SO2 Removal in the Filter Cake of a Jet-Pulsed Filter - American

Ind. Eng. Chem. Res. 2002, 41, 5459-5469

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SO2 Removal in the Filter Cake of a Jet-Pulsed Filter: A Combined Filter and Fixed-Bed Reaction Model Andreas Kavouras,*,† Bernd Breitschaedel,† Gernot Krammer,† Aurora Garea,‡ Jose A. Marques,‡ and Angel Irabien‡ Institut fu¨ r Apparatebau, Mechanische Verfahrenstecknik und Feuerungstechnik, Technische Universita¨ t Graz, Inffeldgasse 25/I, A-8010 Graz, Austria, and Department of Chemical Engineering and Inorganic Chemistry, ETSII y T., University of Cantabria, Avenida Los Castros s/n, Santander 39005, Spain

Jet-pulsed filters are frequently used to separate fine solid particles from gas streams. An example for the application of the filter as both a solid separator and a fixed-bed reactor is a dry flue gas cleaning process, where the dry solid sorbent Ca(OH)2 forms a filter cake that captures a major part of the SO2 and HCl out of the flue gas. One important phenomenon concerning the formation of the filter cake on jet-pulsed filters is imperfect cake removal. Here a jet pulse tears off the entire filter cake from only a fraction of the exposed filter area, and only part of the total filter area is subjected to the jet-pulse cleaning. This property of jet-pulsed filters has a great influence on the chemical reaction simulation between gas and solid in the filter cake because the gas velocity through the cake, the cake thickness, and the residence time distribution of the solid forming the cake differ widely over the entire filter area. A recently developed filter model, in which different classes of cake thicknesses are understood to result from different cake generations, is used to determine the distributions of cake thickness, gas velocity, and residence time of the solid over the filter area. With the combination of the filter model and a fixed-bed reaction model using an empirical kinetic equation, the SO2 removal in the fixed bed of the filter cake can be simulated. The combined filter and reaction model was successfully validated with an experiment from a pilot plant for dry flue gas cleaning, where solid Ca(OH)2 was used as a sorbent. A sample of the partially reacted sorbent from the pilot plant had been used to derive the empirical kinetic equation for SO2 sorption in fixed-bed laboratory experiments. 1. Introduction Fabric or ceramic filters are frequently used for the separation of fine dust particles from gas streams. Usually the cake is removed from the filter by jet pulses. The cleaning is mostly controlled by the upper and lower pressure drop, so that once the upper pressure drop is reached, the cleaning pulses are started and carried on until the lower pressure drop is restored. In general, neither the entire filter area is exposed to the pulses nor is the entire cake actually torn off from the exposed areas. Patchy cleaning, which means that the cake either breaks off completely or stays on the cloth unchanged, is generally observed with jet-pulsed filters.1-5 Imperfect cleaning causes not only a highly nonuniform distribution of the cake thickness over the filter area but consequently also a severely uneven distribution of the filtrate stream over the filter area. In a recent study a transient model was presented based on the assumption of rectilinear, parallel gas flow through the filter cake.6 The filter model deals with the case of a constant overall gas stream. With the model for steady-state, periodic filter operation, one can determine the distributions of the cake thickness and gas velocity over the filter area as well as the distribution of the residence time of the solid in the cake. Ju et al.7 proposed a similar model which, however, deals with the case of filtration at constant pressure drop. * Corresponding author. E-mail: [email protected]. Tel.: 0043/316/873-7489. Fax: 0043/316/873-7492. † Technische Universita¨t Graz. ‡ University of Cantabria.

In the process of dry flue gas cleaning, a solid sorbent [mostly Ca(OH)2] is injected into the flue gas in a duct or fluidized bed and the solid is removed downstream by a jet-pulsed filter. A major part of the overall SO2 and HCl removal of the flue gas takes place in the fixed bed of the filter cake.8 Some types of processes use the filter alone without a fluidized bed as a reactor. A prior attempt to model SO2 removal in the jetpulsed filter was made by Chisholm and Rochelle,9 who examined the reactions of SO2 and HCl in a growing filter cake starting from the perfectly clean filter cloth. Marques et al.10 also simulated SO2 removal in a growing filter cake. In both studies a full breakthrough of SO2 at the start of the filter cycle is simulated. This was not found in the experiment of the present study. Neither author took into account the maldistribution of the solid load over the filter area and its residence time distribution. In the recent decades a large number of kinetic studies on the dry reactions between SO2 and Ca(OH)2 have been reported. Based on laboratory experiments, different effects were deemed to be crucial for the sorbent reactivity with SO2 and the maximum sorbent utilization: fly ash addition to the sorbent,11 activation with water,12 competitive carbonation and sulfation,13 and the presence of HCl and NOx in the flue gas.9 As a consequence, extreme discrepancies were also found in the reaction rates and final solid conversions of the Ca(OH)2 sorbent with gaseous SO2 in laboratory experiments, depending on the sorbent treatment and the experimental gas atmosphere (compare Chisholm and Rochelle,9 Garea et al.11 and Krammer et al.14).

