A new model for bubbling fluidized bed reactors

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1 chemical engineering research and design Contents lists available at ScienceDirect Chemical Engineering Research and Design j ourna l h omepage: A new model for bubbling fluidized bed reactors M.P. Jain a,, D. Sathiyamoorthy a, V. Govardhana Rao b a Bhabha Atomic Research Centre, Mumbai , India b Indian Institute of Technology Bombay, Mumbai , India a b s t r a c t Various mathematical models have been proposed in the past for estimating the conversions of reactant gases in fluidized bed reactors. A new mathematical model is being proposed in this paper that gives relatively better results compared to the prevailing models for bubbling fluidized bed reactors utilizing Geldart B particles. The new model is named as JSR Jain, Sathiyamoorthy, Rao model and it is a modified version of bubble assemblage model of Kato and Wen This paper discusses the development of JSR model and its verification by using data from chemical engineering literature on fluidization and also experimental data from hydrochlorination of silicon in a fluidized bed reactor. The new model is tested for five processes having operating temperatures from 130 C to 450 C, operating velocities from m s 1 to 0.19 m s 1 and solid particle sizes from 65 to 325 mesh The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Fluidization; Modelling; Reactors; Powder; Particles; Compartments 1. Introduction Initially two phase models consisting of bubble and emulsion phases and then three phase models having one more additional phase called cloud phase were proposed. Examples of two phase models are Davidson and Harrison 1963 and Patridge and Rowe 1966 models, and examples of three phase models are Kunii and Levenspiel model 1968 and Kato and Wen model Davidson and Harrison model had limitations with respect to high interphase mass transfer, and Patridge and Rowe model due to excess bubble-cloud area than actual. Therefore, both the two phase models could not provide satisfactory results. Models by Fryer and Potter 1972 and Werther 1980 were proposed. Fryer and Potter model is known as countercurrent back-mixing model CCBM. The CCBM model did not become popular because of the difficulties associated with numerical solutions of the governing equations. The model used constant size bubble while it is a fact that bubble diameter changes as it rises in the fluidized bed. Werther 1980 model took an analogy from gas liquid behaviour. In the this model the reactant gas from the gas phase to solid phase is assumed to be transported in a manner similar to the diffusion of a gas through a thin film into the bulk of a liquid in a gas liquid interacting system. Kunii and Levenspiel 1968 and Kato and Wen 1969 models have been popularly used for design of bubbling fluidized bed reactors. There is still some scope for improvement for both these models as reported by Chavarie and Grace A new model JSR, i.e., Jain, Sathiyamoorthy and Rao has been proposed to improve and scale up the gas solid bubbling fluidized bed reactors. The JSR model has been further tested using four reaction systems, viz. ammoxidation of propylene, hydrogenation of ethylene, oxidation of ammonia, decomposition of nitrous oxide by using data from chemical engineering literature. All the four reactions are confirmed to have first order as that of hydrochlorination of silicon metal. Experiments were carried out by us on hydrochlorination of silicon in a fluidized bed reactor in order to verify the predictions of the new JSR model. Silicon powder used in our experimental work belongs to classification Geldart B. The conversions of reactant gases in fluidized bed conditions are predicted utilizing JSR, Kunii and Levenspiel, and Kato and Wen models and compared Minimum fluidization velocity Minimum fluidization velocity for classification Geldart B particles can be evaluated with a good accuracy from the correlation of Delebarre, Re 2 mf + 29, 400ε 3 mf 1 ε mf Re mf = Ar 1 Corresponding author. Tel.: address: mpjain2000@yahoo.com M.P. Jain. Received 3 December 2012; Received in revised form 3 September 2013; Accepted 15 September /$ see front matter 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

