Development of a Countercurrent Multistage Fluidized-Bed Reactor

Ind. Eng. Chem. Res. 2009, 48, 1629–1637

1629

Development of a Countercurrent Multistage Fluidized-Bed Reactor and Mathematical Modeling for Prediction of Removal Efficiency of Sulfur Dioxide from Flue Gases C. R. Mohanty,† G. Malavia,‡ and B. C. Meikap*,‡ Department of Chemical Engineering, Indian Institute of Technology, Kharagpur, 721 302 West Bengal, India, and State Pollution Control Board, Bhubaneswar, 751 012 Orissa, India

A bubbling countercurrent multistage fluidized-bed reactor for the sorption of sulfur dioxide by hydrated lime particles was simulated employing a two-phase model, with the bubble phase assumed to be in plug flow and with the emulsion phase either in plug flow (EGPF model) or in perfectly mixed flow (EGPM model). The model calculations were compared with experimental data in term of percentage removal efficiency of sulfur dioxide. Both models were applied to understand the influence of operating parameters on the reactor performance. The comparison showed that the EGPF model agreed well with the experimental data. From the perspective of use of a multistage fluidized-bed reactor as air pollution control equipment in industry, the model could be considered general enough for predicting the performance of reactors for gas-solid treatment. Introduction Fluidization is a well-known technique for contacting solids and fluids and finds wide application in the petroleum, metallurgical, and chemical industries. Fluidization has many advantages including amenability of controlled operations on a large scale and high transfer rates. However, considering the flow of solids, a continuous fluidized-bed reactor behaves as a continuously stirred tank reactor, and the residence time distribution of the solids is very wide, which is not desirable if a homogeneous product is required. An alternative approach to narrow the solids residence time distribution is to use multistage fluidized-bed reactor (MFBR). In a vertical reactor, solids are fed by means of a screw feeder down to the bottom, countercurrent to the gas, which is distributed by a distributor assembly fitted at the bottom of the reactor. The gas-solid mass-transfer resistance in the fluidizedbed reactor is so small that it can be neglected, and excellent temperature control is also achievable because of the vigorous mixing of solid particles in the bed.1 This reactor also has characteristics of low reaction temperature and sufficient reaction time, compared with other reactors. In this article, a two-phase model has been developed for the sorption of sulfur dioxide on calcium hydroxide particles in a multistage fluidized-bed reactor, and simulation results are compared with empirical data. Mathematical Model For normal operating velocities (3-8 times the minimum fluidization velocity, umf), a fluidized-bed reactor can be approximated as a bubbling bed.2,3 Bubbling fluidized beds have been extensively studied, and a variety of models of varying degrees of complexity have been proposed in the literature.3-9 Generally, for modeling of a fluidized-bed reactor, either a twophase model comprising emulsion and bubble phases3-7 or a three-phase model including an additional cloud phase is considered.9 For Geldart B type particles, at higher values of the ug/umf ratio (where ug is the superficial velocity of air), the * To whom correspondence should be addressed. Tel.: +91-3222283958. Fax: +91-3222-282250. E-mail: [email protected]. † State Pollution Control Board. ‡ Indian Institute of Technology.

presence of a cloud phase can be considered negligible.10 The two-phase model was used successfully for the drying of moist air by alumina particles in a counterflow multistage fluidizedbed reactor.11 Therefore, it was decided to derive a model for the hydrodynamic behavior of gas for an MFBR based on the same assumptions with slight modification.12 The details of this model can be found elsewhere.13 Mixing in a fluidized-bed reactor is difficult to characterize, and in the literature, both phases (i.e., the emulsion and the bubbles) have been modeled either as plug flow or as perfectly mixed. The assumption of plug flow for the bubble phase is usually valid; however, it is not at all clear whether the emulsion phase should be modeled as being perfectly mixed or in plug flow. The literature suggests that a multistage fluidized-bed reactor behave as a plug-flow reactor. However, in the present study, both flow regimes (plug and perfectly mixed) were considered for the emulsion phase together with the plug-flow regime for the bubble phase. Kinetics. At low temperature, the primary reaction that has traditionally been proposed in the flue gas desulfurization process is Ca(OH)2+SO2 f CaSO3·0.5H2O + 0.5H2O ∆H°298 ) - 238 kJ/mol (1) This reaction is first-order with respect to sulfur dioxide and calcium hydroxide. The rate constant can be expressed according to Arrehenius’ law as

