INTRODUCTION
Generally, high CO_{2} content in the Natural Gas (NG) potentially leads to many disadvantages including reduction in NG heating value and contribution to pipeline corrosion problems. Since most NG contains 7090% of CH_{4} and 020% of CO_{2}. Thus CH_{4} was considered as only component representing NG and CO_{2} as only impurity in this study. Various separation techniques are applicable for the removal of carbon dioxide, including adsorption, absorption and membrane separation. Pressure Swing Adsorption (PSA) system has been identified as one of the potential system for efficient removal of CO_{2} from natural gas especially in producing high purity natural gas.
Several studies have been carried out to determine the most suitable adsorbent
for the removal of CO_{2} from its mixtures using the PSA system. Cavenati
et al. (2004, 2006) have used 13X zeolite
to selectively remove CO_{2} from CH_{4}/CO_{2}/N_{2}
mixture. The 13X zeolite was found to be suitable for CO_{2} separation,
due to higher adsorption capacity of CO_{2} on 13X zeolite which is
much higher than for the other gases and on testing of several adsorbent. Similar
results and conclusions were made by Gomes and Yee (2002).
To avoid the high cost of the experimental setup for industrial scaleup,
much interests and attentions have been devoted to the modeling of kinetic and
equilibrium adsorption phenomena in the fixed bed adsorption column. Several
popular mass transfer models are available in the literature for adsorption
beds, such as porediffusion model, Linear Driving Force (LDF), etc. Details
of these models were elaborated by Ruthven (1984), Yang
(1987) and Ruthven et al. (1994). Simplified
models are often obtained by using appropriate approximation in order to get
substantial saving in computation time. Due to that, LDF model has been used
by several researchers to predicate the kinetics of the CO_{2} adsorption
inside fixed bed column. Dong et al. (1999) conducted
the separation of ternary gas mixture consisting of CO_{2}CH_{4}N_{2},
with three different adsorbents, activated carbon and 13 X zeolite and Carbon
Molecular Sieve (CMS). The mass transfer between the two phases was simulated
using LDF model under set of model assumption including negligible pressure
drop, axial and radial dispersions. Besides Gomes and Yee
(2002) has investigated the feasibility of CO_{2} removal using
PSA. A numerical simulation was carried out using Linear Driving Force (LDF)
model to describe the adsorption kinetic. A good agreement was shown in the
model prediction as well as a great purity of nitrogen gas recovered.
Recently, there has been intense interest in linking engineering models with rigorous simulation tools, parallel with the significant improvement in computational resources and codes. Simulation approaches potentially provides an attractive alternative to costly and timeconsuming experimentation.
Computational Fluid Dynamics (CFD) simulation is appropriate to be used when
the process performance is dictated by the fluid dynamics. CFD has been proposed
as a reliable tool to model and simulate hydrodynamic, mass and heat transfer
phenomena for the design and optimization of process equipment (Natarajan
et al., 2005; Coussirat et al., 2007).
Numerous CFD studies have been reported on the fluid flow and heat transfer
in the packed bed reactors elsewhere (Baleo et al.,
2000; Nijemeisland and Dixon, 2001; Coussirat
et al., 2007; Guardo et al., 2007).
Nevertheless, the CFD studies related to fixed bed adsorption have been found
to be limited. Hence, there is a potential applicability of CFD to model transport
phenomena and adsorption mechanism in packed bed CO_{2} adsorption column.
The aim of present study is to model and simulate the hydrodynamics and adsorption
phenomena for the CO_{2}CH_{4} mixture in the fixed bed adsorption
column filled with zeolite 13X. The effects of several important operating parameters
were varied to study the influence of these parameters toward CO_{2}
adsorption efficiency. In this study, the adsorption isotherms of pure CO_{2}
and CH_{4} on 13X zeolite were measured at constant temperature using
gravimetric apparatus at maximum pressure of 6 bar. Full set of equilibrium
data was fitted with the LDF model for the integrated CFD modeling.