10.1021/ie020281e CCC: $22.00 © 2002 American Chemical Society Published on Web 09/27/2002

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Table 1. Experimental and Design Parameters of the Filter Experiment in the Spittelau Pilot Plant ϑ φ

80 (°C) 0.28

cCO2 cO2

6.5 (vol %) 18.5 (vol %)

Atotal η RHcj RT ∆pcloth

92 (m2) 2.104 × 10-5 (Pa‚s) 2.2 × 108 (1/m2) 8.485 × 108 (1/m) 200 (Pa)

FSolid m ˘ Solid,Filter mSolid,Filter,max V˙ τ

2456 (kg/m3) 0.050 28 (kg/s) 108.5 (kg) 1.055 (m3/s) 435 (s)

Table 2. Chemical Analysis of the Sorbent Sample from the Pilot Plant Spittelau xCaSO3 xCaSO4 xCaCl2

0.222 (mol/mol) 0.072 (mol/mol) 0.075 (mol/mol)

xCaCO3 xCa(OH)2 cCa

0.354 (mol/mol) 0.276 (mol/mol) 0.008 35 (mol/g)

The fixed-bed reaction algorithm is based on the mass balance equations for SO2 of the solid and gas phases in the filter cake. This algorithm considers a moving boundary due to the growth of the filter cake. The source/sink term in the mass balance equations is formed by an empirical kinetic equation,15 which was derived using a solid sample from the pilot-plant experiment that is modeled in this study. The concentration of SO2 in the flue gas up- and downstream of the filter was measured at the modeled operational point of the pilot plant to evaluate the combined filter and reaction model. The present study reveals how a jet-pulsed filter acts as a dust removal unit and a chemical reactor simultaneously. This is demonstrated for SO2 removal from flue gas. 2. Pilot-Plant Experiments Experiments were performed in the pilot plant Spittelau, Vienna, Austria,16,17 which has the new dry flue gas cleaning process Turbosorp is under study. The solid sorbent was dispersed into a fluidized bed and was separated downstream in a jet-pulsed filter, which was operated at a constant flue gas stream. The jet-pulsed filter was controlled by a constant upper and lower pressure drop. Once the upper pressure drop was reached, the jet pulses were started until the lower pressure drop was restored. The tubular cloth filter consisted of seven rows of filter tubes with eight tubes in each row. In the jet-pulse cleaning, one row of tubes was cleaned at a time in a set cyclic pattern with an interval of 5 s between single pulses. The temperature of the flue gas entering the filter housing was measured continuously during the experiment and was found to be approximately constant. During the experiment, the relative humidity was measured using an online Siemens Ultramat 5F. The relative humidity φ was also fairly constant. The medium temperature and relative humidity are given in Table 1. The concentration of SO2 was measured upstream and downstream of the filter by two online Siemens Ultramat analyzers. The flue gas upstream of the jet filter was highly loaded with dust, which was separated in a quartz wool filter before the gas was led onto an H2O condenser and the SO2 analyzer. The quartz wool filter was heated to 180 °C, which prevented further reaction of the gas with the solid gathering in the quartz wool. The measurement of SO2 upstream of the jet filter can only be performed for a limited time span, after which the quartz wool filter must be replaced. The SO2 concentration at the filter inlet is further reduced before the flue gas reaches the filter bags. Because the solid holdup in the gas phase of the filter

Figure 1. Cake area load for the model areas versus time: model simulation.

housing is less than 1% of the solid holdup in the filter cake, this further SO2 reduction is considered negligible. Additionally, the concentrations of CO2 and O2 in the outlet of the filter were measured continuously, and they were found to remain constant (see Table 1). Extensive macroscopic data pertaining to the filter were measured. In particular, the overall gas volume stream, the stream of solid sorbent caught at the filter cloth, the solid holdup on the filter cloth at the end of a filter cycle, and the cake resistance parameter of the filter cake were determined experimentally. Furthermore, the essential design parameters of the filter are known. This set of data (Table 1) was also used to set the open model parameters of the filter model.6 3. Filter Model The filter model6 proposes a cyclic evolution of the cake generations on the filter cloth, where at the start of a filtration cycle a cake is “born” on the clean areas. This cake partly survives the jet pulses at the end of the following filtration cycles and its thickness grows, until it breaks off from the entire remaining filter area. Consequently, the model areas classified by their respective cake thicknesses must decrease in size monotonically, so that the model area representing the newly cleaned patches is the largest. For one steady-state, periodical filter cycle, the pressure drop curve is approximated by the open filter model parameters, of which there are three. Figure 11 shows the model approximation of the pressure drop curve for one filtration cycle. For the experiment presented here, eight model areas were found by the filter model application, where each model area represents one generation of the filter cake. Figure 1 shows the cake area load for these eight model areas through one filtration cycle. It can be seen from Figure 1, that there is already a cake present on the newly cleaned patches at the start of a filtration cycle. This cake, which was found by the model application, is assumed to form out of fresh sorbent during the jetpulse cleaning procedure. Figure 2 shows the superficial gas velocities through the eight model areas during one filtration cycle. The maldistribution of the solid load over the filter area is accompanied by a severely uneven distribution of the gas velocities as well, so that the younger, thinner cakes are pervaded by the gas much faster than the older

Ind. Eng. Chem. Res., Vol. 41, No. 22, 2002 5461 Table 3. Parameters of the Empirical Kinetic Equation of Garea et al.15 at a Relative Humidity of 30% k [kmol/(m2‚s)] R

Figure 2. Gas velocities through the model areas versus time: model simulation.