( RTE )

k1 ) A0 exp -

(2)

where the activation energy of the reaction is 32 kJ/mol and the pre-exponential factor is A0 ) 2.314 m3/mol · s.14 Model Development. The assumptions made in developing the model for the MFBR are summarized as follows: (1) The total bed consists of two phases, namely (i) a solids-free bubble phase and (ii) a solids-rich emulsion phase. (2) All gas in excess of that required for minimum fluidization passes through the bed as bubbles. (3) The bubble phase does not contain any solids. (4) The bubble phase is in plug flow, and the gas in the bubbles is perfectly mixed. (5) The bubbles are spherical, of

10.1021/ie801615c CCC: $40.75  2009 American Chemical Society Published on Web 12/22/2008

1630 Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009

Figure 1. Schematic of the EGPF model.

Figure 2. Schematic of the EGPM model.

constant size, and evenly distributed in the bed at any time. (6) As the bubbles rise, they exchange gas with the rest of the bed (the emulsion phase). (6) Interphase mass transfer results from two independent mechanism, namely, bulk flow of gas and diffusion. (7) The mass-transfer resistances between the particles and the dense-phase gas are neglected. (8) The solid particles are perfectly mixed in the emulsion phase (the emulsion phase is perfectly mixed), but gas in the emulsion phase is considered to be either (i) perfectly mixed (EGPM model) or (ii) in plug flow (EGPF model). The following additional assumptions were made: (1) The mean particle size is constant throughout the bed. (2) The

emulsion of solids at the top of the bed is neglected. (3) All stages operate under same conditions of fluidization. (4) The solids holdup is the same on each stage. (5) All particles entering the first stage present the same concentration of active species. Thus, the assumptions led to two distinct models: (i) the EGPF model and (ii) the EGPM model. Figures 1 and 2 present schematics of both models. Equations of the Model. (a) Mass Balance at the Exit. The mass balance for the reactant gas at the exit is uCi ) umfCpi + (u - umf)Cbi(H)

(3)

Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009 1631

Rearranging the terms, the concentration of gas leaving the ith stage becomes Ci ) βCbi(H) + (1 - β)Cpi

sorbent, CR0, on the particles entering the first stage of the reactor as

(4)

where β is the fraction of gas flow associated with the bubble phase, i.e., β ) 1 - umf/u. (b) Mass Balance of Sulfur Dioxide in Bubble Phase. The mass balance on sulfur dioxide through the bubble phase of the ith stage is independent of the assumption relative to the behavior of gas in the emulsion phase. Consider an element of thickness dz, at a height of z in the bed, containing N × dz bubbles. The material balance is written for a unit horizontal cross-sectional area by considering the total bed height, H, and setting the rate of change of the reactant concentration equal to the rate of loss of the reactant by exchange dCbi NbQ(Cpi - dCbi) ) NbVbub dz

(5)

CRi ) CR0 exp(-k1

( )

(6)

(c) Emulsion Phase. (i) EGPM Model. The material balance is written for a unit horizontal cross-sectional area by considering the total bed height, H. Combining inlet and outlet terms, one obtains

∫

H

0

∫ N Q dz + r˜ ∫ (1 - NV ) dz H

NbQCbi dz + umfCi+1 ) umfCpi + Cpi

0

b

Cpi )

umfCpi + NbQCbi dz ) umf(Cpi + dCpi) + NbQCpi dz + ri(1 - NbV) dz

H

0

Cpi dz

(13)

(14)

The term in parentheses remains constant over the entire emulsion phase, so that the reaction rate can be considered as first-order, i.e. ri ) (k1CRi)Cpi ) kCpi

(15)

(f) Analytical Solution of the Model Equations. (i) Bubble Phase. Integrating eq 6 from 0 to H with boundary conditions Cbi ) Ci+1 at z ) 0 and Cbi ) Cbi(H) at z ) H gives Cbi(z) ) Cpi + (Ci+1 - Cpi)eQz/ubVb

(16)

