Minimum Fluidization Velocities of Binary- Solid Mixtures: Model Comparison

Transcription

1 Vol:4, No:3, 00 Minimum Fluidization Velocities of Binary- Solid Mixtures: Model Comarison Mohammad Asif International Science Index, Chemical and Molecular Engineering Vol:4, No:3, 00 waset.org/publication/5950 Abstract An accurate rediction of the minimum fluidization velocity is a crucial hydrodynamic asect of the design of fluidized bed reactors. Common aroaches for the rediction of the minimum fluidization velocities of binary-solid fluidized beds are first discussed here. The data of our own careful exerimental investigation involving a binary-solid air fluidized with water is resented. The effect of the relative comosition of the two solid secies comrising the fluidized bed on the bed void fraction at the inciient fluidization condition is reorted and its influence on the minimum fluidization velocity is discussed. In this connection, the caability of acking models to redict the bed void fraction is also examined. Keywords Bed void fraction, Binary solid mixture, Minimum fluidization velocity, Packing models I. INTRODCTION HE first known alication of the liquid fluidization of a T solid mixture has been reorted long ago in the mineral dressing for the searation of ores []. It was noted that when solid articles differ in the size, the classification dominates. The difference in the density, on the other hand, leads to the henomenon of sorting. The otential alication of the liquid fluidization of mixtures nowadays is cited in the searation of lastics [] [3]. Even more diverse is the alication of the fluidization of solid mixtures is in the gas-solid systems. An imortant alication in this connection, for examle, has been the thermo-chemical rocessing of the biomass as can be seen from the work of Corella and co-worker [4] [5] and Berruti et al. [6]. In this alication, an inert solid secies, often sand, is used to achieve the fluidization of the biomass and control its residence time besides imroving the heat transfer. Another interesting alication has been the addition of the Geldart s grou B articles to imrove the fluidization of grou D articles which show slugging behavior [7]. Similarly, it has also been shown that the quality of fluidization can be significantly imroved by introducing a small amount of Grou A articles in the cohesive owder which falls under the Geldart s grou C classification [8]. The minimum fluidization velocity is a crucial hydrodynamic feature of fluidized beds as it marks the transition at which the behavior of an initially acked bed of solids changes into a fluidized bed. Its accurate secification is therefore indisensable for a successful initial design and subsequent scale-u and oeration of the reactors or any other M. Asif is with the Chemical Engineering Deartment, King Saud niversity, Riyadh 4, Saudi Arabia (Phone: ; fax: ; massif@ksu.edu.sa). contacting devices based on the fluidized bed technology. Industrial ractice on fluidized beds usually involves the fluidization of solids over a wide range of article-sizes and/or systems with two or more comonents. In these cases, each article fraction or each solid secies has its own minimum fluidization velocity. Characterizing the minimum fluidization velocity in cases where the fluidization mass consists of different kinds of solid articles is quite challenging in view of the comlex article-article and fluid-article interactions. Several aroaches have been recommended in the literature, which can be broadly classified into the following two main categories. The first category is the direct extension of the aroach being commonly used for determining the minimum fluidization velocity of the single solid secies, which consists of equating the effective bed weight with the ressure dro redicted by the Ergun equation [9]. Substituting the averaged values of article roerties, i.e. the mean diameter and the mean density instead of the mono-comonent roerties lead to the minimum fluidization velocity of the solid article mixtures. This can be written as: ( ) ε Re + 50ε ε Re Ga = 0 where the Reynolds number and the Galileo number are defined as follows: ( ρ d μ ) 3 f ( s f ) Re = f ( ρ ρ ρ μ ) Ga = d g Note that the over-bar reresents the mean, and the subscrit reresents the inciient or minimum fluidization condition. Symbols ρ f and ρ s are fluid and solid densities, resectively while other symbols have the usual significance. The following definitions of the mean-diameter and the meandensity are used in the above equation: ( X ) ρs = Xρs+ ρs (4) X X (5) = + d ψd ψd where, X and ψ are the volume fraction and the shericity () () (3) International Scholarly and Scientific Research & Innovation 4(3) scholar.waset.org/ /5950