MATERIALS AND METHODS
Experimental setup for adsorption kinetic data: Adsorption equilibrium and kinetic of pure gases was performed in a (Rubotherm) gravimetric adsorption unit consists of two major components, which are Magnetic Suspension Balances (MSB) unit and the gasdosing unit. A setup of the equipment is shown in Fig. 1. The gasdosing unit governs the amount and pressure of the gas in the system while the adsorption isotherm and kinetics are obtained from the magnetic suspension balance unit. The pressure of the system depends on the outlet pressure of the gas cylinder only without additional compressor. The temperature of the system is controlled by an electrical jacket heater and internal heat exchanger. The Magnetic Suspension Balance (MSB) is a very sensitive balance that is able to weigh samples contactless with a balance located at ambient conditions. The adsorbent sample is located in the measuring cell and can be coupled or decoupled from the balance by a contactless magnetic suspension coupling. The pressure of the system is governed by pressure transducer (PIRC) and dynamic valve for pressure range at 20150 bar and another from 120 bar to acquire data at low and high pressures, respectively.
The 13X zeolite were supplied by Zeochem, Switzerland. Some of characteristic parameters of the adsorbent are summarized in Table 1, together with the experimental data of carbon dioxide adsorption equilibrium at 298 K.

Fig. 1: 
Rubotherm MSB gravimetric adsorption measurement unit 
Experimental setup for model validation: The adsorption dynamic studies for model validation were carried out using twobed Gas Adsorption Column Unit (GACU) developed inhouse. The adsorption beds were made of stainless steel with a length of 0.3 and 0.038 m Internal Diameter (ID) and wall thickness of 0.007 m. The beds were packed with 13X zeolite particles. The column designed for pressure up to 20 bar and temperature up to 923 K. Two pressure transducers were located at the feed and bed ends in order to measure bed pressure variation, in this study the pressure drop of the column was very small (<0.1 bar) and cannot detected accurately with the pressure transducer. The feed flow was controlled by a mass flow controller (Brook, 5851i±0.05 NL min^{1}). In order to keep the pressure in the adsorption bed constant, manual backpressure regulator (Swaglelok 4R3A) was installed with RIX micro boost compressor. The concentration variations of the effluents at the adsorption and desorption steps were analyzed by Gas Chromatography (GC) analysis system. Sampling in the GC was carried out automatically via a Gas Sampling Valve (GSV) at specific time (2 min). The feed gases for the adsorption process were nitrogen (as inert gas), carbon dioxide and methane supplied from gas cylinder. All gas used has purity more than 99.9% and were supplied by MOX Sdn. Bhd. The details of the operating conditions are shown in Table 1.
Mathematical model: The dynamics behavior of the fixedbed adsorption
column can be modeled and characterized using the integrated CFD model. In order
to formulate a generalized model corresponding to the adsorption mechanism,
following assumptions were made:
• 
The heat transfer within the bed is neglected 
• 
Competitive adsorption between CO_{2} and CH_{4} was assumed 
• 
The Linear Driving Force (LDF) model was used for representing the mass
transfer into the pellets 
• 
The mass transfer coefficient is lumped of the external fluid film resistance
and marcropore diffusion 
• 
The porosity was uniform and constant 
• 
Instantaneous equilibrium between the bulk and pellet concentrations 
Governing equations for adsorption column Continuity equation The general
3D continuity equation for unsteadystate fluid flow is:
Navierstokes equations
To represent the fluid flow through the porous medium, additional sources term,
S_{ix}, S_{iy}, S_{iz} were added to Eq.
24 to model the flow resistance in 3D dimensions as follows:
Navierstokes equation in xdirection
Navierstokes equation in ydirection
NavierStokes Equation in zdirection
The porous medium momentum source term S_{i} calculates the pressure gradient in the packed bed and creates a pressure drop that is proportional to the fluid velocity (or velocity squared) as shown below:
Where:
where, C_{2 }and α, are the inertia resistance and viscous resistant
coefficient, which estimated using Eq. 6 and 7.