2 472 chemical engineering research and design Nomenclature A reactant gas Ar Archimedes number, d 3 p f s f g/ 2 g, C A concentration of reactant gas in cloud phase, kg mol m 3 C e concentration of reactant gas in emulsion phase, kg mol m 3 C b concentration of reactant gas in bubble phase, kg mol m 3 C E concentration of reactant gas at reactor exit, kg mol m 3 concentration of reactant gas at entry of reactor, kg mol m 3 C bh concentration of reactant gas in bubble phase at height h, kg mol m 3 C bhi concentration of reactant gas in bubble phase at height h in ith compartment, kg mol m 3 C En concentration of reactant gas at exit of nth compartment, kg mol m 3 C En 1 concentration of reactant gas at exit of n 1th compartment, kg mol m 3 D molecular diffusion coefficient of gas, m 2 s 1 d bi initial bubble diameter, m d b bubble diameter, m d p particle diameter, m d t reactor ID, m maximum bubble diameter, m F a parameter used in Eq. 5, g gravitational acceleration, m s 2 h i height of ith compartment, m ID internal diameter of reactor, m K bc volume rate of gas exchange between bubble and cloud phases per unit bubble volume, s 1 K be volume rate of gas exchange between bubble and emulsion phases per unit bubble volume, s 1 K bei volume rate of gas exchange between bubble and emulsion phases in ith compartment per unit bubble volume, s 1 K ce volume rate of gas exchange between cloudwake and emulsion phase per unit bubble volume, s 1 K r apparent fixed bed reaction rate constant, m 3 /m 3 catalyst s 1 K f apparent fluidized bed reaction rate constant, m 3 /m 3 catalyst s 1 L mf initial height of the solid bed, m M a parameter defined by Eq. 20 t time, s Re mf Reynolds number at minimum fluidization velocity Re mf = d p U mff /g, U o, superficial velocity of fluidizing gas, m s 1 U mf superficial gas velocity at incipient fluidization, m s 1 U b bubble velocity, m s 1 U br bubble rise velocity, m s 1 x a parameter defined by Eq. 35 in appendix X A conversion of reactant gas, X AJSR conversion of reactant gas by JSR model, X AKL conversion of reactant gas A by Kunii and Levenspiel model, or, X AKW conversion of reactant gas A by bubble assemblage model, a parameter defined by Eq. 9, ˇ a parameter defined by Eq. 12, c ratio of volume of solids in cloud-wake region to volume of bubbles in bed e ratio of volume of solids in emulsion phase to volume of bubbles in bed b ratio of volume of solids in bubble phase to volume of bubbles in bed ı I bubble fraction of the HCl gas in the ith compartment a parameter defined by Eq. 14, ϕ a parameter defined in Eq. 22, s density of solid particle, kg m 3 f density of the reactant gas, kg m 3 ε A fractional change in volume between nil and complete conversion of reactant A ε mf fraction of bed at incipient fluidization g viscosity of the reactant gas, kg m 1 s 1 Re mf = [{600ε 3 mf 1 ε mf } Ar] ε 3 mf 1 ε mf 2 The above equation includes bed voids at minimum fluidization and helps better prediction of minimum fluidization velocity. 2. Development of an improved new mathematical model Various phases in a bubbling bed model are shown in Fig. 1, and it is similar to Kunii and Levenspiel model. Three phases have been considered in the bubbling bed model. The model considers all bubbles of equal size throughout the bed and no counter-diffusion in the estimation of predicted conversion of the reactant. Kato and Wen 1969 have proposed a model in which a bubbling bed is divided into several hypothetical compartments of different sizes based on factors like particle density, gas velocity and particle diameter. New model brings important concepts of both Kunii and Levenspiel, and Kato and Wen models together. Assumptions for new model 1. The model assumes bubbles of perfectly spherical shape. 2. It is assumed that in the cloud zone, wake is not a separate entity. 3. The reactant is assumed to diffuse from bubble phase to emulsion phase. 4. In any compartment the mass transfer is assumed to occur from a bubble of diameter equivalent to the compartment height. The emulsion phase is considered to be at incipient state of fluidization and considered to be well mixed up with constant voids. 5. The solid particles present in the bubble are neglected and hence the reaction with the gas in the bubble phase is assumed to be nil. The model is discussed here in five steps as follows, i Derivation of equation for compartment height

