Our study aimed to design a prototype for a desalination unit coupled with a solar collector, utilizing TRNSYS 16, to address the needs of both Bouzaréah in northern Algeria and Ghardaïa in southern Algeria. The desalination unit is composed of vacuum membrane distillation (VMD) coupled with a solar collector, and the photovoltaic has been designed according to the climatic conditions of each region. In this work, the approach adopted is to integrate a model developed in the literature into a simulation environment (TRNSYS) coupled with the CODE-BLOCKS compiler and FORTRAN programming language to create a new component (i.e., VMD process). Simulation results showed that the optimum permeation flux obtained through the desalination unit is relatively higher in Ghardaïa than in Bouzaréah, with a flow exceeding 30 kg/h.m2. The permeation flux and the power to load reached their maximum values with the charge of solar irradiation 48 kg/h.m2 and 6300 kJ/h, respectively, for Ghardaïa at the sun irradiation value 800 W/m2 and temperature of 34 °C. Results showed that Ghardaïa had a higher GOR value than Bouzaréah over the year (10.947 vs. 8.3389). Moreover, both locations recorded thermal recovery ratio values exceeding 1, indicating the high efficiency of the desalination unit.

  • A model that describes the evolution of feed temperature and permeation flux through the membrane was integrated into TRNSYS as a VMD module.

  • Empirical correlations were developed based on experimental results recorded at a meteorological station in two different cities.

  • The plant was designed to conduct annual simulations in two different cities under specific operating conditions.

Ac

Solar collector area (m2)

Am

Membrane area (m2)

A′, B

Constant coefficients

A

Condenser area (m2)

B

Membrane permeability coefficient (mol/Pam2s)

C

Parameter model

Cp

Specific heat (J/kgK)

Gh

Global solar radiation (W/m2)

Gβ

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

Average value of global solar radiation

Ig

Measured value of global solar radiation

kB

Boltzmann constant (J/K)

Kn

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

Pf

Vapor pressure at the feed side (Pa)

Pp

Vapor pressure at the permeate side (Pa)

R

Gas constant (J/g mol)

Rb

Conversion factor

Rc

Nonlinear correlation coefficient

Tf, av

Average temperature (K)

Mean daily minimum temperature (K)

Mean feed temperature (K)

Membrane interface temperature (K)

Ta

Ambient temperature (K)

Tic

Inlet fluid temperature in a collector (K)

Toc

Outlet temperature of the collector (K)

TP

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

TR

Ambient brine water temperature (K)

Tc

Condensate temperature at the condenser outlet (K)

Tcwi

Cooling water temperature at the inlet (K)

Tcwo

Cooling water temperature at the outlet (K)

U

Condenser heat transfer coefficient (W/m2 K)

Ti

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

dp

Pore size (μm)

h

Solar elevation angle (deg)

Enthalpy of water at the hot membrane interface

hf

Convective heat transfer coefficient (W/m2 K)

Hot feed flow rate (kg/h)

mf

Feed mass flow rate (kg/s)

mcw

Mass flow rate of cooling water (kg/s)

ms

Mass flow rate of condensing steam (kg/s)

Mass flow rate (kg/s)

n

Parameter model

rp

Mean pore radius (μm)

t

Time (hour)

xw

Mole fraction of water

x

Dryness fraction of steam

xNaCl

Mole fraction of sodium chloride

Greek letters

ΔHv

Latent heat of vaporization (J/kg)

γw

Activity coefficient of water

δ

Solar declination (deg)

δ′

Standard deviation

δm

Membrane thickness (m)

Water viscosity (kg/m s)

λi

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.

Correlations for evaluating monthly average hourly global solar radiation

Perrin de Brichambaut's formulas can be employed to calculate the global solar radiation value for a surface perpendicular to the solar rays, corresponding to the solar rays after passing through the atmosphere. The variation of global solar radiation was simulated according to Perrin de Brichambaut's model, which is used by Hakem et al. (2013, 2014) to express the monthly global solar radiation on a flat surface, as given by Hakem et al. (2013, 2014):
formula
(1)
where h is the solar elevation angle, and the parameters A′ and B′ are constant coefficients of the model. This study estimated the model's parameters from experimental data recorded in the Ghardaïa region. This model is based on experimental data gathered between 2014 and 2015. Global solar radiation data measurements on a horizontal surface were registered every 5 min. In Equation (1), h (i.e., the solar elevation angle) and the parameters A′ and B′ (i.e., constant coefficients of the model) have been calculated from measurement data. Climate's database contains information about ambient temperature and daily solar radiation. These meteorological data required by the model are provided by the Regional Weather Station in Algeria. In addition, the Excel file format allows for storing the database. The file is a directory containing records of tape identification information. This file also includes variables set in the data file, including the day of the year, the hour, ambient temperature, and solar radiation. We point out that data processing, such as results, is diagnosed to extract erroneous data and identify missing data.
Chauvenet's criterion was used to eliminate erroneous data. For this purpose, the gap between the theoretical (GH) and evaluated (Ig) values was calculated according to Equation (2):
formula
(2)
Furthermore, the representative standard deviation was chosen for assessing the quality of fit and is given by Equation (3):
formula
(3)
where n is the number of data points.

