Author Contributions
Conceptualization, M.M. and M.R.I.; methodology, M.M. and M.R.I.; software, M.R.I.; validation, B.L., M.R.I. and Y.Y.; formal analysis, M.R.I. and B.L.; investigation, M.R.I. and B.L.; resources, M.M. and C.-C.C.; data curation, M.R.I. and B.L.; writing—original draft preparation, M.R.I.; writing—review and editing, M.R.I., B.L., Y.Y., C.-C.C. and M.M.; visualization, M.R.I. and B.L.; supervision, M.M. and C.-C.C.; project administration, M.M.; funding acquisition, M.M. and C.-C.C. All authors have read and agreed to the published version of the manuscript.
Disclaimer
This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
Figure 1.
Control volumes of feed and permeate sides for different MD modules. Mass, momentum, and energy balances are made over the control volume of thickness . and represent mass and heat flux through the membrane, respectively; and feed and permeate bulk temperature, respectively; and membrane surface temperature on the feed and permeate sides, respectively; temperature on the permeate side; , , , , and temperature at the membrane-air gap interface, the air gap-condensate film interface, the condensate film-cooling plate interface, and the cooling plate-coolant interface, respectively; and concentration in the feed bulk solution and on the feed side of the membrane, respectively; and permeate velocity at the inlet and outlet, respectively; and air velocity at the inlet and outlet, respectively; and coolant velocity at the inlet and outlet, respectively; and vacuum on the permeate side.
Figure 1.
Control volumes of feed and permeate sides for different MD modules. Mass, momentum, and energy balances are made over the control volume of thickness . and represent mass and heat flux through the membrane, respectively; and feed and permeate bulk temperature, respectively; and membrane surface temperature on the feed and permeate sides, respectively; temperature on the permeate side; , , , , and temperature at the membrane-air gap interface, the air gap-condensate film interface, the condensate film-cooling plate interface, and the cooling plate-coolant interface, respectively; and concentration in the feed bulk solution and on the feed side of the membrane, respectively; and permeate velocity at the inlet and outlet, respectively; and air velocity at the inlet and outlet, respectively; and coolant velocity at the inlet and outlet, respectively; and vacuum on the permeate side.
Figure 2.
Saturated temperatures of water equivalent to vapor pressure depression, moisture content of air, and vacuum pressure. The values of a and b are 0.988 and 0.0492, respectively, obtained from the exponential curve fitting of vapor pressure vs. temperature from the Antoine equation.
Figure 2.
Saturated temperatures of water equivalent to vapor pressure depression, moisture content of air, and vacuum pressure. The values of a and b are 0.988 and 0.0492, respectively, obtained from the exponential curve fitting of vapor pressure vs. temperature from the Antoine equation.
Figure 3.
Flowchart for performance calculation of MD-based desalination.
Figure 3.
Flowchart for performance calculation of MD-based desalination.
Figure 4.
Variation in (solid lines—left y-axis) and (dashed lines—right y-axis) along the length at different feed salinities for (a) DCMD, (b) VMD, (c) SGMD, and (d) AGMD.
Figure 4.
Variation in (solid lines—left y-axis) and (dashed lines—right y-axis) along the length at different feed salinities for (a) DCMD, (b) VMD, (c) SGMD, and (d) AGMD.
Figure 6.
GOR–flux performance for permeate condition in DCMD with varying distillate flow rate of 1200–2000 kg/h and temperature of 20–40 °C. Note that GOR and flux are calculated from the DCMD-based desalination process at each condition.
Figure 6.
GOR–flux performance for permeate condition in DCMD with varying distillate flow rate of 1200–2000 kg/h and temperature of 20–40 °C. Note that GOR and flux are calculated from the DCMD-based desalination process at each condition.
Figure 7.
GOR–flux performance for permeate pressure in VMD with varying permeate pressure of 3.5–8.5 kPa and module length of 1–3 m. Note that GOR and flux are calculated from the VMD-based desalination process at each condition.
Figure 7.
GOR–flux performance for permeate pressure in VMD with varying permeate pressure of 3.5–8.5 kPa and module length of 1–3 m. Note that GOR and flux are calculated from the VMD-based desalination process at each condition.
Figure 8.
GOR–flux performance for permeate conditions in SGMD with varying (a) airflow rate of 400–1300 kg/h and (b) RH of 0–90%. Note that GOR and flux are calculated from the SGMD-based desalination process at each condition.
Figure 8.
GOR–flux performance for permeate conditions in SGMD with varying (a) airflow rate of 400–1300 kg/h and (b) RH of 0–90%. Note that GOR and flux are calculated from the SGMD-based desalination process at each condition.
Figure 9.
GOR–flux performance for permeate conditions in AGMD with varying coolant temperature of 20–50 °C for (a) air gap thickness of 1–4 mm and (b) coolant flow rate of 1250–2000 kg/h. Note that GOR and flux are calculated from the AGMD-based desalination process in each condition.
Figure 9.
GOR–flux performance for permeate conditions in AGMD with varying coolant temperature of 20–50 °C for (a) air gap thickness of 1–4 mm and (b) coolant flow rate of 1250–2000 kg/h. Note that GOR and flux are calculated from the AGMD-based desalination process in each condition.