3 chemical engineering research and design Fig. 1 Transport of reactant from a bubble to emulsion with a hypothetical compartment of partitioned gas fluidized. The fluidized bed is assumed to be made up of several hypothetical compartments of size h i which is same as the diameter of a single bubble in that compartment. Kato and Wen 1969 have mentioned in their paper that they are applying Kobayashi et al correlation with possibility of some error in the calculation of compartment height and this correlation can be used till a better correlation is found out. Vishwanathan et al also analysed and expressed the similar views. Empirical equation by Mori and Wen 1975 correlated bubble diameter and reactor tube diameter for Geldart B and D powders as given below, 0.3h d bi = d o exp d t The range of conditions are d t 1.3 m, U mf 0.20 m s 1, 60 d p 450 m, U o U mf 0.48 m s 1. Bubble diameter is calculated for ith compartment from Eq. 3. Maximum limit for reactor diameter is 1.3 m but according to GOLFERS 1982 Eq. 3 can be used for higher diameters also for designing and scaling up purposes. This equation will be used to find out compartment height as the bubble diameter has been considered to be equal to the height of i th compartment at a particular level in the fluidized bed. Therefore, 3 a Mass balance of reactant gas A over the cloud phase in a particular compartment: Transfer of A to cloud wake = reaction in cloud wake + transfer of A to emulsion K bc C b C c = c K r C c + K ce C c C e 6 Symbols have their usual meaning and have been described in nomenclature. No counter diffusion and no bulk flow are considered here in the above equation. b Mass balance of A over the emulsion phase in a particular compartment: Transfer of A to emulsion = reaction of A in emulsion K ce C c C e = e K r C e 7 or C e = or, K ce C c ek r + K ce C e = C c 9 From Eq. 6, 8 d bi = h i for i = 1 to N compartments Putting the value of d bi in Eq. 3, rearranging and integrating 1 = hi h i 1 [ ] 1 { } dh 4 0.3h dbm d o exp d t Taking, 0.3/d t = p and 1 d o / expph i 1 = F. On simplifying details are given in the appendix, h i = 1 ln [F + 1 F exppd p bm ] 5 ii Developing an expression for mass transfer of reactant gas A from bubble to cloud and cloud to emulsion K bc C b = C c { c K r + K ce 1 + K bc } 10 Therefore, C c = or C b K bc { c K r + K ce 1 + K bc } 11 C c = ˇC b 12 Therefore, C e = ˇC b 13 Taking, ˇ = C e = C b 14

4 474 chemical engineering research and design The terms and ˇ are calculated from the values of K bc, K ce, c, e and K r. K bc and K ce are calculated similar to the model of Kunii and Levenspiel and correlations are given below, K bc = 4.5 U mf 0.5 g D d b d b and Umf DU br K ce = 6.77 d 3 b 16 iii Estimation of bubble phase exit concentration of A Mass balance in bubble phase in h i size compartment Rate of change of reactant concentration in the bubbles = Loss of reactant by exchange to emulsion Solid particles inside the bubbles are neglected and it is it is assumed that no reaction takes place in bubbles. Only bubble to emulsion reaction takes place for reactant gas A in the compartment i dc b dt = K be C b C e 17 Here, for a particular compartment i, 1/K be = 1/K bc + 1/K ce dc b = K be C b C e dt 18 Putting the value of C e from Eq. 14 and value of dt by its definition in Eq. 18 dc b = K bec b C b dh 19 U br Integrating, and taking, K be 1 /U br = M C b = exp M h i 20 iv Exit concentration for reactant A from the ith compartment Referring to Fig. 2 mass balance for reactant gas A is given below. Only bubble and emulsion phases are considered here and gas volume in cloud phase is negligible U o C E = U mf C e + U o U mf C b 21 Taking, U o U mf /U o = ϕ C E Cb {1 ϕ + ϕ} For each compartment C Ei Cbi = {1 ϕ + ϕ} Fig. 2 Reactant gas flow through a compartment in a fluidized bed. or, C Ei = {1 ϕ + ϕ} exp M h i 24 v Evaluation of overall conversion Concentration of reactant A exiting after all the n number of compartments, i.e., whole reactor is estimated as C E CE1 CE2 CE3 CEn = 25 C E1 C E2 C En 1 Then conversion of reactant gas A is found out as given below, X A = 1 C E 26 Eq. 26 is to be used along with other equations given above for finding out overall conversion of a gaseous reactant in a fluidized bed reactor. The model can be used for gas solid bubbling fluidized bed reactors involving Geldart B particles. Data from literature for four processes utilizing fluidized bed reactors have been tested particularly oxidation of ammonia, ammoxidation of propylene, hydrogenation of ethylene and nitrous oxide decomposition and also our experimental data for hydrochlorination of silicon. It was found that JSR model gives satisfactory results compared to other prevailing models. 3. Verification of new model by taking experimental data from literature Data for four chemical reactions published in literature has been picked up to study the universality of JSR model. The properties of the materials used and flow rates of reactants are converted from standard conditions to operating conditions. Data from experimental work for hydrochlorination of silicon is used as a fifth case for testing JSR model.

