Breakthrough analysis for adsorption of sulfur-dioxide over zeolites

Breakthrough analysis for adsorption of sulfur-dioxide over zeolites

Chemical Engineering and Processing 43 (2004) 9 /22 www.elsevier.com/locate/cep Breakthrough analysis for adsorption of sulfur-dioxide over zeolites...

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Chemical Engineering and Processing 43 (2004) 9 /22 www.elsevier.com/locate/cep

Breakthrough analysis for adsorption of sulfur-dioxide over zeolites Arun Gupta, Vivekanand Gaur, Nishith Verma * Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 2028016, India Received 31 July 2002; received in revised form 13 December 2002; accepted 15 December 2002

Abstract The adsorption experiments were carried out under dynamic conditions for the removal of trace sulfur-dioxide (SO2) in nitrogen by 5A zeolites. The experiments were conducted to characterize the breakthrough characteristics of SO2 in a fixed bed under different operating conditions including temperature, pellet size, concentration levels, and gas flowrate. At a reaction temperature of 70 8C, the breakthrough time was found to be maximum. The adsorption isotherm was found to be linear over the gas concentration range from 1000 to 10 000 ppm. The exothermic heat of adsorption assuming Arrehenius type of temperature dependence of the equilibrium constant was determined to be 9.8 kc/mol. The mathematical model was developed to predict the breakthrough profiles of SO2 during adsorption over the biporous zeolites (containing both macro and micro-pores). The model incorporates all resistances to mass transfer, namely: diffusion in the gas film around pellets in the bed, diffusion in the binder-phase of zeolites and within the crystals, and adsorption/desorption at the interface of binder-phase and crystals. The model was successfully validated with the observed experimental breakthrough data. The study showed potential application of 5A zeolites in controlling SO2 emissions at trace levels. # 2003 Elsevier Science B.V. All rights reserved. Keywords: Zeolites; Breakthrough; Adsorption; SO2; Air pollution

1. Introduction There are two types of solid (ad)sorbents commonly used in controlling SO2 emissions: one is non-regenerative. The common examples are CaO and MgO obtained from different sources such as hydroxide, carbonate and acetates. The other is regenerative, such as zeolites, silica gel, and charcoal. A number of studies pertaining to the use of non-regenerative type of sorbents have been reported in open literature [17 /20]. These range from the theoretical analysis for understanding the mechanism and kinetics of the sorption process to the development of novel materials having relatively higher reactivity for SO2, to the improvement in the solid / gas contact patterns. Despite significant progress made over the last few years in exploiting the non-regenerative type of materials, the premature termination of the sorption process due to pore-blocking by the product

* Corresponding author. Tel.: /91-512-597629; fax: /91-512590104. E-mail address: [email protected] (N. Verma).

sulphate layers remains the major inherent drawback of these materials. The chemical reaction being irreversible, the commercial value of the spent solids is also often marginal. It is in this context that zeolites have been in the recent forefront of many researchers. The major advantage of using zeolites is their ability for the successive regeneration. The reaction temperature is also relatively lower. Successfully commercialized in early seventies in the area of bulk gas separation due to their molecular sieving properties, the application of zeolites in air pollution control has just begun to emerge. It may, however, be pointed out that zeolites in the latter application are used due to their adsorption characteristics rather than molecular sieving actions. Reviewing recent works reported in open literature, it is fair to say that a limited number of studies have been carried out on the adsorption of SO2 over zeolites. Among some of the pertinent studies, Kopac [1] has investigated adsorption properties of SO2 on molecular sieve 13X under equilibrium conditions in a temperature range of 523/673 K and reported a significant adsorption of SO2 below 523 K. The adsorption equilibrium constants were experimentally determined over the

0255-2701/03/$ - see front matter # 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0255-2701(02)00213-1

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temperature range based on the linear adsorption isotherm assuming first order adsorption and desorption rates. In another study, Kopac et al. [2] carried out a comparative study on different types of zeolites molecular sieves and concluded that the adsorption of SO2 decreased in the order of AW300 /4A /5A zeolites. Among some of the studies concerned with the synthesis aspect, Lin and Deng [3] have reported development of a wide variety of zeolites from fly ash, having significant SO2 adsorption characteristics. On the same line, Srinivasan and Gruyzeck [4] have developed sodalite, a chemical adsorbent (CuO /Al2O3) prepared by sol /gel process. Among the studies concerning theoretical analysis, mainly to establish the mechanism of SO2 adsorption over zeolites, [21] developed a simplified mathematical model for a single and multi-component adsorbate system assuming the Langmuir /Freundlich isotherm. Two diffusional resistances to mass transfer: film and macropore were assumed to be in series and incorporated in an overall mass transfer coefficient using the linear driving force (LDF) approximation. The micropore resistance was, however, neglected. Comparing the model results with the experimental data on breakthrough curves, the authors concluded that macropore diffusion is the controlling step in the overall mass transport of SO2 in hydrophobic zeolites. In contrast, disagreement between the model predictions and the adsorption data on H2O on zeolites was attributed due to micropore (crystalline) diffusion, and probably surface diffusion of moisture, which were not included in the model. Kopac and Kocabas [5] have carried out the breakthrough together with adsorption equilibrium analysis on the adsorption of SO2 on a monoporous adsorbent like silica gel. In the equilibrium study, various types of isotherms were used to explain the adsorption data. The salient finding of the study was to demonstrate the suitability of the Freundlich and DRK isotherms in explaining the data. The deactivation model as proposed by Suyadal et al. [6] for the adsorption of hydrocarbon on activated carbon (monoporous) was adopted to explain the SO2 adsorption on silica gel. The removal of SO2 by the activated charcoal adsorbents has also been studied by Gail and Kast [7]. In their study, the sorption was modeled as a combination of physical adsorption and oxidation (catalytic conversion) over porous charcoal. In addition, the authors successfully simulated the breakthrough profiles of a fixed bed reactor based on the single-pellet experimental data. Tsibranska and Assenov [8] have proposed a mathematical model for adsorption in biporous particles. The primary objective was to determine the effects of particle size vis-a`-vis bed column diameter on the breakthrough characteristics. The model assuming the Langmuir isotherm accounted for macro and micro-pores diffusion within the particle. Microparticle size distribution and concentration pro-

