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# Modeling of Solar-Powered Desalination

Written By

Zafar Abbas, Nasir Hayat, Anwar Khan and Muhammad Irfan

Submitted: February 1st, 2022 Reviewed: February 25th, 2022 Published: April 16th, 2022

DOI: 10.5772/intechopen.103934

From the Edited Volume

## Distillation Processes - From Conventional to Reactive Distillation Modeling, Simulation and Optimization [Working Title]

Dr. Vilmar Steffen

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## Abstract

The scarcity, global, and local demand of pure water for SDGs become prominent issue. The global emissions of CO2 and GHGs have put pressure to develop the solar-powered desalination plants. This article discussed the selection of site for the solar thermal desalination in Pakistan keeping the eye on sustainability and modeling and cost analysis of single solar stills technology at Lyari River in Karachi, Pakistan. Pakistan is among the water-deficit countries having 35% of population having lack of pure drinkable water. The plenty of solar irradiance and saline water in Pakistan make it very favorable for solar-powered desalination. The solar stills technology is one of the best technologies to meet the local demand of pure water. The modeling is composed of governing equations based on the law of conservation of mass and law of conservation of energy. The solar irradiance at Lyari River is taken from MERRA–2. The result depicted that the hourly production of distill water is 1 kg/m3 and 8 kg/m3 with and without the FRL lens. The cost of distill water produced from the solar stills having FRL lens is 33% less as compared with solar stills without FRL lens.

### Keywords

• SDGs
• GHGs
• desalination
• solar powered
• solar stills

## 1. Introduction

Water is the resource that sustains all life on the planet earth and key element of sustainable development [1]. The rapid growth in population, and industrial and economic development needs high demand of water. The need of freshwater for drinking and potable water in arid areas is increasingly important issues in most part of the world. In 2000, the world annual demand for water is 4000 billion cubic meter. By 2030, it is estimated to increase over 58% [2]. Water availability per person in Pakistan was 5,600 cubic meter in 1960, and it is reduced to 1000 cubic meter in 2018. The demand of water in Pakistan is important because of its agrarian nature of economy and the agriculture sector shares 24% of gross domestic product (GDP). The regional conflicts on the availability and use of water have pressure on the demand of water. The water sources in Pakistan are surface water, rainfall, glaciers, and groundwater. Surface water consists of rivers, lakes, dams, and runoff during and after heavy rains. Mostly, the groundwater is the source in urban areas except in Karachi, Hyderabad, and some part of Islamabad use surface water. Water for rural areas is also from groundwater source except in saline groundwater areas where irrigation canals are used for domestic purpose [3]. Currently, the water availability per capita in Pakistan is 1000 cubic meter. According to Population Action International, 1993, the countries with water availability below 1000 cubic meter experience chronic water stress [1]. Presently, more than 65% people of total population have access to safe drinking water including 85 and 55% urban and rural areas, respectively. The 35% of population has lack of drinkable water in Pakistan [3]. According to WHO, a drinkable water should have dissolved salt concentration less than 500 ppm. The normal seawater and brackish water have dissolved salt and ion concentration of 3500 ppm and 1000 ppm. Therefore, desalination of seawater and brackish water is the way to make the water drinkable. Most of the desalination plants use conventional methods of energy. But the fossil fuel methods of energy sources have adverse impact on environmental sustainability by producing air pollution, global warming, and GHGs emission. The utilization of fossil fuels for the desalination plants is contributing in CO2 emissions. The total installed power plant for the desalination processes is responsible for the emission of 76 million tons (Mt) of carbon dioxide per year. In 2040, the emission of CO2 is expected to 218 million tons per year [4]. The cuse of fossil fuels for desalination plant is neither sustainable nor environment friendly. Therefore, there is a need of alternative sources of energy to achieve the world demand of freshwater. At a same time, the alternative source should be sustainable and environmental friendly. The renewable energy sources of energy are the alternatives to power desalination processes. Thus, the solar power desalination is one of the most suitable alternatives for desalination plant that meets water demand and also environmental friendly.

