A Review of CFD Modelling and Performance Metrics for Osmotic Membrane Processes
Abstract
:1. Introduction
2. Development of New Spacer Designs
3. Existing CFD Models and Their Challenges
3.1. Reverse Osmosis (RO) Modelling
3.2. Forward Osmosis (FO) and Pressure Retarded Osmosis (PRO) Modelling
4. Hybrid RO Desalination Systems
5. Module Performance Metrics
5.1. Reverse Osmosis (RO)
5.2. Forward Osmosis (FO) and Pressure Retarded Osmosis (PRO)
5.3. CFD-Derived Metrics
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
Symbol | |
A | Membrane permeability [m Pa−1 s−1] |
B | Solute permeability [m s−1] |
D | Solute diffusivity [m2 s−1] |
dh | Hydraulic diameter [m] |
fglob | Fanning friction factor |
hch | Membrane channel height [m] |
K | Diffusion resistivity within the membrane porous layer [s m−1] |
kmt | Mass transfer coefficient [m s−1] |
Jw | Transmembrane volumetric water flux [m s−1] |
Js | Solute mass flux [kg m−2 s−1] |
L | Membrane channel length [m] |
Mloc | Local mixing index [s−o] |
n | Membrane surface normal vector |
Q | Volumetric flow rate [m3 s−1] |
Qp | Permeate flow rate across membrane [m3 s−1] |
p | Pressure [Pa] |
Δp | Transmembrane hydraulic pressure difference [Pa] |
Δpch | Channel pressure drop [Pa] |
PD | Power density [W m−2] |
Pn | Power number |
R | Membrane intrinsic rejection |
Rr | Recovery rate |
S | Structural parameter [m] |
SE | Specific energy [J m−3] |
SEC | Specific energy consumption [J m−3] |
Sh | Sherwood number |
SCE | Spacer configuration efficacy |
SPC | Specific power consumption [W m−3] |
SPMP | Spacer performance ratio |
t | Membrane thickness [m] |
ueff | Effective velocity [m s−1] |
ux | Flow velocity in x-direction [m s−1] |
uy | Flow velocity in y-direction [m s−1] |
uz | Flow velocity in z-direction [m s−1] |
Velocity vector [m s−1] | |
vp | Perturbation velocity vector [m s−1] |
w | Solute mass fraction |
x | Distance in the bulk flow direction, parallel to membrane surface [m] |
y | Distance from the bottom membrane surface, in direction normal to the surface [m] |
z | Distance in the direction perpendicular to both x and y [m] |
Greek letters | |
ε | Porosity |
γ | Concentration polarisation modulus |
ηid | Ideal energy efficiency of desalination |
μ | Dynamic viscosity [kg m−1 s−1] |
π | Osmotic pressure [Pa] |
ϕ | Osmotic pressure coefficient [Pa] |
Φ | Mass transfer enhancement factor |
ρ | Fluid density [kg m−3] |
σ | Reflection coefficient |
T | Tortuosity |
τ | Wall shear stress [Pa] |
Subscript | |
b | Value for the bulk flow |
d | Value for the draw solution |
E | Value for enhanced condition |
f | Value for the feed solution |
in | Value at the domain inlet |
out | Value at the domain outlet |
m | Value at membrane layer/surface |
NE | Value for non-enhanced condition |
p | Value for the permeate |
s | Value for the support substrate |
slit | Value in empty channel |
spacer | Value in spacer-filled channel |
t | Value for wall-tangential shear |
w | Value on the membrane surface (wall) |
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Authors | Research Type | Geometry Analysed | Main Findings | Observations |
---|---|---|---|---|
Koutsou and Karabelas [56] | CFD and experimental | Submerged spacer with circular node with varying mesh length and attack angle. |
|
|
Han et al. [66] | CFD | Net type symmetric spacer with different diameter and pillar shape nodes. |
|
|
Kerdi et al. [55] | CFD and experimental | Effect of spacer perforation on hydrodynamics. |
|
|
Sreedhar et al. [52,63] | Experimental | 3 TPMS-based spacers for UF and RO processes. |
|
|
Experimental | 6 TPMS spacers for UF, and the effect of grading spacer voidage on one of TPMS spacers. |
| ||
Ali et al. [58] | CFD and experimental | Net-type symmetric spacer with small diameter (df/hch = 0.42) and column shape nodes. |
|
|
Researchers | Significance | Findings | Observation |
---|---|---|---|
Tan and Ng [114] |
|
|
|
Gruber et al. [116] |
|
|
|
Park and Kim [41] |
|
|
|
Sagiv et al. [115] |
|
|
|
Heon et al. [111] |
|
|
|
Lee et al. [109] |
|
|
|
Lian et al. [36] |
|
|
|
Alshwairekh et al. [119] |
|
|
|
Qing et al. [6] |
|
|
|
