Assessment of the Use of Solar Desalination Distillers to Produce Fresh Water in Arid Areas

: Water is an important resource for human beings, yet there are inhabited places tormented by the scarcity of it. The present study is concerned with places where, seemingly, the best way to get water is through solar distillers. These places should have, typically, high values of solar irradiation and a lack of human and economic resources to build and operate complex equipment. A set of sites scattered around the world was chosen, and then the presumed productivity and thermal e ﬃ ciency that solar distillers would have if they were installed at these places was calculated. The mathematical model used with this purpose assumes steady state operation; the values of mass of water distilled and distiller e ﬃ ciency were calculated for every hour, but the results presented are annual averages. Then, an economic study was made based on local costs of construction materials for the distillers, the work force, and the prices of water to predict the payback time of solar distillers. Finally, a study on environmental impact, particularly in terms of greenhouse gas (GHG) emissions, was made to compare reverse osmosis (RO) with solar distillation. For the sites studied, typical values of annual water output are in the range of 414 dm 3 / m 2 , for É vora, up to 696 dm 3 / m 2 , for Faya Largeau; the minimum e ﬃ ciency was found for É vora, as 11.5%, and the maximum e ﬃ ciency was found for Tessalit, as 15.2%. Payback times are very high, regardless of the areas of the globe where solar distillers are implanted. Regarding the GHG emissions, solar distillation is preferable to RO.