5 chemical engineering research and design Table 1 Comparison of experimental and predicted conversions of propylene to acrylonitrile. S. no. U/U mf Bed height, m X Aexp X AJSR X AKL X AKW Ammoxidation of propylene This is a well known process for manufacturing acrylonitrile which is used for production of acrylic fibre, styrene co-polymers and nitrile rubber. JSR model is tested for ammoxidation of propylene in a fluidized bed reactor. The exothermic reaction takes place as follows, CH 2 CH CH 3 + NH O 2 CH 2 CHCN + 3H 2 O kcal 27 A stream from refinery is introduced along with ammonia and air into a catalytic fluidized bed reactor. The catalyst used is molybdenum-bismuth. The temperature of the reaction is C and pressure atm. A few seconds contact time is available. The reactor affluent is scrubbed with water to remove the desired products in an aqueous solution which is further fractionated to give wet acrylonitrile and acetonitrile. Both are further purified by azeotropic and conventional distillation. Experimental work of Stergiou et al is taken for testing of JSR model. Reaction rate constant for fixed bed condition is reported to be 0.38 s 1 at 450 C by Sawyer and Martel The data for flow rates and conversion of propylene and other parameters are given below, Table 2 Comparison of experimental and predicted conversions on hydrogenation of ethylene. S. no. U o, m s 1 k, s 1 X Aexp X AmodelJSR X AKL X AKW Oxidation of ammonia Massimila and Johnson 1961 have worked on the oxidation of ammonia reaction for fluidization studies. The solid catalyst used was manganus bismuth oxide on alumina spheres. The solids particles size was mesh. The temperature and pressure of the reaction were 250 C and 1.1 atm, respectively. Inlet composition of the gas was 10% ammonia and 90% oxygen. The reaction takes place as follows, 2NH 3 + 2O 2 N 2 O + 3H 2 O 29 The equipment consists essentially of a heated reactor, cylinders of air, oxygen and ammonia, flow metres for gases, thermocouples, sample valves etc. The reactor had m Bulk density of catalyst = 1000 kg m 3. Minimum fluidization velocity = m s 1. Number of holes per unit area = 1.4. Reaction temperature = 450 C. Reaction pressure = atm. The JSR model is applied and the results are given in Table 1 and Fig. 3. Fig. 3 Model versus experimental conversion of propylene Hydrogenation of ethylene Heidel et al carried out hydrogenation of ethylene in a fluidized bed reactor. Nickel coated solid catalyst is used in the reactor. The reaction takes place as given below, C 2 H 4 + H 2 C 2 H 6 28 This experiment was carried out when hydrogen is in excess to maintain the superficial gas velocities in the fluidized bed reactor. Copper on silica alumina is used as a catalyst in three sizes from 0 42, and m. Inlet composition of the feed is 70% hydrogen and 30% ethylene. The reaction takes place between 130 C and 150 C. The experimental data taken from a paper by Werther 1980 is shown along with results in Table 2. The analysis of the data has been carried out and results are shown in Fig. 4. Fig. 4 Model versus experimental conversion of ethylene.

