Modeling of the fixed - bed adsorption of carbon dioxide and a carbon dioxide - nitrogen mixture on zeolite 13X

THERMODYNAMICS

Modeling of the fixed-bed adsorption of carbon dioxide and a carbon dioxide- nitrogen mixture on zeolite 13X

T. L. P. Dantas^I,III,*; F. M. T. Luna^II; I. J. Silva Jr.^II; A. E. B. Torres^II; D. C. S. de Azevedo^II; A. E. Rodrigues^III; R. F.P.M. Moreira^I

^IFederal University of Santa Catarina, Department of Chemical and Food Engineering, Laboratório de Energia e Meio Ambiente (LEMA), Phone: + (55) (48) 33319448, Ext. 211, Fax: + (55) (48) 33319687, Campus Universitário, Trindade, P.O. Box 476, 88040-900, Florianópolis-SC, Brazil

^IIFederal University of Ceará, Department of Chemical Engineering, Grupo de Pesquisa em Separações por Adsorção, (GPSA), Phone: + (55) (85) 3366-9611, ext. 28, Campus do Pici, 60455-760, Fortaleza-CE, Brazil. E-mail: [e-mail]; [e-mail]; [e-mail]; [e-mail]

^IIIUniversity of Porto, Faculty of Engineering, Department of Chemical Engineering, Laboratory of Separation and Reaction Engineering (LSRE), Associate Laboratory LSRE/LCM, Phone: [phone], Fax: [phone], Rua Dr. Roberto Frias s/n, P.O. Box 4200-465, Porto-Portugal. E-mail: [e-mail]

ABSTRACT

In this study, the fixed-bed adsorption of carbon dioxide and a carbon dioxide-nitrogen mixture on zeolite 13X was investigated. The adsorption equilibrium and breakthrough curves were determined at different temperatures-301-306 K, 323 K, 373 K and 423 K. A model based on the LDF approximation for the mass transfer, considering the energy and momentum balances, was used to describe the adsorption kinetics of carbon dioxide and a carbon dioxide-nitrogen mixture. The model acceptably reproduced all of the breakthrough curves and can be considered as adequate for designing a PSA cycle to separate carbon dioxidenitrogen mixtures.

Keywords: Adsorption; Carbon dioxide; Nitrogen; Zeolite 13X; Modeling.

INTRODUCTION

The emission of CO₂ from power plants that burn fossil fuels is the major reason for the increase in the concentration of this gas in the atmosphere. The amount of carbon dioxide in the atmosphere is currently increasing globally by around six billion tons per year (Zhao et al., 2007).

The capture and storage of carbon dioxide is a technically feasible method of making significant reductions in carbon dioxide emissions. Capturing carbon dioxide involves separating the CO₂ from other flue gases. The technological advances that are being developed around the world capture carbon dioxide from flue gases by using different schemes: postcombustion, pre-combustion and oxy-fuel processes.

Several studies have been conducted worldwide in the field of CO₂ capture by adsorption, indicating that this technique is attractive as a post-combustion treatment of flue gas. Strategies like PSA (pressure swing adsorption) and TSA (temperature swing adsorption) processes have been proposed and investigated for adsorption in a cyclic process (Cavenati et al., 2006; Chou and Chen, 2004; Gomes and Yee, 2002; Grande and Rodrigues, 2008). Pressure swing adsorption technology has become an interesting alternative due to low energy requirements and cost advantages. The PSA processes can be operated at high temperatures and overcome the need to cool the fuel gas to ambient temperature prior to the removal of carbon dioxide (Gaffney et al., 1999).

The capture of carbon dioxide by adsorptive processes is mainly based on preferential adsorption of this gas on a porous adsorbent. Thus, the first and most important step is to find a suitable adsorbent. In industrial processes, zeolite 13X is frequently used as an adsorbent due to its high adsorption capacity (Lee et al., 2002; Siriwardane et al., 2001). For any such case, the basic information required is the adsorption equilibrium behavior of the pure components, in this case carbon dioxide. The design of a PSA system also requires the development of a model that can describe the dynamics of the adsorption on a fixed-bed with the selected adsorbent.