cakes. This feature is vital for modeling the chemical reactions in the jet-pulsed filter. The filter model is based on the concept of patchy cleaning. This means that after a filtration cycle a fraction of a filter cake is removed totally from the filter cloth and the rest of the cake remains unchanged on the filter. Consequently, the cake thicknesses (compare Figure 1) and profiles of the solid conversion of the remaining filter cakes stay unchanged during the cleaning procedure. Accordingly, the reactions in the filter cakes of different generations can be simulated starting from the cleaned filter area with its initial solid layer of fresh sorbent. More details of the filter model and the application of the data to reactions modeling are given in Kavouras and Krammer.6 4. Empirical Kinetic Equation Different authors have shown that the reactivity of pure calcium hydroxide in artificial flue gas, containing SO2 but no HCl, decreases sharply when a small fraction of the solid is converted.13,14 Then the sorbent is virtually inert. Chisholm and Rochelle9 have shown that the presence of HCl in the flue gas leads to sorbent conversions close to 100% at relative humidities of practical relevance. Izquierdo et al.8 found that mixing the additive CaCl2 to Ca(OH)2 had a similar effect not only on the maximum sorbent conversion but also on the reactivity of the sorbent. Garea et al.11 demonstrated that there is a positive influence of the additive fly ash on the utilization and reactivity of the Ca(OH)2 sorbent with SO2. Furthermore, it was observed that the reactivity of a partially spent sorbent can be partly restored by an exposure of the sorbent to relative humidities above 90%.12 In the pilot-plant experiment, the sorbent was brought into contact with a water spray in the fluidized bed, which is situated upstream of the tubular cloth filter, to activate the sorbent and to reach higher solid conversions. The pilot-plant experiment was performed with flue gas at a typical operating point of dry flue gas cleaning processes of coal-fired power plants. The raw flue gas contained approximately 100-200 mg/m3 of HCl and 700-850 mg/m3 of SO2, which was reduced to 350-600 mg/m3 at the filter inlet. In addition, fly ash originating from the flue gas was mixed into the solid sorbent.

7.1 × 10-6 1.55

β

2.87

To overcome the uncertainties concerning the sorbent reactivity due to fly ash content, exposure to gaseous HCl, and its contact with liquid water, a sample of the sorbent was taken from the pilot plant and its reactivity was tested directly to provide a suitable basis for this study.15 Thus, at least the initial reactivity of this sorbent sample with SO2 can be assumed to be representative of the pilot-plant experiments. In the dry flue gas cleaning process under study, the reactive Ca(OH)2 sorbent is dispersed into the flue gas in abundance, and it is strongly recycled in order to increase the sorbent utilization. As a consequence, the solid conversion is minute within one pass through the plant. Therefore, the solid conversion of a sorbent sample is basically independent of the location of sampling. The sorbent sample of the filter experiment was taken from the solid stream leaving the filter. A part of this sample was analyzed chemically by standard techniques.15 The results of these analyses are given in Table 2 in terms of molar conversion of Ca(OH)2, which is the basis of the species CaCO3, CaCl2, CaSO3, and CaSO4. In Table 2 the total number of moles of calcium per unit mass of solid sorbent is given too. In Garea et al.15 derived the empirical kinetic equation (1) for the pilot plant sorbent sample. The kinetic data were obtained from the SO2 breakthrough curves of the fixed-bed experiments, where an artificial flue gas was led through the fixed bed. This artificial flue gas consisted of N2, CO2, O2, water vapor, and SO2, but there was neither HCl nor NOx present in the flue gas.

rSO2(ySO2,xS) ) kySO2(1 - βxS)R

(1)

The additional conversion of the pilot-plant sorbent sample toward CaSO3 and CaSO4, which was examined in the fixed-bed experiments and for which the empirical kinetic equation is employed in the combined filter and reaction model, is small. Therefore, it is assumed that the sorbent composition and its reactivity in the filter cake of the flue gas cleaning plant are approximated by the fixed-bed experiments, even though no HCl was present there. The relative humidity φ plays a major role in dry desulfurization processes. In Garea et al.15 performed a number of fixed bed experiments with relative humidities in the range from 20 to 45% and variable concentrations of SO2 in the gas phase. Kinetic parameters to eq 1 were obtained from a fixed-bed experiment at a relative humidity of 30% and an SO2 inlet concentration of 1240 mg/m3 at 80 °C. These parameters are given in Table 3. Except for the SO2 fixed-bed inlet concentration, these conditions approximate the flue gas properties in the pilot-plant experiment (compare Table 1). Yet, the dependence of the reaction rate on the SO2 concentration has been identified as first order previously.9,13 In the empirical kinetic equation (1), the solid conversion xS ) xCaSO3 + xCaSO4 starts at the initial conversion of the solid sample, which was found to be 0.294 (see Table 2). All SO2 and HCl concentrations specified in this study apply to standard temperature and pressure, which is the temperature 273.15 K and the pressure 101 325 Pa.

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Table 4. Parameters for the Reaction Modeling in the Filter Cake dSolid FSolid Sm FGas DDisp

3 × 10-6 (m) 0.9 2456 (kg/m3) 16000 (m2/kg) 0.0345 (kmol/m3) (1.156-1.162) × 10-5 (m2/s)

The concentrations given are on a “wet” basis of the flue gas before water condensation. The empirical kinetic equation of Garea et al.15 is based on dry SO2 values measured after water condensation. Because in this study SO2 concentrations are used on a wet basis including water vapor, eq 1 was multiplied in the model by the balancing factor 1/(1 yH2O). In this factor the mole fraction of the water vapor in the flue gas can be calculated from the data in Table 1 at standard pressure. 5. Mass Balance Equations and Parameters Removal of SO2 out of the flue gas through the reactive filter cake takes place when the flue gas pervades the fixed bed of the filter cake. The molar fraction of SO2 in the gas phase in the fixed bed is denoted as ySO2, which is ySO2,0 for the still uncleaned flue gas. The solid conversion xS in the fixed bed is defined as the moles of Ca forming CaSO3‚0.5H2O or CaSO4‚2H2O out of Ca(OH)2 or CaCO3 related to the total number of moles of Ca. There are mass balances for SO2 in the gas and solid phases in the filter cake. The gas stream enters the filter cake at a moving boundary. For the gas-phase balance, the convective and reactive (source/sink) terms, dispersion effects, and the instationary term are taken into account. For the solid-phase balance, only the reactive (source/sink) term and the instationary term are relevant because the solid phase is fixed. The rate of dispersion in the gas phase is considered to be linearly dependent on the concentration gradient, and the dispersion coefficient depends on the flow regime.19 The phenomenon of dispersion in fixed beds with very low fluid velocities consists of diffusion, which is predominant in the filter cake, and back-mixing due to microscopic Taylor dispersion,20 which is of no importance. The dispersion coefficient of SO2 depends, in particular, on the superficial gas velocity, the porosity of the fixed bed, the particle size of the powder making up the fixed bed, and the diffusion coefficient of SO2. The dispersion coefficient in the fixed bed was calculated according to the scheme provided in the VDI Wa¨rmeatlas.21 Its value was updated after every time step (although it was almost constant), and the range of the dispersion coefficient in the filter cake together with other parameters is given in Table 4. The complete one-dimensional gas-phase balance of SO2 in the filter cake is given by

