DETERMINING THE RELIABILITY OF PASSIVE SOLAR DISTILLATION BASINS AND PREDICTING THE PROPER STORAGE VOLUME TO MEET YEAR-ROUND POTABLE WATER DEMAND

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1 DETERMINING THE RELIABILITY OF PASSIVE SOLAR DISTILLATION BASINS AND PREDICTING THE PROPER STORAGE VOLUME TO MEET YEAR-ROUND POTABLE WATER DEMAND Noe Santos, M.S., E.I. 55 Maryland Pkwy, Box 515 Las Vegas, NV Aly Said, PhD, P.E. 55 Maryland Pkwy, Box 515 Las Vegas, NV Dave James, PhD, P.E. 55 Maryland Pkwy, Box 5199 Las Vegas, NV Nanda Venkatesh, M.S. 55 Maryland Pkwy, Box 515 Las Vegas, NV ABSTRACT A study has been performed to evaluate and model the reliability of passive solar distillation systems consisting of distillation basins and water storage tanks. The genetic algorithm (GA) optimization method was used to optimize several objective functions to accurately predict daily production from local weather data. The best objective function was capable of predicting daily production with a mean absolute error as low as 11%. A system dynamics model (SDM) was created to forecast daily production and reservoir storage volume. The SDM indicated a minimum basin area requirement of 1.5 m /per capita in order to meet daily water demand over the five year period for the latitude and weather of the Mojave Desert. The SDM also indicated that a storage volume of L per capita would be sufficient to buffer both weather related, daily, and seasonal climate variations in distillate production and to provide a reliable year-round supply. 1. INTRODUCTION Both water transportation costs and distillation processes such as multistage flash, multiple effect, vapor compression, reverse osmosis, electrolysis, phase change, and solvent extraction will see their price per unit of water increase drastically as fossil fuel demand exceeds supply. Solar distillation is a possible low-cost alternative technology that can both distill brackish or polluted water into drinkable water and reduce the fossil fuel dependence associated with many distillation plants(1). Due to relatively low and variable energy fluxes from the sun, solar stills require a relatively high amount of land area compared to other technologies in order to provide reliable potable water supplies. The ability to improve the accuracy and reliability of predicted distillate yields that result from meteorological variations would facilitate the sizing of solar still installations to meet water demands. With the current state of single-basin still technology producing one to seven liters per square meter of still area per day, a community requiring m 3 /day of drinking water () would require 3 to hectares of still area, respectively. Figure 1 illustrates an example of a common single basin solar still model. 1

2 Cover Glass Reflected Rays Raw Water Fig. 1: Basic solar still design concept (3) For reliable supply, combined still basin area and water storage volume must be designed and constructed to meet system demand when solar radiation (insolation) is low due to either seasonal or daily weather variations. It is the purpose of this paper to present an approach for predicting basin yield from varying daily and seasonal weather conditions, and also to use system dynamics modeling to predict water storage volume.. BACKGROUND Evaporation Condensation Distillate Collection Trough Sun Radiation Most current solar still research has emphasized the effects of modifying solar still design or introducing new still components to increase the evaporation rate of the distilland. Published modifications include using internal/external condensers (-5), using black walls with cotton cloth (1), the use of black dye and charcoal in the distilland (), multi-wick solar stills (7), and condensing cover cooling techniques (). Previous research to accurately model solar still performance includes iteration methods (9), numerical methods (1), and computer simulation (11). Despite the various analysis techniques, all of these techniques rely on internal heat and mass transfer models (HMT) which were first applied to heated parallel plates by Dunkle (1) in the 19s and revisited by other researchers such as Tiwari and Tiwari (13). Dunkle and Tiwari and Tiwari s models (1-13) rely on water properties such as water density, specific heat, thermal conductivity, viscosity, latent heat of vaporization, partial saturated vapor pressure, and derived heat and mass transfer coefficients. The coefficients are derived by processing large amounts of real-time measurements of outer/inner glass temperature, vapor temperature, distilland temperature, internal solar still humidity, ambient air temperature, ambient air velocity, total and diffused radiation, and distillate production. Because of the large amounts of real time data, usually recorded at sub-hourly intervals, required to validate the HMT models, the ability to forecast distillate production is limited by the ability to record the data and convert the information into heat and mass transfer coefficients. While HMT models have been successfully generated, the amount of monitoring equipment and data processing would usually put such models out of reach for most rural communities. The first part of this study aims to replace traditional HMT modeling, with predictive models that rely on average daily weather observations and distilland volume as the input data and the total daily distillate production as the target variable. The second part of this study aims to calculate water yields and required storage volume for five years using a system dynamics approach. While, multivariable regressions have previously been successfully applied to predict solar distillate yields (1), modeling techniques that do not depend on assumed normal data distributions may be suitable for use in predicting solar still yields. Artificial Neural Networks have previously been successfully applied to solar still yields (1-17). Genetic algorithms, an alternative non-parametric technique, will be evaluated in this study..1. Genetic Algorithms Genetic algorithms (GAs) were first developed by John Holland and his students and colleagues in the 19s and 197s to both understand adaptation as it naturally occurs throughout nature and apply the mechanisms as computer models (1). Genetic algorithms are capable of solving constrained and unconstrained optimization problems based on processes that drive biological evolution (1). Genetic algorithms require an assumed fitness or objective function to optimize by finding the minimum error of the objective function (1). The value of the objective function for any chromosome/individual is known as the score or fitness. The GA performs a series of iterative computations to create successive new populations until the minimum of the objective function is found (15). 3. EXERIMENTAL MATERIALS AND METHODS The original solar still experimental data was collected between February and August 7 using single basin solar stills from two different manufacturers (3). The experimental site was located on the roof of the Howard R. Hughes College of Engineering building at the University of Nevada, Las Vegas (3.11 N, W). Hourly weather data were obtained from the U.S. National Weather Service (NWS) station located at the McCarran International Airport; located 1.5 miles south of the test site. Hourly temperature, wind speed and direction data were processed

