Effect of column diameter on dynamics of gas-solid fluidized bed: A statistical approach

Indian Journal of Chemical Technology Vol. 16, January 2009, pp. 17-24 Effect of column diameter on dynamics of gas-solid fluidized bed: A statistical approach Y K Mohanty*, G K Roy & K C Biswal Department of Chemical Engineering, NIT, Rourkela 769 008, India Email: yashobantkumar@yahoo.com Received 21 November 2007; revised 3 October 2008 Experiments have been carried out to study the effect of column internal diameters on fluctuation and expansion ratios. Three cylindrical columns with internal diameters as 099, 127 and 1524 m have been used to predict the effect of column diameters on fluctuation and expansion ratios. Factorial design (statistical approach) has been developed to predict fluctuation and expansion ratios in a gas-solid fluidized bed with varying gas-flow rates, internal column diameters and static bed heights. The values of fluctuation and expansion ratios predicted using the developed model have been found to agree well with the corresponding experimental ones. Columns with larger internal diameters give less fluctuation in the lower mass velocity range (G f < 2.5 G ) and vice-versa. The expansion ratio bears an inverse relation with the column internal diameter. Keywords: Gas solid fluidized beds, Fluctuation ratio, Expansion ratio, Factorial design, Column diameter Over the last five decades, fluidized beds have found extensive applications compared to fixed ones, and become a versatile fluid-solid contacting device in chemical, biochemical, metallurgical and thermal power generating industries. The chief advantage of fluidization lies in the fact that solid particles are vigorously agitated by the fluid passing though the bed, thus resulting in little or no temperature gradient even with highly exothermic or endothermic reactions. In spite of many advantages claimed for the fluidization phenomenon, the efficiency and quality of large scale and deep gas-solid fluidized beds are seriously affected by bubbling and slugging behaviour, when the gas velocities are higher than the minimum fluidization velocities. The first attempt to correlate fluctuation ratio with bed characteristics was given by Leva 1 : m Gf r = e (1) G where slope, m, was related to particle diameter. Present address. Department of Chemical Engineering,G.I.E.T, Gunupur, Rayagada, India Bed fluctuation and expansion ratios have been widely used to quantify fluidization quality. Fluctuation ratio is defined as the ratio of highest and lowest levels, which the top of the fluidized bed occupies for any particular gas flow rate above the minimum fluidization velocity 2. Davis 3 suggested that the design and analysis of industrial experiments is one of the important and suitable method to process the experimental data for the development of model equations The oscillations beyond certain limiting value of (G f -G )/G are due to slugging. Since slugging is affected by aspect ratio, h s /D c, the fluctuation ratio is dependent on this. A special characteristic of gassolid fluidized bed reactor is the formation of gas bubbles, which are responsible for particle circulation in the bed. For any fluidization unit, the velocity at which fluidization starts and the velocity at which slugging or enhanced rate of entrainment occurs, are the two limits of the operating range. At higher velocities, most of the gas bypasses the bed in the form of bubbles. Thus much of the gas entering the bed bypasses the solids. Therefore, the overall efficiency of the bed decreases, since a small portion of the gas finds its way up through the dense phase portion of the bed at a much lower velocity. The bubble phase is exposed entirely to a different

