CFD study on the effects of different temperatures and feed velocities for CO 2 , CH 4 , and C 2 H 4 adsorption using 5A molecular sieve

. The removal of carbon dioxide (CO 2 ) from natural gas is a practical measure in dealing with problems such as CO 2 emissions into the atmosphere and reducing the cost of gas processing operations. Adsorption is a promising technology currently used, specifically pressure swing adsorption (PSA) method. In this paper, the adsorption column packed with 5A molecular sieve was simulated using COMSOL Multiphysics software for the separation of CO 2 from natural gas components, which are methane (CH 4 ) and ethylene (C 2 H 4 ). The effects of different temperatures on adsorption time were investigated and the optimum adsorption time was determined by the purity of CH 4 and C 2 H 4 at the column outlet. This study will be beneficial for optimising the design and process configuration of PSA.


Introduction
In the atmosphere, the concentration of greenhouse gases keeps on increasing to an alarming level due to the rise of worldwide demand for energy that is bound to a strong dependence on fossil fuels. Fossil fuels such as coal, oil, and natural gas (NG) are the major contributors to the emission of anthropogenic carbon dioxide (CO2) to the atmosphere, leading to global warming, a challenging issue to both researchers and industries [1]. Nevertheless, NG is considered as the cleanest fossil fuel compared to oil and coal [2,3]. It has been used for residential, commercial, and industrial heating [2,4,5]. NG reservoirs are usually found with other impurities, mainly CO2, which eventually enhances the formation of carbonic acids and dry ice, and causes corrosion and clogging of delivery pipelines. CO2 concentration above 2% or 3% significantly reduces the heat capacity of the gas and makes it economically less viable [6,7]. Therefore, to utilise crude NG, CO2 must be removed so ______________________ that it will comply with the necessary technical standards before supplying NG to the market. For such reason, several separation technologies are widely used to remove CO2 from NG such as absorption, adsorption, cryogenics, and membrane separation. Adsorption has been reported as the most feasible emerging alternative to remove CO2, specifically pressure swing adsorption (PSA) method [8,9].
PSA is a transient cyclical process in which CO2 is adsorbed from the NG stream and CO2 accumulates on the surface of a solid material called adsorbate. The solid adsorbent is purified using the difference in pressure to desorb/remove CO2 and the gas is compressed for storage. Adsorption technology depends on the strong integration of both material science and process engineering. Ideal adsorbent materials with inherent characteristics have high working capacity, high selectivity, fast adsorption and desorption kinetics, chemical stability, and recyclability. The characteristics can be optimised by suitable design and process configuration. Although there are numerous studies regarding the equilibrium of adsorption on different adsorbents, it is important to study the column dynamic behaviour of a packed bed based on different operating parameters prior to designing an optimum adsorption process configuration with a selected adsorbent. The study was conducted to investigate the effects of three different temperatures (29.85, 99.85, and 299.85 °C) on the adsorption time and also the effects of different feed velocities on the adsorption of CO2, methane (CH4), and ethylene (C2H4) on 5A molecular sieve using COMSOL Multiphysics version 5.3. The optimum adsorption time or breakthrough time is determined when the concentration found at the outlet reaches the limiting permissible value of 0.01-0.05 of the initial concentration. As an addition to the study, the effects of feed velocity and optimum bed height were also investigated.

