Simulating two Algerian cities' desalination plants coupled with solar energy systems using TRNSYS

A_c

Solar collector area (m²)

A_m

Membrane area (m²)

A′, B′

Constant coefficients

A

Condenser area (m²)

B

Membrane permeability coefficient (mol/Pam²s)

C

Parameter model

C_p

Specific heat (J/kgK)

G_h

Global solar radiation (W/m²)

G_β

Global solar radiation on an inclined surface (W/m²)

Average value of global solar radiation

I_g

Measured value of global solar radiation

k_B

Boltzmann constant (J/K)

K_n

Knudsen number

L′

Latent heat (kJ/kg)

L

Length (m)

M

Molecular weight (g/mol)

P

Average pressure in the membrane pores (Pa)

P₂, P₃, P₄

Parameters models

P_f

Vapor pressure at the feed side (Pa)

P_p

Vapor pressure at the permeate side (Pa)

R

Gas constant (J/g mol)

R_b

Conversion factor

R_c

Nonlinear correlation coefficient

T_{f, av}

Average temperature (K)

Mean daily minimum temperature (K)

Mean feed temperature (K)

Membrane interface temperature (K)

T_a

Ambient temperature (K)

T_ic

Inlet fluid temperature in a collector (K)

T_oc

Outlet temperature of the collector (K)

T_P

Process temperature or feed temperature at the input module (K)

T_R

Ambient brine water temperature (K)

T_c

Condensate temperature at the condenser outlet (K)

T_cwi

Cooling water temperature at the inlet (K)

T_cwo

Cooling water temperature at the outlet (K)

U

Condenser heat transfer coefficient (W/m² K)

T_i

Predicted value of the ambient temperature

Measured value of the ambient temperature

Average value of the ambient temperature

Coefficient confidence interval

V

Volume (m³)

Z

Parameter model

d_p

Pore size (μm)

h

Solar elevation angle (deg)

Enthalpy of water at the hot membrane interface

h_f

Convective heat transfer coefficient (W/m² K)

Hot feed flow rate (kg/h)

m_f

Feed mass flow rate (kg/s)

m_cw

Mass flow rate of cooling water (kg/s)

m_s

Mass flow rate of condensing steam (kg/s)

Mass flow rate (kg/s)

n

Parameter model

r_p

Mean pore radius (μm)

t

Time (hour)

x_w

Mole fraction of water

x

Dryness fraction of steam

x_NaCl

Mole fraction of sodium chloride

Greek letters

ΔH_v

Latent heat of vaporization (J/kg)

γ_w

Activity coefficient of water

δ

Solar declination (deg)

δ′

Standard deviation

δ_m

Membrane thickness (m)

Water viscosity (kg/m s)

λ_i

Mean free path traveled by the transported molecule (μm)

Kinematic viscosity (kg/m s)

v

Velocity (m/s)

ζ

Membrane porosity

σ

Collision diameter of water (m)

τ

Pore tortuosity

In Algeria, drinking water is a precious commodity. According to the Ministry of Water Resources, renewable natural water supplies are projected to be roughly 15 billion m³ per year or around 404 m³ per capita per year, near the upper limit of 500 m³ per capita per year in 2012, generally referred to as a scarcity threshold that signals emerging inherent crisis (Hamiche et al. 2015). The National Agency of Dams and Transfers reportedly inspected 80 dams with a potential of around 8 billion m³. In addition, almost all the data were available only for 47 major dams (Soltani et al. 2021).