In this study, the adsorption of carbon dioxide and a carbon dioxide-nitrogen mixture on zeolite 13X packed in a fixed-bed was studied. The Linear Driving Force (LDF) model, considering the energy and momentum balances, was used to describe the kinetics of the carbon dioxide and the carbon dioxide-nitrogen mixture adsorption on zeolite 13X.

EXPERIMENTAL SECTION

The gases used for the carbon dioxide breakthrough curves were provided by White Martins S.A/Brazil: Helium 4.5 (99.99%) and standard mixtures of carbon dioxide/helium (20% CO₂/He v/v) and carbon dioxide/nitrogen (20% CO₂/N₂ v/v). Pure CO₂ (99.99%) and N₂ (99.995%) were supplied by Air Liquid S.A. (Portugal). The adsorbent used was zeolite 13X (TradeShinli, China) and its characterization (BET area, pore size distribution and micropore volume), as well as information on the adsorption equilibrium of the pure carbon dioxide and pure nitrogen components, have been reported in a previous study (Dantas et al., 2008).

Fixed-Bed CO₂ and CO₂/N₂ Mixture Adsorption

The experimental breakthrough curves were obtained by passing the appropriate gas mixture (20% CO₂/He v/v or 20% CO₂/N₂ v/v) through the column packed with zeolite 13X. The solid adsorbent was pre-treated by passing helium over it at a flow rate of 5x10^{- 7} m³.s^{- 1} at 593K for 2 hours. These breakthrough curves were obtained at 301K, 323K, 373K and 423 K. The total gas flow rate was maintained at 5x10^-7 m³.s^{- 1} for the CO₂ breakthrough curves and at 10x10^{- 7} m³.s^{- 1} for the CO₂/N₂ breakthrough curves. The reversibility of the adsorption was studied in desorption experiments by passing pure helium through the packed column at a total flow rate of 5x10^{- 7} m³.s^{- 1}. The gas flow was controlled by a mass flow unit (Matheson, USA). A Model CG35 gas chromatograph (CG Instrumentos Científicos, Brazil) equipped with a Porapak-N packed column (Cromacon, Brazil) and with a thermal conductivity detector (TCD) was used to monitor the carbon dioxide and nitrogen concentration at the bed exit, using helium as the reference gas. The column was located inside a furnace with controlled temperature. The experimental system (column and furnace) was considered to be adiabatic because it was isolated with a layer of 0.10 m of fiberglass and with a refractory material. The properties of the adsorbent and of the fixed-bed are given in Table 1.

Fixed-Bed CO₂ Adsorption from a CO₂/N₂ Mixture in a Nitrogen-Saturated Fixed-Bed

The solid adsorbent was previously treated by passing nitrogen over it at a flow rate of 1.67x10^{- 5} m³.s^{- 1} at 593K for 12 hours. After this pre-treatment, the temperature of the fixed bed was adjusted to the desired value (306 K, 323 K, 373 K or 423 K) under a N₂ atmosphere. The CO₂/N₂ mixture (10% CO₂/N₂ v/v) was then fed to the column at a total gas flow rate of 3.5x10^{- 5} m³.s^{- 1}. The gas flow was controlled by mass flow controllers (Teledyne Brown Engineering, USA). At the end of the column, the carbon dioxide concentrations were periodically analyzed using a GA-40T Gas Analyzer (Madur Electronics, USA). The temperature inside the column was continuously monitored using a K-thermocouple placed at 0.17 m and 0.43 m from the bottom of the column. The column was located inside a convective furnace and thus the system was considered to be non-adiabatic. The characteristics of the fixed bed and the column are presented in Table 2.

MODEL DESCRIPTION

The model used to describe the fixed-bed dynamics was derived from the mass balance taking into account the energy balance. For the model used to describe the fixed-bed dynamics of the adsorption of the CO₂/N₂ mixture and of CO₂ from the CO₂/N₂ mixture in a nitrogen-saturated fixed-bed, the momentum balance was also considered. The model was based on the following assumptions:

(i) The flow pattern is described by the axially dispersed plug flow model;

(ii) The mass transfer rate is represented by a linear driving force (LDF) model;

(iii) The gas phase behaves as an ideal gas mixture; and

(iv) Radial concentration and temperature gradients are negligible.