2 Vol:4, No:3, 00 International Science Index, Chemical and Molecular Engineering Vol:4, No:3, 00 waset.org/publication/5950 shae factor of the solid comonent of the binary-solid mixture, resectively. Note that (4) reresents the surface-tovolume mean-diameter whereas (5) is the volume-average article density. Since the above-mentioned aroach is based on averaging the hysical roerties, namely the diameter and density of the two solid secies, it is also commonly termed as the roerty-averaging aroach. However straightforward, the roerty-averaging aroach is reorted to be limited for cases where the solid secies do not significantly differ in their roerties. One reason for the failure of this aroach may be due to the fact that when the solid article secies that differ significantly in their sizes are resent together in the same acking environment, the mixture shows a substantial degree of the volume contraction. As a consequence, the ressure dro in the acking, being a strong function of the void fraction, is also affected. This in turn leads to an incorrect rediction the minimum fluidization velocity of the mixture. Although this issue has been aarently realized sometimes ago [0], any attemt in this direction aears to be relative recent []. What is therefore needed for the correct rediction of the minimum fluidization velocity of the mixture using this aroach is to have a riori reasonable estimate of the void fraction of the mixture besides averaged article roerties. It is worthwhile at this stage to discuss the literature concerning the aarent total volume that a acking of a mixture of two or more solid secies will occuy. A good deal of literature concerning acking models deending uon the erceived mechanism of acking behavior of the solid mixture containing two or more comonents has been reorted [] [6]. However, two models based on the Westman [7] equation, which is valid for a binary-solid mixture, are resented here. The well-known Westman equation is given as: V V X V V X V X V X + G V V V V X V X + = V where, ( ε ) V = is the secific volume of the acking of binary solid mixture while V and V are secific volumes of mono-comonent beds of secies and secies, resectively. The arameter G deends uon the size ratio of the two comonents of the acking. It is easy to see that setting G = in the above equation yields the well-known serial model: V = XV + XV (7) (6) which simly states that the volume occuied by the bed of a mixture of solids is the sum of volumes occuied by monocomonent beds. sing a large base of data, Yu et al. [8] have roosed the following functional form of the arameter G in the Westman equation: ( r ) r 0.84 = G ( r > 0.84) where r is the size ratio (smaller to larger) of the two solid secies. On the other hand, Finkers and Hoffmann [9] have recently suggested another exression for the arameter G in the Westman equation. Their aroach makes use of the structural ratio rather than the diameter ratio, and is equally alicable for both sherical and non-sherical articles. This is given by: (( ε ) ) 3 r k k G = rstr + ( ε ); rstr = ε where a value of exonent k = has been recommended by the authors. The second category of aroaches consists of alying the averaging aroach directly to the minimum fluidization velocity data of mono-comonent beds. Among early researchers, Otero and Corella [0] roosed the following averaging rocedure involving the minimum fluidization velocities of the constituent solid hases: ( ) = X + X (8) (9) (0) where and are minimum fluidization velocities of comonents and, resectively. And, X is the fluid-free volumetric fraction of the larger comonent. On the other hand, assuming the binary-solid fluidized bed as consisting of two comletely segregated mono-comonent layers, others recommended using the following harmonic averaging of minimum fluidization velocities []: X = + X () Though inherently erceived to be alicable for segregated beds, this aroach has been shown to hold good even if the comonents are substantially mixed []. Introducing a more general exression for such averaging aroaches, Asif and Ibrahim [3] suggested the following general exression for averaging: () ( ) = + X X where = - yields the harmonic averaging, whereas = International Scholarly and Scientific Research & Innovation 4(3) scholar.waset.org/ /5950

3 Vol:4, No:3, 00 leads to the arithmetic averaging. sing the data of their own exeriments, they found that = -0.5 in general gave suerior redictions. Although based on minimum fluidization velocities of constituent solid hases, Cheung et al. [4] roosed a slightly different aroach. Their emirical correlation is given by: can be seen in Fig.. The minimum fluidization velocity in this case is found to be 0.7-mm/s and the bed void fraction, evaluated from the bed height, is = X (3) 6 International Science Index, Chemical and Molecular Engineering Vol:4, No:3, 00 waset.org/publication/5950 The exerimental data of Formisani [0] were found to show good agreement with the above equation. Having briefly reviewed both tyes of aroaches resented above, it is worthwhile to comare