Assessment of Appropriate Geometry for Thermally Efficient CO₂ Adsorption Beds

Abstract

Carbon capture is one of the recently raised technologies to mitigate greenhouse gas emissions. Adsorption was introduced as an energy-efficient carbon capture process, and the literature primarily shows the utilization of circular cross-sectional adsorption beds for this purpose. In this regard, this paper investigates different shapes of adsorbent beds to determine the thermal and adsorption uptake enhancements. Three geometries are considered: circular, square, and triangular cross-sectional beds. Mg-MOF-74 is used as an adsorbent, and numerical simulation is developed using a user-defined function coupled with ANSYS-Fluent. The results show that the triangular cross-sectional bed exhibits better adsorption capacity and thermal management compared to other beds. For example, the triangular cross-sectional bed shows 6 K less than the circular one during the adsorption process. It is recommended that the triangular cross-sectional bed be used for temperature swing adsorption when pumping power is not important. The square bed comes second after the triangular one with a lower pressure drop, suggesting such beds as good candidates for pressure swing adsorption. The square bed could be an excellent choice for compact beds when CO₂ uptake and pumping power are both important.

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 CO₂ from flue gas.

Different adsorbents were investigated in the literature to separate CO₂ from N₂ and flue gas, including activated carbons, zeolites, and metal–organic frameworks (MOFs) [4,5,6,7,8]. Silica materials were also suggested for CO₂ separation [9]. The adsorption capacity of such adsorbents is influenced by separation conditions such as pressure, temperature, and moister [10]. Tests of zeolite13X, zeolite 4A, and activated carbon showed higher CO₂ uptake for activated carbon at high pressures (50–300 psi) [11]. For instance, at 25 °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 CO₂ uptake due to a high adsorption surface area [13,14]. Pentyala 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 highest CO₂ 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 CO₂ 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 CO₂ 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 CO₂ from a gas mixture of 15 vol% CO₂ and 85 vol% N₂. 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 CO₂ uptake behaviors. The study of bed geometry is important to show the best geometry that can improve the CO₂ capture performance. The optimal beds could be used for industrial scales and in actual CO₂ separation plants.

2. Adsorption Beds and Model Description

The three beds investigated (with circular, square, and triangular cross-sections) are shown in Figure 1. The metallic tubes are filled with a porous adsorbent, i.e., Mg-MOF-74, and the inlet flue gas (N₂ + CO₂) is introduced to the bed to capture CO₂ and let N₂ exit during the adsorption process. The bed is assumed to be cooled by the atmosphere during the adsorption process, while a heating process carries out the desorption process. Half of the beds are simulated since the process is symmetry, using three-dimensional geometries shown in Figure 1. The three beds have the same cross-sectional area and volume.

2.1. Governing Equations

To simulate adsorption, flow, and energy balances, the following governing equations are used.

The overall mass balance is given by [31]:

$$\epsilon \frac{\partial \left(\rho \right)}{\partial t}+\nabla \cdot \left(\rho \overrightarrow{v}\right)=-\left(1-\epsilon \right){\rho }_p{\displaystyle {\sum }_i{M}_i\frac{\partial q_i}{\partial t}}$$

(1)

where ρ is the gas mixture density, ε is the bed porosity, v is the velocity vector, M is the gas molar mass, q is the adsorption uptake, and t is the time. The mass balance of each gas can be given by:

$$\epsilon \frac{\partial \left(\rho y_i\right)}{\partial t}+\nabla ·\left(\rho \overrightarrow{v}{y}_i\right)=-\nabla \left(\epsilon \rho D_{disp,i}\nabla y_i\right)-\left(1-\epsilon \right){\rho }_P{M}_i\frac{\partial q_i}{\partial t}$$

(2)

Here, y is the molar fraction of species. The quantity ∂q_i/∂t represents the adsorption kinetic, which is expressed from the linear driving force (LDF) model [32,33]:

$$\frac{\partial q_i}{\partial t}=k_{L,i}\left(q_i^{*}-q_i\right)$$

(3)

Here, q_i* is the equilibrium uptake of species i, q_i is the actual uptake of species i, k_L,i is the kinetic constant. q_i* is estimated using the dual-site Langmuir model [16]:

$$q_i^{*}=\frac{q_{m,i1}{K}_{eq,i1}{y}_{i}P}{1+K_{eq,i1}{y}_{i}P}+\frac{q_{m,i2}{K}_{eq,i2}{y}_{i}P}{1+K_{eq,i2}{y}_{i}P}$$

(4)

where q_m,i1 and q_m,i2 are the uptake limits and K_eq,i1 and K_eq,i2 are constants.

$$K_{eq,i}=k_0{e}^{-\left(\frac{\mathrm{\Delta }{H}_i}{RT}\right)}$$

(5)

Here, k₀ is the temperature-independent constant, ΔH_i is adsorption heat, R (8.314 J/mol/K) is the gas constant, and T is the tested gas temperature (K).