With these assumptions, the fixed-bed model is described by the following equations (Eq. 1-7). The mass balance for each component is given by Eq. (1) (Ruthven, 1984):

where ε is the bed porosity, C_i is the concentration of component i in the gas phase, D_L is the axial dispersion coefficient, u is the superficial velocity, and ρ_p is the particle density. The rate of mass transfer to the particle for each component is given by Eq. (2):

where K_L is the LDF overall mass transfer coefficient, q_i* is the adsorbed equilibrium concentration, i.e., q_i* =f(C_i) given by the isotherm, and is the average adsorbed concentration. The total concentration C is given by:

where P is the total pressure, T_g is the gas phase temperature and R is the universal gas constant. The Ergun equation considers the terms of the pressure drop and velocity changes:

where µ_g is the gas phase viscosity, ρ_g is the gas phase density and d_p is the particle diameter.

The energy balance is:

where C_g is the molar specific heat of the gas phase, λ_L is the axial heat dispersion coefficient, C_s is the solid specific heat, (-ΔH_i) is the adsorption heat for the i^th component at zero coverage, h_w is the internal convective heat coefficient between the gas and the wall, d_int is the bed diameter, and T_w is the wall temperature. The solid phase energy balance is expressed by:

where h_f is the film heat transfer coefficient between the gas and the adsorbent. For the column wall, the energy balance can be expressed by:

where ρ_w is the column wall density, C_p,w is the column wall specific heat, α_w is the ratio of the internal surface area to the volume of the column wall, α_wl is the ratio of the logarithmic mean surface area of the column shell to the volume of the column (Da Silva and Rodrigues, 2002), U is the overall heat transfer coefficient between the column wall and the external air, and T_∞ is the furnace

external air temperature.

For an adiabatic system, the last term of Eq. (7) must not been considered. The boundary conditions are the following:

The initial conditions for the adiabatic system are:

The initial conditions for the non-adiabatic system are the following:

The mathematical model was solved with the commercial software gPROMS (Process System Enterprise Limited, UK), which uses the method of orthogonal collocation on finite elements for resolution. The bed was divided into fifty sections with three collocation points for each element of the adsorption bed.

Estimation of the Model Parameters

According to Ruthven and Farooq (1993) and Sircar and coworkers (1999), the kinetics of the diffusion of nitrogen into zeolite 13X is controlled by molecular diffusion in the macropores. In this study, it was considered that the diffusion of both nitrogen and carbon dioxide into the zeolite 13X is controlled by molecular diffusion in the macropores. In fact, when the LDF overall mass transfer coefficient was evaluated considering micropores, macropores and Knudsen diffusion, the fitting of the model to the experimental data was not satisfactory (Dantas, 2009).

The LDF overall mass transfer coefficient is related to the effective diffusivity of the macropore molecular diffusion-controlled system by the following relationship:

where r_p is the particle radius, ε_P is the particle porosity, τ_P is the particle tortuosity, q₀ is the value of q (concentration at the solid phase) at equilibrium with C_o (adsorbate concentration in the feed at feed temperature T_i ) expressed in the appropriate units. The q₀ value was determined by using the apparent Henry constant in the low pressure region, since Eq. 15 is appropriate when the adsorbent operates within Henry's law. The molecular diffusivity ( D_m,i ) is evaluated from the Chapman-Enskog equation. A particle tortuosity ( τ_p ) of 2 was assumed and a value of 0.37 for the particle porosity was used (Cavenati et al., 2004).

The axial dispersion coefficient was evaluated using the correlation of Wakao and Funazkri (1978):

where ε is the term corresponding to the stagnant o contribution to axial dispersion. For low Reynolds numbers, the value of this term has an important effect on the fixed-bed dynamics. For Reynolds numbers lower than 1 (Re < 1), a value of 0.23 was used for this term and, for higher Reynolds numbers (Re > 10), a value of 20 was used for this term. These values are consistent with those previously observed by other authors who used this correlation to model a fixed-bed adsorption process in the gas phase with similar Reynolds numbers (Cavenati et al., 2006; Delgado et al., 2006).

