A solar desalination plant consisting of solar parabolic collectors, steam generators, and MED unit was simulated technoeconomically and optimized using multiobjective genetic algorithm. A simulation code was developed using MATLAB language programming. Indirect steam generation using different thermal oils including THERMINOL VP1, THERMINOL66, and THERMINOL59 was also investigated. Objective function consisted of 17 essential parameters such as diameter of heat collector element, collector width, steam generator pinch, approach temperatures, and MED number of effects. Simulation results showed that THERMINOL VP1 had superior properties and produced more desalinated water than other heat transfer fluids. Performance of the plant was analyzed on four characteristic days of the year to show that multiobjective optimization technique can be used to obtain an optimized solution, in which the product flow rate increased, while total investment and O&M costs decreased compared to the base case.
Limited sources of clean potable water have motivated humans to find alternative sources to resolve the problem. Industrial desalination plants are among the best technological solutions for clean water production from sea water. Traditional plants use fossil fuels to provide required steam but, nowadays, using solar collectors has become more attractive to prevent global pollution. For example, in the southwestern part of USA, in 2010, only about 1.0 Gm^{3}/year of water demand was provided by solar desalination technologies, while, in 2014, this portion reached 3.0 Gm^{3}/year, which shows 200% increase during 4 years. Prediction says that this value would be increased to 12.0 Gm^{3}/year by 2050 [
Multiobjective optimization technique based on the genetic algorithm was proved to be a reliable tool for technoeconomic improvement of plants and has been used by many researchers. Najafi et al. [
In the case of solar applications, there are some studies that use genetic algorithm to find optimal solutions, which include the study performed by Silva et al. [
It is important to note that there are various types of desalination technologies including [
multistage flash (MSF),
multiple effect boiling (MEB) or multieffect desalination (MED),
vapor compression (VC),
freezing,
humidificationdehumidification (HD),
solar stills,
membrane processes.
Industrial desalination technologies either use phase change or involve semipermeable membranes to separate the solvent or some solutes. Therefore, desalination techniques may be classified into the following categories: phase change or thermal processes and membrane or singlephase processes.
In the phase change or thermal processes, distillation of seawater is achieved by utilizing a thermal energy source. Thermal energy may be obtained from a conventional fossil fuel source, nuclear energy, nonconventional solar energy source, or geothermal energy. In the membrane processes, electricity is used for either driving highpressure pumps or ionizing salts contained in the seawater.
Some researchers have focused on “humidificationdehumidification (HD)” technologies for solar desalination. For example, Kabeel and ElSaid [
Some others have studied solar stills, for example, Ranjan and Kaushik [
However, commercial desalination processes based on thermal energy are multistage flash (MSF) distillation, multipleeffect desalination (MED), and vapor compression (VC), which could be thermal (TVC) or mechanical (MVC) vapor compression.
On the other hand, according to a survey conducted under a European research project [
At the present study, solar MEDTVC technology as the combination of multipleeffect desalination (MED) and thermal vapor compression (TVC) was investigated. The plant was designed for a moderate town with demand of 2000–5000 m^{3}/day. Multiobjective genetic algorithm optimization technique was used to find optimum parameters of a solar desalination plant, which is schematically shown in Figure
multiobjective optimization of a solar desalination plant using genetic algorithm,
considering maximum water production and minimum costs as the multiobjective function for the optimization,
investigating the effect of different thermal oils on the plant efficiency and water production rates,
performance of solar desalination plant have been analyzed at four characteristics days of the year, including spring equinox, summer solstice, fall equinox, and winter solstice,
sensitivity analysis on solar collector acceptance angle,
plotting Pareto curve, finding the optimum parameters, and comparing them with the design parameters,
exact calculation of radiative heat loss for the parabolic collector.
Schematic diagram of the solar desalination plant.
Mathematical modeling of solar parabolic collectors has been performed by many researchers (e.g., [
Figure
Onedimensional steadystate energy balance and for a crosssection of an HCE.
The effective incoming solar energy (solar energy minus optical losses) is absorbed by the absorber selective coating
Fourier’s law of conduction through a hollow cylinder describes the conduction heat transfer through the absorber wall [
If there is a wind, the convection heat transfer from the glass envelope to the environment will be forced convection. The Nusselt number in this case is estimated with Zhukauskas’ correlation for external forced convection flow normal to an isothermal cylinder [
Other terms in (
An MED unit includes multiple effects which are similar to each other in terms of energy and mass balance. Figure
Heat and mass balance diagram for
Consider
Consider
Consider
The main objective of MED simulation is to calculate desalinated water flow rates
The formula presented by Han and Fletcher [
Total capital investment (TCI) is the sum of fixed capital investment (FCI) and other outlays including startup cost (SUC), working cost (WC), cost of licensing, research, development (LRD), and allowance for funds used during construction (AFUDC) [
In addition to equipment case, other installation costs like piping should be considered. The cost for piping includes the material and labor costs of all items required to complete the erection of all the piping used directly in the system. This cost represents 10–70% of the purchasedequipment cost. The following relation can be supposed to calculate piping cost [
Collector cost estimation was performed using correlations in [
Considering plant lifetime,
Maximum desalinated water production rates as well as minimum total capital investment were the main items of the objective function in the present study. Thus, the objective function could be formulated by a combination of desalinated water mass flow rate and desalinated water cost:
As mentioned in Table
Lower and upper bounds of decision variables.
Decision variable  Lower bound  Upper bound 