Overview
Needless to say, water is of paramount importance to almost all forms of life. Some think tanks concerned with geostrategic matters have even predicted that in the near future, wars will be waged because of lack of water.
The regions of the planet already distressed by water shortage are located in vast deserts in the north of Africa, Namibia, the outback of Australia, central Asia, North and South Americas, and some tiny islands in the middle of oceans. Moreover, because of climate change such places are appearing with increasing frequency.
It is not simply water that worries human beings, since water, namely, brackish water, is abundant and widespread; what worries human beings is the scarcity of fresh water. Yet, there are several ways to get fresh water from brackish water.
Desalination through distillation is a way to obtain fresh water from brackish or salted water. There are several methods to desalinate water, grouped by the authors of [1] as thermal and non-thermal; the current paper focuses only on the solar distillers, which follow a thermal method. The reason for this choice stems on the obvious link between water shortage and poverty, and so it seems realistic to desalinate water through simple and cheap methods, resorting to long-lasting facilities with almost no maintenance requirements, constructed with materials found locally; a solar distiller may last up to 25 years without major repairs [2].
Ultimately, a solar desalination distiller consists of a cover made of transparent material, placed over a basin filled with salted water (see Figure 1). According to Belessiotis et al. [1], the cover is normally roof-shaped, double-shaped, and symmetric, but can also be asymmetric or single sloped, and there can be two covers. Solar radiation successively crosses the cover; energy is absorbed by the water in the basin; water evaporates; and vapor rises to the underside of the cover, cooler than the upper side of the cover, condenses, and then slides, preferably without falling back into the basin, to the gutters bordering the distiller. The productivity of such installation is assessed by the mass of fresh water yielded by unit area of the distiller and unit of time.
Sustainability 2019, 11, x FOR PEER REVIEW 2 of 16 realistic to desalinate water through simple and cheap methods, resorting to long-lasting facilities with almost no maintenance requirements, constructed with materials found locally; a solar distiller may last up to 25 years without major repairs [2]. Ultimately, a solar desalination distiller consists of a cover made of transparent material, placed over a basin filled with salted water (see Figure. 1). According to Belessiotis et al. [1], the cover is normally roof-shaped, double-shaped, and symmetric, but can also be asymmetric or single sloped, and there can be two covers. Solar radiation successively crosses the cover; energy is absorbed by the water in the basin; water evaporates; and vapor rises to the underside of the cover, cooler than the upper side of the cover, condenses, and then slides, preferably without falling back into the basin, to the gutters bordering the distiller. The productivity of such installation is assessed by the mass of fresh water yielded by unit area of the distiller and unit of time. The cover is usually of glass, and less often of plastic films. Glass covers have the drawback of being breakable and, according to the authors of [3], should have a hematite content lower than 0.01%. Plastic covers can be made of treated polyvinylchloride and tetraphalate-polyethylene; their durability is less than 15 years, and their adaptability to any desired shape of the distiller is the highest of their class [1]. Phadatare and Verma [4] found that the productivity of distillers covered with glass is 30% to 35% higher than the productivity for distillers covered with Plexiglas.
The slope of the cover must guarantee that the condensed droplets of water, due to their surface tension, do not fall back into the basin but slide to the gutters, to be collected; this slope is normally under 20° [2]. The gutters have a slight slope too, just enough to prompt the flow of the distilled water into a reservoir that feeds consumers of such water. If the basin is shallow, its depth ranges from 10 to 20 mm; if the basin is deep, its depth goes up to 100 mm [4]. The widths are around 2 m and the lengths can reach 100 m [4].
The floor of the basin bottom liner must be waterproof, free of toxic components, withstand temperatures up to 90 °C, have a thermal absorptivity above 0.95 (see Table 1), and a polished surface. From Belessiotis et al. [1], it is normally made of one of these materials: concrete, wood impregnated with epoxy resins, aluminum, magnesium alloys, hard plastic ultraviolet resistant as Plexiglas, etc. To increase its absorption of solar heat, the upper side of the floor of the basin is covered by one of these materials: black paint (without volatile components that could evaporate with the water), spongy materials, butyl rubber, black polyethylene, asphalt, jute, etc.
The frame that supports the glass/plastic cover has to be robust and cling to the ground to withstand inclement weather, such as sand storms, but some of its parts must be removable to allow The cover is usually of glass, and less often of plastic films. Glass covers have the drawback of being breakable and, according to the authors of [3], should have a hematite content lower than 0.01%. Plastic covers can be made of treated polyvinylchloride and tetraphalate-polyethylene; their durability is less than 15 years, and their adaptability to any desired shape of the distiller is the highest of their class [1]. Phadatare and Verma [4] found that the productivity of distillers covered with glass is 30% to 35% higher than the productivity for distillers covered with Plexiglas.
The slope of the cover must guarantee that the condensed droplets of water, due to their surface tension, do not fall back into the basin but slide to the gutters, to be collected; this slope is normally under 20 • [2]. The gutters have a slight slope too, just enough to prompt the flow of the distilled water into a reservoir that feeds consumers of such water. If the basin is shallow, its depth ranges from 10 to 20 mm; if the basin is deep, its depth goes up to 100 mm [4]. The widths are around 2 m and the lengths can reach 100 m [4].
The floor of the basin bottom liner must be waterproof, free of toxic components, withstand temperatures up to 90 • C, have a thermal absorptivity above 0.95 (see Table 1), and a polished surface. From Belessiotis et al. [1], it is normally made of one of these materials: concrete, wood impregnated with epoxy resins, aluminum, magnesium alloys, hard plastic ultraviolet resistant as Plexiglas, etc. To increase its absorption of solar heat, the upper side of the floor of the basin is covered by one of these materials: black paint (without volatile components that could evaporate with the water), spongy materials, butyl rubber, black polyethylene, asphalt, jute, etc.
The frame that supports the glass/plastic cover has to be robust and cling to the ground to withstand inclement weather, such as sand storms, but some of its parts must be removable to allow cleaning and repairs in the distiller.
The bottom and sidewalls of the basin are insulated from the ground to lower, as much as possible, the heat losses from the distiller. The most suitable insulation materials have low conductivity, are easily applicable to this kind of basin, withstand the operation of the distiller without deformations, do not release chemicals harmful into water up to 90 • C, and are waterproof. Pumps, storage tanks, pipes, fittings, etc., are considered ancillary components. Pipes and fittings can be of the same material, such as polyvinyl chloride (PVC) or any other plastic material not damaged by temperatures up to 90 • C; pipes and fittings either of galvanized steel or copper for brackish water, and stainless steel for distilled water, can be used as well. Normally, plastic materials are cheaper than stainless steel.
The sealing between cover and basin is necessary because the volume limited by the surface of the water, the underside of the cover, and the tops of the distiller must be air tight to reduce convection losses. Good sealing materials are easily applied, non-toxic, and have very low absorptivity.
The maintenance requirements of such distillers are cheap and easy. The maintenance consists mostly in removing leaves, dust, and sand from the cover; occasionally glasses break, and then have to be replaced. Some parts must be removable to allow cleaning and repairs in the basin.
Such distillers must endure bad weather conditions, such as strong winds and sand storms. Solar desalination distillers operate in either batch or continuous mode. In batch mode, the amount of water evaporated from the basin during one day is offset, at the next sunrise, by new salt water. To avoid scaling or algae, every two or three days the basin is emptied and then refilled with new saltwater. As the temperature of the water in the basin increases, the productivity of the distiller increases; this is the reason why during the morning and the night such productivity is low but near noon it is at a maximum. Besides, shallow basins do not store sensible heat as do deep distillers. The productivity of distilled water by shallow distillers is in phase with the value of irradiation received by the distiller and so, from sunset to sunrise, distillation stops; however, as deep distillers store heat, distillation extends after sunset, although at low rate. In continuous mode, the basin is continuously fed by saltwater in a way to keep the amount of water in the basin constant.