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

The coefficient has been read from the Standard Normal Table for a 95% confidence interval. Once the erroneous values had been eliminated, a new adjustment was made to determine the coefficients B′ and c′. The quality of the fit is estimated by evaluating the corresponding nonlinear correlation coefficient Rc that is given by Equation (4):
formula
(4)
where Ig and are the measured and average values of global solar radiation, respectively.

Correlations for estimating the monthly average hourly ambient temperature

Hakem et al. (2013, 2014) developed an ambient temperature model depending on time:
formula
(5)
where Tmin is the minimum daily temperature; P2, P3, P4, and C are constants related to the measurement sites. The ambient temperature measurements were registered every 30 min at the Weather Station during 2014–2015 in Ghardaïa. The following study concerns the estimation of the correlation coefficients using the method developed by Hakem et al. (2013, 2014).
The minimum of the function was estimated using the simplex method and nonlinear least squares method for establishing the coefficients depending on the time of day. The nonlinear adjustment relationship was assessed by calculating the value of the coefficient of determination using Equation (6):
formula
(6)
where Ti and are the predicted value and the measured value of the ambient temperature, respectively. is the average value of the ambient temperature.
VMD is a process that involves heating saltwater and transferring its molecules across a membrane interface. The saltwater molecules are separated from the feed solution via executing pressure on the permeate side higher than the saturation pressure on the feed side. Heated saltwater molecules are transferred through a membrane interface and separated from the feed solution by applying pressure on the permeate side that exceeds the saturation pressure on the feed side. Finally, these molecules are condensed at the outside of the membrane module. The model of the temperature in the feed side of the membrane built on the heat balance equation has been proposed in our previous research (Irki et al. 2020) and can be written as:
formula
(7)
where is the mass flow rate, Cp is the specific heat, represents the mean feed temperature, which is given by (Wang et al. 2009), Jv is the mass flux of the vapor through the membrane, Am is the area of the membrane, hf is the heat transfer coefficient, is the feed side of the membrane interface temperature, and is the enthalpy of water at the hot membrane interface. In addition, is the average temperature between membrane interfaces and the feed side boundary layer, and is given by . The solar thermal collector is linked to the module VMD comprising mf (kg) of water originally at the temperature with time increments Δt.
The membrane interfaces temperature can be estimated from the equation of heat balance (Wang et al. 2009):
formula
(8)
where hf is the heat transfer coefficient. The partial vapor pressure difference determines the mass flux of vapor across the membrane and is written as:
formula
(9)
where Pf and Pp are the vapor pressures at the feed and permeate sides, respectively, and B is the membrane permeability coefficient. Khayet & Matsuura (2011) have given the partial pressure of water as follows:
formula
(10)
where xw is the water molar fraction, γw is the activity coefficient of water, and Ps is the saturated vapor pressure at the feed/membrane interface.
For dilute NaCl aqueous solution on the feed side, the partial pressure of water vapor is defined (Khayet & Matsuura 2011):
formula
(11)
where xNaCl is the solute molar fraction. The Antoine equation is broadly utilized for evaluating Ps (Khayet & Matsuura 2011):
formula
(12)
By substituting Equations (11) and (12) into Equation (9), we find:
formula
(13)
The correlation for evaluating the coefficient of the activity coefficient of water γw in a NaCl solution is (Khayet & Matsuura 2011):
formula
(14)
The Knudsen number (Kn) bears out the mass transport mechanism in membrane operation. It is a dimensionless number and is described as the ratio of the mean free path (λi) of the transported molecules to the pore size of the membrane (Belessiotis et al. 2016):
formula
(15)
where λi (μm) and dp (μm) are the transport molecules' mean accessible paths and pore size, respectively. The mean free path is calculated using Equation (16) (Belessiotis et al. 2016):
formula
(16)
where kB is the Boltzmann constant, is the average pressure in the membrane pores, and δm is the collision diameter of water.
Knudsen's diffusion dominates when collisions with pore walls are more frequent than collisions between diffusing molecules (Kn > 10 and rp < 0.05λ) (Khayet & Matsuura 2011). The membrane permeability coefficient B could be calculated using Equation (17):
formula
(17)
where rp is the average pore radius of all pores is assumed to be uniform, M is the molecular weight, R is the gas constant, ζ is the membrane porosity, τ is the pore tortuosity, and δ is the membrane thickness.
