Properties of Sodium Carbonates Beds at Incipient Fluidization and Terminal Velocities of Solids

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1 Properties of Sodiu Carbonates Beds at Incipient Fluidization and Terinal Velocities of Solids M. HARTMAN*, O. TRNKA, V. VESELÝ, and K. SVOBODA Institute of Cheical Process Fundaentals, Acadey of Sciences of the Czech Republic, CZ65 02 Prague Received 26 July 2000 An 8.5 c i.d. colun was eployed to easure in air the iniu fluidization velocity and the terinal velocity of different sodiu carbonates particles of ean size ranging fro 0.4 to Based upon the aassed experiental data, correlations were developed to estiate these fundaental fluidization characteristics which delineate odes of gassolid contacting. The need to reduce the eission of different acidic pollutants to the atosphere has led to extensive re search on their reoval fro waste and flue gases. While largescale cleaning processes usually eploy relatively inexpensive calciu or agnesiubased sorbents, potential of Na2C03 should also be explored. Such very effective aterials can be eployed for cap ture of gaseous, weak acidic pollutants and difficult odours. Experiental results of Svoboda et al [] and Mocek et al [2] on lowteperature sorption of ni trogen oxides by Na2C03based sorbents are quite proising. A practical way of contacting gases (or liquids) with particulate solids is provided by a fluidized bed. Because of intensive solids ixing, teperature fields are nearly unifor within the whole volue of bed. Hot or cold spots do not occur in the bed and the heat transfer as well as the ass transfer are usually rapid. The ode of fluidization or the regie of fluidized beds varies widely fro the state of iniu fluidiza tion to pneuotransport in dependence on the size, density, and shape of particles, on the flow rate and physicocheical properties of an eployed fluid. The regies are so different that they cannot be repre sented by a single hydrodynaic odel [3]. Fro an engineering point of view, two basic hy drodynaic states of a given bed should always be considered: the onset of fluidization which occurs at the iniu fluidization velocity [4] and beginning entrainent that is ore or less close to the teri nal (free fall) velocity of the sallest particles in the bed [5]. Moreover, knowledge of the iniu fluidiza tion akes it possible to odel the perforance of a fluidizedbed (bubbling) reactor since it perits the prediction of the aount of gas which passes through the bed in the for of bubbles. While soe data on the fluidized beds of liestonebased aterials can be found in the literature [6, 7] there is little known about fluidized beds with sodiu carbonate particles. In the present study, the inves tigation has been undertaken to explore the particle density and porosity, the iniu fluidization and entrainent velocities for sodiu carbonate decahydrate (SCD, N a 2 C 0 3 0H 2 O), for its calcination (de hydration) products sodiu carbonate onohydrate (SCM, Na2CC>3 H 2 0 ) and anhydrous sodiu carbon ate (ASC, N a 2 C 0 3 ). EXPERIMENTAL The present study was conducted with an anal, grade sodiu carbonate decahydrate (SCD) produced by Fluka (Switzerland) and its calcines (onohydrate (SCM) and anhydrous carbonate (ASC)). The par ticles of SCM and ASC were prepared by dehydrat ing particulate SCD at 30 C and 70 C, respectively, for 2 h in a uffle furnace in a slow strea of dried air. On dehydrating, the particles were sieved carefully and aintained in airtight containers. The true (skeletal) and apparent densities of these aterials were deterined by the heliu and ercury pycnoetry (AutoPore, Microeritics, USA). The physicocheical properties of the three explored solids are presented in Table. The particles coprised six very narrow, carefully sieved fractions: (dp = 0.42 ), {a\> = ), (ďp = ), (áp = 0.45 ), (ďp = ), and (dp = 0.75 ). The Czech Stan dard series of sieves was eployed, in which the aper tures of the adjacent sieves are arranged in ultiples of approxiately.25. The screen size or sieve size, dp, used in this work *The author to who the correspondence should be addressed. Che. Pap. 55(3)49 53 (200) 49