files within the microparticle were also taken into account. The comparison between the experimental breakthrough curves obtained for the adsorption of SO2 in natural clinoptilolite and model predictions showed a good agreement for larger size pellets where macroparticle diffusion control was assumed to be of importance. The model predictions for the smaller pellets were, however, found to be less satisfactory. In the present study, the dynamic adsorption of SO2 by 5A commercial zeolites has been investigated, both experimentally and theoretically. The primary objective is to explore the suitability of zeolites materials in separating trace SO2 (less than 1%) from nitrogen by adsorption under a wide range of experimental conditions, including adsorption temperature, SO2 inlet gas concentration, and particle size, and determine the optimum conditions for the maximum adsorption (longer breakthrough time). A mathematical model is developed mainly to predict breakthrough characteristics of the zeolites materials in a fixed bed and ascertain the key operating parameters that control the adsorption process so as to scale-up and design a suitable adsorber for industrial use. The theoretical analysis in the model takes into account gas film diffusion, intraparticle diffusion within the bi-pores of zeolites (macro and micro) and adsorption/desorption within the pores. The main objectives of the present study can be summarized as follows: (a) design, fabrication and setup of an experimental test bench to carry out the adsorption study (b) determining the optimal adsorption temperature for zeolite (c) determining breakthrough characteristic of the materials under varying operating conditions such as particle diameter (0.1/1.2 mm), flue gas concentration (1000 /10 000 ppm), amount of the adsorbents (1 /10 g) and flow rate of the gas (0.1 /1 slpm) (d) development of a mathematical model to characterize the mechanistic steps involved in the entire removal process, and (e) model parametric study.

2. Theoretical analysis Zeolite solids are available in the pellets form. These pellets are made by compressing zeolite crystals together, usually with a small percentage of binder to join the crystals together. This results in a porous structure having macro and micro-pores. A schematic representation of such a biporous particle is described in Fig. 1. The crystals are of the order of 0.1 /1 mm, and the zeolite pellets are of that of 1 mm. The void between the microparticle contributes to the micro-pores of the particle. These pores act as conduit to transport molecules from the surrounding into the interior of the particle. Once inside the particle, molecules adsorb at the pore-mouth of the micropores and thence the adsorbed species diffuse into the interior of the crystal

A. Gupta et al. / Chemical Engineering and Processing 43 (2004) 9 /22

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Fig. 1. Schematic diagram of the experimental set up to study SO2 breakthrough over zeolite pellets in a packed bed.

through the micro-pores of the crystal. The diffusion process in the macro and micro-pores follows the combination of the molecular and Knudsen mechanisms while that inside the crystal follows an intra crystalline diffusion mechanism. It may be pointed out that the overall mechanistic steps involved in the adsorption over zeolites and the other regenerative adsorbents such as charcoal and silica gel are identical. The difference lies in the internal structures of these adsorbents. While zeolites have biporous structures, charcoal and silica gel have monoporous structures. Thus, in the case of the former, adsorption is usually controlled by intra crystalline diffusion, while in the case of the latter the macropore diffusion prevails. The mathematical model developed to explain the breakthrough of SO2 in the packed bed consisting of the zeolite pellets is based on the following assumptions: 1) Temperature is uniform throughout the bed, pellet and crystals. 2) The adsorbing species (SO2 in this case) is at trace levels (B/1%) and N2 is a non-adsorbing (inert) gas. 3) Pressure-drop along the bed length is negligible under the experimental conditions studied. This (isobaric condition) was found to be true as described later in the Section 3. The assumption of constant pressure in the reactor also derives from the fact that the concentrations in the present study were at trace levels (less than 1%).

Referring to the study by Scholl and Mersmann [9], the authors have shown that during physical gas adsorption in single particle adsorbents, the intraparticle total pressure may change, which should be incorporated in modeling of adsorption. However, the authors have also concluded that such pressure may be assumed to be constant as long as the concentration levels are low. On the other hand, this might not be true in cases where the adsorption concentrations are high or where the total pressure varies during operation as in the case of a pressure swing adsorption (PSA) system. 4) Instantaneous equilibrium exists between the gaseous SO2 species in the macro-pores of the binderphase and the adsorbed phase within the crystal at the binder/crystal interface. Such assumption has also been made in other independent works for most cases of the physical gas phase adsorption [10 /12]. 5) There is a constant fluid velocity through out the bed. This assumption follows from those made in (2 /4), i.e. low concentration level and negligible pressure-drop in the bed. The insignificant change in the axial flow velocity in comparison with the time change (unsteady-state) of the concentration of the adsorbing species at trace levels in the isobaric column (a ‘quasi-static’ assumption) has been mathematically shown by Yang [13]. For the sake of brevity the detailed mathematical steps are not reproduced here.