Cbi(H) ) Cpi + (Ci+1 - Cpi)e-X

(17)

where X ) QH/ubVb is the number of times a bubble is purged as it rises through the bed or the number of times the gas within the bubble is exchanged with the particulate phase during the passage of the bubble through the bed. (ii) EGPM Model. Integrating eq 7 from 0 to H with boundary conditions Cbi ) Ci+1 at z ) 0 and Cbi ) Cbi(H) at z ) H, we obtain Cpi )

(8)

dCpi + NbQ(Cpi - Cbi) + K1Cpi(1 - NbV)dz ) 0 (9) dz

where the SO2 concentration in the emulsion phase, Cpi, and r˜ are functions of z. (d) Mass Balance on the Sorbent Particles. At any time, over the ith stage, the disappearance rate of calcium oxide (species R) according to the rate kinetics can be written as (10)

(i) EGPM Model. The calcium hydroxide concentration is CRi ) CRio exp(-k1Cpiτi)

∫

ri ) (k1CRi)Cpi

Rearranging the terms, we obtain

∂CRi ) -k1CRiCpi ∂t

1 H

(e) Sulfur Dioxide Concentration in the Exit Gas Stream from the ith Stage. The rate of SO2 disappearance from the ith stage can be expressed as

(7)

where the SO2 concentration in the emulsion phase, Cpi, is independent of height z. H is the height of the expanded bed, assumed to be equal to the height of the downcomer over the distributor, and r˜ is the average rate of disappearance of SO2 in the entire emulsion phase. (ii) EGPF Model. We now consider that the gas is in plug flow through the emulsion phase with all the other assumptions the same. The material balance over a unit cross-sectional area of dense phase considering an infinitesimal height dz is then given by

umf

(12)

b

H

0

for j ) 1-i

pjτj)

(ii) EGPF Model. The sulfur dioxide concentration of the gas varies throughout the emulsion phase, but at any time, the solid particles, which are perfectly mixed, have an equal probability of contacting an element of gas volume, whose concentration, Cpi, lies between Ci+1 and Cpi(H). Therefore, it can be accepted that, considering all particles, the sulfur dioxide concentration of gas is Cpi, which is defined by the equation

Combining the inlet and outlet terms and rearranging gives dCbi Vbub ) Cpi - Cbi dz Q

∑C

(11)

where τi is the mean residence time of solids in stage i. It can be expressed as a function of the initial concentration of

(

Ci+1(1 - βe-X) KHmf 1 - βe-X + u

)

(18)

Cbi(H) ) Cpi + (Ci+1 - Cpi)e-X

(19)

Inserting the above expressions for Cpi and Cbi(H) into eq 4 gives the SO2 exit concentration from the ith stage for the EGPM model. (iii) EGPF Model. Integrating eq 9 from 0 to H with the boundary conditions Cbi ) Ci+1 and dCbi/dz ) 0 at z ) 0 and Cbi ) Cbi(H) at z ) H gives Cpi(H) )

(

)[

Ci+1 H m1i 1 + m2i em2iH m1i - m2i X H m2i 1 + m1i em1iH X

(

)

(

Cbi(H) )

) ]

Ci+1 (m em2iH - m2iem1iH) m1i - m2i 1i

In these equations, m1i and m2i are defined by

(20)

(21)


m1i or 2i )

[(

1 X + Ki 1 X + Ki ( 2 H(1 - β) 2 H(1 - β)

)

2

-4

XKi H (1 - β) 2

]

(22)

where Ki is the number of reaction units in the emulsion phase Ki ) k1CRi

Hmf U

(23)

The mean concentration of emulsion gas is given by Cpi )

(

)[

Ci+1 m1i 1 H 1 + m2i (em2iH-1) H m1i - m2i m2i X m2i H 1 + m1i (em1iH-1) m1i X

(

)

(

)

]

(24)