Figure 10.
Vapor permeabilities in different mass transport regions of the AGMD process. CKN, CMol, Cmem, Cgap, and Cov denote the vapor permeability corresponding to Knudsen diffusion, molecular diffusion, diffusion inside the porous membrane, mass transfer through the air gap, and overall mass transfer through the membrane and air gap.
Figure 10.
Vapor permeabilities in different mass transport regions of the AGMD process. CKN, CMol, Cmem, Cgap, and Cov denote the vapor permeability corresponding to Knudsen diffusion, molecular diffusion, diffusion inside the porous membrane, mass transfer through the air gap, and overall mass transfer through the membrane and air gap.
Figure 11.
Flux, vapor permeability, and vapor pressure difference profile with varying gap thickness.
Figure 11.
Flux, vapor permeability, and vapor pressure difference profile with varying gap thickness.
Figure 12.
Thermal efficiency () of different MD configurations.
Figure 12.
Thermal efficiency () of different MD configurations.
Figure 13.
Partial condensation of vapor in VMD and SGMD-based desalination process.
Figure 13.
Partial condensation of vapor in VMD and SGMD-based desalination process.
Figure 14.
Flux vs. STEC in MD-based desalination.
Figure 14.
Flux vs. STEC in MD-based desalination.
Figure 15.
Qualitative summary of various MD configurations versus various key efficiency, operating, and economic parameters.
Figure 15.
Qualitative summary of various MD configurations versus various key efficiency, operating, and economic parameters.
Table 1.
Mass transfer mechanism in MDs.
Table 1.
Mass transfer mechanism in MDs.
| Diffusion Flux | Viscous Flux |
---|
| Knudsen | Molecular | |
---|
DCMD | ✓ | ✓ | ✕ |
VMD | ✓ | ✕ | ✓ |
SGMD | ✓ | ✓ | ✕ |
AGMD | ✓ | ✓ | ✕ |
Table 2.
Balance equations in the permeate channel of DCMD and SGMD and coolant channel in AGMD.
Table 2.
Balance equations in the permeate channel of DCMD and SGMD and coolant channel in AGMD.
| Mass | Momentum | Energy |
---|
DCMD | | | |
SGMD | | | |
AGMD | | | |
Table 3.
Vapor permeabilities in membrane and air gap.
Table 3.
Vapor permeabilities in membrane and air gap.
Membrane | Air Gap | System |
---|
Knudsen | Molecular | Combined | | |
---|
| | | | |
Table 4.
Equivalent saturation temperature () for partial pressure of water in the permeate side.
Table 4.
Equivalent saturation temperature () for partial pressure of water in the permeate side.
DCMD | VMD | SGMD | AGMD |
---|
| | | |
Table 5.
Validation of MD modules.
Table 5.
Validation of MD modules.
MD Modules | DCMD | VMD | SGMD | AGMD |
---|
Data source | [17] | [16] | [18] | [15] |
Number of data | 10 | 4 | 15 | 16 |
Module geometry | | | | |
Length (mm) | 400 | 85 | 85 | 100 |
Width (mm) | 150 | 39 | 39 | 50 |
Channel height (mm) | 1 | 2 | 2 | 2 |
Air gap (mm) | – | – | – | 5–13 |
Membrane | | | | |
Type | PTFE | PTFE | PTFE | PTFE |
Pore size (μm) | 0.22 | 0.20 | 0.20 | 0.2 |
Thickness (μm) | 110 | 30 | 30 | 100 |
Porosity (%) | 83 | 80 | 80 | 80 |
Tortuosity | 2.13 | 2.91 | 2.91 | 1.5 |
Operating condition | |
Feed (temperature, salinity, flow rate) | 40–60 °C | 50–60 °C | 40–80 °C | 40–80 °C |
10 g/L | 0–123 g/L | 0 g/L | 0–43 g/L |
92–302 kg/h | 72–80 kg/h | 15–74 kg/h | 87–92 kg/h |
Permeate (temperature, flow rate, vacuum, and RH) | Distillate | Vacuum | Air 30% RH | Coolant |
93–301 kg/h | 6.5 kPa | 20 °C | 20 °C |
20 °C | | 0.06–0.35 kg/h | 90 kg/h |
%ARD | 11.63 | 9.82 | 12.10 | 7.44 |
Table 6.
Geometry of the modules and operating of MD desalination processes.
Table 6.
Geometry of the modules and operating of MD desalination processes.
MD Modules | DCMD | VMD | SGMD | AGMD |
---|
Module geometry | | | | |
Length (m) | Depends on MD configurations |
Width (m) | 6 | 6 | 6 | 6 |
Channel height (mm) | 2 | 2 | 2 | 2 |
Air gap (mm) | – | – | – | 1 |
Operating condition | | | | |
Feed (feed temperature, flow rate) | 85 °C @1634 kg/h |
Feed salinity | 60–300 g/L of NaCl |
Permeate | Distillate | Vacuum | Air 30% RH | Coolant |
20 °C | 3.5 kPa | 20 °C | 20 °C |
1634 kg/h | | 930 kg/h | 1634 kg/h |