3 to generate daily average values, The average daily wind direction was modified to range between to ±1 degrees from north. This modification was necessary to prevent a large numerical change when prevailing wind direction changed slightly between northwesterly and northeasterly. Input data resolutions were to the nearest tenth of a degree Celsius, tenth of a meter/second, tenth of a degree on compass heading, and tenth of a liter. The original distillate production data were collected in a series of several experiments that compared two single basin solar stills, and varied both cover glass type and distilland volume (3). Solar still production data presented in this study were gathered from two solar stills known as SS1 and SS. Only data from experiments using a standard.3 cm (.15 inch) tempered window plate glass were used in this modeling study. SS1 has a rectangular basin area of.97 m and a body composed of sheet aluminum with.5 cm. thick polyisocyanurate foam board, coated with FDA approved silicone sealant in layers with un-bonded glass fiber cloth for insulation (3). Cover glass sealing was accomplished with closed cell high-density neoprene window seal. SS1 has two inlets for filling and drainage and a glass cover slope of. SS1 was operated between February and July 7 with a break in operation between July and November. SS has a rectangular basin area of.77 m and a fiberglass exterior foamed in place insulation, with a black vacuum-formed inner liner. The sealing is in the form of a u-channel molding wrapped around the perimeter of the still, clamping the cover glass against the d-section seal bonded to the fiberglass box (3). SS has two inlets for filling and drainage and a glass cover slope of 9. SS was operated between February and March 7 with a break in operation in May. Daily distillate volumes, resolved to the nearest tenth of a liter, were collected from SS1 and SS by directly measuring the volume of produced distillate at around hours for the duration of the study. Daily distillate volume data were combined with the daily average weather and distilland volume data to prepare the input data sets used in the GA optimization method. Figure shows an example plot of long term daily insolation and distillate production for SS. Although there is a fairly strong correlation over time between distillate production and insolation, there are a quite a few cases where solar still distillate production varies considerably for the same amount of insolation. This variation is hypothesized to occur due to effects that other weather variables, such as wind speed and ambient temperature, have on still performance. The GA objective functions used in this study were first developed using the -7 weather data and the SS1 and SS distillate production data (1). Input data for the GA optimization included total global insolation, ambient temperature, wind speed, wind direction, cloud cover and distilland volume (1). The GA optimization process calculates the best coefficients and exponents to minimize the error of the objective function (1). Several different objective functions were chosen to correlate daily production with daily weather data and the distilland volume (1). Linear (L), power (P), exponential (E), and sinusoidal (S) functions were used to approximate daily production. Separate GA models were generated for SS1 and SS. GA optimization modules available in MATLAB (1) were used for this study. The fitness of each function was by calculating the mean absolute error () between predicted and actual production at each iteration of the optimization process (1). The optimization was conducted by instructing the modeling process to terminate when either maximum iterations exceeded 1 or the change in relative error for two successive iterations fell below 1x1-9 (1). Daily Total Insolation (J/m ) 3.5E+7.E+7.1E+7 1.E+7 7.E+.E+ Dec-5 Jun- Jan-7 Jul-7 Insolation Date of Operation Distillate Production Fig : Example data: SS long-term production (3). GENETIC ALGORITHM MODELING RESULTS Tables 1 and illustrate the accuracy of the five best optimized objective functions for SS1 and SS, respectively. Results are presented as Mean Absolute Error () and percentage of predicted results the corresponding values. Results are shown for model calibration (generation of optimized model 1 Daily Distillate Production (L/m ) 3

