https://doi.org/10.1016/j.ccst.2022.100028
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A two-dimensional (2D) axisymmetric model was developed in a cylindrical coordinate system. Fig. 3 shows a schematic diagram of the HFMC that was used in this work for numerical modeling. The HFMC comprised of three different domains: shell and tube as well as membrane sides (Rezakazemi et al., 2012; Shirazian et al., 2012a). The governing momentum and mass transfer equations for each section of the model are expressed in section 3.1 and 3.2, respectively. In this model, the solvent flows into the tube side at z=0, whereas the gas mixture flows counter-currently through the shell side of the HFMC at z=Lf. The model considers the non-wetting condition where the pores are not wetted by solvent.
Fig. 3. The schematic of the HFMC used in the model (a) geometry; (b) gas and liquid behavior
The chemical and physical properties along with the working conditions of the HFMC are presented in
Table 2. The chemical and physical properties along with the working conditions of the HFMC
| Parameter | Unit | Value | Ref. |
|---|---|---|---|
| Inner hollow fiber radius, (r1) | mm | 0.32 | (Rezakazemi et al., 2019) |
| Outer hollow fiber radius, (r2) | mm | 0.45 | (Rezakazemi et al., 2019) |
| Length of fiber, (Lf) | cm | 40 | (Rezakazemi et al., 2019) |
| Number of fiber (n) | – | 590 | (Nakhjiri and Heydarinasab, 2020) |
| Porosity (ε) | – | 0.52 | (Nakhjiri and Heydarinasab, 2020) |
| Mass transfer coefficient (km) | ms−1 | Dco2_shell.ε(τ.δ)−1 | (Rezakazemi et al., 2019) |
| Gas flow rate (Qin_gas) | mLmin−1 | 100 | (Nakhjiri and Heydarinasab, 2020) |
| Inlet CO2 concentration (C0) | ppm | 1400 | (Rezakazemi et al., 2019) |
| Gas temperature (Tgas) | K | 298 | This study |
| DCO2_shell | m2s−1 | 1.33e-5 | (Rezakazemi et al., 2019) |
| DCO2_mem | m2s−1 | Dco2_shellετ−1 | (Ghasem, 2019b) |
| DN2 | m2s−1 | 4e-5 | (Ghasem, 2019b) |
| DCO2_solvent | m2s−1 | 9e-10 | (Nakhjiri and Heydarinasab, 2020) |
| CO2 loading factor (m) | molCO2molsolvent−1 | 0.788 | This study |
| Liquid flow rate (Qin_liq) | mLmin−1 | 25 | (Nakhjiri and Heydarinasab, 2020) |
| Pressure (Pt) | bar | 1 | (Ghasem, 2019b) |
| Physical properties of solvent(20 wt% MDEA + 10 wt% KLys) | |||
| Density of solvent | gcm−3 | 1.0291 | This study |
| Viscosity of solvent | mPa.s | 1.9417 | This study |
| Adsorption properties of ZIF-8 | – | ||
| Qm | mmolg−1 | 11.77 | (Yang et al., 2014) |
| Kd | bar−1 | 0.071 | (Yang et al., 2014) |
| Density of particle | grcm−3 | 0.96 | (Hunter‐Sellars et al., 2021) |
The particle-particle and particle-liquid interactions can be neglected, due to low amount of nanomaterials. The laminar parabolic velocity distribution was employed for the solvent flow in the tube side while the gas flow in the shell side was defined by means of Happel’s free surface model (Huang and Zhang, 2013). The following assumptions were made in this work:
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Steady-state and isothermal conditions.
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Incompressible and Newtonian fluid flow for the liquid phase.
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Radial convection is negligible.
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The gas phase is an ideal gas.
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The application of Fick’s diffusion to represent the membrane mass transfer.
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Membrane pore distribution is assumed to be uniform.
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