Inserting the above expressions for Cpi and Cbi(H) into eq 4 then gives the SO2 exit concentration from the ith stage for the EGPF model. Estimation of Hydrodynamic Parameters. To solve the sets of model equations, it is necessary to relate several parameters appearing in the equations, including the bubble volume fraction, the bubble size, and the interphase mass- and heat-transfer coefficients, to the design and operating parameters. Correct evaluation of these parameters is crucial for the accurate simulation of the operation of an industrial fluidized-bed reactor. Several empirical correlations have been proposed for estimating these parameters. For the purpose of this study, an illustrative set was chosen. This set of hydrodynamic correlations is listed in Table 1. Experimental Technique and Procedure Figure 3 presents a schematic of the multistage fluidizedbed reactor developed and used in this study. The configuration of this staged gas-solid fluidized-bed reactor is similar to that of a sieve-tray distillation column. The reactor consisted of a three-stage fluidization column having provision for solid and air feeding from the top and bottom, respectively, along with other auxiliary equipments used for experimentation. Each stage of the column was made up of a Perspex cylinder with an internal diameter of 0.10 m and a length of 0.305 m. Stainless steel plates (G1-G3) were used as internal baffles sandwiched between the flanges of two stages, and each plate was drilled with perforations having 8.56% total grid openings.17 The grid plates were fixed with fine wire mesh (100 mesh size) to prevent weeping of the solid particles through the openings. Each section was provided with a downcomer consisting of a Perspex cylinder with an internal diameter of 0.025 m (D1-D4), and the downcomers were fitted to the gas distributor by a special threading arrangement having the provision for adjusting the weir height as desired. The downcomers were further fitted with

a cone at the exit end to reduce the upflow of the gas through the downcomer and, consequently, widening the stable operating range. Pressure tapings were provided just below the grid plate and near the air outlet and were outfitted with weir mesh filters to prevent any solid particles from entering the tapings. Four manometers were provided to measure the pressure drop at every stage as well as the total pressure drop. To generate a synthetic air-SO2 mixture with a composition similar to that of the exhaust of sulfuric acid plants, copper smelters were made by mixing compressed air from an air compressor and SO2 gas from a SO2 cylinder. Provision was made to feed the air-SO2 mixture at the base of the fluidizedbed reactor. The air-SO2 mixture was generated by mixing air and SO2 in an air-jet ejector assembly. Compressed air from the compressor was used as the motive fluid in the ejector to aspirate and thoroughly mix air with SO2 from the SO2 gas cylinder. The ejector was mounted with a downward slope of 30° with the air nozzle perfectly aligned along the axis of the ejector throat to ensure an axially symmetrical jet. The air nozzle was fixed at a projection ratio (which is the ratio of the distance between the nozzle tip and the beginning of the parallel throat to the throat diameter) of 3.78, which was determined experimentally to give the highest possible mass ratio of aspirated gas. Compressed air at the desired pressure and flow rate was forced through the air nozzle and regulated by a valve. Simultaneously, the SO2 was routed at a controlled rate through the SO2 gas regulator and into the ejector. The air-SO2 gas mixed intensely in the mixing throat of the ejector, and the mixture was fed into a predistributor fitted at the bottom of the column. A precalibrated rotameter (F) was used to measure the gas flow rate. A conical hopper was attached at the bottom of the column for the storage of solids exiting from the bottom stage through the downcomer. The gas leaving the column from the top stage was passed through a standard cyclone (C) and then into the exhaust system. The solids from the screw feeder were fed to the first-stage downcomer of the reactor. Necessary precautions were made to ensure that no air from outside intruded into the column during operation. Tables 2 and 3 list the physical and chemical characteristics of the hydrated lime considered for the study. Experiments were conducted by setting the gas flow rates ranging from 31.27 × 10-2 to 56.4 × 10-2 kg/m2 · s and corresponding solid flow rates ranging from 71 × 10-3 to 141.5 × 10-3 kg/m2 · s. The weir heights of the downcomers were kept at 0.03 and 0.07 m, and the corresponding gaps between the downcomer bottoms and the grid plates were kept at 0.015 and 0.035 m. We previously carried out a detailed hydrodynamic study of the reactor with hydrated lime.17 For each gas flow rate, the

