Optimization Study of Small-Scale Solar Membrane Distillation Desalination Systems (s-SMDDS)
Abstract
:1. Introduction
2. System and Modeling
3. Equipment Sizing
Parameter | Value |
---|---|
Total membrane area (m2) | 2.8 |
Single sheet membrane width (m) | 0.36 |
Single sheet membrane length (m) | 0.39 |
Membrane material (porous + supporting) | PTFE + PP |
Membrane thickness (μm) | 30/170 |
Membrane pore diameter (μm) | 0.2 |
Membrane porosity | 0.8 |
Height of hot fluid channel (mm) | 1 |
Height of cold fluid channel (mm) | 1 |
Thickness of air gap (mm) | 1 |
4. Cost Analysis
- The installation cost is 25% of the purchased equipment costs.
- The instrumentation and control cost is 25% of the total purchased equipment cost.
- Zero land cost.
- Zero pretreatment cost.
- The annual interest rate and plant lifetime for amortization of the capital cost or determining the annual fixed charge are 5% and 20 years.
- The annual operating and maintenance (O&M) cost is estimated to be 20% of the plant annual fixed charge.
- The membrane replacement rate is 20% per year.
Equipment | Purchased Cost ($) | Notes |
---|---|---|
Solar collector | With rack. | |
Thermal storage tank | Carbon steel. | |
Plate heat exchanger | for anti-corrosion material of construction; 1 m2 ≤ AHE ≤ 5 m2 | |
Pump | for anti-corrosion material of construction; | |
Membrane module | Flat sheet AGMD membrane module as the product based on [7] and modified cost index; |
5. Dynamic Optimization
- the desired distilled water production rate (FDW);
- the solar radiation profile (IS);
- the parameters for pseudo-steady-state analysis; ΔTSmax, ΔTlm, ΔTLoop1, ΔTLoop2;
- the maximum temperature of S2 ( TS2 < 95 °C).
6. Results and Discussion
6.1. Optimal Solutions and Performance
FDW (kg/day) | 100 | 200 | 300 | 400 | 500 | 600 |
---|---|---|---|---|---|---|
Unit cost with 1:1 dilution ($/m3) | 15.70 | 8.54 | 6.55 | 6.01 | 5.92 | 7.05 |
STEC (kWh/m3) | 109.29 | 213.88 | 393.18 | 572.63 | 758.87 | 1424.76 |
PR | 5.91 | 3.02 | 1.64 | 1.13 | 0.85 | 0.45 |
RR (%) | 5.49 | 5.33 | 4.60 | 4.29 | 4.07 | 2.75 |
ASC (m2) | 1.36 | 5.35 | 14.76 | 28.70 | 47.57 | 107.21 |
VST (m3) | 0.07 | 0.28 | 0.76 | 1.48 | 2.46 | 5.54 |
AHX (m2) | 1 | 1 | 1.01 | 1.66 | 2.55 | 2.97 |
FS3 (kg/h) | 85.67 | 216.49 | 219.49 | 360.82 | 554.60 | 645.10 |
FS8 (kg/h) | 0 | 0 | 0 | 0 | 0 | 0 |
FS9 (kg/h) | 93.73 | 183.85 | 313.24 | 442.19 | 578.05 | 1015.95 |
FS11 (kg/h) | 0 | 0 | 0 | 0 | 0 | 0 |
FDW (kg/day) | 200 | 400 | 600 | 800 | 1000 |
---|---|---|---|---|---|
Unit cost with 1:1 dilution ($/m3) | 14.24 | 7.84 | 5.95 | 5.23 | 5.16 |
STEC (kWh/m3) | 100.88 | 242.76 | 371.43 | 533.41 | 713.76 |
PR | 6.40 | 2.66 | 1.74 | 1.21 | 0.91 |
RR (%) | 5.56 | 5.07 | 4.81 | 4.55 | 4.57 |
ASC (m2) | 2.52 | 12.17 | 27.95 | 53.54 | 89.58 |
VST (m3) | 0.13 | 0.63 | 1.44 | 2.77 | 4.63 |
AHX (m2) | 1 | 1 | 2.77 | 4.60 | 3.53 |
FS3 (kg/h) | 188.00 | 217.58 | 601.76 | 999.64 | 1536.21 |
FS8 (kg/h) | 0 | 0 | 0 | 0 | 0 |
FS9 (kg/h) | 180.95 | 399.48 | 591.36 | 824.45 | 1121.01 |
FS11 (kg/h) | 0 | 0 | 0 | 0 | 0 |
Items | This study | Banat and Jwaied [6] (compact/large) | MEDESOL [7] 2,3 | Saffarini et al. [8] |
---|---|---|---|---|
Capacity (kg/day) | 500 | 100/500 | 73 | 700 |
Unit cost 1 ($/m3) | 5.92 | 15/18 | 15.67 | 18.26 |
Equipment size | ||||
Membrane area (m2) | 11.5 | 10/40 | 2.3 | 7 |
Solar collector area (m2) | 47.57 | 5.73/72 | 2.6 | N/A |
Heat exchanger area (m2) | 2.55 | 0/N/A | $846 | N/A |
Thermal storage tank (m3) | 2.46 | N/A | N/A | N/A |
Cost data | ||||
Membrane module | $4730 | $1080/$4320 | $808 ($360/m2) | $350/m2 |
Solar collector | $5985 w/ rack | $900/$8700 w/ rack | $385 ($150/m2, w/o rack) | $160/m2 (w/o rack) |
Piping and tanks | $275 | $200/$500 | $62 | $250 |
Heat exchanger | $2730 | 0/$1500 | $846 | $750 |
Pumps | $1000 | $300/$700 | $150 | $700 |
Monitoring and control | 3680 | $3328/$10,510 | $385 | $4500 |
- For the systems reported in the literature, the sizes of equipment units and operating conditions are either not rigorously determined or are determined by a steady state analysis with a constant solar radiation intensity.