Researchers | Significance | Findings | Observation |
---|---|---|---|
Nagy [122] |
|
|
|
Straub et al. [120] |
|
|
|
Wang et al. [43] |
|
|
|
Sagiv et al. [123] |
|
|
|
Soltani and Struchtrup [121] |
|
|
|
Location | RO | FO | PRO |
---|---|---|---|
Inlet | |||
Outlet | |||
Wall (non-membrane, spacer) | |||
Side openings |
| ||
Inlet/Outlet (periodic) | N/A | N/A | |
Membrane permeation | Selective layer: Porous layers: Whole membrane: | Feed side: Draw side: | |
Impermeable membrane | Jw calculated using kmt | N/A | N/A |
Hybrid System | Reference | Main Findings | Obstacles |
---|---|---|---|
FO–RO hybrid system | Kim et al. [132] |
|
|
PRO–RO hybrid system | Kim et al. [14] |
|
|
RO–PRO hybrid system | Senthil and Senthilmurugan [136] |
|
|
FO–RO–PRO hybrid system | Fane [22] |
|
|
Indicator Metric | Mathematical Description | Unit | Description | Observation |
---|---|---|---|---|
Concentration polarisation [153] | - | Ratio of solute concentration at the membrane wall to the concentration at the inlet bulk. | The formulation of CP index varies depending on the choice of membrane processes used (viz. RO vs FO). | |
Ideal energy efficiency of desalination [22] | - | Ratio of Gibbs free energy of mixing of salt/water mixture versus specific energy consumption for desalination. | Current technologies have efficiencies just below 50% of the ideal thermodynamic limit. | |
Fanning friction factor [154] | - | Dimensionless measurement of pressure loss across the membrane channel. | Only related to hydrodynamics, not mass transfer. | |
Local mixing index [155,156] | s−2 | Mixing dependence on fluid stretching and folding. | The relationship between the degree of stretching and folding measured, and mass transfer enhancement is unclear. | |
Mass transfer coefficient [157] | m/s | Diffusion rate constant of water through membrane wall. | Give quick prediction of the degree of mass transfer enhancement. Typically, the values are of the order of 10−5 m/s. | |
Mass transfer enhancement factor [158] | - | Relative change in concentration polarisation due to enhancement techniques. | Positive values indicate increased mass transfer, whereas negative values indicate a decrease in mass transfer and flux. | |
Power density [120] | W/m2 | Power generated per membrane area (for PRO application). | High power density is favourable to minimize the membrane area required for generating power. | |
Recovery rate [46] | - | Ratio of volumetric permeate to feed flow rate. | Provides quick prediction of total water produced depending on types of feed water used (viz. brackish vs seawater). | |
Sherwood number [159] | - | Ratio of mass transfer by convection to mass transfer by diffusion. | Only diffusivity term that reflects the solute characteristics and does not take into consideration other membrane properties parameters (e.g., surface charge). | |
Spacer configuration efficacy [142] | - | Ratio of mass transfer increment by spacer filaments to power consumption. | The limitation of this concept is that it does not show much dependence on Reynolds number. | |
Specific energy consumption [29] | kWh/m3 | Ratio of energy consumption to volumetric permeate flow rate. | Most commonly used for predicting energy usage but does not reflect the actual processing cost. | |
Wall shear stress [160] | Pa | Rate of change of velocity near the membrane surface. | Proxy indicator for anti-fouling tendencies. |
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Toh, K.Y.; Liang, Y.Y.; Lau, W.J.; Fimbres Weihs, G.A. A Review of CFD Modelling and Performance Metrics for Osmotic Membrane Processes. Membranes 2020, 10, 285. https://doi.org/10.3390/membranes10100285
Toh KY, Liang YY, Lau WJ, Fimbres Weihs GA. A Review of CFD Modelling and Performance Metrics for Osmotic Membrane Processes. Membranes. 2020; 10(10):285. https://doi.org/10.3390/membranes10100285
Chicago/Turabian StyleToh, Kang Yang, Yong Yeow Liang, Woei Jye Lau, and Gustavo A. Fimbres Weihs. 2020. "A Review of CFD Modelling and Performance Metrics for Osmotic Membrane Processes" Membranes 10, no. 10: 285. https://doi.org/10.3390/membranes10100285