∂2ySO2 N˙ i ∂ySO2 )+ DDisp ∂t AiFGas ∂h ∂h2 1- F S r˘ (y ,x ) (2) FGas Solid m SO2 SO2 S ∂ySO2

The spatial coordinate in the filter cake is termed h and runs between 0 and the transient surface of the filter cake H(t).

The ideal gas law was used to calculate the molar density of the gas FGas at ambient pressure and the temperature of the filter experiment (see Tables 1 and 4). For the calculation of the mole stream of flue gas N˙ from the volume stream V˙ (Table 1), also the ideal gas law was applied. The mass balance equation for the solid conversion is given in eq 3 and is formulated according to Garea et al.15. Here, for the molar mass of the calcium sorbent, the value of CaSO4 is assumed. The stoichiometric coefficient vS in the mass balance equation of the solidphase equation (3) is unity.

dxS ) vSSmMCaSO4r˘ SO2(ySO2,xSO2) dt

(3)

Depth filtration occurs with clean, needled felt filter media on the newly cleaned patches at the start of the filter cycle.22 However, this is considered neither in the filter model nor in the reaction model. The mass balance equations of the gas and solid phases are only applied to the filter cake but not to the filter medium, although some sorbent may be deposited in the structure of the filter medium during the phase of depth filtration. The thickness of the filter cake on model area Ai grows in the differential time dt by the differential length dhi according to eq 4.

dhi cSolid V˙ i ) dt 1 - Ai

(4)

The initial condition of the solid phase of filter model area A1 for the differential eq 3 was the following: at t ) 0, xS ) xS,0 for h ) 0 to H. The simplifying assumption is adopted that the solid sorbent of the initial solid layer on the newly cleaned patches consists of fresh sorbent out of the flue gas alone, although removed cake is reentrained into the newly forming cake during the jetpulse cleaning procedure.6 The initial condition of the gas phase of filter model area A1 is found through an initialization step, where the quasistationary profile of the SO2 concentration of the gas phase in the fixed bed is calculated. Determination of this initial condition is based on the unvarying initial condition of the solid phase (at t ) 0, xS ) xS,0 for h ) 0 to H). Thus, the actual profile of the SO2 gas concentration in the fixed bed at the start of the filter cycle is provided as the initial condition. The initial conditions of the older cake generations are equal to the final gas- and solid-phase profiles of the preceding generations; i.e., the gas- and solid-phase profiles of model area A1 at the end of the filter cycle are the initial conditions for model area A2. One possible way of representing the boundary condition at the moving boundary is to enjoin a total stream ySO2,0N˙ i into each model area because this stream is actually given by the experiment. Here, both convection and dispersion across the interface of the filter cake and the free gas phase are mechanisms of mass transport. Yet, the grid value at the boundary (i.e., in the first cell outside the filter cake) would be smaller than ySO2,0. If this were not the case and the fixed boundary condition were ySO2 ) ySO2,0 (this in fact being the measured SO2 concentration of the flue gas at the inlet of the filter housing), dispersion as an additional mechanism to

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convection conveys SO2 into the filter. Using the upwind scheme for convection, this would result in an erroneous total stream of SO2 into the filter cakes, higher than the total stream ySO2,0N˙ . However, compared to the fixed boundary condition explained below, this representation of the boundary condition through mixed convection and dispersion is computationally more laborious and it also has no further influence on the grid cells inside the fixed bed. A fixed boundary condition at the moving boundary was finally chosen, and it is equal for all model areas: for h ) H, ySO2 ) ySO2,0 and xS ) xS,0 for all times. Care must be taken that, in the numerical implementation of eq 2, the dispersion flux at the boundary between the free gas phase and the filter cake is switched off. The total mass stream of SO2 into the filter from the free gas phase is thereby considered to be convective alone, calculated by the upwind scheme. This ensures that the total stream ySO2,0N˙ i enters the first grid cell of each model area, in concordance with the experiment. For the second boundary condition (at the interface between the filter cake and the filter cloth), there is no physically substantiable assumption at hand. To circumvent this second boundary condition, the dispersive flux from the filter cake into the filter medium was set to zero. In this case no boundary value ySO2 beyond the last cake cell needs to be known for the calculation of the dispersive flux between the last cake cell and the filter medium. This assumption implies that if the grid were extended outside the cake the grid value of the first cell outside the filter cake would be the same as the last grid value inside the reactive cake, when the upwind scheme was used for convection. It is clear that a further reduction of the SO2 concentration in the first filter medium cell in contrast to the last cake cell is not plausible because in the filter medium no SO2 capture through the sorbent takes place. The chosen boundary condition is thus highly plausible. The parameters used for the fixed-bed reaction simulation are given in Table 4, and other parameters regarding the filter experiments can be found in Table 1. The stated porosity of the filter cake (see Table 4) is a typical value for Ca(OH)2 forming a filter cake in flue gases as reported by Naffin.23 The length scale of the fixed bed is affected by the uncertainty of the cake porosity. The value for the average sorbent particle diameter dSolid in Table 4 is typical of commercially available lime. It is relevant only for the calculation of the dispersion coefficient. With the parameters given, the particle diameter has a negligible influence on the dispersion coefficient. 6. Numerical Implementation of the Mass Balance Equations In this section the basic outlines of the finite volume code, which was developed using the scheme of Patankar,24 are reported. The filter cake of each model area is divided into cells, which are considered to be homogeneous. The boundaries between the cells are immovable, and they are located midway between two grid points. The special feature of the method delivered by Patankar24 is the calculation of the mole fluxes between two cells j and j + 1 through convection and diffusion. A detailed discussion of this issue with polynomial approaches is given by Lim et al.25