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2.1. Mass balance in the packed bed reactor

crystals, the following equation is obtained:

Since the SO2 concentrations were at ppm levels, the exothermic heat of adsorption was negligible and isothermal condition was assumed. The assumption of isothermality in the case of adsorption/desorption of species at trace levels, unlike in the case of bulk separation where concentration levels are typically higher, has also been justified in an independent work [14]. Thus, considering an isothermal plug flow system in a packed bed of spherical pellets, a SO2 balance in the bed of porosity, eb results in the following equation:

a

@Cb @t



Vz @Cb eb @z



Dz @ 2 Cb eb

@z2



1 eb

a f (z)

(1)

The terms in Eq. (1) are transient, convection, axial dispersion and diffusion flux, respectively. The last term represents diffusion of the gas from the bulk into the macropores of the zeolite pellets and is calculated as f (z) Km (Cb Cp j RR ): p

Here, a *,external surface area per unit volume of the 3(1  b ) / /gas film mass transfer co-efficient; Cp, pellet Rp concentration of the reactant gas in the macropores of the pellet. The initial and boundary conditions for Eq. (1) are: Cb  0 z0; Cb Cb0 @Cb 0 z1; @z

t0; t0;

(2) (3) (4)

Here, the theoretical analysis was carried out assuming that only one species (SO2) adsorbs, as the other species (N2) is non-adsorbing (inert gas). This resulted in the development of Eq. (1). However, it can be shown mathematically that in the case of co-sorption of two components in the binary mixture, the form of the equation may still remain the same if the concentration of the strong adsorptive species (SO2) is at trace levels, and the pressure-drop in the bed is negligible. The detailed equations to substantiate the above statement are described in Appendix F. 2.2. Mass balance at any location R within the macropore volume of the binder-phase Consider that crystals are uniformly distributed in the binder-phase, as depicted in Fig. 1 and the adsorption of SO2 by the binder-phase is negligible in comparison with that at the crystal outer surfaces (interface between the binder-phase and crystal) [12]. In such case, incorporating radial diffusion within the macro-pore volume of the binder-phase, and adsorption at the pore-mouth of the

@Cp 1 @(R2 NR ) @ q¯ 3(1a) 0  2 R @R @t @t

(5)

The terms in the Eq. (5) are transient, diffusion flux in the radial direction of the binder-phase (pellet), and the rate of adsorption at the pore-mouth (or opening) of the crystals, respectively. Here, a , void fraction of the macro-pores; NR molar diffusion flux in the radial direction of the pellet q concentration of the adsorbate inside the crystal /q ¯ average concentration of the adsorbate inside the crystal

2.3. Adsorption isotherm In the proposed model, a linear isotherm of the form q /KCp is assumed which correlates the adsorbate concentration within the crystal with the gaseous phase concentration within the macro-pore volume of the binder at the crystal /binder-phase interface. Here, K may be considered as the equilibrium or partition coefficient between the macro and micro-pores volume. The isotherm can also be seen as an equilibrium condition obtained by equating first order adsorption and desorption rates: @q

ka Cp kd q where; at equilibrium @t K  ka =kd q=Cp :

(6)

2.4. Mass balance at any location r within the micro-pore of the crystal Mass balance in the crystal is given by the following solid diffusion equation: @q Dc @(r2 @[email protected])  @t r2 @r

(7)

where Dc is the diffusivity of the adsorbate within the crystal. The governing Eqs. (1), (5) and (7) form the basis of the model developed in this study for predicting the adsorbents performance, especially breakthrough characteristics in the bed. As these equations are coupled partial differential equations, independent variables being time (t ), axial (z ) and radial directions (both in r and R ), an approach is adopted in the present work to simplify numerical computations and significantly reduce the CPU time. Essentially, in this approach radial (r and R ) concentration profiles within the solid pores

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(both macro and micro) are averaged assuming parabolic concentration profiles and the average gas phase concentration within the pores of the pellet and the average adsorbate phase concentration within the crystals are determined [13,15]. The salient advantage of this mathematical approximation is the reduction of second order PDEs to first order PDE with variation only in z direction. Moreover, the number of the governing equations to be solved is also reduced to two. The detailed computational steps are described in Appendices B, C, D, E and F. As a consequence of this approximation, the simplified governing equations, one for the gas phase in the bed and the other for the adsorbate in the pellet are obtained as follows: @Cb @t



 @Cp

Vz @Cb eb @z

Dz @ 2 Cb eb @z2





15(1  eb )Km Dp (Cb  Cp )

(8)

eb R2p (Km  5Dp =Rp )

(Cb  Cp )Km

@t (Km  5Dp =Rp )a   27Dc K(1  a) 15Dp  0 R2C R2p

(9)

Eqs. (8) and (9) are the governing equations to predict the breakthrough characteristics of the bi-porous adsorbents like zeolites in a fixed packed bed under isothermal condition. The required initial and boundary conditions for Eq. (8) remain the same as given by Eqs. (2) /(4). The corresponding conditions for Eq. (9) are as follows: t0;

Cp  0

t0;

R 0;

(10) @Cp @R

0

Time

t 

Cb Cb0 t

; C  p

tresidence

Cp Cb0

; tresidence 

1 Vz

;

Distance in axial direction z z l Radius of the pellet

R

R Rp

Introducing these dimensionless variables in governing Eqs. (8) and (9), the following non-dimensionalized form of the equations are obtained: @C b @t

g

g

@C b 1 @ 2 C b  h(C bC p) @z Pe @z2

(12)

1 eb

;

Pe 

eb Vz l Dz

;

15(1  eb )Km Dp l   ; and 5D eb R2p Vz Km  p Rp   Km l 27Dc K(1  a) 15Dp d    5D R2c R2p Vz Km  p a Rp h

(14)

Here, Pe is nothing but the Peclet number, which compares convective flux to that by dispersion in the empty packed bed. h can be construed as the resistance to the overall mass transfer determined by the gas film mass transfer coefficient and macro-pore diffusivity within the pellet. An inspection of the coefficient d reveals that it is a product of two terms. The first term includes the effects of film mass transfer and diffusion within the pellet in the similar manner as in h . The second term includes the effects of adsorption equilibrium and two time-scales of diffusion: one in the macropore and the other within crystal volume. Furthermore, it may also be noted from Eqs. (13) and (14) that for a zeolite pellet to be ‘sink’ for the adsorbing species, the second term must be negative. Thus, for a zeoilte /SO2 system, the above term puts a constraint on, or in other words, defines a upper limit for the value of equilibrium constant K as: KB

C  b

(13)

where, the dimensionless coefficients are defined as:

(11)

The following dimensionless variables were used to make the governing equations dimensionless: Gas concentration

@C p d(C C )0 b p @t

13

15Dp R2c R2p 27Dc (1  a)

(15)

For a given zeolite pellet and the adsorbing gas, the variables on the right hand side of the above inequality are known. Assuming typical values for these variables, Rp /0.5 mm, Rc /2/107 m, Dp /2.0 /106 m2/s, Dc /1/1014 m2/s, and a /0.3, the upper limit of the equilibrium constant K is theoretically calculated to be 26. Eqs. (12) and (13) are the non-dimensionlized forms of the governing equations that were numerically solved to predict breakthrough times in a packed fixed bed consisting of the bi-porous zeolite adsorbents. These equations containing two dependent variables C b and Cp as a function of time and axial location were solved simultaneously by the finite difference formulation using the NAG Fortran library. On a Pentium III machine the CPU time of computation was found to be less than a minute.