18 INDIAN J. CHEM. TECHNOL., JANUARY 2009 condition than the dense phase gas because of the difference in the gas-solid contact. The increase in the size of bubbles results in poorer gas-solid contact. Hence in order to maintain good fluidization, gas bubbles should be kept as small as possible and interchange of gas should take place between the bubble phase and the dense phase. The ultimate size of the bubbles formed depends upon the size of the fluidized bed, gas velocity, relative density of the gas and the solid, gas entry configuration and the size of the solid. Bed fluctuation and quality being interrelated, previous investigations on quality have been aimed at development of correlations for fluctuation ratio in terms of static and dynamic parameters of the system for cylindrical 4 and conical beds 5. Singh et al. 6 presented fluidization quality in terms of fluctuation ratio with some bed parameters for conical beds. Biswal et al. 7 suggested the following correlation for fluctuation ratio in terms of static and dynamic parameters of the bed in a conical vessel. r hs = 143. D c 415 D d c p G 153 (2) Sanyal and Cesmebasi 8 studied the effect of various momentum transfer coefficient models on bubble dynamics in a rectangular gas fluidized bed and found that it is not possible to see a repetition of well-defined bubble formation after the first bubble which is the result of starting transient behaviour in any of the cases. The gas seemed to choose a slender channel to pass through the bed and there was considerable lateral diffusion resulting in a general lifting of the bed. Kumar and Roy 9 predicted a model equation by using the statistical approach method for the bed fluctuation ratio as under: r = 1.668 + 309X 1 + 173X 2-114X 3 + 112X 4 + 079X 1 X 2 (3) Singh and Roy 10 studied the minimum bubbling velocity, fluidizing index and range of particulate fluidization for gas-solid fluidization in cylindrical and non-cylindrical beds and concluded that under similar operating conditions, minimum bubbling velocity and the fluidization index are maximum in the case of either semi-cylindrical conduit or hexagonal conduit and minimum in the case of square one. It is further concluded that the range of uniform fluidization is maximum in the case of semicylindrical bed for identical operating conditions. Singh and Roy 11 studied the effect of various system parameters on fluctuation ratio in the case of columns of different shapes, viz. square, hexagonal, semi-cylindrical and cylindrical bed as follows. for square bed: dp r = 2. 55 Dc 09 for hexagonal bed: dp r = 2. 3 Dc 06 Dc ρ hs ρ D c ρ f hs ρs for semi-cylindrical bed: dp r = 2. 323 Dc 05 and for cylindrical bed: dp r = 2. 55 Dc 09 f s Dc ρ hs ρ Dc ρ hs ρ f s f s 04 05 G G 04 04 G G 05 (4) 06 (5) 07 (6) 05 (7) Mohanty et al. 12 have found that a distributor plate having 10% open area of cross-section of the column cross-section gives a better result in terms of fluctuation and expansion as compared to 6, 8 and 12% open areas of cross-section. As equivalent diameter (D c ) changes with bed configuration (for non cylindrical columns) for identical cross-sectional area, the wall effect term (d p /D c ) has an appreciable effect on fluctuation ratio. Singh 13 also studied that under similar operating conditions, fluctuation ratio was found to be maximum in the case of square bed and minimum in the case of semi-cylindrical bed. It was also found that for a bed of a given configuration, the fluctuation ratio becomes maximum at a particular velocity ratio (G f /G ) and thereafter it either decreases or remains constant with velocity ratio.