The momentum equation is given by [31]:

$$\epsilon \frac{\partial \left(\rho \overrightarrow{v}\right)}{\partial t}+\nabla \cdot \left(\rho \overrightarrow{v}\overrightarrow{v}\right)=-\nabla p+\nabla \cdot \stackrel{=}{\tau }+\rho \overrightarrow{g}+S_{momentum}$$

(6)

Here, $\stackrel{=}{\tau }$ is the stress tensor, $\overrightarrow{g}$ is the gravitational acceleration vector, and S_momentum is the momentum source term that can be calculated based on the Ergun equation [31].

$$S_{mementum}=-\left(\frac{\mu }{\kappa }{v}_i+C_2\frac{1}{2}\rho \left|\overrightarrow{v}\right|v_i\right)$$

(7)

where μ is the dynamic viscosity, κ is the bed permeability, and C₂ is the inertia resistance.

For the energy equation, adsorption bed and external solid wall energy conservation equations are expressed as:

$$\frac{\partial }{\partial t}\left[\epsilon \rho E_g+\left(1-\epsilon \right){\rho }_b{E}_s+\nabla \cdot \left(\overrightarrow{v}\left(\rho E+P\right)\right)\right]=\nabla \cdot \left(k_{eff}\nabla T-{\displaystyle \sum _i{h}_i\overrightarrow{J_i}+\stackrel{=}{\tau }\cdot \overrightarrow{v}}\right)+\left(1-\epsilon \right){\rho }_b{\displaystyle \sum _i\mathrm{\Delta }{H}_i\frac{\partial q_i}{\partial t}}$$

(8)

$$\frac{\partial }{\partial t}\left({\rho }_w{C}_w{T}_w\right)=\nabla \left(k_w\nabla T_w\right)$$

(9)

where E_g is the total gas energy, E_s is the total adsorbent energy, ρ_b is the density of the bed, h_i is the enthalpy of sensible heat, $\overrightarrow{J}$ is the diffusion flux, k_eff is the bed’s effective thermal conductivity (as given in the below Equation [18]), ρ_w is the wall density, C_w is the wall specific heat capacity, k_w is the wall thermal conductivity, and T_w is the local wall temperature.

$$k_{eff}=\epsilon k_g+\left(1-\epsilon \right)k_s$$

(10)

k_g is the gas thermal conductivity, and k_s is the adsorbent thermal conductivity. Because the adsorption process is cooled by atmospheric air by radiation and convection (Equation (11)), the Nusselt number and heat transfer coefficients can be calculated by Equation (12) [34]:

$$k_w\nabla T_w=h_{ext}\left(T_w-T_{amb}\right)+\sigma ϵ\left(T_w^4-T_{amb}^4\right)$$

(11)

$$Nu=\frac{h_{ext}{D}_o}{k_{air}}={\left[0.60+0.387\frac{R{a}^{1/6}}{{\left[1+{\left(\frac{0.559}{P{r}_{air}}\right)}^{9/16}\right]}^{8/27}}\right]}^2$$

(12)

Here, σ = 5.67 × 10⁻⁸ W/m²·K⁴ is the Stefan–Boltzmann constant, $ϵ$ is the wall emittance (assumed as 0.88), T_amb is the ambient temperature (taken as 298 K), D_o, h_ext is the heat transfer coefficient_, and k_air is the thermal conductivity of the air. Pr_air and Ra denote the Prandtl number and Rayleigh number, respectively. The detailed values for the bed geometry, Mg-MOF-74 properties, adsorption isotherms parameters, and inlet conditions are given in

Table 1. Thermal properties, adsorbent bed construction, and applied boundary conditions.

