International Journal of Theoretical and Applied Nanotechnology (IJTAN)

ISSN: 1929-1248

1. Introduction

Because of the undesirable effects of CO₂ in gaseous mixtures, separation of carbon dioxide from methane is an   important technical challenge in economic and environmental affairs. CO₂ is present in atmosphere, natural gas and by-products of industrial processes. The presence of CO₂ decreases the energy content of natural gas and because of its acidic property in the presence of water, CO₂ causes corrosion in storage and transportation systems. Therefore, according to the increasing trend in consumption of natural gas, containing CH₄ as the major component, removal of CO₂ has a vital role in the industries dealing with natural gas processing (Baker, 2002).

For the separation of CO₂ from natural gas, several technologies, such as absorption, cryogenic distillation, membrane separation, and adsorption, have been used. Among several technologies, adsorption-based methods are promising because of their simple and easy control, low operating and capital investment costs, and superior energy efficiency (Bae et al., 2008).

Gas separation based on adsorption has been well developed, in which the selection of a sound adsorbent is the key for specific separation. Although materials for gas adsorptive separation have been established and a diverse range of useful sorbents are available for CO₂ separation, there is still plenty of room to optimize the performance of these materials and investigate a wider range of new sorbents (Li Jian et al., 2011). A variety of solid physical adsorbents have been considered for CO₂ capture including microporous and mesoporous materials (carbon-based sorbents such as activated carbon and carbon molecular sieves, zeolites, and chemically modified mesoporous materials), metal oxides, and hydrotalcite-like compounds, amongst others (D'Alessandro et al., 2010). Recently, ilico-alumino-phosphates have been recognized as a new family of zeolitic-like materials that have potential applications in separations, gas storage, and catalysis (Ashraf et al., 2011).

Silicoaluminophosphates (SAPO) called zeo-type molecular sieves, are from ALPOs categories and have similar structure to zeolites except than substitution of Si instead of Al in their cages. SAPO molecular sieves have excellent efficiency in catalytic and separation processes such as adsorption and membrane processes. The kinetic diameter of the gas component is the key parameter in its ability to diffusion into the pores of the adsorbents. Within many types of SAPOs, SAPO-34 with a three-dimensional  structure  and  pore  diameter  of 0.38  nm  is  one of the best candidates for  selective adsorption  of  CO₂,  with 0.33 nm kinetic diameter, from CH₄, with 0.38 nm diameter (Ashraf et al., 2010).

Now, various types of column packing ar­­­e available and one of the new packing materials used is made of core-shell particles. These particles are made of a non-selective solid core surrounded by a porous selective thin layer as the shell (Kostka et al., 2011). Horváth and Lipsky suggested the use of core-shell particles instead of fully porous particles as packing materials for chromatographic columns and demonstrated the value of the concept by reporting important analytical results in the ion-exchange analysis and/or the purification of nucleosides (Guiochon and Gritti, 2011). Ever after, the experimental  and  theoretical  analysis  of  the  efficiency  of chromatographic  columns  packed  with  core-shell  particles were discussed in literatures such as Kostka et al. (2011) and Gritti et al. (2011). Guiochon and Gritti (2011) reviewed the origin, purpose, development and properties of columns packed with core-shell particles to explore their perspectives.

The advantage of inert core adsorbents is increasing density by the incorporation of heavier inert core for stable expansion at high flow rate in expanded bed. These types of core-shell adsorbents have been recently used in expanded bed to capture bio-macromolecules directly from crude particle-containing feedstock (Jahanshahi et al., 2002). Recently, Ashraf Talesh et al. (2011) have reported fabrication of a kind of core-shell adsorbent for CO₂ separation from natural gas.

Adsorption process is an economic and effective method with wide usage in separation of gaseous mixtures. As a consequence of this applicative interest, a great amount of work has been devoted to the modeling of these processes such as Siahpoosh et al. (2009) and Zheng et al. (2010). The dynamic mathematical models are required to simulate the gas adsorption processes, mainly to study the behavior of the new adsorbents during adsorption-desorption cycles and optimization purposes. Proper modeling of adsorption units requires good understanding of the simultaneous mass, momentum and heat transfer which occur in the adsorption bed. Modeling of these phenomena needs the simultaneous solution of partial differential equations coupled with algebraic equations. Analytical solutions of the mathematical model are only available when approximations are used; otherwise, numerical solutions should be employed.

Lots of works are done in modeling of dynamic gas adsorption in the packed columns with conventional adsorbents rather than core-shell ones. Li and Xiu (2004) derive analytical solutions to predict breakthrough and elution curves for fixed-bed columns packed with inert core adsorbents regarding linear adsorption isotherm where the axial dispersion, mass transfer and intraparticle diffusion are considered. Shams (2001) modeled the transient behavior of adsorption/desorption from a fixed-bed packed with thin-film-coated spherical particles/hollow spheres when axial dispersion and external mass transfer resistance are negligible.