The gas phase viscosity was estimated from Wilke's equation (Bird, 1060). The mass and heat transport parameters were estimated according to correlations reported in the literature (Bird, 1960; De Wash and Froment, 1972; Incropera and De Witt, 1996). The correlations used to evaluate the mass and heat transport parameters are summarized in Table 3. The values for some of the physical and transport properties of the gas phase, used for the calculation of the breakthrough simulation parameters, are shown in Table 4.

RESULTS AND DISCUSSION

Adsorption Equilibrium of Carbon Dioxide and Nitrogen

The basic information required to describe the fixed-bed dynamics of the adsorption of carbon dioxide and a carbon dioxide-nitrogen mixture is the adsorption equilibrium behavior of the single components. The adsorption equilibria of the pure components on the zeolite 13X used in this study have been previously reported (Dantas, 2009). The CO₂ and N₂ adsorption equilibrium data were fitted using the Toth model (Eq. (17)) (Toth, 1971; Do, 1998) and the temperature dependence of the equilibrium was described according to the Van't Hoff equation (Eq. (18)).

In this study, the adsorbed equilibrium concentration of carbon dioxide on zeolite 13X was estimated as a function of the feed concentration from a mass balance in the fixed bed. For each experimental breakthrough curve, the adsorbed equilibrium concentration is given by:

where C_F is the feed concentration, V is the bed volume, Q_F is the feed volumetric flow rate and t_st is the stoichiometric time given by: o equilibrium concentrations of nitrogen could not be measured due to the very fast breakthrough time, which generates large errors in the adsorbed equilibrium estimates.

The resulting adsorbed equilibrium concentrations are given in Table 5. The differences between some of the values are attributed to the different methodologies used. It can be observed that the zeolite 13X adsorption capacity for CO₂ in the CO₂/He and CO₂/N₂ mixtures is very close to that predicted by the Toth isotherm using the fitting parameters previously reported (Dantas, 2009). This is to be expected if the active sites for N₂ and CO₂ are independent. The amount of CO₂ adsorbed predicted by the multicomponent Toth isotherm has a higher deviation (28.58%) than that predicted by the pure gas Toth isotherm (14.53%).

Thus, the pure component equilibrium isotherms predicted very well the equilibrium of each component in the CO₂/N₂ mixture. Moreover, this solid adsorbed carbon dioxide to its total capacity. This assumption agrees with Siriwardane and coworkers (2001), who observed the same results for adsorption of CO₂/N₂ mixtures on 13X zeolite. Table 6 shows the equilibrium parameters of the Toth model for carbon dioxide and nitrogen adsorption on zeolite 13X.

Breakthrough Curve Modeling

Fixed-Bed CO₂ Mixture Adsorption

For the carbon dioxide breakthrough curves, a set of experiments was performed changing the initial temperature of the bed (runs 1 to 4) and the results were simulated using the model described above. Because the feed consists of a small concentration of a single adsorbable component (carbon dioxide), the velocity through the bed was considered to be constant. As mentioned previously, the system was also considered to be adiabatic. Figure 1 shows a comparison between the experimental and theoretical curves obtained for CO₂ adsorption on zeolite 13X under the conditions of runs 1 to 4. It can be observed that, when the temperature is increased, the carbon dioxide breakthrough times are shorter due to the exothermic nature of the adsorption. It was also observed that the simulated curves reproduce adequately the experimental data for the different feed concentrations and temperatures studied, suggesting that the assumptions on which the model is based could be valid for this system. The LDF overall mass transfer coefficients calculated and used in these simulations are shown in Table 7.

The simulated temperature profiles at the end of the bed are shown in Figure 2 for the conditions of run 1 and run 4 where the large and small temperature peaks are expected. It can be observed that the temperature peaks are very large. In Figures 2 (a) and 2 (b), the temperature peaks correspond to the differences of around 35 K and 5 K, respectively. This is due to the high heat of adsorption for carbon dioxide on zeolite 13X and heat effects during the adsorption process must therefore be considered.