Like most other Mediterranean countries, Algeria will face severe water shortage as its population and industrialization grow. The environmental equilibrium's destabilization is provoked by overcrowded coastal towns, inequalities between rural and urban regions, drought times, and rising emissions (Sadi & Kehal 2002). Algeria has limited potential for water supply development, especially in the northern areas, where around three-quarters of its population live. Total rainfall is estimated to be 100 billion m³, of which about 85% is lost by evaporation, and the remainder (12.5 billion m³) is returned to the sea or the Chotts (Sadi & Kehal 2002). The country has been experiencing many of its worst droughts and floods during the last decades (Schilling et al. 2020). The average annual temperature has risen by 1.45 °C, and the level of rainfall has decreased by 10 (Boudiaf et al. 2020). Most dams have lost some capacity because of mud deposits and lack of proper upkeep. Water treatment plants' dysfunction has been mainly caused by a lack of optimized operating conditions and maintenance (Sadi 2004). Thus, the water crisis could be modulated by removing mud from the dams and implementing desalination plants with optimal operating conditions and maintenance.

In Algeria, rainfall is often the most substantial available water resource, even if it fluctuates from over 2,000 mm/y on the northern heights and near the Mediterranean coast to its lower level, around 100 mm/y in the Sahara's North (Sadi & Kehal 2002). In the southern part of the country, there is a groundwater source with plenty of solar energy, especially in the desert basin of Ghardaïa (Sadi 2004). The government has set a target of generating 40% of its electricity from renewable energy sources by 2030 as part of its ambitious program to promote the development of renewable energy systems (Zahraoui et al. 2021).

Groundwater is the most critical source, providing more than 90% in the Sahara and 55% in the north. The remainder is provided by surface water and desalination plants (Ali Rahmani & Brahim 2017). Water management issues can be resolved by implementing a new approach to expand water supply sources, obtaining water from nonconventional sources. Reverse osmosis (RO) is currently the most widely used method for desalination worldwide, with over 60% of desalination plants using this technology. Its popularity is primarily due to its energy efficiency compared to thermal desalination processes. Indeed, RO requires significantly less energy than thermal processes' high temperatures and pressures, making RO a more cost-effective and environmentally friendly option for desalination, although it has limitations and challenges.

Desalination technologies are becoming more critical for providing access to clean water. However, developing sustainable techniques requires facing two challenges: minimizing energy consumption and ensuring pure water accessibility. Minimizing energy consumption procedures include improving the energy efficiency of the existing technologies, developing new technologies requiring less energy, and using renewable energy sources to power desalination plants (Drioli et al. 2015). The vacuum membrane distillation (VMD) configuration is used primarily to separate aqueous volatile organic compounds, and intensive studies have been recently carried out for its application in desalination. In VMD, a vacuum is applied by a pump at the membrane module's permeate side, resulting in water withdrawal from the evaporation of water, and vapor condensation takes place outside the module. Using VMD combined with solar energy leads to promising findings, even if some environmental constraints may be resolved, conducting to more significant benefits (Khayet & Matsuura 2011).

Wang et al. (2009) coupled a solar energy collector with a hollow fiber membrane VMD module to produce water from underground water. They found that at high permeate fluxes, the power consumption of the vacuum pump of 0.18 kW and the feed circulation pump of 0.37 kW were reduced compared to the heat power consumption. Bouguecha et al. (2005) evaluated small-scale desalination prototypes using air-gap membrane distillation (AGMD) accompanied by the sensible heat of geothermal water as the energy source. Their findings indicated that the experimental specific energy consumption was 30.83 kWh/m³, while the theoretical values ranged from 11.1 to 13.9 kWh/m³. They attributed this difference to the lower efficiencies and permeate fluxes observed in the second and third stages of the AGMD system, which were coupled to geothermal resources operating at lower temperatures.

Criscuoli et al. (2008) assessed the energy requirements of the direct contact membrane distillation (DCMD) and VMD laboratory systems using plate-and-frame membrane modules with an effective membrane area of around 40 cm². They investigated longitudinal and transversal flow dispositions and various MD-working parameters to evaluate energy efficiency. They found the lowest specific energy consumption values of 3,546.3 kWh/m³ for longitudinal flow in DCMD and 1,108.4 kWh/m³ for cross-flow VMD membrane modules. Increasing the feed temperature from 53.9 to 59.3 °C in a cross-flow module with a membrane pore size of 0.2 mm and a thickness of 91 mm at a feed flow rate of 150 L/h and downstream pressure of 10 mbar led to higher permeate flux from 29.7 to 51.5 kg/h m², resulting in a lower 354.6–441.8 W, while the specific energy consumption is 2,984.8–2,144.7 kWh/m³.