MOHANTY et al.: EFFECT OF COLUMN DIAMETER ON DYNAMICS OF GAS-SOLID FLUIDIZED BED 19 Experimental Procedure The experimental set-up consists of an air compressor of an adequate capacity, an air accumulator for storage of air at constant pressure and a silica gel column placed after the accumulator to arrest moisture (Fig. 1). Rotameters have been used to measure the airflow rate. A distributor plate of 10% open area of cross-section of the column crosssection has been used for experimentation. Three fluidizers 099, 127 and 1524 m in internal diameters and 96 m in height each, with one of its ends fixed to the Perspex flange, have been used for the experiment. Two pressure tappings have also been provided to measure the bed pressure drop through a differential manometer in which carbon tetrachloride is used as the manometric fluid. For a particular run, data for bed fluctuation and expansion at varying flow rates and bed heights have been noted. Static bed height, column internal diameter and mass velocity of air are the variables that affect fluctuation and expansion ratios. Thus, the total number of experiments required at two levels, viz. maximum and minimum, for three variables is eight for responses in the case of the factorial design method. Each experiment is repeated three times and the average of the three values are reported as the response value. The various values of a factor examined in an experiment are known as levels. The set of levels of all factors employed in a given trial is called the treatment combination. The treatment combination gives a full description of the conditions under which the trial is carried out, so far as these are affected by the various factors being studied. The numerical result of a trial based on a given treatment is called the response corresponding to that treatment. Qualitative models for bed fluctuation and expansion ratios in the gas solid fluidized bed have been developed. The scope of the experiment is presented in Table 1. Development of model and correlations It has been found 12 that the fluctuation and expansion ratios are the functions of static bed heights, particle sizes, densities and mass velocities. Here an attempt has been made to correlate the fluctuation and expansion ratios in terms of bed heights, column internal diameters and mass velocities. The ratio between the highest and the lowest bed heights of a fluidized bed in expansion gives fluctuation ratio, r. It is mathematically expressed as: r = h 2 /h 1. On the other hand, expansion ratio, which is a measure of the ability of the bed to expand, is the ratio of the average of the highest and lowest bed heights to the static bed height for a particular gas flow rate. Mathematically, expansion ratio, R, is: R= (h 2 +h 1 ) / 2h s. In the present work, a mathematical model has also been developed for the prediction of fluctuation and expansion ratios. The model equations are assumed to be linear and take the general form: Y= a 0 + a 1 A + a 2 B + a 3 C +... + a 7 ABC (8) Fig. 1 Schematic representation of experimental set-up: 1. Compressor 2. Storage tank 3. Silica gel column 4. Rotameter 5. Fluidized column 6. Calming section 7. Manometer 8. Valve 9. Pressure gauge Table 1 Scope of the experiment Properties of the bed materials Materials d p 10 3, m ρ s 10-3, kg/m 3 Dolomite 55 2.817 Density of fluid, ρ f 1.18 kg/m 3 at 25 0 C Diameter of column, D c 099 m, 127 m, 1524 m Bed parameter Initial static bed height, h s 10 2, m 8, 10, 12 Flow property Column diameter (m) G (kg/m 2 s) G f (kg/m 2 s) 099 51 595 to 1.87 127 364 416 to 1.404 1524 36 396 to 9

20 INDIAN J. CHEM. TECHNOL., JANUARY 2009 The coefficients 3 a 0, a 7 are calculated by the Yate s technique = α y a i i i. (9) N where Y stands for fluctuation and expansion ratios; A, B, C and D are the factorial design symbols, a i is the coefficient (i = 0 7), y i is the response, α i is the interaction level of variables 3,12 and N is the total number of treatments. The levels of variables are calculated as under: Level of aspect ratio = (A-868) / 344 Level of wall effect = (B-00455) / 00095 (10) Level of mass velocity = (C-1.94) / 61 The experimental data based on factorial design, nature of