Sites with Distillation Distillers
There is a long record of facilities to desalinate water through solar distillation. Some of these plants are shown in in Table 1.
In 1872, such a desalination plant was built at Chacabuco, (Las Salinas, Chile), which is described in detail by the authors of [5][6][7]. It operated for three decades to provide drinking water for animals used in nitrate mining [5]. Additionally, at Daytona Beach (Florida, USA), a similar facility was built, operated by Battele Memorial Institute of Cleveland [8][9][10]. In addition, numerous studies have been published, such as that by the authors of [11][12][13].
The Table 2 contains some sites, scattered around the world, which are seemingly suitable to solar harnessing facilities in general. The purpose of the present work is to assess the performance of specific distillation plants eventually set up on such sites.

Analyses
The solar distillation process to obtain water was analyzed in three respects: thermal efficiency, economics, and carbon emissions.

Thermal Efficiency
Belessiotis et al., Cooper, Duffie, and Beckman [1,2,5], among others, proposed two energy equations, one for the basin and another for the cover, with almost the same terms.
In the current study, the energy equation applied to the basin is where the subscripts c, w, b, and grd stand for cover, water, basin, and ground, respectively; the energy equation applied to the cover, neglecting the variation of internal energy and the solar energy absorbed by it, is where the subscript a stands for the atmosphere. In the right-hand side of Equation (2), the sky is assumed as a plate. Normally, for shallow and well-insulated basins, a steady-state operation can be assumed and, accordingly, the right-hand side of Equation (1) can be neglected.
According to Cooper [34], the total (all the wavelengths) and directional (angles of incidence of 0 • , 30 • , 45 • , and 60 • ) values of absorptivity, transmissivity, and reflectivity for the glass cover, the water in the basin and the basin liner are given at Table 3. The angle of incidence, θ, is measured from the normal to the surface.
Dunkle [35] proposes that assuming that both the water surface and the lower side surface of the cover are diffuse and gray; the value of 0.9 includes the view factor between these surfaces and their emissivities. For the evaporation with and the mass of water evaporated per unit of time is . M evap = 9.15 × 10 −7 h c (p wb − p wc ). (6) For the convection between the basin and the lower side surface of the cover For the convection between the upper surface of the cover and the atmosphere, which is normally a mixture of free and forced convection, McAdams recommends to adopt the convection coefficient as the maximum between 5 Wm −2 K −1 and the value obtained with 8.6V 0.6 L c −0.4 ; so with V representing the velocity of wind, expressed in meters per second, and the characteristic length, L c , representing the cube root of the volume of the distiller, expressed in meters. Then The radiation exchange between the upper face of the cover and the sky is The temperature of the sky was obtained by The value of Q grd is negligible, since it depends on the construction quality of the basin, which can be controlled by the builder of the basin; a well-insulated basin is usually assumed.
The performance of the distiller was assessed through the efficiency calculated with