5  50 

5  50 

20  80 

1  5 

1  5 

1  5 
No. effect (—)  3  10 

1  8 

10  50 

10  50 

20  80 

8  15 

200  400 

20  80 
Thickness (mm)  10  25 

3.5  8 

1  3.5 
Validation of the developed code was proved by comparison of the obtained results with the reported data of Dudley et al. [
Effect of HTF average temperature on collector efficiency in compaction with measured data of Dudley et al. [
To validate the code, the simulation results for a MED unit including 7 effects were compared with the operational data of Kamali and Mohebinia [
Data validation for MED simulation.
Parameter  Unit  Operational data [ 
Simulated results  Difference (%) 

Number of effects  —  7  7  Assumption 
Length of tubes  M  4.1  4.1  Assumption 
Motive steam pressure  Barg  10  10  Assumption 
Motive steam temperature 

170  170  Assumption 
Motive steam mass flow rate  tons/h  8  8  Assumption 
Number of tubes in each effect  —  1996  1973  −1.17 
Sea water flow rate  tons/h  420  429  2.10 
Desalinated water flow rate (tons/d)  tons/d  1536  1557  1.35 
Mathematical models were used for a desalination plant located in city of Ahwaz in the southeastern part of Iran. Table
Environmental conditions and constant parameters for simulation.
Constant Parameter  Unit  Value 

Latitude 

31.30 
Elevation from sea level  m  17.00 
Average relative humidity  %  60.00 
Average ambient temperature 

15.00 
Mirror’s Clearness efficiency  %  0.94 
Reflection efficiency  %  0.93 
Solar absorber pipe inside diameter  mm  65.00 
Solar absorber pipe outside diameter  mm  75.00 
Pipe material  —  steel 321H 
Collector width  m  5.76 
Collector acceptance angle 

135 
Properties of different thermal oils are mentioned in the Appendix. It is important to note that there is a higher limit of temperature for different oils to prevent oxidation. These limits are also presented in the Appendix. These temperature limits would affect the maximum collector pipe length, as will be discussed in the following sections.
To reach proper accuracy, total pipe length was divided into 4000 small distances. As the first comparison criterion, different maximum temperature limits were considered for different oils (according to the Appendix); therefore, different pipe lengths were considered for different oils, as shown in Table
Comparison of solar field parameters for different thermal oils considering maximum temperature limit for different oils.
VP1  THERMINOL 66  THERMINOL 59  

Length (m)  2455.50  1381.00  1107.50 

399.02  344.04  314.04 

45.60  23.15  18.97 
Dp_{Total} (bar)  46.55  24.27  19.46 
Pressure drop versus pipe segments for different thermal oils.
Total pumping power is calculated from the following equation:
Therefore pumping power is proportional to both pressure drop and total pipe length. As seen from Figure
Considering both pipe length and pressure drop, from data of Table
Variation of fresh desalinated water flow rate during the autumnal equinox for different thermal oils.
As the second comparison criterion, outlet temperature was considered 314°C for all oils which corresponded to the maximum acceptable temperature of THERMINOL 59. With this assumption, simulation results are summarized in Table
Comparison of solar field parameters for different thermal oils considering outlet temperature of 315
VP1  THERMINOL 66  THERMINOL 59  

Length (m)  1255  1107.0  1107.50 

314.00  314.00  314.04 

21.81  18.49  18.97 
Dp_{Total} (bar)  22.27  19.38  19.46 
Bracket radiative and convective heat losses at the pipe inlet and outlet are indicated in Figure
Heat loss mechanism at inlet and outlet of the collector pipe.
Inside heat transfer coefficient versus pipe segment for different thermal oils.
Sum of heat losses during pipe segments is shown in Figure
Total heat loss versus pipe segments for different thermal oils.
Since the intention is to gain maximum solar energy, it is a good idea to use the oil with maximum temperature limit: THERMINOL VP1. Although it involves the greatest heat losses and maximum pumping power, its performance in producing higher desalinated flow rates is more attractive in technical and economic terms. Therefore, this oil was selected for the rest of calculations.
Figure
Variation of outlet HTF (selected THERMINO VP1) temperature versus wind velocity.
It is a general rule for MED units that, up to a specific limit, using more number of effects which means more heat transfer areas and more capital costs leads to producing more desalinated water with the same steam flow rate. This comment is verified by Figure
Variation of heat transfer area and desalinated water flow rate versus number of effects.
As stated previously, the intention was to optimize the solar MED plant using genetic algorithm (GA) with 17 decision variables (Table
Values of decision variables for the design and optimized case.
Decision variable  Design case value  Optimized case value 


