utilised for the prediction of fluctuation ratio, expansion ratio and pressure drop. The factorial design and analysis INDIAN CHEMICAL ENGINEER

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approach is suitable in these circumstances as it can take into account the individual and interaction effects among the variables.

References 1. 2. 3. 4. 5. 6. 7.

Ghosh, A. and Saha, R.K., Indian Chem. Eng., 29, p. 50 (1987). Saxena, S.C., Chatterjee, A. and Patel, R.C., Powder Tech., 22, p. 191 (1979). Swain, P., Nayak, P.K. and Roy, G.K., Indian Chem. Eng., 38, p. 39 (1996). Kumar, A. and Roy, G.K., Inst. Engs. India, 82, p. 61 (2002). Murthy, J.S.N. and Chandra Sekhar, P., Indian Chem. Eng., 46, p. 84 (2004). Singh, S.P. and Singh, A.N., Indian Chem. Eng., 45, p. 268 (2003). Davis, O.L., Design and Analysis of Industrial Experiments, Longman Publishers (1978).

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