- The systems reported in this study are designed via dynamic optimization. For the fixed membrane module sizes, all other equipment units are optimally sized. The flow rates of all of the streams are also optimally determined, including the optimal time-varying flow rate of the solar collector circulation flow (S1). The flow rate of S1 varies with solar radiation and leads to the higher temperature of the hot fluid in the MD module through the heat transfer via the thermal storage tank and the heat exchanger.
6.2. Sensitivity of Pseudo-Steady-State Parameters
ΔTSmax (°C) | 5 | 10 | 15 |
---|---|---|---|
Unit cost ($/m3) | 7.74 | 5.92 | 5.12 |
ΔTlm (°C) | 5 | 10 | 15 |
Unit cost ($/m3) | 5.92 | 5.77 | 5.71 |
ΔTLoop1 (°C) | 15 | 20 | 25 |
Unit cost ($/m3) | N/A | 5.92 | 5.91 |
ΔTLoop2 (°C) | 20 | 25 | 30 |
Unit cost ($/m3) | 5.82 | 5.92 | 6.03 |
6.3. Operation Performance of Optimal Systems
6.4. Effect of Membrane Characteristics
7. Conclusions
Symbol
A | Area (m2) |
a | Amortization factor |
AGMD | Air gap membrane distillation |
Cp | Heat capacity (J/kg K) |
C | Cost ($ or $/year) |
DCMD | Direct contact membrane distillation |
Dh | Hydraulic diameter (m) |
Dm | Molecular diffusivity (m2/s) |
DK | Knudsen diffusivity (m2/s) |
F | Flow rate (kg/h) |
H | Height (m) |
h | Heat transfer coefficient (W/m2 K) |
I | Intensity of solar radiation (W/m2) |
i | Interest rate |
k | Mass transfer coefficient (m/s) |
K | Thermal conductivity (W/m K) |
L | Length of the equipment (m) |
LGMD | Liquid gap membrane distillation |
M | Mass of the fluid in the equipment (kg) |
MD | Membrane distillation |
Mw | Molecular weight of water (kg/kmol) |
m | Mass flow rate (kg/s) |
N | Mole flux of water (kmol/m2 s) |
Nu | Nusselt number |
n | Plant life (years) |
P | Pressure (Pa) |
Pr | Prandtl number |
Qh | Heat flux by convection or conduction (J/m2 s) |
QN | Heat flux of the sensible heat transfer with the mass flux (J/m2 s) |
q | Heat transfer rate (J/s) |
R | Gas constant (Pa m3/kmol K) |
Re | Reynolds number |
T | Temperature (K) |
TAC | Total annual cost ($/year) |
t | Time |
U | Overall heat transfer coefficient (W/m2 K) |
V | Volume |
VMD | Vacuum membrane distillation |
W | Width of the equipment (m) |
x | Flow direction |
y | Mole fraction |
Greek Letters
ΔHVL | Enthalpy for vapor-liquid phase change (J/m2 s) |
ΔHvap | Heat of vaporization (J/kmol) |
ΔT | Temperature difference (K) |
Δt | Time period (hour) |
δ | Thickness (m) |
ε | Porosity of the membrane |
η | Collector efficiency |
τ | Tortuosity of the membrane |
Subscripts
ag | Air gap |
air | Air |
CC | Capital cost |
CL | Cold liquid |
cp | Cooling plate |
CONL | Condensing liquid |
DW | Distilled water |
f | Fluid |
fixed | Fixed |
HL | Hot liquid |
HX | Heat exchanger |
lf | Liquid film |
lm | Logarithmic mean |
max | Maximum |
MD | Membrane distillation |
m1 | Hot fluid-membrane interface |
m2 | Membrane-air gap interface |
mem | Membrane |
mr | Membrane replacement |
O&M | Operating and maintenance |
PS | Pseudo state |
S | Solar |
sat | Saturation |
SC | Solar collector |
ST | Thermal storage tank |
v | Vapor |
vap | Vapor |
w | Water |
Highlights
- The design and operation of s-SMDDS for minimum-cost water production are obtained.
- A pseudo steady state approach is proposed for equipment sizing.
- Effect of increasing membrane mass transfer coefficient on water production cost is analyzed.
Acknowledgements
Author Contributions
Conflicts of Interest
References
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Chang, H.; Chang, C.-L.; Hung, C.-Y.; Cheng, T.-W.; Ho, C.-D. Optimization Study of Small-Scale Solar Membrane Distillation Desalination Systems (s-SMDDS). Int. J. Environ. Res. Public Health 2014, 11, 12064-12087. https://doi.org/10.3390/ijerph111112064
Chang H, Chang C-L, Hung C-Y, Cheng T-W, Ho C-D. Optimization Study of Small-Scale Solar Membrane Distillation Desalination Systems (s-SMDDS). International Journal of Environmental Research and Public Health. 2014; 11(11):12064-12087. https://doi.org/10.3390/ijerph111112064
Chicago/Turabian StyleChang, Hsuan, Cheng-Liang Chang, Chen-Yu Hung, Tung-Wen Cheng, and Chii-Dong Ho. 2014. "Optimization Study of Small-Scale Solar Membrane Distillation Desalination Systems (s-SMDDS)" International Journal of Environmental Research and Public Health 11, no. 11: 12064-12087. https://doi.org/10.3390/ijerph111112064