Economics
In order to carry out the feasibility study of a project, it is very important to make an economic analysis of it. Firstly, this requires predicting expenditures (investments, costs, and expenses) and revenues and, secondly, the analysis of some economic indicators (TCO, NPV, IRR, and payback period). The presently studied facilities consist of distillers with an area arbitrarily set as 1 m 2 , and therefore the costs considered are per square meter of installation. Costs of components were obtained through the CYPE, a price generator digital platform [36].
Total cost of ownership (TCO) is a financial estimate designed to evaluate direct and indirect costs related to purchase and capital expenditures (CAPEX), in addition to operating and maintenance costs (OPEX), and can be expressed through CAPEX covers only the cost of building the equipment. OPEX includes maintenance and operating costs, considering an annual inflation rate of 2% [37,38].
Considering that the equipment has a lifespan of 20 years, the cost of water per 1 m 3 is given by with n representing the operation years and M evap-yearly representing the mass of fresh water obtained yearly. The net present value (NPV) is the balance of all cash inflows and outflows over the estimated useful life of a project, updated to the present moment, considering an inflation rate for the stipulated period. NPV can be calculated using where Fa n is the update factor for period n, R n the revenue for period n, and G n the expenditure for period n.
The value of Fa n is calculated through where i is the inflation rate and n the years of operation. The internal rate of return (IRR) represents the return on an investment, expressed as a percentage rate. The IRR can be viewed as the rate required for NPV to be zero, and calculated by where F n is the cash flow for period n. The payback period represents the time it will take a project to generate returns that equal the investment, and can be calculated using

Carbon Emissions
The parameter analyzed was the CO 2e emissions, defined by IEA 2018, corresponding to the production of 1 m 3 of fresh water. This parameter only encompasses the CO 2e produced by the operation of getting fresh water. Two alternative scenarios were studied: (i) the production of water through reverse osmosis (RO), currently the most widespread desalination process [39], and (ii) the production of water through solar distillation, the process presently studied. Obviously, RO consumes electric energy unlike solar distillation. Other methods to get fresh water were excluded from this analysis due to their technical complexities or operational costs, which renders them inappropriate for small and poor communities, the main target of this study. Table 4 contains values of total emissions of CO 2e and of the total electricity produced by the countries, where the sites studied are located. Specific emissions of CO 2e were calculated with both these values; these specific emissions depend on the energy mix of the country. Whenever there were no reliable values either of CO 2e emissions or the amount of electricity generated, counterpart values of the nearest country were assumed, such as in the cases of Atar, Dikhil, and Faya Largeau.  (31,684,028 kWh to get 8,106,322 m 3 of potable water); it is plausible to assume this same value for other countries, whenever RO is concerned.

Thermal Efficiency
Results concerning output were obtained for the locations indicated at Table 2, with climatic data drawn from reference [42], equations (1) and (2), and the assumption of steady state operation for the basin and the cover.
Hourly values of Q evap , , and Q rad(c−a) were calculated with hourly values of V, T a , T sk , and T wb drawn from the referred climatic site and with the above-mentioned equations, from (1) to (11). The values of absorptivity of water, transmissivity, and reflexivity of the glass cover were assumed as the averages of the homologous values contained at Table 3. The unknowns were the temperature of the basin, T b , and the temperature of the cover, T c , determined by a solver for nonlinear equations. Lastly, hourly values of the efficiency of the solar distiller, η, were obtained as well. Annual values shown in the following graphs were calculated with the counterpart hourly values. Figure 2 shows the annual output of distilled water for the sites studied, whereas Figure 3 shows the annual efficiency of solar distillation plants for the same sites.  Among the chosen sites of Table 2, the most and the least suitable for setting up solar distillation plants are, respectively, Faya Largeua and Évora. For both these sites, Figure 4 shows the monthly output of water and includes the monthly average air temperature, whereas Figure 5 shows the monthly output of water and includes the monthly average value of G.  Among the chosen sites of Table 2, the most and the least suitable for setting up solar distillation plants are, respectively, Faya Largeua and Évora. For both these sites, Figure 4 shows the monthly output of water and includes the monthly average air temperature, whereas Figure 5 shows the monthly output of water and includes the monthly average value of G. Among the chosen sites of Table 2, the most and the least suitable for setting up solar distillation plants are, respectively, Faya Largeua and Évora. For both these sites, Figure 4 shows the monthly output of water and includes the monthly average air temperature, whereas Figure 5 shows the monthly output of water and includes the monthly average value of G.   Figure 6 shows for the site with the highest water output, Faya Largeua, the monthly values of water output for two different situations: the minimum value and the actual value of the convection coefficient ℎ ( ) (see Equation (8)).   Figure 6 shows for the site with the highest water output, Faya Largeua, the monthly values of water output for two different situations: the minimum value and the actual value of the convection coefficient ℎ ( ) (see Equation (8)).  Figure 6 shows for the site with the highest water output, Faya Largeua, the monthly values of water output for two different situations: the minimum value and the actual value of the convection coefficient h (c−a) (see Equation (8)).
It is clear from previous figures that the productivity and the efficiency of solar distillers are higher for higher values of either irradiation G or average temperature T m . Besides, the productivity and the efficiency of solar distillers increase as the convection coefficient h (c−a) drops. Generally, for the sites studied, when h (c−a) drops from the actual to the minimum value, the increase of productivity is around 10%: for the case of Faya Largeua, such an increase is 12.3%. Thus, some expedients should be adopted to decrease, or even eliminate, the velocity of the wind over the distillers. Such expedients can be hedgerows, concrete barriers, etc. It is clear from previous figures that the productivity and the efficiency of solar distillers are higher for higher values of either irradiation G or average temperature . Besides, the productivity and the efficiency of solar distillers increase as the convection coefficient h(c-a) drops. Generally, for the sites studied, when ℎ ( ) drops from the actual to the minimum value, the increase of productivity is around 10%: for the case of Faya Largeua, such an increase is 12.3%. Thus, some expedients should be adopted to decrease, or even eliminate, the velocity of the wind over the distillers. Such expedients can be hedgerows, concrete barriers, etc.