the effects and its analysis are presented for fluctuation and expansion ratios in Tables 2 and 3 respectively. The following Eqs (11) and (12) have been developed for fluctuation and expansion ratios (neglecting smaller coefficients). r = 1.1185-0185A + 0047B + 0535C 0185AC +0152BC (11) R= 1.659-1726A - 1363B + 5143C 1371AC + 1163BC (12) Results and Discussion Three cylindrical columns of different internal diameters, viz. 099, 127 and 1524 m have been considered for experimentation. The variables considered in this experimentation are: dolomite of the size 00055 m, static bed of heights 08, 1 and 12 m, and mass velocity ranging up to 3 times the minimum fluidization mass velocity. Fluidization quality greatly varies when scaling up from laboratory scale to industrial scale is done. Keeping this fact in view, in the present experimentation, columns having diameters falling in the intermediate range have been considered to ensure that the findings equally suit the industrial needs. Statistical design and analysis has been used in the present work. The statistical approach requires a far less number of experimental data as compared to the other conventional methods for the development of model equations. This approach can also explicitly find out the individual as well as the interaction effect of each of the variables quantitatively on the response. When a bed of particles is fluidized by an upward flow of air, the surface of the bed is pushed up to a higher level. Any further expansion beyond this point can be attributed to the presence of gas bubbles that are responsible for an increase in bed volume. Table 2 Factorial design and analysis Sl. No Name of the variable Variable general symbol Factorial design symbol Minimum level (-1) Maximum level (+1) Magnitude of variables 1 Aspect ratio h s /D c A 524 1.212 808, 629,524, 1.01, 787, 656, 1.212, 944, 7877 2 Wall effect d P /D c B 0036 0055 0055, 00433, 0036 3 Mass velocity G f /G C 1.33 2.55 1.133 to 3.142 Table 3 Analysis of fluctuation and expansion ratios data, (r) and (R) Sl. No. Treatment combination A (h s /D c ) B (d p /D c ) C (G f /G ) r exp R exp 1 1 524 0036 1.33 1.075 1.206 2 a 1.212 0036 1.33 1.076 1.125 3 b 524 0055 1.33 1.055 1.156 4 c 1.212 0055 1.33 1.054 1.095 5 ab 524 0036 2.55 1.2 2.75 6 ac 1.212 0036 2.55 1.104 2.104 7 bc 524 0055 2.55 1.218 2.218 8 abc 1.212 0055 2.55 1.166 1.625 (Columns indicating A, B and C are common)

MOHANTY et al.: EFFECT OF COLUMN DIAMETER ON DYNAMICS OF GAS-SOLID FLUIDIZED BED 21 It is evident from Eq. (11) that the fluctuation ratio varies directly with mass velocity of air and the wall effect (column diameter), and inversely with the aspect ratio. It is also evident from Figs 2 and 3 that in the lower mass velocity range, i.e. up to two and a half times the minimum fluidization mass velocity, the fluctuation ratio is less in the case of columns having larger diameters compared to that having smaller diameters, as in the latter case the bubble diameter reaches the column diameter and consequently bursts. On the other hand, for columns having larger diameters, the bubbles do not reach column diameter in this mass velocity range and hence the fluctuation ratio is more beyond this limit. Here channelling effect is also prominent for larger diameter columns. It is also evident from the above figures that in the case of columns having smaller diameters the fluctuation ratio first increases and then remains constant in some cases in this mass velocity range. It is evident from Fig. 4 that in the lower mass velocity range, the fluctuation ratio is less for greater static bed height, i.e. for 12 m but in the higher velocity range, the ratio is less for smaller static bed height, i.e. for 08 m. From Figs 5 and 6, it is evident that the expansion ratio decreases with an increase in column diameter but increases linearly with an increase in mass velocity. Again Fig. 7 reveals that expansion goes Fig. 4 Effect of bed height on fluctuation ratio for particle size 00055 m and column diameter 127 m Fig. 2 Effect of column diameter on fluctuation ratio for particle size 00055 m and bed height 08 m Fig. 5 Effect of column diameter on expansion ratio for particle size 00055 m and bed height 08 m Fig. 3 Effect of column diameter on fluctuation ratio for particle size 00055 m and bed height 12 m Fig. 6 Effect of column diameter on expansion ratio for particle size 00055 m and bed height 10 m