Fixed-Bed CO₂/N₂ Mixture Adsorption

Figure 3 shows a comparison between the experimental and theoretical curves obtained for N₂ and CO₂ adsorption on zeolite 13X under the conditions of runs 5 to 8. In Table 7 is possible to observe the LDF Figure 3 shows a comparison between the overall mass transfer coefficient used for these carbon experimental and theoretical curves obtained for N₂ and dioxide and nitrogen breakthrough curves.

The model reproduces very well all of the breakthrough curves, for all feed concentrations, including the experimental breakthrough curves obtained for nitrogen. It was observedthat the adsorbent is very selective toward carbon dioxide, as shownby the difference between the breakthrough times. Aspreviously stated, the theoretical curves for CO₂ and N₂ adsorption on zeolite 13X were simulated by considering the Toth equation for the pure components to describe the equilibrium. The simulation results show that the zeolite 13X capacity for CO₂ adsorption isnotaffected by the presenceof N₂.These results are in line with the observations reported byGoj et al. (2002) obtained by molecular simulation and by Harlick and Tezel(2003). The observations showedmixture isothermsin which the amount of CO₂ adsorption is almost unchanged from the analogous single component isotherm. These results are attributed to the lateral interactions between carbondioxide molecules due to their higher quadrupole moment (Delgado et al., 2006).

Figure 4 shows the simulated temperature profile for the carbon dioxide/nitrogenmixture adsorption on zeolite 13X, at the end of column, under experimental conditionsof temperature of301 K (run 5). The temperature peak correspond toa differencearound 30K, very similar to the temperature peak observed for the CO₂ adsorption only. In the inset, it is possible toobserve that there is a first temperature peakat the beginning of the adsorption. This is to be expected, since, at the beginning, there is also nitrogen adsorption.

Fixed-Bed CO₂ Adsorption from a CO₂/N₂ Mixture in a Nitrogen-Saturated Fixed-Bed

A set of experiments was performed changing the initial temperature of the bed to obtain the breakthrough curves of CO₂ adsorption from CO₂/N₂ mixtures on zeolite 13X in a nitrogen-saturated fixed bed (runs 9 to 12). Figure 5 shows the experimental and simulated breakthrough curves for the CO₂ adsorption. The model was suitable for describing the dynamics of CO₂ adsorption. The LDF overall mass transfer coefficient used to simulate these breakthrough curves can be seen in Table 7.

The system is non-adiabatic and a variation in the fluidphase temperature was noted during the adsorption (Figure 6) at the differential positionof 0.17 m for run 9. The temperature peak is high, even considering that in this system there is a contribution from nitrogen desorption. This is because zeolite 13X is very selective toward carbondioxide; there is a largedifference between the heat ofadsorptionof carbon dioxide and ofnitrogenon thisadsorbent and the presence of nitrogen does not affect the CO₂ adsorption. Moreover, the thermal effects must be considered for all of the CO₂ adsorption systems discussed herein.

CONCLUSIONS

In this study, the fixed-bed adsorption of carbon dioxide on zeolite 13X was investigated. A model based on the LDF for the mass transfer, considering the thermal effects, was able to suitably describe the carbon dioxide breakthrough curves.

The fixed-bed adsorption of carbon dioxide from CO₂/N₂ mixtures on zeolite 13X was also studied. The adsorption dynamics were investigated at several temperatures and under different conditions: considering N₂ adsorption and desorption. It was demonstrated that zeolite 13X adsorbed carbon dioxide and nitrogen to its total capacity and, thus, the equilibrium of CO₂ and N₂ adsorption for CO₂/N₂ mixtures can be very well described by the pure component adsorption isotherms. A model based on the LDF for the mass transfer, considering the energy and momentum balances, was able to describe adequately the adsorption kinetics of carbon dioxide and nitrogen.