2 M. HARTMAN, O. TRNKA, V. VESELÝ, K. SVOBODA T a b l e. Properties of Particulate Sodiu Carbonates Property Mass loss on calcination 0 True (skeletal) density, pt/(kg ~ 3 ) Apparent density, p s / ( k g ~ 3 ) Porosity, e Pore volue, Vp/(3 k g ) SCD SCM ASC x 0 ~ x 0 " 3 $90. $ a) Related to К а г С О з IOH2O as a parent aterial. is the arithetic ean of the aperture of the screen which just lets the particles pass through and the next finer screen below on which they are retained. Exaination with an optical icroscope indicated that the collected particles Ъad approxiately equal axes at right angles to each other. In other words, their nearisoetric for can be assued. While sharp edges could be seen on the SCD aterial, the calcined or dehydrated SCM and ASC particles appeared ore or less round. To take into account the particle shape, the sphericity was eployed as the ost appropriate sin gle easure for characterizing the shape of closetoisoetric nonspherical particles. For the definition and features of the sphericity, a reader is referred to the literature [4, 5, 8]. For exaple, the sphericity, ф = for perfect spheres, and 0 < ф < for other bodies. Particle sphericity was deterined by a procedure based upon easureents of pressure drop across the fixed (static) bed [9]. According to this ethod, the particle sphericity can be expressed fro the widely accepted Ergun equation [4, 0] ( Д Р / Д Я ) ^ [.75( 50( 2 e)p{u2l(e3dp))^3 е) &и/(е 4)=0 () The bed voidage,, was deterined experientally by weighing a ass of particles slowly poured into a glass cylinder. e= lw/[fh(ptpi)] (2) The average values of poured bed voidage for SCD, SCM, and ASC aounted to 0.55, 0.48 and 0.45, respectively. The values of the particle sphericity, ф, fluctuated slightly for different particle size. Repeated easure ents provided average values of the sphericity, ф = 0.63 for SCD, ф = 0.82 for SCM, and ф = 0.85 for ASC. Dried air was used at 20 C as an operation ediu (density, pf =.20 kg ~ 3 ; viscosity, /if =.8 x 0" 5 Pa s). An experiental setup with a glass colun of in side diaeter 8.5 c and height 2 was used. The col un was equipped with an interchangeable gas plate distributor and fluidizing grid. Their free area was var ied to avoid excessive pressure drop. The distance be 50 tween these perforated plates was 3 c. A ring with a height of.5 c was situated just above the fluidiz ing grid for easureents of the pressure drop across the bed. The elutriated particles were separated in a cyclone, and the dust was reoved in a fabric filter. The flow rate of air was gradually increased (or de creased), and the pressure drop of the fluidized bed vs. the velocity of air was recorded. The points of iniu (incipient) fluidization and the terinal velocities of very narrow fractions of SCD, SCM. and ASC particles deterined fro the dependence of pressure drop across the bed vs. gas (air) velocity for a shallow bed of such particles were deterined by experient in a glass fluidization col un [8,, 2]. All tested powders behaved according to the "nor al" curve and began "to bubble" as soon as the in iu fluidization velocity, /щь had been exceeded. The terinal velocities given in this work are the arithetic ean of the velocity at which the decline in pressure drop becoes noticeable and that when practically all the particles are entrained out of the colun. Such values are related to the ean sieve size of the particles. The difference between the end and the beginning of entrainent is a function of the width of a sieved fraction ( ) and varies fro about'0.05 s for the sallest particles to approxiately 0.25 s for the largest ones. Replicate easureents of iniu fluidization velocity and the terinal veloc ity showed reproducibility better than 4 %. RESULTS A N D DISCUSSION The easured iniu fluidization velocities of the SCD, SCM, and ASC particles vary fro s to 0.90 s for particles in the range of These results axe plotted in Fig. as a function of the ean particle size, dp. As can be seen, the presented dependences are not linear. The SCD beds coence fluidizing at the highest superficial gas velocities because of their highest density. In Fig. 2, the experiental data points are replotted in ters of the diensionless variables such as the chiedes nuber,, and the Reynolds nuber, ižef. We can see in this figure that the results for the three tested aterials follow approxiately a single dependence. Che. Pap. 55(3)49 53 (200)