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3. Experimental studies 3.1. Experimental set-up The experimental set-up used in the study may be assumed to consist of three sections as schematically described in Fig. 1: (a) gas-mixing section, (b) test section, and (c) analytical section. In the gas-mixing section two electronic mass flow controllers (Model PSFIC-I, Bronkhorst, Netherlands) were used to control and measure the flowrates of SO2 and N2. A mixture of the gases of the desired concentration was prepared by mixing the two individual streams in a gas-mixing chamber (135 mm long and 25 mm I.D.) made of stainless steel tube. The N2 stream was purified using silica gel purifier to remove moisture in the gas. There was a provision of bypassing the gaseous mixture directly to the analytical section for calibration as well as for the measurement of the inlet concentration of the gaseous mixture entering the reactor (test section). The test section consisted of a vertical inconel made reactor (14 mm I.D. /150 mm L) co-axially mounted in a 200 mm long tubular furnace. The top end of the reactor was connected to the gas line using 1/4 in. swage lock fittings and specially mounted unions made of SS. The temperature of the furnace was controlled using a proportional temperature controller (Blue Bell, Mumbai). The temperature in the reactor was measured using a chromel /alumel thermocouple inserted in a S.S thermo well (O.D. 3mm). The effluent gas stream from the reactor was passed to the analytical section. A manometer was also connected to the two ends of the reactor to measure the pressure-drop across the adsorbent bed. The analytical section consisted of a gas chromatography (GC) connected to a data station. A computer was connected to the data station to store the chromatogram and the peak areas. Thermal conductivity detector (TCD) was used to detect and measure SO2 concentration in the products stream. Activation of the zeolite particles was carried out in a vacuum oven. The vacuum was created with the help of a rotary vacuum pump (Lawrence & Mayo, New Delhi). 3.2. Experimental procedure The zeolite materials (type 5A) were obtained in the form of spherical pellets from Merck Co, Germany, comprising of three size ranges: 1.16, 0.80, and 0.16 mm. For these particle sizes, the ratios of the inside diameter of the reactor to the pellet size were calculated to be 12:1, 35:1, and 280:1, respectively. Tien [16] has recommended a minimum ratio of 10:1 to be able to assume the radial dispersion insignificant in a tubular reactor. In a typical test run, the required quantity of fresh zeolites was first activated in the vacuum oven at 100 8C before feeding into the reactor. The choice of activation

temperature is predominantly dependent upon the vacuum used to drive off the moisture and the time for activation or outgassing. With low vacuum, the required temperature can be substantially decreased. Thus, more than one combination of the activation conditions is possible. In the present work, the fresh samples were activated at 100 8C for 4 h in a vacuum oven operated at 100 mm Hg. After a series of trial runs, this combination of activation conditions was found to be satisfactory for the maximum adsorption of SO2 (longer breakthrough time). Similar temperature ranges for activation have also been reported elsewhere [2]. Mesh and quartz wools were put at both ends of the reactor tube so as to prevent any carry over of the adsorbents. The thermo well for holding thermocouple was then placed co-axially in the center of the reactor tube. First, N2 was allowed to pass through the reactor at a desired flow rate controlled by MFC. The reactor was then heated to the desired reaction temperature and further kept at that temperature for 2 h so that the system was stabilized and a uniform temperature existed in the bed. The required flow rate of SO2 was adjusted using MFC. The concentration of the inlet gaseous mixture was measured by GC prior to the start of the reaction through the line bypassing the reactor. The total pre-reaction time included 2 h to pre-heat the bed to the desired temperature and 2 h to stabilize. The reaction time typically varied between 2 and 6 h depending upon the operating conditions including the flow rates and the amount of the adsorbents used. The product gas was analyzed by a GC using Porapak Qcolumn (6 in. /2 mm I.D.) and TCD (Model 5700, Nucon). Table 1 lists the various experimental conditions used in this study on the adsorption of SO2 by 5A zeolites. In the adsorption experiments, the gas superficial velocity in the tubular reactor was chosen between 0.04 and 0.1 m/s, corresponding to the volumetric gas flowrates range from 0.3 to 1.0 slpm. The pressuredrops across the reactor measured under these conditions were found insignificant, varying between 4 and 10 mm of the heights of liquid CCl4 used as the manometer fluid. These values corresponded to the pressures between 60 and 160 Pa only. The maximum pressuredrop measured in the case of powder zeolites (0.16 mm diameter, particle Reynolds number /1, i.e. viscous flowrange) was not more than 6 cm of the liquid (0.937 kPa) at a superficial velocity of 0.1 m/s. This value compares with 0.69 kPa (/1 atm or /100 kPa) as predicted by Ergun’s equation. The difference between the experimental and theoretical values was attributed due to the pressure-drop across the wool meshes supporting the zeolites pellets and that across the reactor fittings. The above pressure-drop measurements justify the assumption of constant pressure in the bed, made in the theoretical analysis.

