Statistical Model for the Sizing of a Prototype Solar Still Applicable to Remote Islands
2. Solar Still Set-Up and Experimental Methods
2.1. Experimental Setup and Data Collection
- The solar still was positioned in a north-south orientation such that the inclined glass covers were directed east and west while the heat pipe evacuated tube collectors (ETC) were inclined at 23° to the horizontal facing the south.
- The feedwater storage tub was filled with 120 L of water at least one day ahead of the experiment and the topside glass panes, side wall glass panes, fins, basin, and the solar water heater were also cleaned ahead of the experiment.
- Cotton wicks were prepared by cutting a roll of cotton yarn into 145 strands that were 0.002 m in diameter and 0.50 m long and were then placed in the feedwater to soak overnight.
- On the first day of the experiment at approximately 5:30 am, the glass cover was removed and two sets of fins were installed in the basin of the solar still, following which an electronic water pump was used to fill the basin with feedwater to the maximum water level (0.027 m for 60% recovery ratio, 0.040 m for 70% recovery, and 0.077 m for 80% recovery). The high-water level switch (Figure 2) controls the maximum water level by deactivating the water pump and electronic valve A simultaneously. The cotton wicks were then added to the larger rectangular fins (Figure 3).
- The glass cover was then repositioned on the basin and the gaps between the basin and the frame of the glass cover were sealed with foam material to prevent vapor from escaping.
- Hourly measurements of weather parameters such as total global solar radiation (Rad), ambient temperature (Ta), ambient relative humidity (RHa), and windspeed (Ws) were performed using equipment already installed at the test site such as the Eppley precision spectral pyranometers (Model PSP), Young Co. anemometer (Model 05103L), and Dwyer humidity-temperature transmitter (Model 657-1). Data for the fraction of cloud cover (CCr) for Tainan City was obtained from the Central Weather Bureau .
- The data acquisition modules along with the LabVIEW engineering software were used to make hourly measurements of the basin water temperature (TB), inner glass temperature, vapor temperature, and humidity of the solar still.
- The volume of distillate produced were measured at 8 am (overnight) and 5 pm (daytime) daily until the volume of the feedwater in the basin reaches the minimum level (approximately 1 cm above the absorber plate) which was controlled by the low water level switch (Figure 2).
- The low-level water switch activates electronic valve A which allows the residue water to flow into the brine residue storage tub. The volume of the residue water was then measured after which it was placed in an open area to evaporate (Figure 4a) and the mass of the crude salt that remained was measured by gravimetric analysis (drying and reweighing until two consecutive masses were within 1 g of each other and recorded).
- Following the collection of the residue water, the wicks and fins were then removed and cleaned.
- The procedure was then repeated for the next experiment.
2.2. Uncertainty Analysis
2.3. Data Analysis
3. Results and Discussion
3.1. Summary of Data Collected from Experimental Trials at 70% Recovery Ratio
3.2. Effect of Recovery Ratio on the Performance of the Solar Still
3.3. Effect of Recovery Ratio on the Concentration of the Brine Residue
3.4. Modelling of the Daily Distillate Yield
3.4.1. Identification of Outliers
3.4.2. Predictor Variables and Pearson’s Correlation Matrix
3.4.3. Model Building
3.4.4. Model Evaluation
3.5. Application of Typical Meteorological Year (TMY) Data to the Model
3.6. Sizing of the Solar Still Prototype
3.7. Payback Period
Data Availability Statement
Conflicts of Interest
|Constant regression term|
|Coefficient of the kth predictor variable|
|Random error of regression model|
|Standard deviation, Equation (2)|
|ACF||Annual cash flow (NTD), Equation (21)|
|Capital cost (NTD), Equation (21)|
|Cost of fabrication (NTD)|
|Cost of installation (NTD)|
|Mallows test statistic, Equation (12)|
|Durbin-Watson statistic, Equation (15)|
|The ith error term, Equation (16)|
|The ()th error term, Equation (17)|
|ETC||Evacuated tube collector|
|jth predictor variable|
|Number of variables|
|M||Annual freshwater yield (L)|
|MAE||Mean absolute error, Equation (6)|
|MAPE||Mean absolute percentage error, Equation (9)|
|MPR||Market penetration rate (%)|
|Annual solar salt production (kg)|
|MSE||Mean square error, Equation (7)|
|Number of observations|
|NTD||New Taiwanese dollar|
|PP||Payback period, Equation (21)|
|R2||Coefficient of determination, Equation (4)|