Gases mass balance equation: The mass balance for the bulk flow in the fixed bed column is given by Eq. 8:
The adsorption rate ∂q_{i}/∂t was obtained based on the LDF
model (Yang, 1987) as shown:
where, C_{i} is the bulk concentration (kg m^{3}),
is the pellet concentration (kg m^{3}), t is the time (s), ε is
the bed voidage fraction, D_{z,i }is the column 3D dispersion coefficient,
k_{i} is the average mass transfer coefficient for each species and
a the surface area of pellet per volume of bed.
The column dispersion coefficient, D_{z,i } in Eq. 8
can evaluated by Ruthven (1984):
The molecular diffusivity, D_{m }can be calculated by Suzuki
(1989):
where, A = CO_{2} and B = CH_{4}
The concentration inside a spherical pellet
is described by multicomponent Langmuir model (Suzuki, 1989).
As shown in Eq. 12, q_{i} is the average adsorbed
concentration (kg m^{3}), q_{s} is the adsorbent maximum capacity
concentration. Equation 8, 9 and 12
are coupled in order to solve the overall column mass balance by calculating
the concentration within the pellet
with considering the interaction between the two components by using the multicomponent
Langmuir model.
Vant Hoff correlation was used to estimate the equilibrium constant K_{A
}(Suzuki 1989).
where, R is the ideal gas law constant, T is the operation temperature, K_{0} = 0.0206 is the preexponential factor and ΔH_{A }= 15.294 kJ mol^{1} is the heat of CO_{2} adsorption.
Besides, the mass transfer coefficient (k_{A}) for CO_{2} is
given by Yang (1987):
where, Sc, Re and R_{p} are the Schmidt numbers, Reynolds numbers and the pellet radius, respectively.
Energy balance equation: The overall energy balance for the bulk flow
in the fixed bed column including the heat generated by adsorption was given
by Yang (1987):
where, K_{L} is the mixture axial thermal conductivity (W/m.K), ρ_{g} is the mixture density, C_{pg} is the heat capacity and ÄH_{i} is the heat of adsorption (kJ mol^{1}).
BOUNDARY CONDITION AND COMPUTATIONAL METHOD
One of the important sections of CFD modeling is the construction of the mesh geometry topology. The mesh establishes the accuracy of the simulation. It has to be chosen with enough detail to describe the processes accurately and with a degree of coarseness that enables solution within an acceptable amount of time. This study focused mainly on maintaining a 3D topology that described the physical model accurately and has been able to handle the flow specifics of the fixed bed column geometry.
Considering a threedimensional axisymmetric domain, the above set of model
Eq. 115 were solved using commercial software
FLUENT 6.3 (FLUENT, 2003). The generalized balances that
used by the FLUENT 6.3 were the governing equations for conservation of mass
and momentum, which coupled with system mass balance equation.
Table 1: 
Experimental data and simulation boundary conditions 

The basic equations and background of these balances are stated in the FLUENT
6.3 User’s Guide (FLUENT, 2003). In order to simulate
the transport equations and adsorption phenomena in the fixed bed adsorption
column using FLUENT 6.3 software, extra scalars would be needed. Userdefined
scalars (UDS) have been used to implement the flow mass transfer coefficients,
which were modeled using userdefine source terms. To determine the interaction
between the mass and heat balances for the adsorption system (which is an exothermal
process), vant Hoff correlation (Eq. 13) have been used to
represent the interaction between the amounts of mass adsorbed and the temperature
elevation. C programming language has been used to write the codes in the User’s
Defined Functions (UDF) file for customizing the UDS equations.
Table 1 summarizes the experimental parameters and simulation boundary conditions for the CFD model validation.