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4. Results and discussion 4.1. Adsorption temperature for zeolites The tests were carried out on 5A zeolites at various temperatures. Fig. 2 describes the experimentally obtained breakthrough characteristics of SO2 during dynamic adsorption by zeolite carried out at six different reaction temperatures: 35, 50, 60, 80, and 100 8C. The gas flow rate and gas inlet SO2 concentration were kept constant at 300 cm3/min and 10 000 ppm, respectively, under each case. The weight of the test sample was 2.5 gm for the average pellet size of 16 mm. From Fig. 2, it may be observed that there was practically no improvement in the breakthrough time with an increase in the temperature from 35 to 50 8C. In each case the breakthrough occurred in less than 15 min. The total adsorption time (time for the exit gas concentration to approximately reach the inlet concentration, 10 000 ppm) was approximately 30 min. However, the breakthrough and adsorption times were found to considerably increase to 25 and 50 min, respectively, at the bed temperature of 60 8C. Further increase in the temperature to 80 8C resulted in the marginal increase in the breakthrough time. As also observed from the figure, the breakthrough curve shifted to the left as the reaction temperature was increased to 100 8C, indicating an early saturation of the bed. In fact, at temperature as high as 150 8C, the zeolite materials were found to be unsuitable for adsorption as the breakthrough of the bed occurred instantaneously ( B/10 min). This type

Fig. 2. Temperature effects on breakthrough of SO2 over 5A zeolites (w/2.5 g, L/3.5 cm, CSO2 /10 000 ppm, QN2 /300 cm3/min, dp / 1.16 mm).

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of breakthrough characteristic (optimum adsorption at an intermediate temperature) for SO2 over zeolite was observed for all the concentration levels less than 1%. Thus, the adsorption temperature for all test runs hence after in this study was chosen as 70 8C. The model predictions were done under the identical experimental conditions. As described in the section on theoretical analysis, the concentration profiles within the zeolite crystal due to the radial diffusion in the micro-pores of crystals was averaged and the adsorption of SO2 at the interface of the crystals and marco-pores was assumed to be determined by a parameter, called equilibrium constant. This dimensionless constant has been used as an adjustable parameter in the model, wherever necessary, to explain the experimental data. The remaining variables such as the gas film mass transfer coefficient around the pellet, dispersion coefficient in the packed bed and macro-pore diffusivity incorporating Knudsen effects and intra-particle diffusivity were either calculated or estimated based on the typical data reported in the literature [12]. The temperature effects on variation in gas, pore or crystal diffusivities were incorporated, as necessary. Fig. 3 compares the model predicted breakthrough curves with the experimental data. A reasonable good agreement is observed between two results within the experimental and computational errors. The values for equilibrium constant K at 35, 60, and 80 8C were adjusted at 102, 33, and 13, respectively. The decrease in the values of K with increase in the temperature is

Fig. 3. Comparison between model predictions and experimental data: Determination of heat of adsorption for SO2 over 5A zeolites (w/2.5 g, L /3.5 cm, CSO2 /10 000 ppm, QN2 /300 cm3/min, dp /1.16 mm).

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also found to be consistent with an independent equilibrium study [2]. Assuming the Arrhenius type temperature dependence of the equilibrium constant, the exothermic heat of adsorption was calculated to be 9.8 kc/mol as shown in the inset of Fig. 3, which is smaller than that (ca. 12 kc/mol) obtained for the adsorption of lighter hydrocarbons such as propane and butane on 5A zeolite [12]. Table 2 summarizes the values of various variables that were either used in the model, such as crystal radius and crystal diffusivity, or calculated based on the operating conditions, such as mass transfer coefficient, and Reynolds number, corresponding to the experimental operating conditions used in this work. The last column lists the adjusted values of the model parameter K for these conditions to explain the observed breakthrough characteristics of SO2 on 5A zeolites. 4.2. Effect of concentration To observe the effects of SO2 concentration at trace levels on the breakthrough characteristic, the experiments were carried out for varying gas inlet concentrations: 2000, 5000, 7500 and 10 000 ppm; the remaining operating variables (temperature, adsorbent weight and size, gas flowrate) were kept identical in each case. Fig. 4 describes the breakthrough characteristics at these concentrations. As observed from the figure, the breakthrough time considerably decreases from about 3 h to less than 1 h as the concentration increases from 2000 ppm to 1%. As also observed, the decrease in the

Fig. 4. Concentration effects on breakthrough of SO2 over 5A zeolites (w/5.0 g, L/6.5 cm, T /70 8C, QN2 /300 cm3/min, dp /1.16 mm).

breakthrough and adsorption times is relatively larger at higher concentration levels (7500 /10 000 ppm) than lower levels (2000 /7500), indicating the suitability of zeolites in the concentration levels typically less than 1%. The model predictions are observed to be in good agreement with the data under identical conditions. In each case, a marginal change (less than 5%) in the model parameter K (from 30.0 for 10 000 ppm to 31.4 for 2500 ppm) was required to explain the experimentally obtained breakthrough curves, verifying the assumption of the linear adsorption isotherm in this study over the selected concentration range (B/1%). 4.3. Effect of particle size The experiments were carried out for three different particle (pellet) sizes: 0.16, 0.80, and 1.16 mm, under varying gas flow rates and inlet SO2 concentrations. The test samples having a particle size of 0.16 mm were in nearly powdered form, while those having higher size particles were in the spherical pellet forms. The amount of zeolite materials was taken as 5 g in each case. Fig. 5 describes the representative results of the effects of particle sizes on the breakthrough characteristics. In the test run, the inlet SO2 gas concentration and flow rate were kept constant at 10 000 ppm and 300 cm3/min, respectively. As observed from the figure, decrease in the particle size from 1.16 mm (the largest pellet size in this study) to 0.16 mm (the smallest size) resulted in significant increase in the breakthrough and adsorption

Fig. 5. Effects of zeolites particle size on SO2 breakthrough (w /5.0 g, L /6.5 cm, T /70 8C, CSO2 /10 000 ppm, QN2 /300 cm3/min).