Therefore, in this research paper the focus is on the demand of water in Pakistan as the result of rapid growth in population and industrialization. It has become necessary to install the desalination plant in Pakistan by keeping in mind the energy available as well as economic situation. The main ambitions of this research are to select a site having plenty of solar radiations and salt or brackish and suitable solar technology having low capital and operational cost to fulfill the demand of pure water at minimum cost. Thus, the development of mathematical model of solar stills and cost analysis at Lyari River, in Karachi, follows the solution of mathematical model using MATLAB.

## 2. Methodology

The methodology of this research is composed of the selection of site in Pakistan for solar power desalination following the mathematical modeling of the single slope of solar stills and employs modern software for the solution of mathematical model. The governing equations for mathematical model of the solar stills are based on the law of conservation of mass and law of conservation of energy for the system. The equations for convective heat transfer coefficients and radiation heat transfer coefficients are based on the Dunkle’s model. The MATLAB r2019 is employed to solve the equations.

### 2.1 Site selection in Pakistan

The availability of 1900–2200 kWh/m2annual global irradiance makes Pakistan highly favorable for solar power-based desalination [5]. The Balochistan and Sindh province of Pakistan is rich in solar energy with an average daily direct normal irradiance of 5.3–5.6 kWh/m2 and 2.5–3.0 kWh/m2 with sunshine duration of 8–8.5 hours a day [6]. Therefore, in this research paper the site at Lyari River Karachi has been selected for the modeling the single-slope solar stills.

### 2.2 Mathematical modeling of solar stills

The basic assumptions while modeling the solar stills take negligible temperature stratification within the evaporator basin. Temperature is uniform within each still component. Temperature is time dependent. The evaporated water is assumed only pure water; that is, the evaporated water has no dissolved salt or ion. The stills have no vapor leakages. The governing equations are based on law of conservation of mass and law of conservation of energy. The schematic of single slope solar stills is shown in Figure 1.

The law of conservation of mass can be written as [7].

ṁsw=ṁev+ṁbE1

If Xswis the concentration of salt in the feed saline water, Xbis the concentration of salt in the cbrine within the basin. Then, the salt balance is [7].

ṁswXsw=ṁbXbE2

The solubility of salt determines the salt content in the brine. The salt content in the brine is important in practice to avoid the problem of forming layer and blockage. The factor fcfor concentration is defined as the ratio of brine concentration to feed concentration.

fc=XbXswE3

This factor is used to fix a threshold limit to not exceed during evaporation and condensation. By solving Eq. (2)) and Eq. (3), we have the following equation.

ṁb=1fcṁswE4
ṁev=fc1fcṁswE5

Eq. (5) is for the stationary conditions, the rate of evaporated water as a function of rate of feed saline water. Now, the distillated water or recovery rate can be defined as

φ=fc1fcE6

The recovery rate is an important parameter, which indicates the possible amount of distillate water from the saline feed water without scaling [7]. It means that only 40% of saline water can be transformed into distillate water without encrustation and blockage.

The law of conservation of energy gives the following set of equations for the respective components in the solar stills.

The energy balance equation for the outer of the transparent glass cover is as follows [7]:

ρgVgCp,g2AgdTgedt=λgegTgiTgehcgeamTgeTambhrgeskyTgeTskyE7

The energy balance equation for the inner of the transparent glass cover is as follows:

ρgVgCp,g2AgdTgedt=α´gIt+hcswgi+hrswgiTswTgi+ṁevLvAgλgegTgiTgeE8

The energy balance for the seawater inside the basin of solar still is as follows [7]:

ρswVswCp,swAswdTswdt=
α´swIt+hccswTcTsw+ρswDswAswcp,swTsw,incp,bTb,outṁevAswhLcp,bTb,outhcswighrswigTswTgiE9

The convective heat transfer coefficient of between the outer of the transparent glass cover and the ambient temperature depends on the wind velocity. According to McAdams correlation [8], this coefficient is approximated by the following equation.

hcgeamb=5.621+1151.2vTambifv<4.88ms1604.29vTamb0.78if4.88v<30.48ms1E10

The heat transfer coefficient between the saline water and the inner of the transparent glass cover is given by the second form of Dunkle’s model and can be written as [9].

hcswgi=0.884TswTgi+pswpgiTsw2.689×105psw13E11

The radiation heat transfer coefficient between the outer of the transparent glass cover and the sky is given by

hrgesky=εvσT2ge+T2skyTge+TskyE12

σis the Steffen Boltzman constant.