The transition flow takes precedence if 0.1 > Kn > 0.01 and 50 > rp > 0.05λ. Therefore, combining these two mechanisms, Poiseuille flow and Knudsen's diffusion transition, is advisable. The membrane permeability coefficient can be expressed using Equation (18) (Khayet & Matsuura 2011):
formula
(18)
where η is the viscosity. Then, use Tf to determine the vapor mass flux through the boundary layer adjacent to the membrane surface.
On the other hand, VMD is the process of converting seawater into its vapor, transferring the vapor through the membrane, and recovering the liquid by condensing the vapor, usually by leading it into contact with a cold surface. In practice, the heat lost by the vapor is equal to the heat gained by cooling water, and the energy exchange in the condenser may be analyzed in a steady state through Equations (19) and (20) (Khalil 1990; Maivel & Kurnitski 2015):
formula
(19)
formula
(20)
where x is the dryness fraction of steam at the condenser inlet, L is the latent heat at condenser pressure, Tc is the condensate temperature at the condenser outlet, Tcwi is the cooling water temperature at the inlet, Tcwo is the cooling water temperature at the outlet, mcw is the mass flow rate of cooling water, and ms is the mass flow rate of condensing steam.
The condensing temperature is calculated from energy balance, heat on the coolant side (Q1) and heat from the condenser (Q2) given by Equations (21) and (22):
formula
(21)
formula
(22)
Equations (21) and (22) allow deriving condensing temperature Equation (23) (Maivel & Kurnitski 2015):
formula
(23)
where U is the condenser heat transfer coefficient (W/m2K), and A is the condenser area (m2).
The full steam is condensed by a coolant fluid from a closed-circuit cooling. The coefficient of performance (COP) is the ratio of the cooling capacity produced to the total energy input to the cooling system:
formula
(24)
The most critical factors employed for estimating the efficiency of solar desalination units remain the gained output ratio (GOR) of the VMD module and the thermal recovery ratio (TRR) of the solar thermal desalination systems. GOR could be defined as the ratio of thermal energy needed to generate distillate water to the real thermal energy expended in the feed side. Its equation can be written as (Abu-Zeid et al. 2015):
formula
(25)
where is the latent heat of vaporization (J/kg), mf and mp are the feed and permeate flow rate (kg/h), respectively. TRR is described as the heat energy theoretically requested for distilling an amount of distillate divided by the total heat energy utilized by the setup (Abu-Zeid et al. 2015):
formula
(26)
where Ac is the solar collector area (m2), Gβ is the global solar radiation on an inclined surface (W/m2), and is the latent heat of evaporation at the hot membrane interface.

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.

A comprehensive system description for water treatment

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.

A solar collector is an apparatus that absorbs and converts solar radiation into thermal energy, which can then be transferred to a fluid circulating across the collector. This thermal fluid is then passed through a heat exchanger, transferring its heat to the water in a storage tank. Hot water from the storage tank is directed to a VMD system, where a membrane interface transfers vapor molecules. This transfer occurs due to the difference in vapor pressure between the feed and permeate sides of the membrane. After the molecules are transferred, they undergo condensation at an external condenser. This process involves a closed-circuit cooling tower that cools a liquid stream by evaporating water outside coils holding the working fluid. The coolant fluid from the condenser can be cooled using a closed-circuit cooling tower. In a closed-circuit cooling system, a coolant fluid circulates through a loop that includes a vapor condenser and a cooling tower. The vapor condenser allows heat transfer between the coolant fluid and a vapor that needs to be condensed into a liquid state. The coolant fluid absorbs heat from the vapor, causing it to condense into a liquid. After passing through the vapor condenser, the heated coolant fluid flows through coils exposed to the cooling tower. The cooling tower uses evaporative cooling to lower the temperature of the coolant fluid by spraying water onto the coils and blowing air over them. This causes some of the water to evaporate, which removes heat from the coolant fluid and lowers its temperature. The cooled coolant fluid is then directed back to the vapor condenser, which removes more heat from the vapor (Figure 1). Figure 2 depicts the solar energy-coupled seawater desalination plant diagram. The TRNSYS simulation of this unit utilized several existing components and a new component developed specifically for this project. Table 1 summarizes the dimensions and conditions of the various components used in the TRNSYS simulation.
Table 1