Parameter	Value
Bed length, m	0.20
Bed cross-sectional area, cm2	3.1416
Bed density (kg/m3)	297 [16]
Adsorbent thermal conductivity (W/m·K)	0.3 [35]
Adsorbent heat capacity (J/kg·K)	900 [35]
Particle density, ρp (kg/m3)	911 [35]
Bed porosity, ε	0.674 [16]
qm1,CO2 (Equation (4)) (mol/kg)	6.80 [16]
qm2,CO2 (Equation (4)) (mol/kg)	9.9 [16]
qm1,N2 (Equation (4)) (mol/kg)	14.0 [16]
qm2,N2 (Equation (4)) (mol/kg)	0 [16]
Ko1,CO2 (Equation (4)) (1/Pa)	2.44 × 10−11 [16]
Ko2,CO2 (Equation (4)) (1/Pa)	1.39 × 10−10 [16]
Ko1,N2 (Equation (4)) (1/Pa)	4.96 × 10−10 [16]
Ko2,N2 (Equation (4)) (1/Pa)	0 [16]
ΔH1,CO2 (Equation (4)) (J/mol)	−42,000 [16]
ΔH2,CO2 (Equation (4)) (J/mol)	−24,000 [16]
ΔH1,N2 (Equation (4)) (J/mol)	−18,000 [16]
ΔH2,N2 (Equation (4)) (J/mol)	0 [16]
KL,CO2 (Equation (3)) (1/s)	0.1213 [16]
KL,N2 (Equation (3)) (1/s)	0.3055 [16]
CO2 adsorption heat (Equation (8)), ΔHCO2 (J/mol)	−(42,492.6 – 6568.83 q + 3973.75 q2 − 959.838 q3 + 69.1208 q4) J mol−1 (0 < q < 7.5 mmol g−1) [16]
N2 adsorption heat (Equation (8)), ΔHN2 (J/mol)	−18,000 [16]
Inlet velocity during adsorption, m/s	0.1
Pressure outlet during adsorption, kPa	101.3
Inlet temperature during adsorption, K	298
Inlet velocity during desorption, m/s	0
Wall temperature during adsorption, K	Equation (11)
Wall temperature during desorption, K	393

.

2.2. Mesh Independence and Model Validation

The mesh independence is studied for four mesh schemes listed in

Table 2. Mesh independence study in terms of the bed T_avg.

Cells Number	7140	32,000	72,500	102,000
Tavg (K)	312.86	312.17	309.48	309.20

. It could be observed that the mesh number of >72,000 is sufficient to ensure precise results. For this study, the mesh size was taken >100,000 for all investigated cases. The model results are validated against experimental data of our previous work [23], as shown in Figure 2. An excellent agreement is observed between the numerical results and the experimental breakthrough curves of CO₂ and N₂ concentration ratios. The investigated numerical cycle is taken as the stable cyclic one when the difference between adsorption and desorption uptakes remains constant.

3. Results and Discussion

The results of the investigated three beds are discussed in this section, mainly in terms of CO₂ uptake and bed temperature during the adsorption and desorption processes.

3.1. The General Behavior of Adsorption/Desorption Processes

The overall picture of the adsorption/desorption processes for the three beds can be obtained from the temporal temperature and uptake CO₂ contours of the symmetry plane that shows the sorption behavior along the beds. The adsorption process is given 1100 s to ensure CO₂ saturation (the inlet and surrounding temperatures are 25 °C). After that, up to 1800 s is given for the desorption process under heating from the external surface (120 °C). Figure 3 shows the temperature contours for the circular, square, and triangular cross-sectional beds at some selective adsorption and desorption times. During the adsorption process, the hot spots exist in the middle of the bed and crawl as time passes due to the adsorption process. As the adsorption process is exothermic, the regions that continue adsorbing CO₂ are hot. The places at the bed center are hotter than those closer to external surfaces due to the good cooling process closer to the surfaces. For the desorption process, the hotter zones are closer to the external walls where the heating is applied.

The difference between the three-bed geometries is that the triangular one has hot regions (during the adsorption process) closer to the bottom since the distance between the top region and external surfaces is shorter than that in the middle. Thus, the top region of the triangular bed quickly becomes colder during the adsorption process and hotter during the desorption process.

The temperature distribution along the bed is obtained from the applied conditions and the sorption processes. Figure 4 shows the CO₂ uptake during the adsorption and desorption processes. The CO₂ uptake is higher for colder zones (closer to the surfaces) and increases along the bed; the red zones show the regions that are saturated with CO₂. At t = 900 s, all the beds reach the saturated uptake. Applying the heating process leads to a desorption process that expels the CO₂ out from the bed. As the heating process is applied from the external surfaces, the regions closer to these surfaces are first regenerated. Again, the circular and square beds have similar adsorption and desorption uptake distribution, unlike the triangular one, in which the symmetry plane shows more adsorption/desorption at the top zones closer to the external surfaces.

Despite Figure 3 and Figure 4 showing the sorption behavior along the beds, the difference between beds in terms of higher uptake and better temperature dissipation can not be concluded from such plots. Therefore, the 2D profiles are discussed in the following sections.

3.2. Adsorption Concentration

The adsorption concentration in terms of the CO₂ molar fraction at bed exits is shown in Figure 5. As the inlet CO₂ molar fraction is 0.15, the saturation conditions are reached when the CO₂ outlet has 95% of the CO₂ inlet (y = 0.1425). However, when the CO₂ outlet reaches 5% of the CO₂ inlet (y = 0.0075), this status is called the breakthrough point. The breakthrough point is for the CO₂ separation applications to avoid the release of CO₂ into the atmosphere. This means that, in real applications, the adsorption process should be stopped at the breakthrough point. It is obvious from Figure 5 that the triangular cross-sectional bed has a higher breakthrough time and lower saturation time, which are preferable. The higher breakthrough adsorption time means that the bed is able to adsorb more CO₂, whereas a lower saturation time indicates a quick sorption process. The square cross-sectional bed comes second in terms of this advantage, while the circular one comes last. These results could be explained by the good cooling process during the adsorption process closer to the three corners of the triangular cross-section, which enables the bed to adsorb more CO₂. The cooling process is better for the triangular bed than the square bed.