6 476 chemical engineering research and design Fig. 5 Model versus experimental conversion of ammonia bed. ID and 1.09 m height and was made up of stainless steel. The lower flange was connected to an inlet plenum section and a stainless steel perforated plate distributor placed between the reactor and the inlet section, was used to support the bed and disperse the gas uniformly. The flange supported the cyclone separator used to remove the catalyst particles from the gas stream. The catalyst collected in the cyclone was returned to the reactor at the end of each series of runs. The reactor was heated electrically by four chromel resistance ribbons wound on alundum insulation around the reactor. The temperature of the bottom and upper sections were controlled manually with variacs and the temperature of sections immediately above the porous plate was regulated by an automatic controller. The experimental data and predicted results are given in Table 3 and results are depicted in Fig Decomposition of nitrous oxide Catalytic decomposition of nitrous oxide gas has been chosen as a reaction to test the new model in fluidized bed reactors. This experimental work was carried out by Shen and Johnstone The catalyst activity remains substantially constant over a long period of time. The rate of decomposition is measured in fixed and fluidized beds in the temperature range from 343 C to 426 C. Nitrogen, air or oxygen streams containing 1 2.5% nitrous oxide are used. The reaction is first order. This reaction in fluidized bed reactor is used to verify the JSR model and it is given as, 2N 2 O 2N 2 + O 2 30 The individual gases are flown through filters, pressure regulators and flow metres. The reactor had m ID and 1.09 height. The reactor is made up of SS310. One thermocouple is embedded in the perforated stainless steel support plate distributor and two others are mounted through the column wall in the fluidized bed itself. The reactor is heated electrically by chromel resistance ribbon which is wound in all the three sections around the reactor. The temperatures of the top and bottom sections are controlled manually with variable transformers and the temperature of the middle section which covers the entire catalyst bed is regulated with an automatic controller. The data obtained from literature and also predicted conversions are presented in Table 4. A plot Fig. 6 Model versus experimental conversion of nitrous oxide. showing experimental conversion of nitrous oxide versus predicted conversion is drawn and depicted in Fig Hydrochlorination of silicon Hydrochlorination of silicon is carried out in a fluidized bed reactor as per the following reaction, Si + 3HCl 321 C SiHCl 3 + H 2 H = 115 kcal/mol atm The experimental set-up is made up of SS316L. It consisted of a reactor having m ID and 0.47 m height. The reactor had a perforated plate distributor with 9 holes at the bottom through which HCl gas was supplied and it had a pressure gauge at the top for knowing the internal pressure of the reactor. Approximately kg dried silicon powder of required size was introduced from the top of the reactor up-to an initial height of bed equal to 0.1 m. The gaseous products on exiting the reactor were condensed by a dry ice cooled condenser working at 78 C. The reactor was heated by electric resistance coil and controlled by an ON OFF controller. Temperature of the reactor was measured by a thermocouple. Glass wool was used to insulate the reactor. The temperature of the reaction was 321 C at atmospheric pressure. Heat generated due to reaction was removed by air flowing through a copper coil brazed externally around the reactor. Silicon powder was added to the reactor from a silicon bin so as to keep the bed height constant while the bed gets depleted due to reaction. Condensed reaction product trichlorosilane mainly was weighed after the reaction was over. Some quantity of trichlorosilane still escaped the condenser which was at 78 C. Vapours of uncondensed trichlorosilane were reacted with NaOH solution in a trapping vessel and the contents were analysed and the amount of SiO 2 was estimated to ascertain the extent of trichlorosilane escaping condenser using the stoichiometry of the reaction. Silica was estimated as per the following reaction. SiHCl 3 + 3NaOH SiO 2 + 3NaCl + H 2 + H 2 O 32 Silica thus obtained was washed with hot distilled water several times and dried in an electric oven. The amount of silica obtained and quantity of condensed trichlorosilane were