Table 1. Hydrodynamic and Transport Property Correlations parameter bubble

diameter

bubble velocity bubble rise velocity emulsion phasevolumetric flowrate bubble phasevolumetric flowrate height of bed at rest interphase mass transfer number of bubbles perunitbedvolume bubble volume number of orifices diameter of reactor diffusivity of gaseousreactant

correlation

ref

Db(Z) ) Dbmax - (Dbmax - Db0) exp(-0.3z/DT) Dbmax ) 0.625[A(u - umf)]0.4 ub ) u0 - umf + ubr ubr ) 0.711(gDb)0.5 Qe ) umfA Qb ) (u - umf)A Hmf ) H(1 - NbVb) ) H[1 - (u - umf)/ub] Q ) [3/4umf + 0.975DG0.5(g/Db)0.25]πDb2 Nb ) (u - umf)/Vbub Vb ) πDb3/6 Nd ) 216 DT ) 0.1 m Dg(T) ) 8.0 × 10-26T7.5

15 13 13 13 13 13 13 13 13 16


Figure 3. Schematic diagram of the experimental setup of a three-stage countercurrent fluidized-bed reactor.

inlets SO2 loadings were varied from 500 to 1500 ppm at the inlet. The study was carried out at room temperature around 310 K and a pressure of 1 atm absolute. The

percentage removal of SO2 was calculated for each experimental run according to the equation ηSO2 )

Table 2. Characteristics of Hydrated Lime Adsorbent characteristic

value

average particle diameter (µm) density (kg/m3) minimum fluidization velocity (m/s) specific area of unreacted sorbent (m2/g) average pore diameter (A0) pore volume (cm3/g)

426 2040 0.112 15 98.4 1.213

cin,SO2 - cout,SO2 cin,SO2

× 100

(25)

Likewise, for stage i ηSO2 )

Ci+1 - Ci Ci+1

(26)

1634 Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009 Table 3. Chemical Composition of Hydrated Lime compound

content (wt %)

CaO Ca(OH)2 CaCO3 MgO impurities

25.0 64.4 4.76 3.22 2.62

where Ci and Ci+1 are the sulfur dioxide concentrations in the gas at the outlet and inlet, respectively. In this study, the effects of the superficial gas velocity, superficial solid velocity, and weir height on the removal efficiency of SO2 were investigated. Sampling and Analysis. In the experiments, solid lime was continuously fed from the top to the first stage of the column. Samples at the inlet of the column and outlet of each stage were drawn at flow rate of 1.0 L/min. Under steady-state operating conditions, SO2 gas samples were collected at each point using midget impinges and aspirator bottles. The gas samples were analyzed for sulfur dioxide by the “Tetrachloro Mercurate Method” of the Indian Standard Methods for Measurement of Air Qualities [IS: 5182 (Part VI)]. The method consists of passing a portion of the sampled air through a solution of absorbing medium (sodium tetracholoromercurate) and analyzing the resulting solution spectrophotometrically by UV-visible recording spectrophotometer. An absorbing solution of 0.1 M sodium tetrachloromercurate was prepared by dissolving 27.2 g (0.1 mol) of mercuric chloride and 11.7 g (0.2 mol) of sodium chloride in 1.0 L of distilled water. This solution could be stored at room temperature for several months. The indicator p-rosaline hydrochloride [0.04% (w/v), acid-bleached] was prepared by dissolving 0.20 g of p-rosaline hydrochloride in 100 mL of distilled water and filtering the solution after 48 h. This solution was stable for at least 3 months when stored in the dark and kept cool. The p-rosaline hydrochloride was required to have an assay of 95% percent or better and an absorbance maximum at 560 nm. Twenty milliliters of this solution was pipetted into a 100-mL volumetric flask to which was added 6 mL of concentrated hydrochloric acid. This solution should be pale yellow with a greenish tint. It could be stored at room temperature in an amber bottle for 1 week or for about 2 weeks if refrigerated. When SO2 from the air stream was absorbed in sodium tetrachloromercurate solution, it formed a stable dichlorosulfitomercurate complex. The amount of SO2 was then estimated by the color produced when p-rosaline hydrochloride was added to the solution. The color was estimated by using a spectrophotometer for which a calibration curve had already been prepared (Figure 4). The amount of SO2 in the air sample was obtained from the differences in spectrophotometric values of the blank and test samples and is reported in parts per million (ppm) using the calibration curve. The measurements are reported to the nearest 0.005 ppm at concentrations below 0.15 ppm and to the nearest 0.01 ppm for concentrations above 0.15 ppm. Ozone and nitrogen dioxide interfere if present in air samples at concentrations greater than the SO2 concentration. Interference from nitrogen dioxide was eliminated by including 0.06% sulfamic acid in the absorbing reagent. However, this could result in a different calibration curve of lower sensitivity and in greater losses of SO2 upon shortage of the sample for more than 48 h after o-toludine subsequent to sample collection. Heavy metals, especially iron salts, interfere by oxidizing dichlorosulfitomercurate during sample collection. This interference was eliminated by including ethylenediaminetetraacetic acid in the absorbing reagent. Sulfuric acid and sulfate do not