3.3. Adsorption Uptake

The adsorption uptake represents the ability of the bed to efficiently adsorb or desorb the desirable gas. A greater uptake shows that the bed capacity is high due to good cooling processes, and low uptake during the regeneration process indicates an efficient heating process. Of the three examined beds, the triangular one shows the greatest capacity during the adsorption process (Figure 6a) and the lowest capacity for an adequate desorption process time (Figure 6a). The square cross-sectional bed also has good uptake values. The difference between the three beds is not high (e.g., at t = 10.8 min, adsorption uptake is 6.04 mmol/g for the circular bed, 6.13 mmol/g for the square bed, and 6.17 mmol/g for the triangular bed); however, the square bed is best for large and industrial scales. In addition, for large scales, the triangular cross-sectional beds can be arranged compactly, compared to circular ones, which have cavities between beds. Figure 6 exhibits, in general, an increase in the adsorption uptake with time until the bed is saturated during the adsorption process, and the opposite occurs during the desorption process.

3.4. Temperature Profiles during Adsorption and Regeneration Processes

Temperature values increase in the bed during the adsorption process due to the exothermic phenomenon of the adsorption. An increment in bed temperature has a negative impact on the adsorption capacity, so a bed design that can minimize increases in temperature values is desirable. Figure 7a shows that the outlet temperature of the triangular cross-sectional bed has the lowest temperature values. Its maximum temperature (during the adsorption process) is about 327 K, which is lower than that of the circular bed by 6 K. Figure 7b also emphasizes the merits of the triangular bed in reaching higher temperatures quickly during the desorption process. The triangular cross-section has three corners that raise the bed temperature closer to the surfaces than the core. The core of the circular cross-sectional bed is wider, so the heating process takes time since the thermal conductivity of adsorbent materials is very low (~0.3 W/m·K).

3.5. Pressure Drop

Since the three beds have the same cross-sectional area and length, the pressure drop could be assumed to be the same. However, this is not true because the triangular cross-section has three corners, the square cross-section has four corners, and the circular cross-section has no corners. The beds are also porous, and the particle distribution inside the beds affects the flow resistance and pressure drop. Figure 8 shows a slight pressure drop for the triangular cross-sectional bed that is less than the circular one. However, the square cross-sectional bed has the minimum pressure drop, which suggests that such beds are better suited for pressure swing adsorption rather than temperature swing adsorption. The maximum pressure drop per unit meter is about 108.5 Pa/m for the square cross-sectional bed, 130.5 Pa/m for the triangular cross-sectional bed, and 131.5 Pa/m for the circular cross-sectional bed. According to the above results, triangular cross-sectional beds perform well with temperature swing adsorption when pumping power is not important. When considering both CO₂ uptake and pumping power, one may select the square cross-sectional beds. The advantage of triangular and square beds is their arrangement in the package of a bank of tubes for industrial scales with appropriate cooling clearance between the tubes. Circular cross-sectional beds used in the literature have bed packing arrangements with non-uniform spaces between the tubes.

4. Conclusions

Three beds with different cross-sectional area shapes (circular, square, and triangular) are investigated to enhance thermal characteristics (heating and cooling) during the sorption processes of carbon capture. The cross-sectional area and bed length are the same for systematic comparison. Mg-MOF-74, as an excellent adsorbent, is used in this study. The CFD model is developed by a user-defined function coupled with commercial ANSYS-Fluent software. The model is validated against the experimental work completed previously by the authors. Based on the applied conditions, we present the following conclusions:

• Temperature values along the bed are lower for triangular cross-sectional beds than others, improving the adsorption and desorption processes. About 6 K is the reduction in temperature when a triangular cross-sectional bed is used compared to a circular one.
• Due to an enhancement in temperature cooling and heating of the triangular bed, the CO₂ adsorption uptake has higher values for this bed than others.
• The pressure drop is lower for the square bed, about 17% less than the circular one. The triangular bed has slightly lower values compared to the circular beds.

Based on the above points, triangular cross-sectional beds could be an excellent candidate when pumping power is not important for temperature swing adsorption plants in which a bank of tubes is compact together with proper cooling between them. The circular beds suggested in the literature are less compact. The square beds could be suitable for pressure swing adsorption as the pressure drop is low. Furthermore, the square bed is the correct choice when considering both pumping power and CO₂ uptake.