20  9.41 

20  11.14 

28.75  48.17 

1  2.57 

3  2.31 

4.2  3.16 
No. effect (—)  4  10.00 

4.1  2.42 

16  23.39 

35  29.00 

20  56.08 

9  8.49 

200  210.37 

65  57.07 
Thickness (mm)  15  14.21 

5.76  7.53 

2  3.21 
The optimization results are shown in Figure
Pareto curves for different HTFs with objective function of water production and total capital investment.
Using these Pareto curves, the absolute optimum point of the operation can be determined. In this case, a special code was used to determine the optimum point. Values of decision parameters for optimized case are presented in Table
To better understand the differences between the optimized case and the base case, four characteristic days of the year (i.e., spring equinox, summer solstice, fall equinox, and the winter solstice) were studied. Rates of solar flux on a horizontal surface for these characteristic days were 1010, 1200, 820, and 680 W/m^{2}, respectively. Figures
Comparison between design and optimized case in terms of fresh water production during spring equinox.
Comparison between design and optimized case in terms of fresh water production during summer solstice.
Comparison between design and optimized case in terms of fresh water production during autumnal equinox.
Comparison between the design and the optimized case in terms of fresh water production winter solstice.
For further analysis, both the design case and optimized case are compared in Figures
Comparison between design and optimized case in terms of cost of one cubic meter of produced fresh water during autumnal equinox.
Sensitivity analysis on solar collector acceptance angle.
Therefore, it can be concluded that the genetic algorithm is a powerful tool for optimization of a solar desalination plant in terms of technical and economical items.
To perform a sensitivity analysis, solar collector acceptance angle was reduced from 135 (design case) to 125 degrees and Pareto curves of both cases are plotted in Figure
Decreasing the collector acceptance angle from 135 to 125 degrees leads to considerable increase in cost. A slight variation in solar field parameters indicates that genetic algorithm changes the MED and steam generator design parameters simultaneously to reach the new optimized case.
The simulation results showed that, among three different thermal oils, THERMINOL VP1 needed greater pipe length than others considering the same outlet HTF temperature and produced more desalinated water, while total capital investments were of the same order.
Increasing wind velocity considerably decreased solar filed efficiency. On the other hand, increasing wind velocity from 0.5 to 2.0 m/s led to 10% increase in heat losses.
Using genetic algorithm for the plant optimization resulted in determining an optimized case which produced more desalinated water; meanwhile, its total investment cost was reduced. Pareto curves also indicated that THERMINOL VP1 had less price and higher water flow rates than other oils, which showed that GA well predicted the proper oil as was expected from the previous analysis and knowledge.
Reduction of solar collector acceptance angle from 135 to 125 degrees caused increasing the total cost in high water flow rates, while there was a small effect at low flow rates, indicating that GA led to change in design parameters of the MED unit and steam generator as well as those of solar field simultaneously in order to determine the optimized case.
Consider
Consider
Consider
Parameter for estimation of BPE (°C)
Parameter for estimation of BPE (°C)
Heat capacity (kj/kg·K)
Boiling point elevation (°C)
Inlet diameter tube of absorber
Inlet diameter tube of effect
Inlet diameter tube of condenser
Effects temperature difference (°C)
Mass flux, kg/(m^{2}·s)
Gravitational constant, 9.81 m/s^{2}
Height of condenser Shell
Heat transfer coefficient of tube wall (KW/kg°C)
Tube length (m)
Evaporator length (m)
Number of tubes on one line for effect
Number of tubes on one line for condenser
Number of rows wide
Number of tubes rows deep
Nusselt number
Pinch point (C or K)
Maine steam pressure
Reynolds number
Tube of absorber thickness (mm)
Velocity (m/s)
Specific volume of fluid (m^{3}/kg)
Width of condenser Shell
Capital cost rate ($/s)
Component purchase cost ($)
Specific heat ratio
Density (kg/m^{3})
Maintenance factor
Dynamic viscosity, kg/(s·m)
Surface tension, kg/s^{2}
Heat transfer fluid
Inner absorber pipe surface
Outer absorber pipe surface
Ambient
Sky
Brine
Condenser
Conduction
Convection
Capital recovery factor
Evaporation
Feed seawater
Out
Interest rate
Inlet condition
Component
Tube pinch (mm)
Saturated conditions
Steam high pressure
Seawater
Vapor phase.
The authors declare that there is no conflict of interests regarding the publication of this paper.