22 INDIAN J. CHEM. TECHNOL., JANUARY 2009 Fig. 7 Effect of bed height on expansion ratio for particle size 00055 m and column diameter 127 m down with an increase in bed heights, i.e., less in the case of 12 m static bed height. Equation (12) shows that expansion ratio is a direct function of mass velocity but varies inversely with the aspect ratio and wall effect. The experimental data obtained have been verified with the developed model and also with the model equation developed by Singh and Roy 11, presented in Table 4 for fluctuation ratio. Table 5 represents a comparison of expansion ratio data, calculated through factorial design approaches. It is clearly evident that the developed equations are fit to any number of experimental data. The present model has Table 4 Comparison of fluctuation ratio data D p /D c D c /h s ρ f /ρ s (G f -G )/ G r cal r exp % Deviation r cal r exp % Deviation Used for Eq. (7), other model Present factorial analysis model, Eq. (11) 0055 1.2375 000539 333 1.1187 1.055 6.0435 1.054 1.055-047 0055 1.2375 000539 571 1.1493 1.285-155 1.1724 1.285-8.761 0055 1.2375 000539 2.16 1.2283 1.2 2.366 1.2702 1.2 5.856 0055 99 000539 5 1.1315 1.116 1.396 1.0715 1.116-3.985 0055 99 000539 1 1.1714 1.142 2.582 1.1215 1.142-1.789 0055 99 000539 2 1.2128 1.175 3.217 1.2216 1.175 3.972 0055 825 000539 333 1.1007 1.054 4.436 1.0545 1.054 047 0055 825 000539 1 1.1629 1.166-259 1.1096 1.166-4.8338 0055 825 000539 1.67 1.1931 1.157 3.127 1.1647 1.157 672 00433 1.587 000539 285 1.1105 1.079 2.920 1.0627 1.079-1.501 00433 1.587 000539 857 1.1733 1.238-5.221 1.1217 1.238-9.392 00433 1.587 000539 1.714 1.2147 1.187 2.336 1.2099 1.187 1.936 00433 1.587 000539 2.285 1.2323 1.125 9.539 1.2688 1.125 12.78 00433 1.27 000539 285 1.1006 1.064 3.445 1.0634 1.064-054 00433 1.27 000539 857 1.1629 1.153 862 1.1143 1.153-3.350 00433 1.27 000539 2 1.2132 1.2 1.106 1.2161 1.2 1.348 00433 1.058 000539 285 1.0926 1.062 2.885 1.0640 1.062 192 00433 1.058 000539 857 1.1544 1.172-1.494 1.1070 1.172-5.539 00433 1.058 000539 2 1.2044 1.204 037 1.1930 1.204-907 0036 1.905 000539 222 1.0966 1.055 3.946 1.0654 1.055 990 0036 1.905 000539 666 1.1585 1.142 1.450 1.1067 1.142-3.086 0036 1.905 000539 1 1.1823 1.192-809 1.1378 1.192-4.544 0036 1.905 000539 1.444 1.2042 1.157 4.085 1.1787 1.157 1.880 0036 1.524 000539 222 1.0868 1.064 2.151 1.0667 1.064 253 0036 1.524 000539 667 1.1483 1.16-1.003 1.1029 1.16-4.917 0036 1.524 000539 1.177 1.1814 1.205-1.955 1.1481 1.205-4.715 0036 1.27 000539 222 1.0789 1.062 1.600 1.0679 1.062 560 0036 1.27 000539 667 1.1400 1.129 975 1.0990 1.129-2.651 0036 1.27 000539 1.777 1.1972 1.146 4.472 1.1378 1.146-708 Columns indicating ρ f /ρ s is used only for Eq. (7) and other symbols are as represented in the model equations, i.e. h s /D c, d p /D c, and G f /G