The sky temperature is determined by [10].

Tsky=Tamb0.74+0.006θ0.25E13

Where Ɵ is the dew point temperature given by [11].

θ=273.317.27Inε+17.27Tamb4061Tamb35.85Inε+17.27Tamb4061Tamb35.85E14

εis the relative humidity.

The radiation heat transfer coefficient between the saline water and the sky is expressed as

hrgesky=εeffσT2sw+T2giTsw+TgiE15

Emissivity is given by,

εeff=1εsw+1εg11E16

The equation in the second part of the (Eq. (9)) in given by Dunkle’s model as [9].

ṁevhL=hevAswTswTgiE17

The latent heat of vaporization hLis given by [9].

hL=31462.36TswE18

The evaporative heat transfer coefficient hev is given by [9].

hev=0.016273hcvswgipswpgiTswTgiE19

The evaporative heat transfer coefficients Eq. (11) and Eq. (19) can only be estimated through correlations when the following conditions is satisfied: the aspect ratio 2.5a5.5, the inclination angle 100i300, and Rayleigh number 5×106Ra5×107.

If the above conditions are not fulfilled, then it could be done either experimentally or by using 2D modeling of the problem such as considered in some other systems [12, 13].

The Nusselt number is obtained through a correlation in the form by to express the convective heat transfer coefficients [14].

Nu=cRan=cGrPrnE20

The Grashof and Prandtl number is given by,

Gr=βgρ2L3Tμ2E21
Pr=μcρλE22

The correlation that gives Nusselt number is [14].

Nu=1ifGr<1050.5Ra0.25if105<Gr<2×1070.15Ra0.33ifGr>2×107E23

When the Nusselt number is known, the heat transfer coefficient between the basin liner plate and the saline water can be calculated for an active solar still as

hcvcsw=NucswλswLE24

The convective heat transfer coefficient between the fluid and the plate for an active solar still is calculated as [15].

hcvhc=NuhcλhLE25

The heat loss coefficient is approximated by the following equation [15].

Uloss=λiseisE26

Tb,out can be assumed to be equal to that of the plate Tp for larger length of basin liner for an active solar stills [15].

The MATLAB’s solver for ordinary differential equations (ODEs), MATLAB ode45 function, has been employed for the efficient computation of the differential equations.

The material properties and dimensions of solar still are given in Table 1 and thermophysical properties of glass, basin, and insulation are given in Table 2 in Appendix A.

ParameterValue
Basin Area0.2
Thickness2
Basin MaterialAluminum
InsulationWool
Thickness20
ChannelsPVC
GlassTempered
Glass Area0.234
Thickness glass cover0.04
FRL LensR18
Lens Area0.2839

### Table 1.

Material properties of solar stills.

ParametersValue
Basin absorptivity0.90
Glass absorptivity0.05
Water reflectivity0.05
Glass reflectivity0.05
Glass emissivity0.94
Water emissivity0.95
Specific heat4.002
Glass thermal conductivity1.03
Insulation thermal conductivity0.0363
Water depth0.02
Wind velocity4.6

### Table 2.

Thermophysical properties.

Cost(PKR)Without FRLWith FRL
Capital355019500
Operational1200/year1200/year
Maintenance500/year500/year

### Table 3.

Cost of solar stills with and without FRL lens.

## 3. Results

The hourly production of distill water in kg/hourat Lyari River, Karachi, with and without Fresnel (FRL) lens. The results are depicted in Figure 2.

