Two-dimensional (2D) axisymmetric model for HFMC

A two-dimensional (2D) axisymmetric model was developed in a cylindrical coordinate systemFig. 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., 2012Shirazian 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

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.

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:

Steady-state and isothermal conditions.

Incompressible and Newtonian fluid flow for the liquid phase.

Radial convection is negligible.

The gas phase is an ideal gas.

The application of Fick’s diffusion to represent the membrane mass transfer.

Membrane pore distribution is assumed to be uniform.

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