In this research, the mathematical modeling of the packed bed with core-shell zeolitic particles that have been recently prepared (Ashraf Talesh et al., 2011) is modeled for separation of CO₂ from natural gas. The assumptions of the model are axial dispersion bed and variable velocity of gas, with macropore diffusion resistance with nonlinear equilibrium model of binary gas component at the shell side of the particle, with no adsorption capacity at the core side, and non-isothermal conditions. Furthermore, a comparison between the breakthrough curves, purity and recovery derived by model from core-shell adsorbents would be taken place with conventional one to figure out efficiency of the core-shell particles in improvement of CO₂ separation from natural gas.

2. Mathematical Modeling

2. 1. Simulation of the Fixed Bed Adsorption

In this model we consider an adsorption column packed with conventional or core-shell particles. The model applied to describe the fixed-bed dynamics is derived from the mass, energy and momentum balances, including the following assumptions:

i. The gas phase behaves as an ideal gas mixture.

ii. The flow pattern is described with the axially dispersed plug flow model.

iii. Total concentration does not vary verses the time.

iv. The internal mass transfer rates are assumed to be governed by multi-component molecular diffusion through macropores.

v. Radial concentration and temperature gradients are negligible.

vi. The particles are spherical and they are packed uniformly into the fixed bed.

vii. The core-shell adsorbent consists of a core of uniform thickness on the spherical inert particle.

viii. The bed wall temperature is considered constant.

Based on the above assumptions, the fixed-bed model is described by the equations given below. The transient material balance for component i of the gas mixture over a differential cylindrical control volume in the adsorption column, like as Fig. (1) yields:

(1)

This equation was used to find the distribution of gas composition  along the bed length, where where   is the axial dispersion coefficient,  is the interstitial velocity,  is the bed void fraction, z is the axial distance from column entrance and  is the source/sink term of component i caused by adsorption/desorption.

The overall mass balance for the bulk gas is given by Eq. (2)

(2)

The following equation expresses the component material balance over a spherical control volume in the adsorbent particles:

(3)

Where  is the pore concentration of component i, and  is the solid concentration of component i which is in equilibrium with pore concentration, i.e.,  is effective pore diffusivity of component i and r is the radial distance of the adsorbent.

 is the radius of inert core, and  is the total radius of the adsorbent, as illustrated in Fig. (2); for conventional adsorbents,  is equal to zero.

Boundary conditions of the equation (3) are:

(4)

(5)

 which appears in equations (1) - (2) was substituted by following equation:

(6)

 is the density of active adsorbent,  is the fractional volume taken up by the shell,  and  are the average macropore and solid concentration of component i.

Because adsorption is an exothermic process, heat is generated and hence the adsorbent particle temperature varies, then the generated heat is transferred to the gas phase by convection. The following equations were obtained by writing the differential energy balance in the bed:

(7)

(8)

The above equations were used to find distribution of pellets and gas phase temperatures  along the bed. where  is the molar specific heat at constant volume for the gas phase,  is the molar specific heat at constant pressure for the gas phase, is the thermal axial dispersion coefficient,  is the convective heat transfer coefficient between the gas and pellets,  is the convective heat transfer coefficient between the gas and column wall,  is the solid specific heat,  is the adsorption enthalpy for the component i, at zero coverage,  is the bed diameter, and  is the wall temperature which kept constant.

 Ergun's law is used to estimate locally the bed pressure drop:

(9)

 and  are viscosity and density of gas phase, respectively.

 The extended Langmuir-Freundlich isotherm for multi-component adsorption was used to find equilibrium concentrations:

(10)

The adsorption equilibrium data of pure carbon dioxide and pure methane on conventional and core-shell SAPO-34 at different temperatures (Ashraf Talesh et al. 2011) were used to drive parameters of isotherm equations. The parameters of single adsorption isotherm were implemented in the extended isotherm for the binary adsorption equilibrium. The constants  and  are derived dependent to the temperature and shown in Table (1).

2. 2. Simulation of Cyclic Adsorption

The behavior of the individual steps within the cycle is simulated by varying the boundary conditions of the bed.  The boundary conditions describing the four-step cycles are introduced in Table 2. The four steps which makes up each cycle are: adsorption, depressurization, regeneration, and pressurization.

Table 1. Isotherm parameters

CO2	-15.12	5975	0.088	608	-10.58	3523
CH4	0.8647	704.2	6.314e-5	2155	-0.0248	324.2

Table 2. Boundary conditions for four steps in an adsorption cycle.