The maximum ambient temperature and sky temperature on the hottest day is 39.5°C and 14.7°C. The result is showing that the maximum water temperature with and without Fresnel (FRL) lens is 82.3°C and 47.2°C. And also the maximum glass temperature with and without FRL lens is found to be 80°C and 39.5°C. The production of water is calculated using the temperatures. The maximum water production with and without FRL lens is 8 kg/hour and 1 kg/hour. Using FRL lens, the production of water is 330% more than without using FRL lens.

## 4. Cost analysis

The cost analysis of the solar still with and without FRL lens includes the capital, operational, and maintenance cost. The major contributor is FRL lens that cost 90$. The details of the costs are given in Appendix A. The economic performance is estimated by the following. P=Capital cost+Operational cost/year+Maintenance cost/yearwater production/yearE27 The monthly operating cost is about 1.25$. There is no maintenance cost is required in this case but only the cleaning cost. The accidental cost is not considered in this study. The cost with FRL is 122.3$and without FRL is 22.27$. The production of distilled water per cubic meter with and without FRL is found to be 1.37$and 1.66$, respectively.

## 5. Conclusion

It is concluded that the scarcity of pure water can be compensated by desalination processes to meet the global demand of water as some developing countries have already done. The developed and developing countries have the capacity to install the conventional source of desalination plant but this attitude is greatly impacting on the environmental issues such as global emissions of CO2 and greenhouse gases (GHGs). Currently, the desalination plants are based on the conventional sources of thermal energy. The sustainable development goals (SDGs) can only be achieved using the renewable source of energy for the desalination processes. This will eliminate two main problems: global emissions and scarcity of water. The alternative and most effective source for desalination processes keeping in mind the SDGs is the solar thermal desalination processes. The capital and operational cost of the conventional thermal desalination processes are high enough that under developing countries cannot afford it. Therefore, the solar thermal desalination processes are the best option for those countries. The plenty of solar irradiance, water, and land make Pakistan the best suited area for the solar thermal desalination. Baluchistan, Sindh, and Southern Punjab are the most suitable area for the solar energy applications. The Lyari River at Karachi in Sindh province is one of the most suitable areas for the solar thermal desalination processes. The solar stills technology for the distillation of saline water is one of the most favorable technologies to distill water to meet the water demand of Pakistan at effective cost. The governing equations of mathematical modeling of solar still were based on law of conservation of mass and law of conservation of energy. MATLAB was employed to solve the governing equations of the mathematical model. The result is showing that the utilization of Fresnel (FRL) lens makes the solar stills more productive of distill water as compared with solar stills without Fresnel lens. At the same time, the cost of pure water is less while using FRL lens in the solar stills. The solar stills technology works more efficiently at the remote areas of Pakistan where high-cost desalination plants are far enough to install. And ease of installation, capital, operational, and maintenance cost make it possible to reach to all people.

## Acknowledgments

I pay gratitude to Allah Almighty for His blessings that make possible to complete this research paper. Our heartedly gratitude to our parents and guidance that they support us from childhood to present. Besides their support, it was impossible for us to do so.

It is my pleasure to acknowledge here the personal and institutional support I have received leading to the completion of this work. I am thankful to my team members, Muhammad Irfan and Anwar Khan, student of B.Sc. Mechanical Engineering Department at University of Engineering and Technology, Lahore, for their cooperation.

On the behalf of my team I would like to express sincere gratitude to Professor Nasir Hayat, Chairman Mechanical Engineering Department, University of Engineering and Technology Lahore for his continuous supervision, advice, effort, and worthy suggestions during the entire research project. At Mechanical Engineering Department, University of Engineering and Technology, Lahore, I am grateful to project coordinator Dr. Naseer Ahmad, Associate Professor Mechanical Engineering Department, and his fellows for their valuable and estimable suggestions. And special thanks go to our semester coordinator Dr. Zia ur Rahman Tahir.