Figure 4. Calibration curve of UV spectrophotometer for SO2 concentration at λ ) 560 nm.

interfere. If large amounts of solid materials are present, a filter can be used advantageously upstream; however, a loss of SO2 might occur. In the adsorption experiments, detailed studies were performed to determine the effects of the gas and solids flow rates and the inlet loading of sulfur dioxide on the percentage removal of sulfur dioxide using lime as the scrubbing medium. The range of concentration for SO2 monitoring was 500-1500 ppm, and the accuracy was (10 ppm Results and Discussion The concentration of the gas stream exiting each stage was calculated by solving the equations of the models. The calcium hydroxide concentration (CR0) of the sorbent particles entering the reactor, expressed in moles of calcium hydroxide per unit volume of solids, was determined by analysis. To solve the equations, a simulation program was developed in Matlab, and based on this program, the following results were obtained and compared with experimental values. Effect of Weir Height on Sulfur Dioxide Removal Efficiency. Figures 5 and 6 present the effects of different inlet sulfur dioxide loadings on the percentage removal of SO2 at a particular mass velocity of gas (31.2 × 10-2 kg/m2 · s) and weir height (70 mm). For this set of predictions, the temperature was held at 310 K. It can be observed that the removal efficiency decreased as the inlet sulfur dioxide concentration increased. The percentage removal of SO2 was higher for the EGPF model than for the EGPM model. The percentage removal of sulfur dioxide was 62% for the EGPF model and 59% for the EGPM model for an inlet concentration of 500 ppm at a weir height of 70 mm and a mass velocity of solids of 141.5 × 10-2 kg/m2 · s. The percentage of sulfur dioxide was 51% for the EGPF model and 49% for the EGPM model for the same inlet concentration


Figure 5. Effect of inlet SO2 concentration on percentage removal efficiency of SO2 at hW ) 0.07 m and Gs ) 141.5 × 10-3 kg/m2 · s.


at a weir height of 70 mm and a mass velocity of solids of 71.0 × 10-2 kg/m2 · s. This indicates that decreasing the mass velocity of solids decreases the removal efficiency, as the probability of collision between gas and solid particles decreases as a result of the decrease in solids holdup. Figures 7 and 8 present the effects of the inlet sulfur dioxide concentration on the percentage removal of SO2 at a particular mass velocity of gas (31.2 × 10-2 kg/m2 · s) and weir height (30 mm). Similar trends emerged. The percentage removal of SO2 was again higher for the EGPF model. The percentage removal efficiency of sulfur dioxide was 59% for the EGPF model and 56% for the EGPM model for a 500 ppm inlet concentration at a weir height of 30 mm and a mass velocity of solids of 141.5 × 10-2 kg/m2 · s. The percentage removal efficiency of sulfur dioxide was 49% for the EGPF model and



47% for the EGPM model for the same inlet concentration at a weir height of 73 mm and a mass velocity of solids of 71.0 × 10-2 kg/m2 · s. This indicates that decreasing the weir height decreases the removal efficiency, as the solids holdup in the bed decreases. It can also be observed that a higher solid flow rate (141.5 × 10-3 kg/m2 · s) at a particular gas velocity gives higher sulfur dioxide removal efficiency than lower solid flow rate (71.0 × 10-3 kg/m2 · s) for both models. Effect of Temperature and Inlet Concentration of SO2 on Sulfur Dioxide Removal Efficiency. Figure 9 depicts the effect of temperature on the sulfur dioxide removal efficiency for both models. Because the reaction rate depends on temperature and the overall desulfurization rate increases with increasing temperature, the removal efficiency was around 98% for both models at 120 °C for an inlet concentration of 500 ppm. The difference between the predictions of two models was much


previously for a fixed bed.18 Because this product layer is formed, the diffusion resistance of SO2 from the emulsion phase to the inner untreated calcium sorbent might have gradually increased. Thus, the removal efficiency kept decreasing. At the third stage, the removal efficiency of SO2 was quite low. The slight difference observed between the predictions of the two models tends to indicate that the gas interchange between the bubble phase and the emulsion phase is not the limiting step in this process. This is probably a consequence of the rather small bed height. Conclusion

