Computational Fluid Dynamics Analysis of a Hollow Fiber Membrane Module for Binary Gas Mixture
Abstract
:1. Introduction
2. Materials and Methods
2.1. Assumptions
- Steady-state condition is applied.
- Laminar flow is considered with constant physical properties.
- Ideal gas law is used.
- Without axial mixing of gaseous molecules.
- Fiber diameter in the module is uniform.
- Fiber deformation with high inlet pressure is neglected.
- Solution-diffusion mechanism is used for membrane gas separation.
2.2. Mass Transport Mathematical Modeling
2.2.1. Convection and Diffusion Models
2.2.2. Diffusion
2.2.3. Membrane Model
2.2.4. Flow through Membrane in HFM Module
2.3. Flowchart of Post-Processing Scheme
2.4. Geometry
2.5. Meshing
3. Results
3.1. Air Separation
3.2. Carbon Dioxide Separation
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
List of symbols | |
Acronyms | |
CFD | Computational fluid dynamics |
HFM | Hollow fiber membrane |
N2 | Nitrogen |
O2 | Oxygen |
CO2 | Carbon dioxide |
CH4 | Methane |
Greek Symbols | |
x x | Co-ordinate |
y y | Co-ordinate |
z z | Co-ordinate |
Vx | Velocity in x-direction |
Vy | Velocity in y-direction |
Vz | Velocity in z-direction |
“∇” | Nabla operator |
Latin symbols t time (s) | |
Ra. | Rate of reaction (mol/m3.s) |
N | Molar flux (mol/.m2. s) |
D | Diffusion coefficient (m2/s) |
S | Solubility (mol/m3.pa) |
P | Permeance (mol/m2.s.pa) |
C | Concentration of component (mol/m3) |
P | Partial pressure |
L | Module length (m) |
Do | Module diameter (m) |
Ro | Fiber bundle radius (m) |
δ | Membrane thickness (m) |
C | Gas species concentration (mol/m3) |
D_AB | Diffusivity coefficient (m2/s) |
C_0 | Concentration of inlet (mol/m3) |
C_0,1 | Concentration of outlet (mol/m3) |
P | Permeability of the gas (mol/m2.s.pa) |
S | Membrane solubility (mol/m3.pa) |
pf | Pressure of the inlet side (Pa) |
ph | Pressure of the permeate side (Pa) |
δ | Membrane thickness (m) |
∆C | Concentration gradient (mol/m3) |
∆p | Gradient of the partial pressure of gases (Pa/m) |
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Parameters | Symbols | Hollow Fiber Membrane Module [33,34,35,36,37] | Units | |
---|---|---|---|---|
Inlet pressure | 790.8 | 6895 | Pa | |
Permeate pressure | 101.3 | 138 | Pa | |
Inlet gas | 0.205 O2 | 0.5 CO2 | Mole fraction | |
Permeance | 30.78 × 10−10 | 33 × 10−10 | mol/m2. s.pa | |
Module diameter | Do | 9.5 × 10−3 | 20 × 10−3 | m |
Module length | 0.25 | 0.1 | m | |
Membrane thickness | 0.08 | 0.0004 | mm |
Parameters | Total Elements |
---|---|
Solution time (Study 1) | 625 s |
Number of edge elements | 33,311 |
Number of boundary elements | 779,926 |
Number of elements | 6,376,565 |
Minimum element quality | 7.11 × 10−5 |
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Qadir, S.; Ahsan, M.; Hussain, A. Computational Fluid Dynamics Analysis of a Hollow Fiber Membrane Module for Binary Gas Mixture. Gases 2023, 3, 77-91. https://doi.org/10.3390/gases3020005
Qadir S, Ahsan M, Hussain A. Computational Fluid Dynamics Analysis of a Hollow Fiber Membrane Module for Binary Gas Mixture. Gases. 2023; 3(2):77-91. https://doi.org/10.3390/gases3020005
Chicago/Turabian StyleQadir, Salman, Muhammad Ahsan, and Arshad Hussain. 2023. "Computational Fluid Dynamics Analysis of a Hollow Fiber Membrane Module for Binary Gas Mixture" Gases 3, no. 2: 77-91. https://doi.org/10.3390/gases3020005