Dimensions of various plant parts

ParameterCompleted data
Frikha et al. (2013)GhardaïaBouzaréah
VMD (Type 226) 
 Commercial reference UMP 3247 R 
 Number of fibers (PVDF) 806 
 Internal diameter (mm) 1.4 
 Module length (m) 1.129 
 Membrane's mean pore size (μm) 0.1 
 Area of membrane (m2
 Feed mass flow rate (kg/h) 11,000 12,000 
 Vacuum pressure (Pa) 10,000 
Solar collector (Type 1b) 
 Area of collector (m270 
 Inlet flow rate (kg/h) 852 637 
Heat exchanger (Type 5b) 
 Hot inlet flow rate (kg/h) 1,205 1,033 
 Cold inlet flow rate (kg/h) 844 689 
Tank (Type 4d) 
 Hot inlet flow rate (kg/h) 300 300 
 Cold inlet flow rate (kg/h) 300 300 
Water cooled chiller (Type 666) 
 Chilled inlet flow rate (kg/h) 800 700 
Photovoltaic (PV) panel (Type 94a) 
 Number of modules in series  
 Number of modules in parallel  
 Module area (m2 0.82 0.82 
Pumps (Type 110) 
 Inlet flow rate (kg/h)  300–500 200–900 
Closed-circuit cooling (Type 510) 
 Fluid flow rate (kg/h)  20,000 20,000 
ParameterCompleted data
Frikha et al. (2013)GhardaïaBouzaréah
VMD (Type 226) 
 Commercial reference UMP 3247 R 
 Number of fibers (PVDF) 806 
 Internal diameter (mm) 1.4 
 Module length (m) 1.129 
 Membrane's mean pore size (μm) 0.1 
 Area of membrane (m2
 Feed mass flow rate (kg/h) 11,000 12,000 
 Vacuum pressure (Pa) 10,000 
Solar collector (Type 1b) 
 Area of collector (m270 
 Inlet flow rate (kg/h) 852 637 
Heat exchanger (Type 5b) 
 Hot inlet flow rate (kg/h) 1,205 1,033 
 Cold inlet flow rate (kg/h) 844 689 
Tank (Type 4d) 
 Hot inlet flow rate (kg/h) 300 300 
 Cold inlet flow rate (kg/h) 300 300 
Water cooled chiller (Type 666) 
 Chilled inlet flow rate (kg/h) 800 700 
Photovoltaic (PV) panel (Type 94a) 
 Number of modules in series  
 Number of modules in parallel  
 Module area (m2 0.82 0.82 
Pumps (Type 110) 
 Inlet flow rate (kg/h)  300–500 200–900 
Closed-circuit cooling (Type 510) 
 Fluid flow rate (kg/h)  20,000 20,000 
Figure 1

System component overview of the desalination unit.

Figure 1

System component overview of the desalination unit.

Close modal
Figure 2

Diagram of a seawater desalination station coupled with solar energy.

Figure 2

Diagram of a seawater desalination station coupled with solar energy.

Close modal

Result of estimating the global solar radiation

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)

MonthDayRc
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 
MonthDayRc
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 

The accuracy was critically compared to experimental data. Several approaches in the literature critically compared the accuracy results to experimental data using the correlation coefficient (R2). The correlation coefficient ensures sufficient precision among the methods considered (Gairaa et al. 2016). The south of Algeria is an ideal location for harnessing solar energy thanks to the high levels of sunlight it receives and characterized substantial solar energy potential; this means that all these are suitable locations for solar PV applications. Figure 3 shows the bell-shaped curves that provide a good fit for the distribution of the experimental points for global solar radiation data. Theoretical and empirical results are very similar. Therefore, the dependence relations between variables can be described as a problem of fitting models from point cloud experimental data. The results showed that the maximum solar radiation occurs during summer, with a maximum value around noon of 1,035 W/m2 in June. On the other hand, it appears that the minimum of global solar radiation occurs only in winter. We also noticed that the lowest global solar radiation occurred in December (650 W/m2) at 0 degrees.
Figure 3

Curves representative of the variation of average daily solar radiation with experimental data.