Economics
An economic analysis was made for the sites referred to in Table 2, with the more important results presented in Table 5. The water annual production was drawn from Figure 2. The average costs of water for consumers were obtained from potable water suppliers: TCO, NPV for twenty years, IRR, and payback result, respectively, from Equation (12), Equation (14), Equation (16), and Equation (17).

Economics
An economic analysis was made for the sites referred to in Table 2, with the more important results presented in Table 5. The water annual production was drawn from Figure 2. The average costs of water for consumers were obtained from potable water suppliers: TCO, NPV for twenty years, IRR, and payback result, respectively, from Equation (12), Equation (14), Equation (16), and Equation (17).
It is important to stress that the costs of water presented in Table 5 are subsidized by the abovementioned governments.
Values of Table 5 are, at least, discouraging for poor communities of the Third World tormented by a lack of drinkable water.
Clearly, water can be obtained with distillers made with cheap materials found locally and by local unskilled people; such distillers will be affordable by poor communities, but their performance will be poor. Meanwhile, the performance and economic analyses of such distillers are impossible to calculate because (i) there is an enormous array of materials more or less suitable for the construction of distillers, and consequently, more or less expensive, and (ii) the unskillfulness of people is disputable.
So, the results presented in Table 5, however discouraging, were obtained with the underlying scope to obtain distiller with the highest efficiency, manufactured with prices current at Cabo Verde.
Anyway, from the values of payback of Table 5, it is clear that solar distillers are only suitable for domestic water production where other production methods are unavailable.  Table 6 contains, for the set of sites studied, the values of Greenhouse Gas (GHG) that would be emitted if the production of the water, instead of being through the solar distillers proposed in this study, was by RO. It is considered that the operation of solar distillers does not emit GHG. The water annual production was drawn from Figure 2, and the consumption of electricity to obtain potable water through RO was assumed 3909 kWh/m 3 , the same as in Cabo Verde. Clearly the environmental impact of RO is a drawback of this process when compared with solar distillation.

Conclusions
The scarcity of water is a problem of a growing number of regions of the world, which cumulatively are the poorest regions. Solar distillation has higher efficiency as irradiation increases and thermal losses decrease, which means that it is an acceptable desalination process for arid and hot climates.
Typical values of annual water output are in the range of 414 dm 3 /m 2 for Évora and up to 696 dm 3 /m 2 for Faya Largeau; the minimum efficiency found for Évora was 11.5%, and the maximum efficiency found for Tessalit was 15.2%.
However, the payback times for high performance solar distillers are very high, which excludes solar distillation when economic criteria are the only factors to be considered. Solar distillation is far better than RO, when the environmental impact of GHG is considered. For remote and poor communities, solar distillation is to be considered.
So, as guidelines to decide if solar distillation to obtain fresh water it is important to get positive answers to the following questions: Finally, the present study addresses the shortage of fresh water in the growing number of places that comply with the previous guidelines.