their redictive caability using carefully obtained data for the binary-solid fluidization. II. EXPERIMENTAL The test section used in the resent exerimental investigation consisted of a.5-m tall transarent Persex column of 60- mm internal diameter. It was receded by a erforated late distributor covered with a 05-µm mesh. As an added recaution to eliminate entry effects, a 0.5-m long calmingsection was emloyed receding the distributor. A schematic is shown in Fig.. A flow-through circulation cooler was used to maintain the temerature of the ta water at 0±0. C in the recirculation water tank. This was imortant in view of the fact that any change in the water temerature affects the viscosity, and consequently the ressure dro and the bed height. The flow rate of the water was adjusted using one of three calibrated flow-meters of a suitable range. The bed heights were read visually with the hel of a ruler along the length of the column. The ressure dro along the bed was measured using two different manometers of significantly different ranges. For small ressure dro measurements, an inverted air-water manometer was used. A mercury manometer, on the hand, was emloyed for measuring high ressure dros. The observation included measuring the flow rate, the bed height and the ressure dro across the bed. Two different solid secies were used. The larger lastic articles were cylindrical in shae with equivalent volume diameter of.95-mm and the density of 76-kg/m 3. Its shericity was The smaller article secies was a closely-sized sand samle retained between adjacent sieves with oening of 600-μm and 500-μm. Its density was found to be 664- kg/m 3. Different amounts of solid masses were charged into the test column and several runs for different exeriments were carried out as summarized in Table I. The bed comosition as well as the mean-diameter and the mean-density of the resulting solid mixture are also shown in the table. Both fluidization and defluidization runs were carried out. Since the defluidization runs rovided reroducible results in most cases, the minimum fluidization velocities and the bed void fraction at the inciient fluidization condition were evaluated using the ressure dro data during the defluidization. This Water tank,. Pum; 3. Flow-meters; 4..5-m long test section 5. Distributor; 6. Manometer tas; 7. Recirculation to water tank Fig. Schematic of the exerimental setu TABLE I SMMARY OF EXPERIMENTAL RNS CARRIED OT Mass of solid (g) Fraction Diameter Density Sand Plastic X (m) (kg/m 3 ) International Scholarly and Scientific Research & Innovation 4(3) scholar.waset.org/ /5950

4 Vol:4, No:3, 00 International Science Index, Chemical and Molecular Engineering Vol:4, No:3, 00 waset.org/publication/5950 ) a, (P ro d re u s re P Run (Defluidization) Run (Defluidization) Run3 (Fluidization) Run4 (Fluidization) o, (mm/s) Fig. Deendence of ressure dro on liquid velocity for X = 0.75 III. RESLTS AND DISCSSION In the following, the results of the resent exerimental investigations are first resented in Table II. The minimum fluidization velocity and the bed void fraction are both reorted in the table for different comositions of the bed. Note that the bed void fraction for the larger articles (Plastic) is much higher than the one of the smaller (sand) articles. It is seen that as the fraction of the larger comonent increases, the minimum fluidization velocity also increases. On the other hand, the bed void fraction also shows a rogressive increase as the fraction of larger articles is increased. In the following, we first resent the comarison for both categories of aroaches discussed before. This is shown in Fig. 3. Also reorted in the chart window is the average ercent error. It is seen here that redictions of () with = is better than = -0.5 and = -. This is in variance with what was reorted before that = rovides better descrition [3]. This can be attributed to the greater difference in the hysical roerties of binary mixture considered in their work. Here, the roerty-averaging model however rovides the best redictions. The mean ercentage error is seen to be 0% in this case. Predictions of both = - as well as (3) are seen to be oor here. It is imortant to oint out at this stage that none of the models resented above are fully redictive. While () (3) deend uon mono-comonent values for the rediction of the minimum fluidization velocities of the mixture, the roerty averaging aroach (using Eqs. -5) strongly deends uon the bed void fraction at the inciient fluidization condition. This issue needs to be roerly addressed in order to make the roerty-averaging model fully descritive and exloit its suerior redictive caability. For the case of binary mixtures, one can use (6) in conjunction with one of (7) to (9) to redict the mixture void fraction. The redictions are shown in Fig. 4. It is clear from the figure that (7) does not account for the volume contraction or volume exansion effects associated with mixing of two or more solid secies in the same acking environment. On the other hand, both (8) and (9) are caable of describing the contraction henomenon. But, the degree of contraction redicted by both models is higher as comared to actual values, while (7) roviding a better descrition of the mixture void fraction. TABLE II EXPERIMENTAL RESLTS FOR THE DEPENDENCE OF THE VOID FRACTION AND VELOCITY AT INCIPIENT FLIDIZATION CONDITIONS FOR THE BINARY-MIXTRE Fraction Inciient fluidization X Voidage Velocity Fig. 3 Predictions of minimum fluidization velocities using different aroaches International Scholarly and Scientific Research & Innovation 4(3) scholar.waset.org/ /5950

