# Assessment of Appropriate Geometry for Thermally Efficient CO\({}_{2}\) Adsorption Beds
## 1 Introduction  
Carbon capture and decarbonization are essential technologies for mitigating global warming and saving the earth's ecosystem [1; 2]. Burning fossil fuel is still the primary driver of global energy, and alternative sources are still less mature. The transmission from fossil fuel to clean energy sources will take a significant time. To keep using fossil fuels while minimizing carbon emissions can be achieved with carbon capture and storage [3]. Post-combustion using adsorbents is a promising topic being researched with the aim of separating CO\({}_{2}\) from flue gas.  
Different adsorbents were investigated in the literature to separate CO\({}_{2}\) from N\({}_{2}\) and flue gas, including activated carbons, zeolites, and metal-organic frameworks (MOFs) [4; 5; 6; 7; 8]. Silica materials were also suggested for CO\({}_{2}\) separation [9]. The adsorption capacity of such adsorbents is influenced by separation conditions such as pressure, temperature, and moisture [10]. Tests of zeolite13X, zeolite 4A, and activated carbon showed higher CO\({}_{2}\) uptake for activated carbon at high pressures (50-300 psi) [11]. For instance, at 25 \({}^{\circ}\)C and 300 psi, the uptake reached 8.5 mmol/g for activated carbon and 5.2 mmol/g for 13X. However, zeolites can show better adsorption uptake at low pressures [12].  
On the other side, MOFs showed higher CO\({}_{2}\) uptake due to a high adsorption surface area [13; 14]. [PERSON] et al. [15] demonstrated that among MOFs with different inorganic metals, such as Mg, Ni, Zn, or Co, the Mg metal to produce Mg-MOF-74 has the highestCO\({}_{2}\) uptake and adsorption affinity. However, MOFs are sensitive to the moisture that collapses the organic linkers between the metals. Thus, the dehydration process is necessary for flue gas separation [16; 17; 18].  
A significant amount of research has been conducted on MOf-74 materials [19; 20; 21; 22] and separation processes [23]. Temperature swing adsorption and thermal management are important to improve the separation efficiency and adsorption capacity [23; 24]. Cycling tests were shown to be very important in determining the stable CO\({}_{2}\) uptake [16].  
In terms of the adsorption beds used for carbon capture, the literature usually introduced beds with circular cross-sections for breakthrough studies [25; 26] or separation processes [27; 28; 29]. Circular beds with trapezoidal length beds were also investigated and showed no significant difference from the circular cross-sectional beds [30].  
As discussed above, the literature showed that the MOFs are excellent adsorbents for CO\({}_{2}\) capture, and circular cross-sectional beds always represent the fixed adsorption beds. In addition, based on the authors' best knowledge, no research conducted in the literature was concerned with the bed shapes. Additionally, adsorbents showed low thermal properties that minimize heating and cooling processes. Therefore, the present study compares three-bed geometries (i.e., circular, square, and triangular cross-sectional beds) to investigate the thermal enhancement in adsorption beds to improve the adsorption/desorption processes. Mg-MOF-74 is used as an adsorbent to fill the three beds with the same cross-sectional area and length to separate CO\({}_{2}\) from a gas mixture of 15 vol% CO\({}_{2}\) and 85 vol% N\({}_{2}\). A three-dimensional model to solve the flow, energy, and adsorption balances is developed by a user-defined function code written in C and coupled with ANSYS-Fluent. This study focuses on the thermal and CO\({}_{2}\) uptake behaviors. The study of bed geometry is important to show the best geometry that can improve the CO\({}_{2}\) capture performance. The optimal beds could be used for industrial scales and in actual CO\({}_{2}\) separation plants.