For the finite volume method, the complete mass balance equation with an instationary term and a source/sink term is integrated across the spatial domain over the volume of each cell. A fully implicit Euler method is chosen for time integration. Patankar24 also proposes a linearization of the source/ sink term, which may depend on the grid value ySO2 in a nonlinear way. Linearization accelerates the convergence of the iterative solution of the set of linear equations and was employed in the present study. Thus,

1- F S r˘ (y ,x ) = Sc + SpySO2 FGas Solid m SO2 SO2 S

(5)

The resulting linear equations for the internal grid cells that represent the partial differential mass balance equation of the gas phase are as follows: (t+∆t) (t+∆t) (t+∆t) (t+∆t) (t+∆t) (t+∆t) ySO2,j ) aW,j ySO2,j-1 + aE,j aP,j ySO2,j+1 + b(t+∆t) j (6)

where the coefficients are defined as (t+∆t) aW,j )

N˙ i exp(Pej-1) AiFGas exp(Pej-1) - 1

(7)

N˙ i 1 AiFGas exp(Pej) - 1

(8)

(t+∆t) ) aE,j

∆hj-1,j + ∆hj,j+1 ∆hj-1,j + ∆hj,j+1 (t+∆t) aP,j + ) Sp + 2 2∆t(t+∆t) (t+∆t) (t+∆t) + aE,j (9) aW,j

The Peclet number Pe is defined as follows:

Pej )

Ni(t) ∆hj,j+1 DDispAi(t) FGas

(10)

Patankar24 states a more convenient power scheme as an approximation of the expressions in eqs 7 and 8, which involve exponential functions. This power scheme was used in this work because it is computationally more economical. in eq 6 is defined as The constant coefficient b(t+∆t) j

) Sc b(t+∆t) j

∆hj-1,j + ∆hj,j+1 (t) ∆hj-1,j + ∆hj,j+1 + ySO2,j 2 2∆t(t+∆t) (11)

It should be noted that for a purely convective problem |Pe| f ∞ and eq 6 reduces to the upwind scheme. The equations for the cells on the boundaries of the filter cake can be incorporated by adjusting the dispersion coefficients. The dispersion flux through both boundaries was set to zero, so that on the right-hand boundary the coefficient aE must be calculated with DDisp ) 0 and on the left-hand boundary the coefficient aW is calculated likewise. Starting from the initial condition that a cake of defined thickness and profile of solid conversion is present on the filter cloth, the set of transient gas-phase balance equations (6) of all of the cake cells was solved using a Gauss-Seidel algorithm.26 After several iterations, convergence was reached. The source/sink terms in the coefficients in the set of gas-phase balance

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equations strongly depend on the profile of the solid conversion in the filter cake. The mass balance equations (3) for the solid phase are integrated with a fully implicit Euler method, which leads to eq 12. The implicit eqs 12 were solved by (t+∆t) (t+∆t) (t+∆t) (t) xS,j ) xS,j + vS∆t(t+∆t)SmMCaSO4rSO2(ySO ,xS,j ) 2,j

(12) iteration (i.e., direct substitution with under-relaxation) until convergence of the solid conversions was obtained. The set of ordinary differential equations for the solidphase balance and the partial differential equation for the gas-phase balance (represented by the set of eqs 6 and 12) are interlinked via the source/sink term. In the source/sink term, both the concentration of SO2 in the gas phase and the solid conversion appear. For the integration of each time step, the set of eqs 6 and 12 was solved iteratively. At first guess values for the concentrations in the gas and solid phases of the new time step were chosen. After that the coefficients in the set of linear equations for the gas phase were calculated. Then the set of linear equations for the gas phase was solved by the Gauss-Seidel method. With the gas-phase concentrations, the solid phase eqs 12 were solved and the coefficients in the set of linear equations for the gas phase were updated. The procedure was stopped when (t+∆t) both the solid conversions xS,j and the gas concen(t+∆t) trations in the filter cake ySO at all grid points had 2j converged. At the beginning of every time step, a new cake cell with the initial solid conversion xS,0 has to be considered in the set of eqs 6 and 12 due to the growth of the filter cake. The time steps were decided in such a way that every new cake cell of one filter cycle had the same length. With the restriction that the cells have equal length, the spatial discretization error of every cell remains in the same range because the cells are of the same size. Had constant time steps been used, the cells of filter model area A1 at the start of the filter cycle would have been excessively larger than the cells at the end of the cycle (compare Figure 2). To check the fixed-bed reaction algorithm, the integral balance equations were examined and they were found to agree well (relative error: 10-8).

Figure 3. SO2 concentration profiles in the gas phase along the filter cakes of the eight model areas at the start of the filter cycle.

Figure 4. SO2 concentration profiles in the gas phase along the filter cakes of the eight model areas after 25% of the filter cycle.