7 chemical engineering research and design Table 3 Comparison of experimental and predicted conversion on catalytic oxidation of ammonia. S. no. U o, m s 1 Bed height, m X Aexp X AmodelJSR X AKL X AKW Table 4 Conversion of experimental and predicted conversions of catalytic decomposition of nitrous oxide. S. no. Temp., C U mf, m s 1 k, s 1 U o, m Bed height, m X Aexp X AmodelJSR X AKL X AKW used to back calculate HCl utilized during reaction for estimating conversion of HCl. The total quantity of HCl fed was known by using a rotameter. Packed bed reaction rate constant was estimated by keeping the superficial gas velocity lower than minimum fluidization velocity and then for calculation of reaction rate constant in fluidized bed condition superficial gas velocity was kept above the minimum fluidization velocity. The dry hydrogen chloride gas used was 99.5% pure. The value of silicon powder minimum bed voids ε mf was found to be 0.5 for all particle sizes used in the experiment except 208 m for which it was Density of the silicon particles used was 2065 kg m 3. A sample of tricholorosilane produced was checked in a gas chromatograph and showed 94.4%, purity of trichlorosilane. Other than trichlorosilane it was assumed to be tetrachlorosilane present in the liquid mixture produced. Experimental data obtained for the hydrochlorination of silicon in fluidized bed conditions at optimum temperature of 321 C is presented in Table 5 for bed of silicon metal powder of size m. The initial bed height in all the cases is kept at 0.1 m. Jain et al carried out experiments for the reaction of silicon powder with HCl in the temperature range of C at atmospheric pressure to find out optimum temperature for operation of the reactor to yield near theoretically maximum rate of production of trichlorosilane. This temperature was found to be 321 C for maximum rate of production of trichlorosilane. Hence, subsequently the experiments were carried out at 321 C and atmospheric pressure. The value of packed bed condition reaction rate constant, K r was obtained utilizing separate experimental data and it was found to be approximately 0.7 s 1. In homogeneous reactions rate constant is temperature dependent but in heterogeneous reactions interphase mass transfer coefficients are also taken into consideration to find out fluidized bed condition reaction rate constant. conventional popular models, i.e., Kunii and Levenspiel, and Kato and Wen models, and also the newly proposed JSR model and compared with the experimental values. Values of wake fraction, f w 0.23, and ratio of volume of solids in bubble phase to volume of bubbles in the fluidized bed b were taken from Levenspiel 1991 for Kunii and Levenspiel model. The calculated value of diffusivity of pair of trichlorosilane and HCl was m 2 s 1. The reduction in volume of the dry HCl feed gas due to reaction ε A = 1/3 for complete conversion was considered as well as temperature effect for volume increment of the gas in superficial gas velocity was also considered in all the models presented here for calculation of conversion of HCl to trichlorosilane. The predicted results by models and experimental results are shown in Table 6 and Fig. 7 and it shows that maximum number of new model conversions points are falling on or near y = x line to show that the new JSR model is a comparatively better model for hydrochlorination of silicon. 4. Discussion It is found from calculations that the choice of bubble growth equation critically affects the value of compartment sizes. Mori and Wen 1975 have analysed well and also proposed their correlation for maximum bubble and initial bubble Conversions of HCl gas in fluidized bed reactor Minimum fluidization velocity was calculated for different size of particles used in the experiment. Flow rates were measured at room temperature and corrected to 321 C by assuming the gases to be ideal and considering reduction in overall volumetric flow due to reaction. Conversions of HCl were estimated for various particle sizes using the Fig. 7 Model versus experimental conversion of HCl gas.

8 478 chemical engineering research and design Table 5 Fluidized bed experimental data and off gas analysis for hydrochlorination of silicon metal using HCl gas for different size particles at 321 C. S. no. Particle diameter, m HCl gas flow rate, lpm Conc. of NaOH, in trap, % TCS condensed, kg 10 3 Av. wt. of silica precipitated in trap, kg 10 3 HCl reaction time, s Table 6 Comparison of HCl conversion at 321 C by model prediction and experimental results for different particle size. S. no. d p, m U o, m s 1 U mf, m s 1 U o /U mf X Aexp X AJSR X AKL X AKW diameter. Their correlation gives more realistic bubble size and hence the compartment size also as compared to the value obtained by Kobayashi s correlation Bubble diameter calculation takes care of gas flow rates, minimum fluidization velocity, particle density, particle size, gas density, gas viscosity, temperature of the gas, etc. In JSR model both mass transfer coefficients for bubble to cloud and cloud to emulsion have been considered rather than exchange coefficient value as 11/d b in Bubble Assemblage K W model. Kato and Wen 1969 have used exchange coefficient based on work of Kobayashi et al., Toei et al have reported exchange coefficient to be in the range of 2/d b to 6/d b in their studies. Therefore, it would be better to go for Kunii and Levenspiel method of finding exchange coefficient which is a well established concept. It is important that the new mathematical model utilizes Mori and Wen correlation for bubble diameter and also combined exchange coefficient for reactants in bubble and emulsion phases. Volumetric gas flow rate change due to temperature and reaction are taken into consideration. Minimum