The LDF overall mass transfer coefficient was related to the effective diffusivity for a macropore molecular diffusion-controlled system. The zeolite 13X used in this study has high selectivity for CO₂ and it is suitable for CO₂/N₂ separation processes. The model proposed here can be used to design a PSA cycle to separate CO₂/N₂ mixtures, where pressure drop and thermal effects are very important.

ACKNOWLEDGEMENTS

The authors are grateful to CAPES for financial support and CAPES/GRICES for the International Brazil/Portugal Cooperation Project.

NOMENCLATURE

C total concentration of the gas phase mol.m³ C_F feed concentration mol.m³ C_g molar specific heat at
constant volume for the gas phase J.kg^-1.K^-1 C_i concentration of component
i in the gas phase mol.m³ C_s solid specific heat J.kg^-1.K^-1 C_p,w column wall specific heat J.kg^-1.K^-1 d_p particle diameter m d_ext column diameter m d_int bed diameter m D_{K, i} Knudsen diffusivity of component i m².s^-1 D_L axial dispersion coefficient m².s^-1 D_m,i molecular diffusivity of component i m².s^-1 h_ext external convective heat transfer coefficient W.m^-2.K^-1 h_f film heat transfer coefficient between
the gas and the adsorbent W.m^-2.K^-1 h_w internal heat transfer coefficient between
the gas and the column wall W.m^-2.K^-1 k_f film mass transfer coefficient m.s^-1 k_ext external air conductivity W.m^-1.K^-1 k_g gas phase conductivity W.m^-1.K^-1 k_w column wall conductivity W.m^-1.K^-1 K_L,i LDF overall mass transfer
coefficient of component i s^-1 K_eq equilibrium constant bar^-1 K_o pre-exponential factor bar^-1 L bed length m l column wall thickness m M_i molecular weight of
component i kg.kmol^-1 n parameter of Toth model P total pressure Pa Q_F feed volumetric flow rate m³.s^-1 q_o value of q (concentration at
the solid phase) at
equilibrium with C_o mol.m^-3 average amount adsorbed of
component i mol.kg^-1 q_i* amount adsorbed at
equilibrium of component i mol.kg^-1 q_m maximum amount adsorbed
at equilibrium mol.kg^-1 r_p particle radius m R universal gas constant m³.Pa.mol^-1.K^-1 t_st stoichiometric time s T_g gas temperature K T_s solid temperature K T_w column wall temperature K T_∞ furnace external air
temperature K u superficial velocity m.s^-1 U external overall heat transfer
coefficient W.m^-2.K^-1 V bed volume m³ W bed weight kg

Greek Letters

-ΔH_i adsorption heat for the ith
component at zero coverage J.mol^-1 α air thermal diffusivity at
film temperature m².s^-1 α_w ratio of the internal surface
area to the volume of the
column wall m^-1 α_wl ratio of the logarithmic
mean surface area of the
column shell to the volume
of the
column wall m^-1 β thermal expansion
coefficient K^-1 ε bed porosity ε_p particle porosity λ_L effective axial thermal
conductivity W.m^-1.K^-1 µ_g gas viscosity Pa.s^-1 v air kinematics viscosity at
film temperature m².s^-1 ρ_g gas density kg.m^-3 ρ_p particle density kg.m^-3 ρ_s solid density kg.m^-3 ρ_w column wall density kg.m^-3 τ_p particle tortuosity

Dimensionless Numbers

Nu Nusselt number Pe Peclet number Pr Prandtl number Ra Rayleigh number

(Submitted: June 21, 2010 ; Revised: February 23, 2011 ; Accepted: April 30, 2011)

Permanent Address: Federal University of Paraná, Department of Chemical Engineering, Phone + (55) (41) 33613173, Fax: + (55) (41) 33613277, Centro Politécnico, 81531-980, Jardim das Américas, Curitiba-PR, Brazil. E-mail: [e-mail], [e-mail]

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To whom correspondence should be addressed

Publication Dates

• Publication in this collection
  01 Sept 2011
• Date of issue
  Sept 2011

History

• Accepted
  30 Apr 2011
• Reviewed
  23 Feb 2011
• Received
  21 June 2010