4 coefficients using % of input data) and model validation (evaluation of predictive ability of the generated model coefficients using input data). TABLE 1: AND PERCENTAGE OF RESULTS WITHIN % ERROR FOR SS1 (1) GA Optimized Fitness Function L-IT 1.1%.3% 7.7% 39.% L-I 1.% 1.% 7.7% 9.% PS-IT.5%.% 7.5% 7.% P-IT.7% 5.3%.% 1.7% PS-I.9% 1.%.%.% TABLE : AND PERCENTAGE OF RESULTS WITHIN % ERROR FOR SS (1) GA Optimized Fitness Function L-ITV 1.9% 1.5% 5.%.% L-ITVWD 13.%.%.% 79.% L-ITVW 13.% 19.% 5.% 7.% L-IT 15.7% 11.% 7.% 91.9% PS-I 1.% 17.% 71.% 77.% The results shown in Tables 1 and indicate that the best performing objective functions used linear combinations of insolation and temperature as their inputs. Insolation and temperature (L-IT) produced the lowest calibration and L-I gave the lowest validation for SS1. Insolation, temperature, and distilland volume (L-ITV) gave the lowest calibration and L-IT gave the lowest validation for SS. The models with the highest proportions of predicted results within % error for both model calibration and validation were L-I for SS1 and L-IT for SS.Overall, the L-I GA model performed the best for SS1, with three of four best scores, while the L-ITV model performed best for SS with the lowest calibration and the nd highest calibration and validation percentages of predictions within %. Figures 3 and plot the predicted distillate production against production for the SS1 L-I GA model and the SS L-ITV GA model, respectively. Predicted Production (L/m ) 1 1 Actual Production (L/m ) Fig 3: Predicted vs. actual production for SS1, L-I (1) Coefficients of determination (R value) were calculated for the separate calibration and validation scenarios to determine the percentages of variance explained by the best GA models. For both stills, the best GA models explained more than 9% of the variance for the calibration scenarios, and lower proportions of variance for the validation scenarios. The L-ITV model for SS predicted a higher proportion of the validation variance (about %) than did the L-I model for SS1 (3%). Student s t-test calculations showed that the coefficients of determination for all four scenarios were statistically significant at the p <.5 level. Predicted Production (L/m ) 1 R R -.3 Slope 1 R -.95 R Actual Production (L/m ) Slope 1 Fig : Predicted vs. actual production for SS, L-ITV (1) To evaluate reliability of the models in predicting distillate yield under worst-case weather conditions, the 5 th percentile average daily production by month was calculated for and predicted distillate yields. The difference between predicted and actual (predicted 5 th percentile yield 5 th percentile yield) was computed. The results are plotted in Figure 5 for SS1 and SS (1).

5 Predicted Actual Difference (L/m ) Fig 5: Monthly 5 th percentile prediction errors for SS1 (L-I) and SS (L-ITV) (1) The SS1 error curve shows that the largest 5 th percentile prediction error was -.5 L/m in May 7. The largest error for the SS curve was -.9 L/m in June. Overall the SS1 L-I and the SS L-ITV functions tended to over predict production more often than under predict. 5. SYSTEM DYNAMICS MODEL The goal of this phase of the study was to combine the effects of variations in predicted distillate output resulting from seasonal and daily weather fluctuations with seasonally varying potable water demand to determine required distillation basin area and reservoir size for a household-scale solar still system that could provide a reliable year-round potable water supply. 5.1 System Dynamics Methods SS1 SS1 B SS A system dynamics computer model (SDM) using methods described in (1) was constructed to simulate the combined effects of seasonally varying per-capita potable distillate demand and daily and seasonal variations in distillate production. The SDM assumed a water supply system consisting of single basin solar stills similar to still SS1 and a storage tank. Surplus distillate production would be stored in the tank and stored distillate was consumed when distillate production was insufficient to meet demand. The SS1 L-I GA objective function was used to project future daily solar still production from daily southern Nevada weather observations covering the period from February through March 1. United Nations World Health Organization potable water demand estimates of 5 L/day per capita demand was used during the summer season, L/day per capita demand during the spring/fall season, and 3 L/day per capita demand during the winter season (1). The STELLA system dynamics model (19) was used for computations with th order Runge-Kutta numerical integration to minimize propagation of numerical error. Different combinations of solar still basin area numbers of persons were used as inputs to the model, along with assumed initial amounts of stored distillate volume. If storage fell to zero during the simulation, the model was stopped and reset with a larger initial storage volume. 5. System Dynamics Model Results Figure illustrates results of the STELLA simulations varying distillate output and storage volume for a solar still system used by two people with a total basin area of.5 m. The initial storage volume in the reservoir was set to L (1). Over the four year simulation period the STELLA model showed that surplus water is generally produced during the spring and summer when production is greater than potable demand and a deficit occurs during the fall and winter when potable demand is greater than production. Maximum and minimum stored distillate volumes occurred three months after the corresponding seasonal maxima and minima in distillate production. Storage volume variations did not exhibit the daily fluctuations observed for distillate yield. The STELLA simulation showed a maximum storage volume of 1,13 L and a minimum storage of 7 L, giving a net change of 1,53 liters, or about 57 liters per capita. A storage volume of liters per capita would provide a modest factor of safety. When the STELLA model was operated to accommodate potable demand of 1 people, 1. m of basin area would be required to supply sufficient water. The resulting system would require an initial supply of L before initiating potable demand and would experience a maximum storage of 5 L and a minimum storage volume of 1 L (15). This correlates to a net change of 51 L per capita. For both scenarios, a storage volume of L per capita would provide a modest factor of safety. The authors wish to note that the optimized objective functions were built using weather data from the North American Southwest Region. This region is characterized by hot summers, mild winters, and low relative humidity throughout the year. Further research would be required to verify the performance of the developed objective functions 5