Chen et al. (2021a, 2021b) examined a solar-powered MD system performance under different configurations utilizing an absorption plate to gather solar energy. They devised a two-stage design methodology to reduce the total annual cost via steady-state simulations and increase the produced permeate through dynamic simulation. The simulation results indicated that the price per m³ of freshwater for AGMD, DCMD, and VMD configurations was 2.71, 5.38, and 10.41 USD, respectively. Liu et al. (2021) designed a VMD seawater desalination system integrated with a thermal/photovoltaic (PV) solar system. They showed that the setup could attain a thermal and electrical efficiency of 56.2% and an electrical efficiency of 15.9% while producing a water yield of 0.579 L/h m².

Miladi et al. (2021) studied a VMD plant combined with solar energy utilizing a liquid ring pump distinguished by lower electrical energy consumption, varying between 4.2 and 7.47 kWh/m³ throughout the year. They found that the average daily production oscillated from 598 to 217 kg/day (Miladi et al. 2021). Andrés-Mañas et al. (2018) assessed an original desalination setup built on vacuum multi-effect MD modules and solar energy as a thermal source for desalinating Mediterranean seawater. They placed a heat storage tank before the heat exchanger and after the solar collector. The maximum distillate flux of 8.5 L/h m² was attained at a feed flow rate of 150 L/h at a feed temperature of 75 °C and specific thermal energy consumption of around 200 kWh/m³ (Andrés-Mañas et al. 2018). However, the specific thermal energy consumption of the DCMD unit (2.52 W/g h) is relatively higher than the energy used by VMD (1.07 W/g h) (Criscuoli 2021). They also focused on the effect of different environmental conditions on thermal storage to minimize the impact of disturbances in solar radiation. A quasi-dynamic model simulation was also conducted to analyze the distillate formation profile and the running period over 12 months at various temperatures. They proved that the average flux of (5.5 ± 1) L/h m² was considered the most suitable for the MD unit (Andrés-Mañas et al. 2020).

An appropriate program for energy system simulations is transient system simulation software (TRNSYS). It is one of the most established programs, providing a flexible graphical software environment tool. It is mainly used to simulate the transient behavior of a system, despite most simulations being used to evaluate the performance of systems. These simulation program packages, whose components are tightly integrated and connected to form a system, are modeled in the FORTRAN programming language, making it one of the most versatile tools available (Dall'O 2013). On the other hand, desalination processes have become increasingly coupled with solar energy. Remlaoui et al. (2020) tested DCMD connected to a 2 m² solar energy collector with a 0.82 m² PV panel for producing freshwater from brackish water. They simulated a desalination unit to be tested with solar energy and evaluated design variables using TRNSYS software (version 16). They found that the daily freshwater production in the region of Ain Témouchent (north of Algeria) by the system is about 59.34 L/d m², and the feed saltwater outlet temperature for DCMD and freshwater outlet temperature oscillate, respectively, from 60 to 21 °C and between 20 and 34 °C (Remlaoui et al. 2020). Duong et al. (2017) used TRNSYS (version 17.2) to design a coupled solar thermal-driven DCMD system composed of a 7.2 m² membrane module under counter-current flow and a 22.6 m² of flat plate solar thermal collector. This unit's daily distillate production rate can produce more than 140 kg of distillate daily (Duong et al. 2017). Acevedo et al. (2016) developed a novel model type. They comprised MD in the lab-scale pilot plant capable of generating electricity by integrating PV/thermal collectors with a wind turbine. The sanitary hot water comes from the thermal collectors and evacuated tube collectors, whereas the MD and RO plants provide fresh water. In the MD plant, the suggested base case generated up to 15,311 L per year and achieved an electric energy demand of 1,890 kWh (Acevedo et al. 2016).