Boundary	Z=0	Z=L
Adsorption
Depressurization
Regeneration
Pressurization

*:subscript F indicates the inlet flow in each step

2.3. Model Parameters

The model parameter evaluation is an important aspect included in the basic information required for modelling the adsorption process. The transport parameter values required in the mathematical model are summarized in this section. Molecular diffusivities were calculated by Chapman-Enskog equation (Reid et al., 2001). An average pore diameter of 0.38 nm was considered for SAPO-34 (Hong et al., 2007) and employed for calculating Knudsun diffusivities. Effective pore diffusivities were calculated using Bosanquet relationship (Yang, 1987). The film mass transfer coefficient was evaluated with the following correlation (Delgado et al., 2006):

(11)

is Reynolds number on the base of particle diameter, calculated with the superficial velocity and Sc is the Schmidt number of the gas. The axial dispersion coefficient was estimated by the correlation of Wakao et al. (1978). As low Reynolds numbers were used in this work (below 0.45), the value of the stagnant contribution term taken for this correlation has an important effect on the bed dynamics and we selected the value corresponding to an inert bed (0.23) for this parameter, which has previously been observed by other authors who have used this correlation for modelling the fixed-bed adsorption process in the gas phase using similar Reynolds numbers (Delgado et al., 2006):

(12)

Where  is molecular diffusivity of component i. The viscosity of each pure gas is estimated by the Lucas method, whereas the viscosity of the mixture is evaluated by the Reichenberg method (Reid et al., 2001).

Like the mass axial dispersion coefficient, the one corresponding to thermal axial dispersion was also estimated with the correlation of Wakao et al. (1978) for low Reynolds numbers, assuming a solid thermal conductivity/gas thermal conductivity ratio of 10, resulting in  (Delgado et al., 2006), where Pr is the Prandtl number and  is gas thermal conductivity which is calculated by Stiel and Thodes equation (Reid et al., 2001). The enthalpy of adsorption was replaced by 24 and 16  for CO₂ and CH₄, respectively (Li et al., 2004), heat capacities of the gases are calculated according to the Reid et al., (2001). The value of the wall Nusselt number  was set to 5 (Delgado et al., 2006), and finally the film heat transfer coefficient between gas phase in the bed and pellets is evaluated with the following correlations (Dantas et al, 2011):

(13)

(14)

 is the particle Nusselt number. The transport parameter values required in the mathematical model are summarized in Table (3), based on the feed condition.

Table 3. Transport parameter values for feed condition.

λ	(m2/s)	0.3
hp	(W/m2.K)	24
hw	(W/m2.K)	12
Cp,g	(J/mol.K)	36
		CO2	CH4
Dax	(m2/s)	1.3E-5	1.3E-5
Dp	(m2/s)	0.8E-7	1.1E-7
Kf	(m/s)	0.0053	0.0053

2.4. Numerical Method

The foregoing models require the numerical solution of a set of partial differential equations accompanied with algebraic equations (overall and component mass balance equations, heat balance and momentum balance equation). The set of differential equations is solved using the method of lines (Schiesser, 1991). In this method, all the spatial derivatives are replaced by the finite difference method, whereas the time derivatives left intact. In fact, this is an explicit time stepping finite difference algorithm in which the time step determined automatically and adaptively by the ODE solver of MATLAB programming. The ODE solver was the ODE23tb that is proper for stiff systems which use crude error tolerances (Kiusalaas, 2005). This solver is an Implicit Rung-Kutta method with a first stage that is a trapezoidal rule step and second stage that is a backward differentiation formula of second order.

3. Verification of the Mathematical Model

In order to validate the developed model, the calculated results were compared with the multi-component experimental data of Ashraf Talesh et al. (2011). In their work, nano-sized core−shell particles containing an inert ceramic core and a thin perm-selective zeotype shell ware studied as a core-shell adsorbent for selective separation of CO₂ from methane in natural gas (10% CO₂, 90% CH₄); and their performance were compared with conventional one. The characteristics of the adsorbents are shown in Table (4). Adsorption experiments were conducted at 298 K and 1 atm pressure with feed flow rate adjusted to 10 (NmL/min) (Ashraf Talesh et al., 2011).

Table 4. Characteristics of the adsorbents.