Figure 9. Effect of inlet SO2 concentration on SO2 removal efficiency at different temperatures.

A model based on the assumptions of Davidson and Harrison12 with slight modifications has been developed for simulating the operation of a countercurrent multistage fluidized-bed reactor. The assumption of plug flow of the gas percolating through the emulsion phase leads to slightly better predictions than the assumption of perfect mixing of the emulsion phase. Based on model predictions, it can be shown that increases in the mass velocity of solids, temperature, and weir height result in increases in the sulfur dioxide removal efficiency. The maximum SO2 removal occurred in the first stage of the reactor. Increasing the inlet concentration of sulfur dioxide decreased the desulfurization efficiency. Even though the some of the conclusions are specific to this study, the model developed herein should be considered general enough to be used for predicting the performance of a countercurrent multistage fluidized-bed reactors for gas-solid treatment. Nomenclature

Figure 10. Effect of inlet SO2 concentration on removal efficiency at different stages at T ) 38 °C.

smaller than the difference at higher concentration. As the temperature decreased, the removal efficiency decreased. Stagewise Percentage Removal Efficiency of Sulfur Dioxide. Figure 10 presents a comparison of the percentage removal efficiency of SO2 between the experimental results and the predicted results at different stages at a particular solid flow rate, gas flow rate, and weir height. It can be observed that, at the first stage, the solid reactant was fresh, so that the maximum percentage of inlet sulfur dioxide was absorbed and reacted at the surface of the calcium sorbent. As a result, the removal efficiency was higher than at the other two stages. At the second stage, perhaps the gradual formation a product layer (CaSO3 · 0.5H2O) at the surface of the sorbent decreased the removal efficiency, which was similar to results observed

A ) area of the reactor (m2) Cb ) sulfur dioxide concentration of bubbles (mol/m3) Cbi ) sulfur dioxide concentration of bubbles in the ith stage (mol/ m3) Ci ) sulfur dioxide concentration of gas leaving the ith stage (mol/ m 3) Ci+1 ) sulfur dioxide concentration of gas entering the ith stage (mol/m3) Cin ) sulfur dioxide concentration of gas at the inlet (mol/m3 or ppm) Cout ) sulfur dioxide concentration of exit gas (mol/m3 or ppm) Cp ) sulfur dioxide concentration of emulsion phase (mol/m3) Cpi ) sulfur dioxide concentration of emulsion phase in the ith stage (mol/m3) CR ) calcium hydroxide concentration of emulsion phase (mol/ m3) CRi ) calcium hydroxide concentration of emulsion phase in the ith stage (mol/m3) CR0 ) calcium hydroxide concentration of emulsion phase entering (mol/m3) dp ) particle diameter (m) F ) fractional free area of distributor (%) Ga ) mass velocity of air (kg/m2 · s) Gs ) mass velocity of solids (kg/m2 · s) g ) acceleration due to gravity (m/s2) H ) height of the bed (m) hW ) height of the weir (m) k1 ) reaction rate constant (m3/ mol · s) m1, m2 ) constants Nb ) number of bubbles per unit bed volume (1/m3) Q ) interphase mass-transfer flux (m3/s) r˜ ) average rate of SO2 removal (mol/m3 · s) ug ) superficial velocity of air (m /s)

Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009 1637 us ) superficial velocity of solids (m/s) Vb ) volume of bubble (m3) z ) height in the bed (m) Greek Symbols β ) fraction of gas flow associated with bubble phase mf ) bed voidage at minimum fluidization (1 - ) ) fractional solids concentration ζ ) solids mean residence time (s) ηSO2 ) SO2 removal efficiency (%) Fg ) density of air (kg/m3) Fs ) density of solids (kg/m3) Subscripts a/g ) air/gas b ) bubbles c ) calculated e ) experimental i ) ith stage of column i + 1 ) (i + 1)st stage of column mf ) minimum fluidization p ) particle s ) solids