7. Simulation of the SO2 Capture in the Growing Filter Cake The reaction model was applied to the filter-related data (gas velocities and sizes of model areas) of the simulation results to the filter experiment as depicted by Kavouras and Krammer.6 The average SO2 inlet concentration was determined from the experiment (Figure 11) to be 475 mg/m3 and served as a constant input to the reaction model. The combined filter model and the fixed-bed reaction model yield the gas streams through the single model areas of the filter and their SO2 concentrations. The SO2 concentration profiles in the gas phase along the filter cakes of the eight model areas at the start of the filter cycle are shown in Figure 3. The vertical lines in Figure 3 represent the interfaces between the filter cakes and the free gas phase. The interface between the filter cake and the filter medium is located at the length h ) 0 m for all model areas.


The SO2 concentration profiles in the gas phase along the filter cakes after 25%, 50%, and 100% of the filter cycle are shown in Figures 4-6, respectively. From Figure 3, it can be seen for the spatial coordinate h ) 0 m that virtually only model areas A1 and A2 emit significant concentrations of SO2. By far the greatest part of the SO2 emissionstaking into account the SO2 outlet concentration and the gas volume streams comes from the newly cleaned patches of the filter, i.e., model area A1. From the third model area onward, where the outlet concentration is almost zero at the start of the filter cycle, the model areas capture the oncoming SO2 almost completely.


If the SO2 outlet concentration of model area A1 is compared at different times of the filter cycle, a rapid reduction of the SO2 emission is found at the start of the cycle. After half of the cycle has elapsed, only moderate further reduction occurs (compare Figures 3-6). The profiles of the gas-phase SO2 concentrations in the filter cake are strongly convex. The reduction of SO2 in the filter cake is steep at the interface of the cake and the free gas phase but levels off strongly inside the cake. From the simulation results, it becomes clear that the instationary term in the mass balance equation of the gas phase is negligible. The relevance of the dispersive term depends on the reactivity of the fixed bed: The convective term in the mass balance equation of the gas phase is on the order of magnitude of N˙ i/(AiFGas)ySO2,0/z, when the total incoming SO2 is reduced to almost zero within the length z. Then the dispersive term is on the order of DDispySO2,0/z2, and the division of both terms constitutes a Pe number that is proportional to the length z. Because the filter cake consists of pure sorbent, the reactivity of a unit length of the fixed bed is high, the Pe number is low, and thus dispersion plays a major role (the Pe number for the filter cake, calculated with the total cake thickness, ranged from 0.64 for model area A1 at the start of a filter cycle to 4.56 for model area A8 at the end of a cycle). Yet, for laboratory fixedbed experiments with a large fraction of inert silica in the bed material and only a small amount of the sorbent, the reactivity of a unit length of the fixed bed is low, the Pe number is high, and dispersion is insignificant. Mass transfer through axial dispersion in the filter cake is several times higher than that through convection near the interface between the cake and the free gas phase. At this interface the dispersion term in the gas-phase balance equation is switched off. The kinks in the curves of the SO2 concentration at the interface between the filter cake and the free gas phase (see Figure 3) are due to the irregularity in the dispersion term. Owing to the assumption of purely convective transport of SO2 across the interface, the total mole stream of SO2 into the filter cake is described correctly but the stated SO2 concentration at the interface between the cake and the gas is not. Actually, there is a dispersion/diffusion flux from the free gas phase to the interface between cake and gas, so that the concentration of the uncleaned flue gas must already be smaller at this point than the value ySO2,0 of the uncleaned gas. As a consequence, the assumption of a purely convective stream across the interface between the filter cake and the free gas phase does not lead to consecutive errors because the total mole stream of SO2 into the cake is known and the faulty grid value at the interface has no further influence on the rest of the fixed bed. Further, Thomas et al.22 reported that in reality there is no sharp interface between the homogeneous filter cake and the gas phase. The newly forming cake has a dentritic structure27,28 and is less compact than the older layers of the filter cake,29 so that there is a smooth transition between the filter cake and the gas phase. In general, axial dispersion in the filter cake has a detrimental effect on the SO2 removal of the filter,

Figure 7. Solid conversion profiles along the filter cakes of the eight model areas at the start of the filter cycle.

Figure 8. Solid conversion profiles along the filter cakes of the eight model areas after 25% of the filter cycle.


because an additional mass-transfer mechanism to convection conveys SO2 through the filter cake. Another essential result of the combined filter model and the fixed-bed reaction model is the profiles of the solid conversions in the fixed bed of the filter cakes. The profiles of the solid conversions along the filter cakes of the eight model areas at the start of the filter cycle are shown in Figure 7. Again the vertical lines represent the interfaces between the filter cakes and the free gas phase, and the interface between the filter cake and the filter medium is located at the length h ) 0 m for all model areas. The profiles of the solid conversion along the filter cakes after 25%, 50%, and 100% of the filter cycle are shown in Figures 8-10. Because of the varying gas velocities through the model areas, the profiles of the solid conversions show some peculiarities. The profile of the solid conversion of the cake of model area A1 (initial solid layer) in Figure 7 is flat at the initial value xS,0 at the start of the filter cycle. If the profile of the solid conversion of model area A1 is followed through time (see, e.g., Figure 10), then two segments of the cake can be distinguished. The segment of the initial solid layer, which is already present at the start of the filter cycle, suffers increasing but uneven conversion: Those parts of the initial solid layer that are closer to the gas phase are subjected to