A. Gupta et al. / Chemical Engineering and Processing 43 (2004) 9 /22

times. In fact, in the latter case, the breakthrough occurred in approximately 2 h. For an intermediate particle size of 0.80 mm, the breakthrough and saturation times were observed to be approximately 70 and 120 min, respectively. The noticeable characteristic of the breakthrough responses, especially for the small size particles (nearly powdered form) was the abrupt increase in the concentration levels following the breakthrough of the bed. These effects have again been discussed in the later section of this paper. The BET area measurements were made use along with the model predictions to explain the observed superior performance of the relatively smaller size zeolite materials in this study. The larger size pellets (1.16 and 0.8 mm) were found to have BET area in the range of 170/200 m2/g, while the powdered materials had lower BET area (/70 m2/g). Despite this the increased breakthrough time in the case of smaller size pellets was attributed due to the significant increase in the gas film mass transfer coefficient and interfacial surface area. As observed from Table 2, the mass transfer coefficient for the 0.16 mm zeolite particle was calculated to be 0.45 m/s in comparison with 0.075 m/s for 1.16 mm size particle under the identical gas superficial velocity. With the increase in mass transfer co-efficient due to smaller particle radius, the amount of gas or the flux of SO2 (mol/m2 s) diffusing into the adsorbents increased. This, in turn, resulted in higher adsorption rate. As the particle radius was decreased for the same amount of adsorbent the interfacial area per unit volume (a*) also increased. Hence, there was a combined effect of mass transfer rate as well as the interfacial area per unit volume on the total SO2 flux entering the pores of the pellet, resulting in increased adsorption and breakthrough time. Here, it is essential to point out that relatively longer breakthrough time reflects the comparatively superior performance of the adsorbents. However, the similar inference cannot be made for the shorter breakthrough time observed during adsorption. The latter situation may be consequence of either diffusion controlled adsorption or significantly high reactivity (favorable adsorption isotherm) of SO2 with the adsorbents resulting in immediate saturation of the bed. From Eqs. (12) and (13) it may be seen that a number of phenomenological effects including diffusion within the micro and macro-pores of bi-disperse zeolites materials, and dynamic adsorption/desorption at the crystal /binders interface simultaneously take place. The response of an initial clean bed (i.e. free of adsorbate) to an influent containing an adsorbate has a complex dependence on these effects, in addition to the relative size of crystal to that of a pellet. The following section illustrates the relative importance of these effects in interpreting the breakthrough characteristics obtained during adsorption/desorption of SO2 over zeolites.

17

4.4. Model parametric study There are three resistances to mass transfer as postulated in the model analysis: (1) in the gas film surrounding the pellet (2) within the macro-pore volume (binder-phase), and (3) within the micro-pore volume (crystal volume), characterized by mass transfer coefficient Km, characteristic times of diffusion tp (R2p /Dp) and tc (R2c /Dc), respectively. The first two resistances may considered to be in series as they appear as a sum in both the coefficients h and d of Eq. (14). On the other hand, the effect of the crystal diffusional resistance on adsorption may be ascertained only in comparison with the macro-pore diffusional resistance, as is evident from the expression for d. The quasi-steady state adsorption/ desorption at the crystal /macro-pore interface, characterized by the equilibrium constant K may be considered to be affecting or modifying the characteristic time of crystal diffusion tc. As also seen from the set of governing equations, the adsorbent BET area, Sg does not appear explicitly; however, it has the direct bearing on the macro-pore radius, rpore through the intra-particle porosity and bulk density as, rpore /2a / Sgrb. The pore radius rpore, in turn, determines the macro-pore diffusivity, Dp and, therefore, tp. Fig. 6 describes the comparative effects of gas film transfer and intra-particle diffusion. The simulated conditions including the adsorber’s geometrical dimensions are shown on the figure. The adsorbent particles radius was set at 4.16 mm, which gave a ratio of 12:1 for

Fig. 6. Comparative effects of gas mass film mass transfer and macropore diffusion on SO2 breakthrough (Rp /4.16 mm, Km / 0.0074 m/s, K/133; T/30 8C, CSO2 /10 000 ppm, QN2 /300 cm3/ min, w/1 kg, L /1.9 m, I.D./0.05 m).

18

A. Gupta et al. / Chemical Engineering and Processing 43 (2004) 9 /22

the bed id to the particle radius. The gas film mass transfer coefficient under the prevailing flow conditions in the bed was calculated to be 0.0074 m/s. The simulations were carried out for different BET areas (15 /215 m2/g) so as to obtain varying values of pore diffusivity, Dp and hence, those of KmRp/5Dp from a low value of approximately 1 to a high value of 42. The numerical values of equilibrium constant K , crystal radius Rc and crystal diffusivity Dc were chosen such that both terms in the second product term of Eq. (14) had the same order of magnitude. In other words, the effects of both crystal diffusion and macro-pore diffusion were considered in each of the cases simulated. As observed from the plots on Fig. 6, the breakthrough of the adsorber bed occurs in a relatively shorter time (less than 10 min) in all the cases for which the value of KmRp/5Dp was less than 35, suggesting that the adsorption was controlled by the gas film mass transfer in these cases. As a consequence, insignificant amount of the adsorbate (SO2 flux in this case) reached the adsorbents surface resulting in immediate breakthrough of the bed and, therefore, shorter adsorption time. The breakthrough times appreciably improved as the ratio of KmRp to 5Dp was increased to 40 and greater, suggesting that the resistance to the gas film mass transfer gradually diminished and the adsorption became independent of the film resistance. In such cases the adsorption was controlled by macro-pore diffusion. In fact, for KmRp/5Dp /42 a typical ‘S’ type of sigmoidal curve was obtained with breakthrough and adsorption times of approximately 50 and 150 min, respectively. It may be pointed out that the identical simulated adsorption profiles were obtained if the pellet size was varied instead and the BET area of the adsorbents (or pore diffusivity Dp) kept constant so that the numerical values of the above ratio remained the same as before. For the sake of brevity, these results are not produced here. Fig. 7 describes the simulations results for the similar scenario (comparative effects of two resistances), however, for the smaller size particle (Rp /0.186 mm). The mass transfer coefficient in this condition was calculated to be 0.102 m/s, an increase of almost two orders of magnitude from the previous case. The values of pore diffusivity were accordingly adjusted through the BET areas so as to get the ratios of two effects approximately in the same range as before. As observed from the figure, the effects of gas film mass transfer relative to that of macro-pore diffusion on the breakthrough characteristic are identical as in the previous case (Fig. 6), except the rise in the concentration levels following the breakthrough are relatively sharper. These profiles are also characteristically similar to those observed in the test runs for smaller size particles (powdered form). The comparative effects of macro-pore and crystal diffusion are described in Fig. 8. The simulations were