6 before their use in different latitudes and climates. 1.E+3 Reservoir Volume (L) 9.E+.E+ 3.E+.E+ 1 1 Daily Production (L) () Tiwari, G., Singh, H., and Tripathi, R., Present Status of Solar Distillation, Solar Energy, 3. (3) Venkatesh, N., Performance Evaluation of Single and Double Basin Solar Stills in Las Vegas, NV, M.S.E. Dissertation,, 7. () Fath, H. and Elsherbiny, S., Effect of Adding a Passive Condenser on Solar Still Performance, Energy Conversion and Management, (5) Fath, H., Elsherbiny, S., and Ghazy, A., A Naturally Circulated Humidifying/Dehumidifying Solar Still With a Built-In Passive Condenser, Desalination,. () Tiwari, G., Gupta, S., and Lawrence, S., Transient Analysis of Solar Stills in the Presence of Dye, Energy Conversion and Management, 199. Fig : System dynamics modeled production and reservoir volume requirement for two people.. CONCLUSIONS For daily weather data available for southern Nevada, representative of a temperate zone desert, genetic algorithms were shown to be capable of optimizing objective functions to predict daily solar still production with a mean absolute error as low as 11.% with up to 9% of predictions being the actual value. Linear combinations of daily average insolation, temperature and distillate volume gave the best results for two different types of single basin solar stills. Modeled fifth percentile daily yields, computed by month, tended to slightly over predict yield compared to monthly fifth percentile daily yields. STELLA system dynamics modeling using a genetic algorithm objective function showed that storage volume maxima and minima lagged distillate production by three months, and that to meet per capita demand, a minimum of 1.5 m per capita of basin area and L per capita of storage capacity would be needed to provide sufficient potable water year round. 7. REFERENCES Reservoir Volume Predicted Production (1) Fath, H., Solar distillation: A Promising Alternative for Water Provision With Free Energy, Simple Technology, and a Clean Environment, Desalination, 199. (7) Sodha, M., Kumar, A., Tiwari, G., and Tyagi, R., Simple Multiple Wick Solar Still: Analysis and Performance, Solar Energy, 191. () Abu-Hijleh, B., Enhanced Solar Still Performance Using Water Film Cooling of the Glass Cover, Desalination, 199. (9) Toure, S. and Meukam, P., A Numerical Model and Experimental Investigation for a Solar Still in Climactic Conditions in Abidjan (Cote d Ivoire), Journal of Renewable Energy, (1) Lof, G., Eibling., and Blowemer, J., Energy Balances in Solar Distillation. American Institute of Chemical Engineers Journal, 191. (11) Cooper, P., Digital Simulation of Transient Solar Still Processes, Solar Energy (1) Dunkle, R., Solar Water Distillation, the Roof Type Still and Multiple Effect Diffusion Still. International Developments in Heat Transfer, ASME, Proc. International Heat Transfer, 191. (13) Tiwari, A. and Tiwari, G., Effect of Water Depths on Heat and Mass Transfer in a Passive Solar Still: In Summer Climactic Condition, Desalination,. (1) Santos, N.I. Comparing multivariate regression and artificial neural networks to model solar still production. Proceedings for SOLAR 11, Raleigh, NC, 11. (15) Santos, N.I., Said, A.M., James, D.E., and Venkatesh,

7 N.H. Modeling solar still production using local weather data and artificial neural networks. Renewable Energy, (1), 1. (1) Santos, N.I. Modeling Passive Solar Distillation Production in Las Vegas, Nevada. (Master s Thesis)., 11. (17) Kalogirou, S.A. Artificial neural networks in renewable energy system applications: A review. Applied Energy, 77,. (1) Mitchell, M. Genetic algorithms: An overview. Complexity, 1(1), (19) Sterman, J. D. Business dynamics, systems thinking and modeling for a complex world. Irwin McGraw-Hill, Boston,. 7