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higher SO2 concentrations and undergo a stronger conversion. The second segment of the cake on model area A1 is that of the growing cake. This segment shows a steep decline of the solid conversion when the interface between the free gas phase and the filter cake is approached. The newly deposited cake has the initial conversion xS,0, and a thin layer of the cake neighboring to the interface with the free gas phase captures almost all of the oncoming SO2. The profiles of the solid conversion in the second segment of the filter cake, this segment being the newly deposited sorbent of the respective cycle, have a similar shape for all model areas irrespective of the gas velocity (see also Figure 3, where the concentration profiles in the gas phase are depicted). In Figure 7 there are jumps in the profiles of the solid conversion of model areas A2 to A8 at the interface between the free gas phase and the filter cake of model area A1. These jumps occur at the borderline between the two segments of the initial solid layer and the newly formed cake. Additionally, in Figure 10, there are smaller jumps of model areas A2 to A8 at the interfaces between the cake and the gas phase of model areas A1 to A7. These jumps arise when the filter cake of model area Ai becomes the cake of model area Ai+1 after filter cleaning. Then there is a sudden and sharp decrease of the gas velocity, and the already deposited cake mass near the interface to the gas phase has a better SO2 cleaning capacity than a cake formed with constant, lower gas velocity. Naturally, as the cleaning capacity improves, the solid conversions increase also. From Figure 7 it can be seen that the solid conversion grows near the interface between the filter cake and the free gas phase alone. The profiles of the solid conversions of the older cakes are almost congruent near the filter medium; i.e., there is hardly any reaction going on there. Accordingly, the greatest part of the solid mass, which forms the cake of the older model areas, gives no contribution to the SO2 capture. The conversion of the sorbent achieved during one pass through the filter is low. In the experiment presented here, not more than roughly 2% additional solid conversion was reached in the cakes of the older model areas. Of course, only the sorbent stream caught at the filter undergoes conversion, and the solid stream that, because of sedimentation, falls to the hopper of the filter housing during the filter cycle does not. The experimental and simulated pressure drop curves and the experimental SO2 concentrations at the inlet and outlet of the filter are shown in Figure 11. Besides the simulated transient outlet concentration of SO2, the time-averaged outlet concentration from the simulation and the assumed constant inlet concentration of the filter are depicted in Figure 11. The simulated outlet

Figure 11. Upper plot: experimental and simulated pressure drop. Middle plot: experimental SO2 inlet concentration into the filter and assumed constant inlet concentration. Lower plot: experimental SO2 outlet concentration of the filter and simulation results during one filter cycle.

concentration of the filter is an average calculated from the gas streams through all model areas of the filter at a time. Only this average outlet concentration can be compared to the measured experimental value because a direct measurement of the gas streams exiting the filter cakes of different thicknesses could not be performed. Figure 11 reveals that the medium value of the simulated SO2 outlet concentration (45 mg/m3) is in very good agreement with that of the experiment. However, the measured curve of the SO2 concentration is rather level, and it is approximated only fairly by the simulation result, which shows a strong peak at the start of the filter cycle and a heavy slump shortly afterward. Naturally, one would expect that, at the beginning of a filtration cycle, when parts of the filter are cleaned of the solid, the removal of SO2 will deteriorate sharply, at least for a short time. In the experimental data presented here, the fluctuation of the SO2 outlet concentration has no apparent correlation with the filter cycles though. The SO2 concentration of the flue gas at the filter inlet also fluctuated considerably, and the operation of the pilot plant was not perfectly stable. During the operation of the pilot plant, it was observed that there is a clear correlation between jet-pulse cleaning and a consequent SO2 peak when the plant operates stably. Still, even under perfectly stable plant operation, the measured fluctuation of the SO2 outlet concentration of the filter was only moderate; i.e., there were no sharp SO2 peaks after filter cleaning, in contrary to the simulation results. Part of this discrepancy in the simulated and experimental fluctuation of the SO2 outlet concentrations is due to the imperfect representation of the filter cleaning


procedure in the model. Filter cleaning is treated as instantaneous, whereas in the pilot-plant experiments, it took place stepwise with intervals of 5 s between single jet pulses. This stepwise cleaning of the rows of filter tubes is likely to damp the concentration peak at the start of a filter cycle. Another part of the discrepancy in the simulated and experimental fluctuation of the SO2 outlet concentrations with the filter cycles is caused by the inertia of the SO2 analyzer device. Because of dispersion effects in the H2O cooler, a sharp rise of the concentration of SO2 cannot be detected simultaneously and the actual concentration peaks are damped. Therefore, the marked peak at the start of the filter cycle, shown in the model simulation, is likely to be blurred in practice by the measurement device employed. Consideration of the above issues should help explain why it is hard to compare the fluctuations in SO2 concentrations in the filter outlet between the model and the experiment. For one set of macroscopic experimental filter data, different sets of model parameters with almost equal agreement between the filter model results and the experiment were found (compare Kavouras and Krammer6). However, for the different sets of model parameters, the distributions of the solid load over the filter area were demonstrated to be almost the same. Reaction simulations were carried out for every set of filter model parameters to the filter experiment presented here.6 The simulated time-averaged filter outlet concentrations of SO2 range from 42 to 46 mg/m3 when the inlet concentration was constantly 475 mg/m3. The deviations between the simulation results are very small; therefore, the model results can be termed unambiguous. 8. Conclusions A chemical reaction model of a fixed bed with a moving boundary was introduced. The source/sink term in the mass balance equations of the reaction model was formed by an empirical kinetic equation. The kinetics were decided by means of a solid sample from a filter experiment in a flue gas cleaning pilot plant. Thus, the empirical kinetic equation mirrors the sorbent behavior of the filter experiment. How the reaction model could be applied to the results of a recently developed filter model6 was also pointed out. Thus, the jet-pulsed filter as a chemical fixed-bed reactor was simulated and the combined filter and reaction model successfully validated. Naturally, it is only to be expected that the capture of a gaseous component in the filter cake of a jet-pulsed filter is least thorough at the start of a filtration cycle when parts of the filter cake are removed by the cleaning jet pulses. With the combined filter and reaction model, it was demonstrated that no SO2 peak with a full breakthrough of SO2 occurs at the filter outlet shortly after jet-pulse cleaning. This is due to the imperfect cleaning of the filter medium, prevalent in jetpulsed filter systems. The simulated transient SO2 concentration in the cleaned flue gas shows strong fluctuations. The SO2 outlet concentration ranges from roughly 10 to 170 mg/ m3 when there is a constant inlet concentration of 475 mg/m3. The simulated SO2 concentration at the filter outlet has a marked peak directly after filter cleaning and then slumps sharply. After roughly 50% of the filter