Fig. 7. Comparative effects of gas film mass transfer and macro-pore diffusion on SO2 breakthrough (Rp /0.186 mm, Km /0.102 m/s, K / 133; T/30 8C, CSO2 /10 000 ppm, QN2 /300 cm3/min, w /1 kg, L /1.9 m, I.D./0.05 m).

Fig. 8. Comparative effects of macro-pore and crystal diffusion on SO2 breakthrough (Rp /0.186 mm, Km /30 m/s, K/13; T /30 8C, CSO2 /10 000 ppm, QN2 /300 cm3/min, w/1 kg, L /1.9 m, I.D./ 0.05 m).

carried out for varying ratios of tc and tp. In the expression for d , i.e. Eq. (14), by setting the value of K at 13 and a at 0.3, it can be shown that for the macro-

A. Gupta et al. / Chemical Engineering and Processing 43 (2004) 9 /22

pore diffusion effects to be negligible in comparison with those of crystal diffusion, tc/16tp /1. This is also consistent with the imposed constraint that d must be negative for the adsorption by the zeolite particles. The different values of tc/16tp were obtained by assuming various values for the adsorbent BET area, which determined the pore diffusivity Dp and the corresponding characteristic time of pore diffusion tp. In all these simulated cases, the ratio KmRp/5Dp was calculated to be at least 30, implying that the adsorption was not controlled by the gas film mass transfer. As observed from the figure, the adsorption remained relatively insignificant so long the value of tc/16tp was greater than 2. In each of these cases, the breakthrough occurred in less than 10 min suggesting that the adsorption remained crystal or micro-pore diffusion controlled. The adsorption increased significantly in the cases for which the above values were adjusted to approximately 1 or lower. In such cases both macroand micro-pores diffusion were relatively important and as a consequence, the breakthrough times improved significantly. It may be re-emphasized that due to the assumption of a quasi (pseudo) steady-state adsorption/ desorption at the interface of crystals and binder-phase, the effect of K is essentially to modify the characteristic time of diffusion within the crystals. In other words, Eq. (14) can also be written as   Km l 27 15 d    5D t? t?p Vz Km  p a c Rp where t? may be considered as an effective time of crystal diffusion. Therefore, for the maximum adsorption by the zeolites pellets, the adsorbate’s diffusivity within the crystals is required to be relatively significant, i.e. higher value of t c?. Since d assumes a negative value during adsorption, the effective macro-pore diffusivity is also required to be higher in the same proportion. The simulation results on Fig. 8 have illustrated these remarks.

5. Conclusion A dynamic adsorption/desorption study was carried out on the removal of trace SO2 (B/1% volume concentration) on zeolites. The breakthrough curves were experimentally obtained under several operating conditions, including temperature, gas concentration, and particle size. The maximum adsorption of SO2 was observed at a reaction temperature of around 70 8C. The performance of the zeolites materials in the powdered form was found to be superior, in terms of breakthrough times, to that for relatively larger size pellets, although the breakthrough curves for smaller

19

size particles were observed to be steep. The adsorption isotherm assuming first order adsorption and desorption rates with respect to the gas and adsorbate phase concentrations was found to be linear in the concentration range (1000 /10 000 ppm) studied in this work. The equilibrium constant at 70 8C and exothermic heat of adsorption were determined to be 30 and 10 kcal/mol, respectively. A mathematical model for the zeolites particles assuming biporous structures was developed to predict the breakthrough profiles under varying operating conditions. With the help of the model, the dynamic adsorption of SO2 was explained by the combined effects of gas film mass transfer, diffusion in the macro-pores and within the crystals of the zeolites pellet. These effects were mathematically represented by two dimensionless variables, h and d, in the proposed model. An upper limit for the adsorption equilibrium constant was theoretically obtained in terms of the physical characteristics of the zeolites pellet and crystals as, KB

15Dp R2c R2p 27Dc (1  a)

:

The model simulation results were successfully validated with the experimental data.

Appendix A: Nomenclature a external surface area per unit volume of the particle (m2/m3) C concentration of reactant gas (mol/m3) D diffusion co-efficient of reactant gas (m2/s) k adsorption or desorption rate constant (1/s) K equilibrium constant/partitioning coffecient (dimensionless) Km average mass transfer co-efficient (m/s) L length of the packed bed (m) M molecular weight (kg/kg mol) N flux, (mol/m2 s) Q flow rate (slpm) q concentration of the adsorbate inside the crystal (mole/m3) /q ¯ volume-averaged concentration over the crystal (mol/m3) ¯ volume-averaged concentration over the entire /q pellet (mol/m3) r radial co-ordinate in the crystal (m) R radial co-ordinate in the particle (m) Rp pellet radius (m) Sg BET area (m2/g) t time (s) T temperature (8C) V superficial velocity (m/s) Z axial position in the packed bed (m)