3 FLUIDIZATION AND TERMINAL VELOCITIES OF SOLIDS average deviation and a axiu deviation of ±2.8 % and ±4.7 %, respectively. The coputed lines are also shown in Figs. and 2. Consequently, the correlation (4) is proposed here as a eans of interpolation of J7f within the range of the operating variables involved in this work. We believe that such interpolated and cautiously extrapolated values are reliable enough for engineering design calculations. In contrast to the Ergun relation () derived by consideration of pressure drop [4, 0], Wen and Yu [3] developed a correlation on the basis of drag force considerations. Their correlation, after odification to apply to nonspherical particles, takes the for 2.70^0687 Де т? Äe f tp 2 e 4 j = 0 (5) Fig.. Measured and predicted iniu fluidization velocities: О SCD; D SCM; Л ASC; the lines show predictions of eqn (4) for the respective aterials. /kf Coputed values of t/f fro eqn (5) agree with the experiental values with an average deviation of ±27 %, while the deviations vary fro ±5 to ±32 %. While inforation on the incipient state of fluidization is quite satisfactory, with a nuber of equations and aount of experiented data to be found in the literature, this is not so for the terinal velocity. The reason for this state of the art is the obvious difficulty of easuring the terinal velocity and of describing real gassolid particle systes theoretically. Although we have worked with the very carefully sieved fractions as narrow as possible, they are not rigorously of unifor size and shape. The terinal velocity was related to the ean esh size of particles. It represents, therefore, the paraeter of the bed aterial rather than the true, freefall velocity of a single particle in an indefinite ediu. The easured terinal velocities varied fro about 0.25 s" to approxiately 3 s and are shown in Fig. 3. As can be seen in Fig. 4, the experiental data points for practically a single curve Fig. 2. Measured and predicted points of iniu fluidization. The sybols are the sae as in Fig.. In an effort to represent our experiental findings, we fitted an epirical quadratic expression, based on the Ergun odel [4, 0] *2Íře f + A;iiíe f = 0 (3) to our easured data on the point of iniu fluidization. The nuerical constants were deterined fro the whole set of the collected data by the siplex optiization ethod 56.35Де^ + 66iže f = 0 (4) The Í7 f and Re f values coputed fro eqn (4) agree well with the directly easured values within an Fig. 3. Measured and predicted values of terinal velocities. The sybols are the sae as in Fig., the lines show predictions of eqn (6). СЛвш. Pap. 55(3)49 53 (200) 5

M. HARTMAN, O. TRNKA, V. VESELÝ, K. SVOBODA 50 i / where C D = (24/Äet)(l + 0.73Яе 657 )+ + 0.43/( + 6 300Де 4 " 09 ) (8) 00 50 n Уд A JO 0 20,/з Fig. 4. Measured and predicted values of the Reynolds nuber at terinal velocity.

4 M. HARTMAN, O. TRNKA, V. VESELÝ, K. SVOBODA 50 i / where C D = (24/Äet)(l Яе 657 ) /( Де 4 " 09 ) (8) n Уд A JO 0 20,/з Fig. 4. Measured and predicted values of the Reynolds nuber at terinal velocity. The sybols are the sae as in Fig.. 30 A difference of approxiately 20 % was observed between the predicted and the experiental values indicating that irregular sodiu carbonate particles had a greater drag than the spherical ones. In practice, a situation frequently occurs when the size of particles, which are just entrained under the operation conditions of interest, is to be deterined. Successive approxiations are needed for calculating the size of a particle which has a given terinal velocity when we eploy the above relationship. To avoid the trial and error coputations, the particle size ust be eliinated fro eqn (7). Having introduced the diensionless terinal velocity defined by the equation Re*/ = (4/3)Äe t /C D = U?p/[g( Ps pt)] (9) one can note that the particle size does not occur on the righthand side of eqn (9). On cobining eqn (6) and (9) we get a relationship between the above diensionless terinal velocity and the diensionless diaeter, = (3/4)СЬЯе, of a sodiu carbonate particle or Re t /C D = 3.34 x 0" = 49.8(üe t /C D ) (0) (C D W),/3 Fig. 5. Correlation plot for the terinal velocity. The line represents predictions of eqns (0) and (). when replotted in ters of and Ret. The whole set of the experiental results on the terinal velocity was correlated by the siple equation Re t = 0.64АГ 0733 (6) A very good fit of this relationship to the easured results is evident in Fig. 4. Of course, the epirical correlation (6) developed here has the usual liitations, and it should be applied with caution outside the experiental conditions fro which it was educed. An attept has also been ade to copare our results with the theoretical estiates for spherical particles [5, 4] C D Re 2 t = (4/3) (7) The course of this function is shown in Fig. 5. An operation region in which particles are fluidized, but not elutriated yet, can be expressed by the difference Re t üe f. Such quantities deduced fro the experiental results in this study are plotted in Fig. 6. This contactingode diagra has practical iplications in design of gassolid contacting unit, where elutriation of particles is to be avoided or ensured. Any coercial fluidized bed unit processes particulate aterials of real, ore or less continuous size distribution. This fact can never be overlooked in either design or odelling efforts. CONCLUSION The iniu fluidization velocity and the terinal velocity of sodiu carbonate decahydrate, sodiu carbonate onohydrate, and anhydrous sodiu carbonate were deterined by experient in dependence on the diaeter of particles. Based on the collected experiental data, correlating equations were developed for the two fundaental characteristics of a fluidized bed. An explicit forula was also proposed that akes it possible to estiate the size of a carbonate particle which corresponds to a given terinal velocity under different conditions of operation. The presented find 52 Che. Pap. 55(3)49 53 (200)