MOHANTY et al.: EFFECT OF COLUMN DIAMETER ON DYNAMICS OF GAS-SOLID FLUIDIZED BED 23 Table 5 Comparison of expansion ratio data A B C R cal R exp % Deviation 524 0036 1.33 1.2002 1.206-4809 1.212 0036 1.33 1.1292 1.125 3733 524 0055 1.33 1.1602 1.156 3632 1.212 0055 1.33 1.0892 1.095-5296 524 0036 2.55 2.7356 2.75-5236 1.212 0036 2.55 2.1162 2.104 5798 524 0055 2.55 2.2304 2.218 5590 1.212 0055 2.55 1.611 1.625-8615 1.01 0055 1.5 1.2051 1.185 1.7039 1.01 0055 2 1.4850 1.75-15.14 1.01 0055 2.667 1.8583 2.175-14.55 1.212 0055 1.667 1.2333 1.187 3.9036 1.212 0055 2.166 1.4467 1.625-1968 1.212 0055 2.833 1.732 1.958-11.540 629 0043 1.285 1.1274 1.187-5.0208 629 0043 1.857 1.7276 1.968-12.211 629 0043 2.714 2.6270 2.562 2.5390 787 0043 1.285 1.1157 1.15-2.9788 787 0043 2.142 1.9266 1.9 1.4023 787 0043 3 2.7384 2.3 19.0648 944 0043 1.428 1.2247 1.187 3.1841 944 0043 2.142 1.827 1.667 9.6070 524 0036 1.444 1.3432 1.206 11.4155 524 0036 1.777 1.762 1.512 16.5846 524 0036 2.222 2.3228 2.562-9.3363 656 0036 1.444 1.3202 1.2 10181 656 0036 1.777 1.7105 1.675 2.1246 787 0036 1.444 1.2969 1.125 15.2837 787 0036 1.667 1.5392 1.583-2.7622 787 0036 2.444 2.3836 2.075 14.8739 not considered the density as one of the variable, but still gives better result as compared to the other model and hence can be suitably used for the purposes. For development of the model equations through factorial analysis approach, the intermediate values for the bed fluctuation and expansion ratios have been considered in lieu of the smallest and largest ones, i.e. for ( 1) and (+1). The standard deviations for fluctuation and expansion ratios in percentage have been found to be ± 3.68 and ± 16.58. Conclusions The following observations can be made about the effect of column diameters: Fluctuation ratio is small for columns having larger diameters in the lower velocity range. Fluctuation ratio is small for columns having smaller diameters in the upper velocity range, i.e. when G f 2.5 G. Fluctuation ratio bears an indirect relation with bed height in the lower velocity range. Whereas wall effect (d p /D c ) is prominent in columns having smaller diameters in the lower velocity range, channelling dominate in that having larger diameters in the upper velocity range. Expansion ratio is in inverse proportion to column diameters and bed heights, whereas it bears a direct relation with mass velocity. Factorial analysis approach can suitably be used for the development of model equations, as it

24 INDIAN J. CHEM. TECHNOL., JANUARY 2009 expresses the individual and interaction effects. Apart from this the number of experimental data required is far less as compared to other conventional methods. Nomenclature d p = diameter of particle, m D c = diameter of column, m G f = mass velocity corresponding to fluidization, kg/m 2 s G = mass velocity corresponding to minimum fluidization, kg/m 2 s h S = static bed height, m h 1 = lower height of the expanded bed, m h 2 = upper height of the expanded bed, m r = fluctuation ratio r cal = fluctuation ratio calculated through the developed equations r exp = fluctuation ratio calculated from the experiment R = expansion ratio R cal = expansion ratio calculated through the developed equations R exp = expansion ratio calculated from the experiment Greek letters ρ f = density of fluid, kg/m 3 ρ s = density of solid particle, kg/m 3 References 1 Leva M, Fluidization (McGraw Hill Book Co Inc, London), 1959. 2 Kunii D & Levenspiel O, Fluidization Engineering (Wiley, New York), 1969. 3 Davis O L, The Design and Analysis of Industrial Experiments, 2 nd edn (Longman Publishers), 1978. 4 Agarwal S K & Roy G K, J Inst Eng India, Ch 1, 68 (1987) 35. 5 Krishnamurthy S, Murthy J S N, Roy G K & Pakala V S, J Inst Eng India, Ch 2, 61 (1981) 38. 6 Singh R K, Roy G K & Suryanarayana A, Indian Chem Eng, XXXIII (2) (1991) 26. 7 Biswal K C, Sahu S & Roy G K, Chem Eng J, 23 (1982) 97. 8 Sanyal J & Cesmebasi E, Chem Eng Sci, 49, 23 (1994) 3955. 9 Kumar A & Roy G K, J Inst Eng India, 86 (2005) 119. 10 Singh R K & Roy G K, Powder Technol, 159 (2005) 168. 11 Singh, R K & Roy G K, Indian J Chem Technol, 13 (2006) 139. 12 Mohanty Y K, Biswal K C & Roy G K, Indian Chem Eng, 49(1) (2007) 1. 13 Singh R K, Studies on Certain Aspects of Gas-solid Fluidization in Non-cylindrical Conduits, Ph.D. Thesis, Sambalpur University, India, 1997.