|Adjusted R-squared, Equation (6)|
|Rad||Daily total global solar radiation|
|RHa||Ambient relative humidity|
|RMSE||Root mean square error, Equation (8)|
|RR||Recovery ratio (%), Equation (18)|
|S||Standard error of the regression, Equation (10)|
|SE||Standard error, Equation (11)|
|Selling price of crude solar sea salt (NTD)|
|Selling price of distillate (NTD)|
|SSE||Sum of squares error, Equation (13)|
|Ta||Ambient temperature (°C)|
|TB||Basin water temperature (°C)|
|Temp||Daily average ambient temperature (°C)|
|TDS||Total dissolved solids (mg/L)|
|TMM||Typical meteorological month|
|TMY||Typical meteorological year|
|Standard uncertainty, Equation (3)|
|USD||United States dollar|
|VD||Volume of distillate (L)|
|VF||Volume of feedwater (L)|
|VIF||Variance inflation factor, Equation (11)|
|WHO||World Health Organization|
|Predictor or independent variable|
|Mean of measured values, Equation (1)|
|ith measured value, Equation (1)|
|Mean of the predictor variable|
|The value of the ith predictor variable|
|Response or dependent variable, Equation (19)|
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|Meteorological Factors||Design Factors||Operational Factors||References|
|ambient temperature, sky temperature, global radiation, and wind velocity||-||-|||
|daily solar radiation, average ambient air temperature||-||-|||
|-||-||heat storage material, basin water depth, basin cover thickness and external mirrors|||
|percentage of daylight, ambient temperature, solar radiation, windspeed||glass cover thickness||feedwater salinity, initial water depth|||
|relative humidity, windspeed, solar radiation, ambient temperature||-||feedwater temperature, feedwater flow rate and feedwater TDS|||
|-||inclination angle||feedwater temperature, salt concentration, depth|||
|solar radiation intensity, ambient temperature||-||temperature difference between feedwater and inner condensing cover|||
|-||inclination angle||feedwater temperature|||
|-||quantity of stone used as energy storing medium, area of the double glazing used||feedwater level|||
|solar radiation||-||feedwater temperature|||
|Resistance thermocouple||Thermoway/PT100||0–100 °C||±0.47%|
|Spectral pyranometers||Kipp & Zonen/CMP11||0–1400 W/||±1.41%|
|Anemometer||Vector Instruments/A100L2||0–77 m/s||±1.16%|
|Humidity-temperature transmitter||Dwyer/657-1||0–100% |
|Top-pan balance||Shimadzu/EB-4300D||0–4300 g||±2.5%|
|Trial||Duration (Days)||Average Daily Yield (L/day)||Average Daily Rad (MJ/m2)||Average Daily Ta (°C)||Average Daily CCr||Average Daily Ws (m/s)||Average Daily RHa (%)|
|Parameters||Recovery Ratio (%)|
|Volume of feedwater (L)||46||61||100|
|Total volume of distillate (L)||Overnight||4.229 (15.3%)||7.279 (16.9%)||20.661 (25.8%)|
|Daytime||23.436 (84.7%)||35.690 (83.1%)||59.534 (74.2%)|
|Total||27.665 (100%)||43.001 (100%)||80.195 (100%)|
|Avg. productivity (L/day)||4.61||4.78||5.01|
|Avg. rate of change of productivity (L/day2)||0.768||0.531 (−30.9%)||0.313 (−59.2%)|
|Avg. daily total insolation (MJ/m2)||17.1||17.9||18.6|
|Avg. daily Ta (°C)||26.5||20.6||25.7|
|Avg. daily RHa (%)||75.7||75.0||76.5|
|Avg. daily TB (°C)||40.4||35.2||39.8|
|Recovery Ratio (%)||Mass of Salt (g)||Volume of Water Sample (L)||Concentration of Brine Residue (mg/L)||Change in Concentration (%)|
|60||187.8||2.00 b||93, 900||-|
|70||1, 700.0 a||14.8 a||114, 865||22.3|
|80||441.3||2.00 b||220, 650||135.0|
|Term||Coefficient||SE of Coefficient||p-Value||VIF|
|Number of Variables (k)||R2 (%)||(%)||Mallows Cp||S||Rad||Temp||RHa||Ws||CCr|
|Data Set Used||MAE||RMSE||MAPE (%)||R2 (%)||(%)|
|Month||TMY Year||Monthly Average TMM Values||Daily Average Predicted Yield (L)|
|Rad (MJ/m2)||Temp (°C)||CCr|
|Location||Avg. Yield||Avg. Days per Batch||Avg. Batches per Year||Annual Yield (L)||a Annual Mass of Crude Salt (kg)|
|Location||a Basin Length Requirement||b Basin Size Requirement||c Evacuated Tube Requirement|
|Value (m)||% Increase||Value (m2)||% Increase||Amount||% Increase|
|Location||(NTD)||ACF (NTD)||PP (Years)|
|Dongji Islet||100, 567.5 (USD 3, 419.3)||16, 421.76 (USD 558.3)||6.1|
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Samuel, A.; Chang, K.-C. Statistical Model for the Sizing of a Prototype Solar Still Applicable to Remote Islands. Water 2022, 14, 3510. https://doi.org/10.3390/w14213510
Samuel A, Chang K-C. Statistical Model for the Sizing of a Prototype Solar Still Applicable to Remote Islands. Water. 2022; 14(21):3510. https://doi.org/10.3390/w14213510Chicago/Turabian Style
Samuel, Alinford, and Keh-Chin Chang. 2022. "Statistical Model for the Sizing of a Prototype Solar Still Applicable to Remote Islands" Water 14, no. 21: 3510. https://doi.org/10.3390/w14213510