20

A. Gupta et al. / Chemical Engineering and Processing 43 (2004) 9 /22

Subscript a adsorption b bed c crystal d desorption k Knudsen m molecular p pore or pellet z axial location or dispersion in the packed bed

ing the parabolic concentration profiles q (r ), the solid diffusion Eq. (7) leads to the following LDF approximated equation (Yang et al., 1997): @ q¯ 15Dc  (q½rRc  q) ¯ @t R2c

Taking the volume /average of Eq. (21) over the entire pellet, the following equation is obtained: @ q¯ 15Dc ¯  (q½rRc  q) @t R2c

Superscript * dimensionless variables

q¯½rRc KCp

The detailed computational steps involved in the simplification of the governing equations Eqs. (1), (5) and (7) to obtain Eqs. (8) and (9) are as follows: (1) First, the particle volume averaged quantities in the pores and within the crystals are calculated: R3p

g

2

Cp R dR;

q ¯

3 R3c

g

2

qr dr

(16)

@Cp @t



3 Rp

NR½RR 3(1a) p

@q @t

0

(17)

where, q¯/ /averaged concentration of the adsorbate over the entire pellet and defined as: ¯ q

3 R3p

g qR¯ dR 2

(18)

In the integration of Eq. (5), the following boundary conditions were used: NR /0 at R /0, due to symmetricity. At the surface (R /Rp), the diffusion flux into or out of the pores: NR½RR  Km (Cb Cp½RR ) p

p

(19)

(3) Parabolic concentration profiles were assumed within the pore volume of the pellet and crystals as follows: Cp C DR2

and

qABr2

3 q¯ A BR2c 5

3 Cp C  DR2p 5

(24)

From Eq. (20) the concentration at R /Rp is evaluated as: Cp½RRp C DR2p

(25)

Combining Eqs. (23) /(25) C and D are calculated as:

(2) By integrating Eq. (5) with respect to R and using the volume averaged quantities the following equation is obtained: a

(23)

The volume-averaged concentrations q¯ over the crystal and Cp is obtained by averaging Eq. (20) and using Eq. (16):

Appendix B

Cp 

(22)

where, qjrRc is in equilibrium with Cp at location R in the pellet. (5) Averaging Eq. (6), the adsorption isotherm is rewritten as:

Greek symbols eb bed porosity (dimensionless) a intra-particle porosity (dimensionless) rb bulk density of zeolite (kg/m3) t tortuosity factor (dimensionless)

3

(21)

(20)

(4) This has been mathematically shown that assum-

D C

5 2R2p  5 2

[Cp½RRp Cp ] 3

Cp  Cp½RRp 2



(26)

Substituting the values of C and D in Eq. (20), an expression for the average gas phase concentration in the pore is obtained as:   5 3 5 [Cp½RRp Cp ]R2 (27) Cp  Cp  Cp½RRp  2 2 2R2p (6) Equating radial diffusion flux (concentration gradient) at the pellet surface calculated from Eq. (27) with that from Eq. (19), the gas phase concentration at the surface of the pellet is obtained as: Cp½RRp 

(Km Cb  5Dp =Rp Cp ) (Km  5Dp =Rp )

(29)

Similarly, substituting Eq. (20) in Eq. (23), and identically comparing term by term, A and B are evaluated as follows:

A. Gupta et al. / Chemical Engineering and Processing 43 (2004) 9 /22

A K K B

 5 2

Cp 

5 2R2p

3 2

Cp½RRp



[Cp½RRp  Cp ]R2

the zeolites pellet is given by a combination of both Knudsen (Dk) and molecular (Dm) diffusivities as: (30)

Once the values of A , B , C , and D are obtained, an expression for the average adsorbate concentration q¯ and that for @q/@t can be expressed in terms of Cb and Cp as follows: ¯ q @ q¯ @t

5



[8Cp 3Cp½RRp ] 9Dc KKm

R2c (Km

 5Dp =Rp )

(31) (Cb Cp )

(32)

Finally, by expressing the average adsorbate phase concentration in terms of the bulk gas phase and average gas phase concentration in the macro-pore, the simplified forms of Eqs. (7) and (8) are obtained.

Appendix C The axial dispersion co-efficient in the packed bed, Dz is expressed in terms of Peclet number defined as, Pe / 2Rpm /Dz r . The Peclet numbers are correlated with particles Reynolds and Schmidt numbers through one of the empirical correlations as follows [13]: 1 0:3 0:5   Pe Re  Sc 1  3:8=(Re  Sc) for 0:008B ReB 400 and 0:28BSc B2:2

Appendix D The mass transfer co-efficient Km in the packed bed is calculated using the following correlation for Sherwood number defined as, Sh /2KmRp/Dm [13]: Sh 2:01:1(Sc)0:33 (Re)0:6

Appendix E The effective diffusivity inside the pores is determined using the formula: Dp 

1 D

R2c

K

21

Da t

The combined diffusivity, D inside the macro-pores of



1 Dk



1 Dm

where, Knudesn diffusivity is given as, Dk(m2/s) / 97xRpore (m)[T /M ]1/2.

Appendix F A general mass balance for A (SO2) in the bed will yield the following equation:   @CA @(uCA ) @q o (1o) A 0  @z @t @t An identical equation can be written for B (N2). Assuming that (a) the linear adsorption isotherms for both species A and B are non-interfering: qA /KA CA and qB /KB CB , and (b) the mole-fraction of B is approximately 1, as A is at ppm levels (less than 1%), the above equation(s) can be recast in terms of total pressure P as:   @(PY ) @(uPY ) @(PY ) e  (1e)KA 0 @t @z @t and,   @P @(uP) @P o  (1o)KB 0 @t @z @t . Here, Y is the mole-fraction of SO2. Thus, assuming negligible pressure-drop in the bed and also, insignificant variation with time in the total pressure P during adsorption, it is trivial to show from the last equation that the flow velocity also remains the same along the bed length, i.e. @u/@z/0. As a consequence, the above species balance equation for A in the case of co-sorption of A and B is reduced to the identical form as in Eq. (1).

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