Adsorbent type	Conventional	Core-shell
Average particle diameter (mm)	3	3
Core diameter (mm)	-	2.86
Shell thickness (mm)	1.5	0.07
SAPO-34 solid density (kg/m3)	2260
Average SAPO-34 porosity	0.55

Fig. (3) shows the breakthrough curves of CO₂ and CH₄ for conventional adsorbents. Similarly Fig. (4) shows the comparison of calculated results with the experimental break-through curves of CO₂ at the outlet of the bed for both conventional and core- shell adsorbents. As it can be seen from these figures, there is a good agreement between the calculated results and the experimental data. (The coefficient of determinations (R²) are 0.998, 0.991 for CO₂ and CH₄ breakthrough curves, respectively, on conventional adsorbent, and it is 0.979 for CO₂ breakthrough curve on core-shell one).

4. Results and Discussion

The developed model can be used as a proper tool for simulation and sensitivity analysis of the adsorption beds with core-shell adsorbents. The results of the developed model are discussed in the following sections.

4.1. Effect of Core-Shell Adsorbent on the Bed Performance

The shape and size of the core-shell adsorbent were the same as those of the conventional particles except that it consists of two parts, the inert core and the active layer coated on the inert part. The effect of core-shell adsorbent on the breakthrough curve of CO₂ is presented in fig. (4). Using core-shell adsorbent, influenced both the breakthrough time and shape of the breakthrough curve.

This figure shows that late breakthrough time is achieved by using core-shell adsorbent, also the sharper S shape would be appeared using core-shell adsorbent. By comparison CO₂ breakthrough times of conventional and core-shell adsorbents, it could be observed 1.3 times improvement of CO₂ breakthrough time using core-shell adsorbent. Usually the breakthrough curves reflect the shape of the mass transfer zone (MTZ). As mentioned core-shell adsorbent makes the curve sharper therefore it is concluded that a shorter MTZ exists inside the bed. It is concluded that the effects of core-shell adsorbent on the breakthrough curve discussed above, is dependent to the decrease in intraparticle diffusion resistance.

Decreasing of useless bed length at breakthrough time is another advantage of using core-shell adsorbents. According to following equation and fig. (5) which describes the loading of the bed at breakthrough time, useless bed length percentages using conventional and core-shell adsorbents are obtained 51.1% and 28.3% respectively.

(15)

It is observed that in using conventional adsorbent, approximately half of the adsorbent bed would be useless. While using core-shell adsorbent, the useless bed length at the breakthrough time is reduced by 22%.

Fig. (6) compares desorption curves of conventional and core-shell adsorbents using the model. As shown, the regeneration time of the conventional adsorbent is too long. Analysing the above mentioned figure clarify that the core-shell adsorbent, that means the lower thickness of the active shell, the shorter the regeneration time of the bed. Based on this finding, we can conclude that using inert core adsorbent is an effective way to reduce the regeneration duration that in turn causes a higher productivity of the adsorption column.

4.2. Effect of Core-Shell Adsorbent on the Cyclic Performance

In this section, the simulation results obtained for the PSA process with respect to cyclic performance are presented comparatively in conventional and core- shell nano-adsorbents. As mentioned before, this PSA system undergoes a simple four-step cycle; the four steps making up each cycle are: (1) adsorption, (2) depressurization, (3) regeneration, and (4) pressurization. During the adsorption step, the feed mixture (10% CO₂, 90% CH₄) flows into the bed at high pressure (P_H=10 atm), carbon dioxide continues to adsorb preferentially to adsorbent, and purified methane is released through the bed as the product. In depressurization step the pressure is reduced to low pressure (P_L=1 atm) and the adsorbates begin to desorb from the surface of the adsorbent. In regeneration step, the bed is purged with the recycled product to regenerate the adsorbent. In the last step (pressurization) the bed is pressurized up to high pressure with the recycled product and the cycle is allowed to repeat.

 The performance of a cyclic process is commonly evaluated according to basic parameters of product purity and product recovery defined, respectively, by:

(16)

(17)

The values obtained for these simulations at cyclic steady state are shown in Fig. (7). It can be seen that using core-shell nano-adsorbent affected both purity and recovery. Core-shell nano-adsorbent increased both purity and recovery by over 4% and 17% respectively, compared with conventional one. It is worth noting that the simultaneous increasing in purity and recovery is the point of interest in applying these adsorbents which is because of positive effects of core-shell adsorbents on both adsorption and desorption stages compared with conventional adsorbent as discussed in section 4.1.

5. Conclusions

To enhance the separation efficiency of the light gaseous compounds by adsorption, configuration of the active parts of the adsorbent is a critical object; therefore proper designing the adsorbent particles improves the efficiency of the separation and can reduce useless part of the adsorption bed. In this research, it was observed that using a thin layer of the active adsorbent on an inert core enhanced the efficiency of CO₂-CH4 separation.

We can conclude that designing and fabricating core-shell adsorbents would be a good idea for the cyclic adsorption process to improve the efficiency of the light gases separation.

References