This work aims to design and evaluate the coupling of a solar collector with a VMD module in actual weather conditions during a year in two different cities. The novelty and significant contributions of this study can be summarized as follows: (1) A model describing the evolution of feed temperature and permeation flux through the membrane was integrated into TRNSYS as a VMD module to facilitate the operation of the desalination unit. (2) The empirical correlations have been developed based on experimental results recorded at a meteorological station in two different cities. (3) The plant was designed for conducting annual simulations in two different cities, under specific operating conditions. In addition, the present research concerns the application of TRNSYS to predict the outlet temperature from the collector and permeation flux through the VMD. The TRNSYS software allows researchers to study solar energy systems without performing actual experiments; it includes a method for creating a new component (VMD unit) that does not exist in the standard component library. The model developed in our previous work (Irki et al. 2020) is integrated into the TRNSYS software, coupled with CODE: BLOCK for adding new components to the TRNSYS library to optimally design and operate the desalination unit (Irki et al. 2020). In this study, we have used experimental data from the Meteorological Stations of Ghardaïa and Bouzaréah to predict the global solar radiation incident on a horizontal surface and ambient temperature. Furthermore, we have used the various component models in the TRNSYS for modeling the desalination unit, including a new component developed for this research. Finally, the TRNSYS software was used to simulate calculations for a prototype solar collector coupled with a VMD module in two different cities in Algeria.

The performance of a given solar collector varies as a function of ambient temperature and the amount of solar insolation available. In this study, we coupled the solar thermal collectors with the VMD process for heating salted water by thermal conversion. Two regions' meteorological data must be considered to assess permeation flux through VMD.

Data are filtered when the value deviates more than the value of ⁠.

All the required simulations were realized utilizing MATLAB software.

The model system was developed using TRNSYS, a general-purpose solar energy-simulating program. Using the modular simulation program, TRNSYS as the main computational framework permitted the development of a new component. The TRNSYS advantages are modularity in libraries, flexibility, and component adoption through which the developer can write a new component to extend the program's functionality. Also, TRNSYS has a modular structure, making it possible to incorporate a new mathematical model into the software. In addition, TRNSYS includes a library of component models the developer can use or formulate his own in the same code. Finally, TRNSYS has a modular construction enabling the program to be versatile and allowing users to add components to the TRNSYS library.

Modeling large numbers of systems is daunting; however, modeling through TRNSYS is possible and has been configured to facilitate users adding their components. For this study, the model used has been developed in the literature for estimating permeation flux through VMD. However, this model has been validated with experimental results for the desalination unit produced by Frikha et al. (2013). Therefore, the model was tested under varying operating conditions using data from the desalination unit produced by Frikha et al. (2013), even though the climatic conditions were different from the original conditions of the unit.

All the design and coding processes were performed using the coupled TRNSYS 16/CODE: BLOCK. The new component has also required changes to executable code by running a FORTRAN compiler. Subsequently, we ran the executable file using the text file, then called a dynamic link library (DLL) containing the actual TRNSYS FORTRAN source code, and it will be placed in the standard package for the TRNSYS. Data reader component Type 9c is used to read hourly values of solar radiation incidents on a horizontal surface and ambient temperature for a typical day of the month at a particular location.

Weather data obtained from the typical day-of-the-month empirical formula for Ghardaïa and Bouzaréah cities were used for the simulation. Subsequently, all the collected data was incorporated into a new component. The project of a setup furnishing solar PV system comprises PV power systems and batteries that work with a grid converter. The PV power system consists of two main components. The first is the solar cell lineup, which generates DC power from sunlight. The second component is the line converter, which takes the DC from the solar array and converts it to AC. The battery stores the DC power produced by the solar cell lineup, which can be used to power pumps for pumping water or other devices when the solar panels are not producing enough energy.