Mathematical model
The mass transfer of CO2 adsorption in a packed-bed column at different operating temperature was modelled in this study. Figure 1 shows a two-dimensional geometric model used in the present study for the simulation of CO2 adsorption in a packed-bed column. During the adsorption process, the gas mixture flows into the porous media column and CO2 is adsorbed onto the adsorbent materials. The model was developed using the following assumptions: l The gas phase obeys the ideal gas law. l The adsorbent is considered as a homogeneous phase. l The mass transfer rate during the adsorption process is described by the linear driving force (LDF) model. l The physical properties of the adsorbent are constant. Based on the assumptions, the transient gas-phase mass balance for a differential control volume of the adsorption column can be described by the following equation: (1) Where Ci is the bulk concentration (kg m -1 ), Ɛ is the bed porosity, and q is the component concentration on the solid phase at time t.
The rate of adsorption based on the LDF model is as follows: ( Where ki is the mass transfer coefficient and q * is the component concentration on the solid phase at equilibrium.
The adsorption isotherm is described by the Langmuir isotherm: Where Qm is the maximum capacity of adsorption and K is the equilibrium adsorption constant for the Langmuir isotherm.
K is the equilibrium adsorption constant described by the van't Hoff equation as follows: Where ΔH is the enthalpy change, R is the gas constant, and T is the temperature. Previous experimental work on CO2, CH4, and C2H4 at three different temperatures by Pakseresht (2010) was used as the case study. The results from the work in the form of isotherm data were used to simulate the adsorption process in this study [10].

Computational methodology
The optimum adsorption time to separate CO2 from CH4, and C2H4 was determined through computational fluid dynamics (CFD) using COMSOL version 5.3. The transport diluted species through porous media interfaces was selected as the main physics package that describes mass balance in the bulk flow through the porous material. Table 2 shows the parameters used. A point plotted on the column at the height of 28 inch, approximately at the end of the packed-bed column, was used as a reference point for identifying the presence of gases and the limiting allowed composition. The increase in temperature leads to the decrease of the breakthrough time for each component in reaching the packed-bed column. The trend can be observed from the graph with the shift to the left as the temperature increases. This phenomenon is unfavourable for gas adsorption resulting from less residence time of gas in the column, which leads to low amount of CO2 adsorbed on the adsorbent and subsequently low adsorption capacity. This supports the relation in the van't Hoff equation where equilibrium constant (K) is inversely proportional to the temperature. When the equilibrium constant is small, the adsorption capacity will also be low. The same pattern was also observed in the previous research at low temperature, where the dissipation energy of the adsorption process was more efficient and the bed was provided with a higher adsorption capacity [11,12].

Effects of feed velocity
The evaluation of CO2 concentration in the column at different feed velocities is presented in Figure 3. It shows the variation in the contours along the height of the bed by varying the feed velocity from 100 to 170 cm s -1 with constant CO2 inlet concentration, adsorption time (2,000 s), and temperature (29.85 °C). From the surface plot at 2,000 s, the mass transfer zone for the feed velocity of 100 cm s -1 is at the middle (17 inch) of the bed, whereas the mass transfer zone for the feed velocity of 170 cm s -1 is almost at the end of the packed bed (27 inch). At higher velocity, CO2 would leave the column faster. This is supported by literature that showed a significantly higher CO2 concentration was found at the outlet of the column under higher feed velocity. This indicates lower adsorption capacities because the gas mixture had shorter residence time and left the column before the equilibrium adsorption of CO2 occurred [13,14].
The optimum bed height can be determined from the concentration contours as shown in Figure 3

Conclusion
The study used computational fluid dynamics to simulate the adsorption of CO2, CH4, and C2H4 in a packed-bed column with 5A molecular sieve. The breakthrough curves and concentration contours were used to study the effects of operating parameters on the adsorption dynamics inside the packed-bed column. The operating temperature and feed velocity are the two operating parameters that influence the adsorption process performance, and the parameters were accordingly investigated. The simulation showed that the two variables investigated significantly affect adsorption dynamics. Based on the temperature, the time for the gas mixture to reach the packed-bed column outlet decreases as temperature increases. The residence time of the gases is low; hence, they might leave the column before equilibrium could be achieved, which subsequently reduces CO2 removal efficiency and gives low adsorption capacity. The optimum adsorption time for CO2 is 3,000 s at 29.85 °C, 1,800 s at 99.85 °C, and 100 s at 299.85 °C. Similarly, the results of the change in feed velocity of CO2 with constant operating time, temperature, and feed concentration showed that the mass transfer zone moved faster towards the end of the packed-bed column with higher feed velocity. The optimum bed height for lower velocity is 22 inch.