RESULTS AND DISCUSSION
CFD model validation: The integrated CFD model was used (as described in section II) to determine the CO_{2} concentration factor at the column outlet for different time based on different operating conditions. The results simulated using the CFD model, were compared with the experimental data as shown in Fig. 2. Based on the results, the simulated data demonstrated a good agreement with the experimental data with maximum error less than 2.5%.
Based on the good agreement of the model results, several important operating parameters were varied to study the influence of these parameters on CO_{2} adsorption performance.

Fig. 2: 
Comparison of CO_{2} experimental and simulation breakthrough
curve (Sampled at column outlet) 

Fig. 3: 
Effect of feed velocity on the simulated breakthrough curve
(Sampled at column outlet) 
Effect of feed velocity: Figure 3 shows the effect of feed velocity for CO_{2} adsorption process in the fixed bed adsorption column. The CO_{2} concentration, C, was sampled at the column outlet. The effect of feed velocity was studied at 0.02, 0.04 and 0.06 m sec^{1}, while the CO_{2} inlet concentration, C_{0} in each run was kept constant at 50% of CO_{2} concentration. Based on the figure, as the velocity increases, the breakthrough curve becomes steeper. This signifies that higher CO_{2} concentration is produced in the product stream, under higher feed velocity. At higher velocity, the gas mixture would have shorter residence time in the fixed bed column. Under this condition the gas mixture would leave the column before the equilibrium adsorption of CO_{2} occurs. Thus, higher feed velocity tends to give a reduction in removal efficiency of CO_{2} in the fixed bed adsorption column.
Effect of bed porosity: Figure 4 shows the effect
of bed porosity on the breakthrough curve.

Fig. 4: 
Effect of bed porosity on the simulated breakthrough curve
(Sampled at column outlet) 
The CO_{2 }concentration,
C, was sampled at the column outlet. Based on the figure, as the bed porosity increases from 0.3 to 0.5, higher
CO_{2} concentration is produced at the product stream. This signifies
that the increment of bed porosity leads to a lower performance in CO_{2}
removal, which gives higher CO_{2} concentration at the column outlet.
This trend can be explained by the effect of the fluid flow through a packedbed.
Since the closeness and orientation of the packing has significant effect on
the pressure gradient and velocity magnitude, smaller bed porosity leads to
an increase in the bed velocity and consequently reduces the gas residence time
in the bed.
This would give a higher CO_{2} concentration at the product stream.
Nevertheless, based on the mass balance Eq. 8 and 9,
the porosity has an inverted effect, whereas, smaller bed porosity tends to
increase the adsorption rate and reduce the CO_{2} concentration at
the outlet. Hence, based on Fig. 4, it can be concluded that
the influence of hydrodynamics is more dominant as compared to the effect of
mass transfer for the adsorption of CO_{2} in the fixed bed column.
Effect of CO_{2} concentration on the adsorption process: Figure
5 shows the effect of CO_{2} concentration factor (C/C_{0})
inside the fixed bed adsorption column at different adsorption time (5, 30 and
120 sec). Three different CO_{2} concentrations (10, 30 and 70%) were
varied to study the adsorption capacity, which can be calculated based on column
CO_{2} concentration factor (C/C_{0}), where higher concentration
factor represents lower adsorption capacity. Under the case with 10% of CO_{2}
feed concentration, a rapid increasing of CO_{2} concentration factor
was observed in the adsorption column (from 5 to 30 sec). As the adsorption
process proceeds to 120 sec, the fixed bed adsorption process tends to give
a uniform CO_{2} concentration factor throughout the entire column.

Fig. 5: 
Effect of CO_{2} concentration on the simulated adsorption
process 
The rapid increasing of bed concentration at the beginning of the adsorption
time (5 to 30 sec) was due to the high affinity of the fresh adsorbent to adsorbe,
which derived from the physical Van der Waals and electrostatic Forces (Slejko,
1985). When the adsorption approaches to the equilibrium, the adsorbent
capacity reduces as the bed becomes saturated.