Equation (1) has been programmed using Matlab software and gives correlation coefficient values for a representative day for each month of the year. The standard deviation and correlation coefficient values are depicted in Table 2. As seen in Table 2, the model fits well with experimental data, and the correlation coefficient varies from 0.87 to 0.97. The model is perfectly adapted to a comparison with experimental data. For each typical day of the month, the correlation coefficient is close to unity and suited to fit the data.

Table 2

Correlation coefficients of global solar radiation for the typical day of the month (Ghardaïa)

Month .	Day .	.	.	Rc .
January	17	1,264.9	1.1259	0.914
February	47	1,341.2	1.2534	0.948
March	75	1,228.9	1.2265	0.958
April	105	1,143.4	1.2732	0.949
May	135	1,051.5	1.3557	0.936
June	162	1,062.8	1.3767	0.964
July	198	1,051.2	1.3917	0.969
August	228	1,083.70	1.2898	0.971
September	258	1,109.6	1.2351	0.916
October	288	1,162.4	1.1220	0.909
November	318	1,204.2	1.0613	0.891
December	344	1,238.1	1.1135	0.879

Month .	Day .	.	.	Rc .
January	17	1,264.9	1.1259	0.914
February	47	1,341.2	1.2534	0.948
March	75	1,228.9	1.2265	0.958
April	105	1,143.4	1.2732	0.949
May	135	1,051.5	1.3557	0.936
June	162	1,062.8	1.3767	0.964
July	198	1,051.2	1.3917	0.969
August	228	1,083.70	1.2898	0.971
September	258	1,109.6	1.2351	0.916
October	288	1,162.4	1.1220	0.909
November	318	1,204.2	1.0613	0.891
December	344	1,238.1	1.1135	0.879

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The average solar radiation values during the period 2014–2015 estimated by the model for both summer and winter are 253.87 and 151.23 W/m², respectively. Unfortunately, the essential meteorological parameters data are available only for a few locations. However, Yacef et al. (2014) proposed new integrated empirical models and a Bayesian neural network model to assess daily global solar radiation on a horizontal surface in Ghardaïa from air temperature. They found that the average solar radiation values determined by the developed model for summer and winter are 307 and 162 W/m², respectively. The developed model has been validated using six months of the year 2012. In addition, it has been demonstrated that insolation in the Ghardaïa area where the mean daily global solar radiation measured on a horizontal plane exceeds 250 W/m² for 2 years (2012 and 2013) (Gairaa et al. 2016).

The model (2) used in the ambient temperature predictions has been simulated for different initial conditions using Matlab and gives correlation coefficients value for a representative day for each month of the year. The correlation coefficients of ambient temperature were calculated using the method developed by Hakem et al. (2013) and data recorded in Ghardaïa. The adjustment results are grouped and given in Table 3.

Using a storage tank, the desalination unit can operate consistently regardless of changes in the feedwater flow rate. As a result, the unit can produce a more stable output, leading to a higher average flow over time. This can help to mitigate the effects of interruptions in the feedwater supply, enabling the desalination unit to keep functioning and generating fresh water. A storage tank can also enhance the energy efficiency of a desalination unit by allowing it to run continuously at a constant flow rate. This is beneficial because the unit can be optimized to operate at a specific flow rate, reducing the energy required to produce each unit of freshwater.

Figure 5(a) and 5(b) shows the progression of the feed temperature and permeation flux through VMD during June. Consequently, the permeation flux achieved 32 and 48 kg/h m² when the maximum temperatures were 73 and 80 °C for Bouzaréah and Ghardaïa, respectively. The findings show that the maximum temperature values are reached around midday when solar irradiation is optimum.

It can be seen that the permeation flux increases considerably depending on the feed temperature. Water vapor flows across the porous membrane because of the transmembrane vapor pressure gradient in VMD and condenses at the external condenser to form the distilled water. Our study utilized a VMD module with the exact specifications as the one in Frikha's paper. Still, we altered the hot inlet temperature to account for climate differences in our regions. With these modified operating conditions, we achieved a maximum simulated throughput of 49 kg/h m², while Frikha's study only reached a maximum throughput of 22 kg/h m².