cycle has been completed, further reduction of the SO2 emission levels off and changes only slightly. The range of fluctuation in the simulated SO2 concentration is by far larger than that found in the experiment, where it ranged between 20 and 70 mg/m3. The simulated time average of the SO2 outlet concentration of the filter agrees very well with the experimental data. The simulated value is 45 mg/m3 based on the constant inlet concentration of 475 mg/ m3, and the experimental value is roughly 40 mg/m3. In conclusion, the combination of the filter model and the fixed-bed reaction model, in which an empirical kinetic equation from laboratory experiments is implemented, is suitable to mirror the complex behavior of a jet-pulsed filter in its capacity as a fixed-bed reactor. The application of the combined filter and reaction model revealed that SO2 removal in the filter cake is dominated by the newly cleaned patches of a filter cleaning procedure. The flue gas pervading the older cake generations is cleaned of SO2 almost completely, even at the start of the filter cycle, within a tiny fraction of the total length of these cakes. The solid conversions, achieved after one pass of the sorbent through the filter, are low (in this case roughly 2%). Of course, the solid stream that falls, because of sedimentation, to the hopper of the filter housing does not undergo an additional conversion in the filter. Acknowledgment We express our gratitude to the Austrian Exchange Office (Project 14/99), to the management of the waste incinerator plant Spittelau for their support, to DI Harald Reissner and to Dr. Karl Spiess-Knafl for operating the pilot plant, and to AE Energietechnik GmbH for permission to operate the pilot-plant Spittelau. The spanish research group has been supported by the exchange project Acciones Integradas HispanoAustriaca HU 1998-2001. Nomenclature (t) aE,j ) coefficient for the linear set of mass balance equations, east of grid point j at time step t24 (m/s) (t) ) coefficient for the linear set of mass balance equaaP,j tions, grid point j at time step t24 (m/s) (t) aW,j ) coefficient for the linear set of mass balance equations, west of grid point j at time step t24 (m/s) Atotal ) total filter area (m2) Ai ) model area i of the filter model (m2) b(t) j ) constant factor of the linear set of mass balance equations of the gas phase at grid point j at time step t24 (m/s) cCa ) moles of calcium per unit mass sorbent (mol/g) cCO2 ) concentration of CO2 in the flue gas (vol %) cO2 ) concentration of O2 in the flue gas (vol %) cSolid ) volume concentration of the solid in the gas stream relevant for the filter dSolid ) average sorbent particle diameter (m) DDisp ) dispersion coefficient of SO2 in the gas phase of the filter cake (m2/s) h ) spatial coordinate in the filter cake (m) hi ) spatial coordinate in the filter cake of model area Ai (m) (t) ∆hj,j+1 ) spatial step size of filter cake discretization between grid points j and j + 1 at time step t of one model area (m)

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H(t) ) transient length of the filter cake of one model area (m) k ) kinetic parameter of the empirical kinetic equation15 [kmol/(m2‚s)] MCaSO4 ) molar mass of CaSO4 (kg/kmol) m ˘ Solid,Filter ) solid mass stream to the filter (kg/s) mSolid,Filter,max ) maximum solid mass on the filter cloth (kg) n ) number of model areas of the filter model N˙ ) total mole stream of flue gas through the filter (kmol/ s) N˙ i ) mole stream of flue gas through model area Ai (kmol/ s) ∆pcloth ) pressure drop of the filter cloth alone without cake (Pa) Pej ) local Peclet number midway between grid points j and j + 1 r˘ SO2 ) reaction rate of the solid sorbent with gaseous SO2 [kmol/(m2‚s)] RT ) total resistance of the filter cloth (1/m) Sc ) constant part of the linearized source/sink term24 (1/ s) Sm ) specific surface area of the solid sorbent (m2/kg) Sp ) variable part of the linearized source/sink term24 (1/ s) t ) time (s) ∆t(t) ) time step size of discretization at time step t (m) V˙ ) total gas volume stream through the filter (m3/s) V˙ i ) gas volume stream through model area i (m3/s) xS ) molar conversion of the solid calcium sorbent to CaSO3 and CaSO4 xS,0 ) molar conversion of the solid calcium sorbent to CaSO3 and CaSO4 at the inlet of the filter xCaX ) molar conversion of Ca to CaX [X ) SO3, SO4, Cl2, CO3, (OH)2] in the solid sorbent yH2O ) mole fraction of the water vapor in the flue gas ySO2 ) mole fraction of SO2 in the gas phase ySO2,0 ) mole fraction of SO2 in the flue gas upstream of the filter (t) ySO2,j ) mole fraction of SO2 in the flue gas at grid point j at time step t in the filter cake Greek Symbols R ) kinetic parameter for empirical kinetic equation15 RHcj ) filtrate volume related specific filter cake resistance (1/m2) β ) kinetic parameter for empirical kinetic equation15 η ) dynamic viscosity of the flue gas (Pa‚s) ) voidage/porosity in the filter cake vS ) stoichiometric coefficient for SO2 in the mass balance equation of the solid phase φ ) relative humidity in the flue gas ϑ ) temperature in the flue gas (°C) FGas ) molar density of the flue gas (kmol/m3) FSolid ) solid sorbent density (kg/m3) τ ) duration of a filtration cycle (s)

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Received for review April 12, 2002 Revised manuscript received August 6, 2002 Accepted August 19, 2002 IE020281E

SO2 Removal in the Filter Cake of a Jet-Pulsed Filter - American

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