Comparing with other cases with different CO_{2 }feed concentration, higher CO_{2} feed concentration (70%) tends to give a higher CO_{2} concentration factor (lower adsorbent capacity) for the entire column bed under each of the adsorption time studied. This results exhibit that higher CO_{2} feed concentration tends to achieve bed saturation and equilibrium at a shorter period of time.
Effect of CO_{2} concentration on the temperature profile: Figure
6 shows the evolution of temperature profile at different CO_{2}
concentrations (10, 30 and 50%). The temperature profile was sampled at the
column outlet. Since CO_{2} adsorption is an exothermic process, the
column temperature tends to increase with CO_{2} concentration. This
is exhibited in Fig. 6, where the column initial temperature
(283 k) was found to increase during the range of adsorption period from 283
to 296 K, 309 and 317 K at 10, 30 and 50% of CO_{2} concentration respectively.

Fig. 6: 
Effect of CO_{2} concentration on the simulated temperature
profile (Sampled at column outlet) 
This phenomenon is due to the proportional relation between the adsorbed amount
and the temperature releases. The gradient of the temperature increment is found to be higher at the beginning
of the adsorption (<30 sec), where the adsorption rate of the CO_{2}
is higher at each given concentration. When the adsorption time approaches 60s,
the temperature gradient achieves developed stage, where further increment is
relatively small compared with the adsorption time. This is due to the saturation
of CO_{2} in the adsorbent bed.
CONCLUSION
Integrated CFD model was employed to simulate the transport and adsorption phenomena of the CO_{2}NG fixed bed adsorption column. The hydrodynamics and mass transfer models were validated with experimental data. Under present study, several important operating parameters were studied and the results showed a reasonable manner for the effect of feed velocity, bed porosity and CO_{2} inlet concentration. This study also showed that the hydrodynamics within the packed beds significantly influences the performance and capability of the adsorption process.
NOTATIONS
a 
: 
Surface area of pellet per volume of bed 
C_{0} 
: 
Inlet concentration (kg m^{3}) 
C 
: 
Bed concentration (kg m^{3}) 
C_{2} 
: 
Inertia resistance coefficient (m) 
D_{m} 
: 
Molecular diffusivity (m^{2} sec^{1}) 
D_{p} 
: 
Particles diameter (m) 
D_{z,i} 
: 
The column 3D dispersion coefficient (m) 
K 
: 
Equilibrium constant 
k 
: 
Mass transfer coefficient (sec^{1}) 
M_{A,B} 
: 
Species molecular weight (g mol^{1}) 
P 
: 
Partial pressure (Pa) 
q 
: 
Adsorbent capacity (mmol g^{1}) 
q_{s} 
: 
Maximum capacity (mmol g^{1}) 
t 
: 
Time (sec) 
u 
: 
Gas velocity (xdirection) (m sec^{1}) 
v 
: 
Gas velocity (ydirection) (m sec^{1}) 
w 
: 
Gas velocity (zdirection) (m sec^{1}) 
Greek symbols
ε 
: 
Bed voidage fraction (Porosity) 
ρ_{s} 
: 
Particles Density (kg m^{3}) 
ρ 
: 
Fluid Density (kg m^{3}) 
α 
: 
Viscous resistant coefficient (m^{1}) 
μ 
: 
Fluid Viscosity (Ns m^{2}) 
Ω_{AB} 
: 
Collision integral, a function of k_{B}T/ε_{AB} where
k_{B} is Boltzmann’s constant 
σ_{AB} 
: 
LennardJones constant 
Abbreviation
CFD 
: 
Computational Fluid Dynamics 
LDF 
: 
Linear Driving Force 
UDS 
: 
User’s Defined Scalars 
UDF 
: 
User’s Defined Functions 
NG 
: 
Natural Gas 
ACKNOWLEDGMENTS
The authors gratefully acknowledge the support from University Technology PETRONAS by providing grant and facilities for the research.