Based on the experimental data recorded by the weather station, we observed that the solar panel outlet temperature was higher in October and November than in June and July. The temperature variation may be attributed to changes in the region's climatic conditions. During daytime operation, the storage tank stores the hot salty water required to provide a proximate source of hot salty water to produce steam. The salty water is returned directly to the heat exchanger and circulated to the solar collector to absorb the solar energy. Based on this, intermittent renewable solar energy can supply power to the desalination system. It can not only solve the scarcity of freshwater resources but also permit the reduction of local consumption and environmental pollution.

However, there is a disadvantage of increased risk of pore wetting because of the implementation of vacuum on the permeate side of the membrane module and membranes with smaller pore sizes (i.e., less than 0.45 μm) than other MD variants (Khayet & Matsuura 2011). Therefore, it was suggested that the submerged vacuum membrane distillation (S-VMD) powered by solar energy could achieve higher permeation flux and fouling reduction. However, researchers (Chang et al. 2022) found that permeation flux varied between 2.1 and 5.2 kg/h m², following the solar intensity profile. Therefore, Maa et al. (2022) recommended small-scale flat plate vacuum membrane distillation (VMD-FPC) for small-scale usages built on its more crucial productivity and less space footprint.

Based on Figure 7(a) and 7(b), the PV panel can generate a maximum power of 6,600 kJ/h for Ghardaïa when the sun irradiation value is 1,000 W/m² and the temperature is 24 °C. Similarly, for Bouzaréah, the power to load reaches a maximum of 6,300 kJ/h when the sun irradiation value is 972 W/m², and the temperature is 18 °C. However, it is essential to note that the solar radiation collected by the solar collectors at the latitude and height of the solar energy is higher during winter compared to the summer. This is because the sun's height in the sky affects the angle at which sunlight hits the solar collector. This angle, in turn, determines the amount of solar energy that can be collected and converted into electricity. When the sun is directly overhead, the angle of incidence of sunlight is at its maximum, and the solar collector can collect the maximum amount of energy. However, when the sun is lower in the sky, the angle of incidence decreases, and the solar collector is less efficient in capturing energy. Therefore, the sun's height is critical in determining the amount of solar energy that can be converted into electricity by a solar collector.

Deng et al. (2020) proposed an appropriate experimental design strategy based on response surface methodology for predicting the impacts of different operational parameters on permeate flux and energy consumption. They found that the optimum conditions for the empirical permeate flux are 6.26 L/h m², the corresponding electricity consumption is 0.5 kWh (1,800 kJ), and its corresponding energy effectiveness is 12.52 L/kW m². Zhou et al. (2018) proposed a novel solar VMD regeneration for a liquid desiccant air conditioning system. The PV module provides the energy consumption for the vacuum pump in the VMD regeneration and fans, equal to 582.4 kWh per year (2,096,640 kJ). Still, the PV modules' price slumped the probability of more expansion of VMD regeneration (Zhou et al. 2018).

The coolant fluid enters the condenser at 20 °C; here, this coolant fluid gets heated due to heat transfer, which occurs when the vapor coming from VMD is condensed. The cooling liquid from the condenser flows through a closed-circuit cooling tower, which is used to cool the liquid by evaporating the water outside the coils containing the working liquid. As shown in Figure 8(a) and 8(b), the maximum value of COP with previous conditions equals 3.6.

It is necessary to notice that the COP depends mainly on the evaporating temperature, and these results may be suitable for the desalination plant operation. A COP of 3.6 for condensation in a cooling system indicates that the system can effectively remove heat from the vapor.