Literature Cited (1) Khani, M. H.; Pahlavanzadeh, H.; Ghannadi, M. Two-phase modeling of a gas phase fluidized bed reactor for the fluorination of uranium tetrafluoride. Ann. Nucl. Energy 2008, 35, 2321. (2) Cui, H. P.; Mostuofi, N.; Chaoki, J. Characterization of dynamic gas-solid distribution in the fluidized beds. Chem. Eng. J. 2000, 79, 135. (3) Hatzantonis, H.; Yiannoulakis, H.; Yiagopoulos, A.; Kiparissides, C. Recent developments in modeling gas-phase catalyzed olefin polymerization fluidized bed reactors: The effect of bubble size variation on the reactor’s performance. Chem. Eng. Sci. 2000, 55, 3237. (4) Lu, W. Z.; Teng, L. H.; Xiao, W. D. Simulation and experiment study of dimethyl ether synthesis from syngas in a fluidized-bed reactor. Chem. Eng. Sci. 2004, 59, 5455.

(5) Kiashemshaki, A.; Mostoufi, N.; Sotudeh-Gharebagh, R. Two-phase modeling of a gas phase polyethylene fluidized bed reactor. Chem. Eng. Sci. 2006, 61, 3997. (6) Harshe, Y. M.; Utikar, R. P.; Ranade, V. V. A computational model for predicting particle size distribution and performance of fluidized bed polypropylene reactor. Chem. Eng. Sci. 2004, 59, 5145. (7) McAuley, K. B.; Talbot, J. P.; Harris, T. J. A comparison of twophase and well-mixed models for fluidized-bed polyethylene reactor. Chem. Eng. Sci. 1994, 49, 2035. (8) Alizadeh, M.; Mostoufi, N.; Pormahdian, S.; Soutudeh-Gharebagh, R. Modeling of fluidized bed reactor of ethylene polymerization. Chem. Eng. J. 2004, 97, 27. (9) Kim, J. Y.; Choi, K. Y. Polymer particle mixing and segregation in a gas phase olefin polymerization reactor. AIChE Symp. Ser. 1999, 95, 77. (10) Faltsi-Saravelou, O.; Vasalos, I. A. FBSim: A model for fluidized bed simulationsI. Dynamic modeling of an adiabatic reacting system of small gas fluidized particles. Comput. Chem. Eng. 1991, 15, 639. (11) Hymore, K.; Laguerie, C. Analysis and modeling of the operation of a counter-flow multistage fluidized bed adsorber for drying moist air. Chem. Eng. Process. 1984, 18, 255. (12) Davidson, J. F.; Harrison, D. Fluidized Particles; Cambridge University Press: Cambridge, U.K., 1963. (13) Kunii, D.; Levenspiel, O. Fluidization Engineering, 2nd ed.; Butterworth-Heinemann: Boston, MA, 1991. (14) Ghosh, D. K. Studies on the desulphurization of flue gas by porous solid reactants. Ph.D. Thesis, Indian Institute of Technology, Kharagpur, India, 1987. (15) Mori, S.; Wen, C. Y. Estimation of bubble diameter in gaseous fluidized beds. AIChE J. 1975, 21, 109. (16) Treybal, R. E. Mass Transfer Operations, 3rd ed.; McGraw-Hill: New York, 1980. (17) Mohanty, C.; Meikap, B. C. Pressure drop characteristics of a multistage counter-current fluidized bed reactor for control of gaseous pollutants. Chem. Eng. Process. 2009, 48, 209. (18) Ho, C. S.; Shih, S. M. Ca(OH) 2/fly ash sorbents for SO2 removal. Ind. Eng. Chem. Res. 1992, 31, 1130.

ReceiVed for reView October 23, 2008 ReVised manuscript receiVed November 16, 2008 Accepted November 20, 2008 IE801615C

Development of a Countercurrent Multistage Fluidized-Bed Reactor

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