fluidization velocity of reactant gas is calculated by Delebarre correlation or experimental value used. These are important criteria for finding superficial gas velocities. Therefore, all the above improvements provide a good solution to the problem of modelling for all the reaction systems chosen for the present study. The data for ammoxidation of propylene, hydrogenation of ethylene, oxidation of ammonia, decomposition of nitrous oxide and hydrochlorination of silicon were tested for JSR model and it is found that the model works well for all these reaction systems as shown from Figs Also it can be seen from Fig. 8 that the conversions of gaseous reactants in fluidized bed by JSR model very closely agree with experimental results. Kunii and Levenspiel and Kato and Wen models predict conversions lower than the experimental values in most of the cases. Reasons for predicting low conversions by Fig. 8 Conversion of reactant by model versus experiments all cases together. the two models may be attributed to consideration of correct mass transfer resistance from bubble to emulsion only in case of Kunii and Levenspiel model and accounting for change in bubble size only in the case of Kato and Wen model. JSR model utilizes both these concepts together along with volume change due to temperature and reaction and also Delebarre correlation for minimum fluidization velocity. Majority of the points obtained by utilizing JSR model are either on or near the y = x line in all the figures. In Fig. 8 goodness of fit shows the value of R 2 to be for JSR model. It indicates that new model is working well. 5. Conclusion A new model named as JSR model has been mathematically developed and proved by matching theoretical model and experimental conversions of reactant gases for fluidization

9 chemical engineering research and design of Geldart B particle of sizes mesh. The reactant gas bubbles grow as they rise in the fluidized bed. The calculation of size of the bubbles in hypothetical compartments is an important factor which was achieved by employing Mori and Wen correlation as compared to Kobayashi et al. correlation earlier used in Kato and Wen model. Interphase exchange coefficient K be is obtained by Kunii and Levenspiel method in JSR model. In Kato and Wen model exchange coefficient is assumed to be 11/d b which is not a perfect assumption as Toei et al. have reported mass interchange exchange coefficient differently in their studies. Refining of the calculations with these two parameters, i.e., bubble diameter and interphase mass transfer coefficients and other parameters such as temperature correction for gas flow, volume change due to reactions, calculation of minimum fluidization velocity by Delebarre correlation improve the results. It is found that the JSR model predicts the conversion of reactant gases better than the two prevailing models for solid particles of classification Geldart B and size mesh. where x i 1 = 1 1 d o exp ph i 1 Put 1 d o exp ph i 1 = F x i 1 = 1 F p = 1 F{expp h} 1 F 1 F{exp p h} dx 1 x + dx x 1 F p = [ ln1 x] 1 F{exp p h i } 1 F + [ln x] 1 F{exp p h i } 1 F [ ln ] x 1 F{exp p hi } 1 x 1 F Acknowledgment Authors are grateful to Dr. A.K. Sharma, Head, Food Technology Division, BARC for his help and permission for carrying out work on hydrochlorination of silicon. Appendix A. Appendix The equation for finding compartment height is further simplified from Eq. 4 as follows, hi 1 = hi 1 Therefore, 1 { d o exp ph} dh 33 hi 1 = { } dh 34 hi do exp ph Taking, 1 1 d o exp ph = x 35 Therefore, 1 d o exp ph pdh = dx 36 or dx dh = { } 37 1 do exp ph or dh = = dx p1 x xi x i 1 dx p1 x p = ln { 1 F{exp p h i } } [1 {1 F exp p h i }] ln p = ln {1 Fexp p hi}f [F1 F exp p h i ] expp = {1 Fexp p h i } [F1 F exp p h i ] 1 F [1 1 F] expp {1 F exp p h i = {1 F{exp p h i } 45 exp p h i [F + 1 F expp ] = 1 46 expp h i = [F + 1 F expp ] = 1 47 p h i = ln[f + 1 F expp ] 48 h i = 1 lnf + 1 F exppd p bm 49 References Chavarie, C., Grace, J.R., Performance analysis of a fluidized bed reactor. Ind. Eng. Chem. Fundam. 14 2, Davidson, J.F., Harrison, D., Fluidized Bed Particles. Cambridge Press, London. Delebarre, A., Revisiting the Wen and Yu equations for minimum fluidization velocity prediction. TransIChE, PartA ChERD 82 A5, Fryer, C., Potter, O.E., Countercurrent backmixing model for fluidized bed catalytic reactors. Applicability of simplified solutions. Ind. Eng. Chem. Fundam. 11 3, 338. GOLFERS, Kagaka Kogaku Ronbunshu 8, 464. Heidel, K., Shugerl, K., Fetting, F., Shiemann, G., Chem. Eng. Sci. 20, Jain, M.P., Sathiyamoorthy, D., Rao, V.G., Studies on hydrochlorination of silicon in a fixed bed reactor. I.C.E. 53 2, Kato, K., Wen, C.Y., Bubble assemblage model for fluidized bed catalytic reactors. Chem. Eng. Sci. 24, Kobayashi, H., Arai, F., Shiba, T., Chem. Eng. Tokyo 29, 858. Kunii, D., Levenspiel, O., Ind. Eng. Chem. Fundam. 7, 466. Kunii, D., Levenspiel, O., Fluidization Engineering. John Wiley, New York, pp. 124, 158, 277. Levenspiel, O., Chemical Reaction Engineering, third ed. John Wiley and Sons, New York, pp. 395.

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