However, Sztekler et al. (2020) investigated the influence of heating water temperatures from 55 °C to approximately 80 °C on the COP of a three-bed adsorption chiller. They found that the COP augmented with elevating heat source temperature and had the maximum level for the temperature of heat water of around 80 °C (Sztekler et al. 2020). Further, Sztekler (2021) focused on the impact of the time of the adsorption and desorption methods on the COP of an adsorption chiller with a desalination function (Sztekler 2021). The results show that increased cycle time can significantly augment the COP value.

This study provided information on two crucial performance indicators, i.e., the GOR and the TRR, for high-performance flat plate solar collectors over an annual period (Table 4). As mentioned in Table 4, the average GOR values in Ghardaïa and Bouzaréah were 10.947 and 8.3389, respectively. Higher GOR systems have higher initial costs but lower operating costs due to lower energy consumption. This reduction in operating expenses is only in terms of energy components and does not include maintenance and replacement costs. The results showed that the average TRR values for Ghardaïa and Bouzaréah were 2.2076 and 1.9415, respectively, representing the average ratio of thermal energy recovered from the system to the quantity of incident solar radiation absorbed by the system over a year (Table 4). If TRR is more significant than one, the system can recover more thermal energy than the amount of solar radiation received. In our case, the desalination unit has a heat exchanger capable of transferring more thermal energy to the storage tank than the amount of solar radiation absorbed by the collector.

This work established that the permeation fluxes in Ghardaïa were considerably better than those obtained in Bouzaréah under more challenging and advantageous conditions. However, this also requires a treatment process with a storage tank upstream of the treatment, which presents an additional advantage for both sites. Integrating the model of the VMD process into a simulation environment (TRNSYS) coupled with CODE-BLOCK and FORTRAN programming language allowed us to create a new component (i.e., VMD). Adding a new type 226 in the TRNSYS software makes it possible to evaluate the potential contribution energy efficiency measures can make in delivering our energy goals. A new Type 226 has been added to the TRNSYS software to assess energy efficiency procedures' possible role in achieving our energy goals. Various TRNSYS components are used for modeling this unit, including a new component developed for this work. The permeation flux obtained through the desalination unit with storage-heated water is relatively higher in Ghardaïa than in Bouzaréah, with a flow exceeding 30 kg/h m². The TRNSYS simulation approach involves estimating permeation flux using the relevant explanatory variables and forecasting permeation flux by including the possible future values of the variables in a new compound. The study on high-performance flat plate solar collectors in Ghardaïa and Bouzaréah provided valuable information on their performance indicators.

The results also showed that the average GOR values for Ghardaïa and Bouzaréah were 10.947 and 8.3389, respectively, establishing that the GOR system in Ghardaïa is more efficient in producing energy than in Bouzaréah. The higher GOR value for Ghardaïa could be attributed to its higher solar radiation value. Moreover, the average TRR values for Ghardaïa and Bouzaréah were 2.2076 and 1.9415, respectively, indicating that both systems could recover more thermal energy than the quantity of solar radiation collected by the collectors. Consequently, the desalination unit with the heat exchanger efficiently converted solar energy into thermal energy for desalination purposes. Overall, the study demonstrates the potential of high-performance flat plate solar collectors for desalination purposes in different locations.

Furthermore, the ability of TRNSYS to create and share new components with others can support the development of a new desalination system. Solar energy production aims to achieve the highest power output possible at any given time. Still, the nonlinear power output of PV panels is influenced by variables such as solar radiation and temperature, leading to more complex behavior.

This research has been funded by Scientific Research Deanship at University of Ha'il - Saudi Arabia through project number <<RG-23 030>>.

Conceptualization: N.E., D.G., and S.I.; methodology: E.A., S.H., D.G., and N.E.; formal analysis: S.I., N.E., S.B., M.B., and D.G.; investigation: S.I., N.E., N.K.M., and S.A.; resources: N.E. and D.G.; writing original draft preparation: S.I., S.H., M.B., and D.G.; writing review and editing: N.K.M., S.B., E.A., and D.G.; supervision: D.G. All authors have read and agreed to the published version of the manuscript.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.