5 Vol:4, No:3, 00 bed void fraction can lead to a significantly higher error in the rediction of the ressure dro. This, in turn, introduces the error in the rediction of the minimum fluidization velocity. This issue assumes even greater imortance due to the occurrence of the higher degree of volume contraction as the size ratio of mixture constituents increases. ACKNOWLEDGMENT This work was suorted by the Deanshi of Scientific Research, King Saud niversity. REFERENCES International Science Index, Chemical and Molecular Engineering Vol:4, No:3, 00 waset.org/publication/5950 Fig. 4 Predictions of bed void fractions using different equations at inciient fluidization conditions The rediction of, when ε is calculated from (7) (9) are shown in Fig. 5. The average error associated with each model is also resented in the chart window. The trend already seen in Fig. 4 is once again in fact gets highlighted in this figure. The error associated with (7) is less than both (8) and (9). This is clear indication of suerior redictive caability of (7). Fig. 5 Comarison of redictions of using the roerty averaging aroach. Eq. ( 5) legend refers to exerimental values of ε. IV. CONCLSION It becomes obvious that while the roerty averaging aroach is inherently caable of roviding a good descrition of the minimum fluidization velocity here, it is mainly the accurate rediction of the bed void fraction at the minimum fluidization condition that roves to be the main stumbling block. Its imortance can be easily gauged from the fact that the Ergun equation contains terms with third order deendence on the bed void fraction. As a result, even a small error in the [] N. Estein, "Alications of Liquid-Solid Fluidization," Int. J. of Chem. Reactor Eng., vol., R, 003. [] K. Adham, Classify article using fluidized beds, Chem. Eng. Prog., vol. 9, , 00. [3] X. Hu and J.M. Calo, Plastic article searation via liquid-fluidized bed classification, A.I.Ch.E. J., vol. 5, , 005. [4] I. Narvaez, I., A. Orio, M.P. Aznar and J. Corella, Ind. Eng. Chem. Res., vol. 35,. 0-0, 996. [5] A. Olivares, M.P. Aznar, M.A. Caballero, J. Gil, E. Frances and J. Corella, Ind. Eng. Chem. Res., vol. 36, , 997. [6] F. Berruti, A.G. Liden and D.S. Scott, Chem Eng. Sci., vol. 43, , 988. [7] A. Ajbar, K. Alhumaizi, A.A. Ibrahim and M. Asif, Hydrodynamics of gas fluidized beds with mixture of grou D and B articles, Can. J. Chem. Eng, vol. 80,. 8-88, 00.. [8] A. Ajbar, K. Alhumaizi and M. Asif, Imrovement of the fluidizability of cohesive owders through mixing with small roortions of Grou A articles, Can. J. Chem. Eng., vol. 83, , 005 [9] S. Ergun, Chem. Engng. Prog., vol. 48, , 95. [0] B. Formisani, Powder Technol., vol. 66, , 99. [] Z. Li, N. Kobayashi, A. Nisjimura and M. Hasatani, Chem. Eng. Comm., vol. 9, , 005. [] T. Stovall, F. De Larrad and M. Buil, Powder Technol., vol. 48,. -, 986. [3] A.B. Yu and N. Standish, Powder Technol., vol. 55,. 7-86, 988. [4] A.B. Yu and N. Standish, Ind. Eng. Chem. Res., vol. 30, , 99. [5] A.B. Yu, R.P. Zou and N. Standish, Modifying the linear acking model for redicting the orosity of non-sherical article mixtures, Ind. Eng. Chem. Res., vol. 35, , 996. [6] N. Ouchiyama and T. Tanaka, Ind. Eng. Chem. Res., vol. 8, , 989. [7] A.E.R. Westman, The acking of articles: Emirical equations for intermediate diameter ratios, J. Am. Ceram. Soc., vol. 9,. 7-9, 936. [8] A.B. Yu, N.Standish and A.McLean, Porosity calculation of binary mixture of nonsherical articles, J. Am. Ceram. Soc., vol. 76, , 993. [9] H.J. Finkers and A.C. Hoffmann, "Structural ratio for redicting the voidage of binary article mixture," A.I.Ch.E..J., vol. 44, , 998. [0] A.R. Otero and J. Corella, Anales de la RSEFQ, vol. 67,. 07-9, 97. [] E. Obata, H. Watanbe and N. Endo, J. Chem. Eng. Jaan, vol. 5,. 3-8, 98. [] J. Rincon, J. Guardiola, A. Romerero and G. Ramos, J. Chem. Eng. Jaan, vol. 7,. 77-8, 994. [3] M. Asif and A.A. Ibrahim, Minimum fluidization velocity and defluidization behavior of binary-solid liquid-fluidized beds,. Powder Technol., vol. 6,. 4-54, 00. [4] L. Cheung, A.W. Nienow and Rowe, P.N., Chem. Eng. Sci., vol. 9, , 973. International Scholarly and Scientific Research & Innovation 4(3) scholar.waset.org/ /5950