I would like to thanks all the researchers and coordinators of the websites that their research articles are easily available at the respective websites. It is my pleasure that to express thank to Maja Bozecevic, Author Service Manager at IntechOpen, which is world-leading publisher of Open Book Access.

## Conflict of interest

There is no conflict of interest for this publication.

## Nomenclature

 Asw Area of saline water (m2) Ag Area of glass cover (m2) Ab Area basin (m2) A Aspect ratio (dimensionless) c Constant in Nusselt correlation (dimensionless) cp,b Specific heat of brine (J kg−1 K−1) cp,sw Specific heat of saline water (J kg−1 K−1) cp,g Specific heat of glass (J kg−1 K−1) eg Thickness of glass cover (mm) egs Thickness of insulation material Fc Feed concentration factor (dimensionless) I(t) Solar Intensity (Wm−2) IO Constant solar intensity (Wm−2) I Inclination angle of glass cover (degree) Gr Grash of number G Acceleration of gravity (m s−2) Hl Height of the higher side of the still (m) Hr Height of the lower side of the still (m) H Mean height of the still (m) hL Latent heat of vaporization (kJ kg−1) hev Evaporative heat transfer coefficients (kJ kg^−1) hcge-amb Convective heat transfer coefficient between outer glass cover and ambient (Wm−2 K−1) hcsw-gi Convective heat transfer coefficient between saline water and inner glass (Wm−2 K−1) hge-sky Heat transfer coefficient between outer glass cover and sky (Wm−2 K−1) ṁsw Mass flow rate of Saline water (kg m−3) ṁb Mass flow rate of brine (kg m−3) mw Mass yield hourly (kg m−3) ṁev Mass rate of produced vapor (kg m−3) Nu Nusselt number (dimensionless) N Exponent in Nusselt correlation (dimensionless) Pr Prandtl number (dimensionless) pgi Partial pressure of the water at the interior of the glass cover (Pa) psw Partial pressure at saline water surface temperature (Pa) Ra Rayleigh number (dimensionless) Tamb Ambient temperature (K) Tb,out Brine output temperature (K) Tge Temperature at the outer side of cover glass (K) Tgi Temperature at the inner side of cover glass (K) Tsw Temperature of saline water (K) Tsw,in Inlet temperature of saline water (K) Tsky Sky temperature (K) t Time (s) tc Time period for calculation of the yield (s) Uloss Loss factor per unit surface (W m−2 K) Vg Volume of glass cover (m3) Vsw Volume of saline water (m3) v Wind speed (m s−1) w Width of the solar stills (m) xb Concentration of salt in brine (mg l−1) xsw Concentration of salt in feed saline water (mg l−1) αc, Fraction of solar energy absorbed by basin liner material (dimensionless) αg, Fraction of solar energy absorbed by glass cover material (dimensionless) αsw, Fraction of solar energy absorbed by saline water (dimensionless) β Coefficient of volumetric thermal expansion (K−1) βsw Coefficient of volumetric thermal expansion for saline water (K−1) ϵeff Effective emissivity (dimensionless) ϵg Emissivity of cover glass (dimensionless) ϵsw Emissivity of saline water (dimensionless) φ Feed recovery rate (dimensionless) Γ Yield (kg) λ Thermal conductivity (W m−1 K−1) λg Thermal conductivity of glass cover (W m−1 K−1) λsw Thermal conductivity of saline water (W m−1 K−1) λin Thermal conductivity of insulation material (W m−1 K−1) μ Viscosity (N s m−2) μsw Viscosity of saline water (N s m−2) ρ Density ρg Glass cover density (kg m−3) ρsw Saline water density (kg m−3) σ Stefan-Boltzmann^’ s constant (5.6697 × 10−8) (W m−2 K−4) θ Dew point temperature (K) ε Relative humidity (dimensionless) ∆T Temperature difference in transfer by natural convention (K)

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Written By

Zafar Abbas, Nasir Hayat, Anwar Khan and Muhammad Irfan

Submitted: February 1st, 2022 Reviewed: February 25th, 2022 Published: April 16th, 2022