5 FLUIDIZATION AND TERMINAL VELOCITIES OF SOLIDS 0 2 Re i ^ ^ Rei Transport ^tt0^ ^ ^ ^ Ftuidized bed ^ ^ Re f Rčf Reynolds nuber at iniu fluidization velocity (= C/fdpPfM) Ret Reynolds nuber at terinal velocity of a particle (= U t dppf/fif) U { iniu fluidization velocity s i U t terinal velocity s i W ass of particles kg Greek Letters КГ 2 ^ / ^ Fixed bed» i 0^ 0 J 0< 0 : Fig. 6. Contactingode diagra for sodiu carbonates particles. The lines represent predictions of eqns (4) and (6). f /f Pf Ps Ф bed voidage bed voidage at the point of iniu fluidization fluid viscosity Pa s, kg/( s) fluid density kg 3 particle density kg ~ 3 particle sphericity, shape factor REFERENCES ings can readily be eployed in successful design and operation of dense and circulating fluidized beds. Acknowledgeents. Financial support provided by the Grant Agency of the Czech Republic under the Grant No. 203/g8/00 and by the Grant Agency of the Acadey of Sciences of the Czech Republic under the Grant No. A40727 is gratefully acknowledged. C D dp ďp F 9 H АН ДР SYMBOLS chiedes nuber (= <Qgpf{ps Pf )//*f) drag coefficient of a particle particle diaeter ean particle over the very narrow size range crosssectional area of vessel 2 acceleration due to gravity (= s~ 2 ) bed height increent of bed height pressure drop across the fluidized bed s 2 Pa. Svoboda, К., Veselý, V., Hartan, M., and Jakubec, K., Atos. Protection 4, 30 (990). 2. Мосек, К., Stejskalová, К., Bach, Р., Basti, Z., Spirovová, I., and Erdös, E., Collect. Czech. Che. Coun. 6, 825 (996). 3. Hartan, M., Beran, Z., Svoboda, К., and Veselý, V., Collect. Czech. Che. Coun. 60, (995). 4. Hartan, M. and Coughlin, R. W., Collect. Czech. Che. Coun. 58, 23 (993). 5. Hartan, M. and Yates, J. G., Collect. Czech. Che. Coun. 58, 96 (993). 6. Pata, J. and Hartan, M., Ind. Eng. Che., Process Des. Dev. 7, 23 (978). 7. Pata, J. and Hartan, M., Ind. Eng. Che., Process Des. Dev. 9, 98 (980). 8. Hartan, M., Trnka, O., and Svoboda, К., Ind. Eng. Che. Res. 33, 979 (994). 9. Svoboda, К. and Hartan, M., Ind. Eng. Che., Process Des. Dev. 20, 39 (98). 0. Ergun, S., Che. Eng. Prog. 48, 89 (952).. Yates, J. G., Fundaentals of FluidizedBed Processes. Butterworths, London, Kunii, D. and Levenspiel, O., Fluidization Engineering. 2nd Edition. Butterworth Heineann, Boston, Wen, C. Y. and Yu, Y. H., Che. Eng. Prog., Syp. Ser. 62, 0 (966). 4. Turton, R. and Levenspiel, O., Powder Technol. 47, 43 (986). Che. Pap. 55(3)49 53 (200) 53

U ms = U mf (gD c ) 0.5

U ms = U mf (gD c ) 0.5 Indian Journal of Cheical Technology Vol. 15, January 2008, pp.85-89 Prediction of iniu slugging velocity, bubbling bed index and range of bubbling fluidization in cylindrical and non-cylindrical gas-solid