Figure 3

Curves representative of the variation of average daily solar radiation with experimental data.

Close modal

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).

Results of estimating the ambient temperature

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.

Table 3

Correlation coefficients of ambient temperature for the typical day of the month (Ghardaïa)

CP2P3P4TminRc
January 28.70 8.674 2.027 1.6775 4.987 0.97 
February 19.41 12.28 4.77 1.001 6.088 0.94 
March 24.87 12.296 3.290 1.172 12.83 0.99 
April 23.53 13.769 4.302 0.865 15.91 0.99 
May 15.328 13.143 5.399 0.694 24.04 0.98 
June 13.605 4.546 0.642 20.32 25.50 0.99 
July 9.649 11.036 2.757 0.6125 34.014 0.95 
August 16.195 13.411 7.211 0.7358 22.658 0.84 
September 20.384 13.054 4.180 0.851 22.209 0.98 
October 27.32 10.67 2.803 1.337 19.156 0.99 
November 28.326 9.609 2.381 1.507 12.444 0.99 
December 5.020 2.3781 1.0012 3.1789 7.8592 0.97 
CP2P3P4TminRc
January 28.70 8.674 2.027 1.6775 4.987 0.97 
February 19.41 12.28 4.77 1.001 6.088 0.94 
March 24.87 12.296 3.290 1.172 12.83 0.99 
April 23.53 13.769 4.302 0.865 15.91 0.99 
May 15.328 13.143 5.399 0.694 24.04 0.98 
June 13.605 4.546 0.642 20.32 25.50 0.99 
July 9.649 11.036 2.757 0.6125 34.014 0.95 
August 16.195 13.411 7.211 0.7358 22.658 0.84 
September 20.384 13.054 4.180 0.851 22.209 0.98 
October 27.32 10.67 2.803 1.337 19.156 0.99 
November 28.326 9.609 2.381 1.507 12.444 0.99 
December 5.020 2.3781 1.0012 3.1789 7.8592 0.97 

Figure 4 shows the experimental data for the mean temperature and the fit of the temperature prediction model to the data for March, June, September, and December. These bell-shaped curves show that the agreement between the estimated and experimental temperature values is broadly satisfactory; in other words, the model is well-fitted by the experimental data. Further, Figure 3 depicts that the lowest and peak of the average temperature are 38 °C in June at 14.30 and 16 °C in December at 14.30, respectively. The average ambient temperature throughout the summer reached 35 °C compared to the winter period, which revealed a decrease in the average temperature of about 18 °C. Djeffal et al. (2021) used the details from the two weather stations located on the terrace of the research unit for the five selected years (2012–2016). They found that the average ambient temperatures recorded by Ghardaïa station ranged from 35 to 17 °C during summer and winter for the period selected during 2012–2016. There is increasing evidence that the impact of climate change is the occurrence of extreme weather conditions, which are wreaking havoc in many countries worldwide. Consequently, the differences in ambient temperature and solar radiation have affected the average values during the winter and summer.
Figure 4

Curves representative of the variation of average ambient temperature with experimental data.

Figure 4

Curves representative of the variation of average ambient temperature with experimental data.

Close modal

Results of TRNSYS simulations

The following results have been obtained via TRNSYS simulation. Figure 5 presents the evolution of the solar collector's outlet fluid temperatures, the VMD's feed temperature, the storage tank's average temperature, and the permeation flux variation for Bouzaréah and Ghardaïa, respectively. As seen in Figure 5(a) and 5(b), the maximum output temperatures of the solar collector were found to be 106 and 152 °C for Bouzaréah and Ghardaïa, respectively, at noon for June. The storage tank reaches a very high output temperature of 100 °C for an initial mass flow rate across the solar collector and heat exchanger at 1,205 and 844 kg/h for Bouzaréah and 1,033 and 689 kg/h for Ghardaïa, respectively. The coolant fluid is circulated across the solar collector to a heat exchanger, where the collected solar heat is transferred via a water loop to the storage tank.
Figure 5

Evolution of the outlet fluid temperatures of the solar collector (Toc), the feed temperature in the VMD (Tf), the average temperature in the storage tank (Tav), and variation of the permeation flux for the Bouzaréah (a) and Ghardaïa (b), respectively.

Figure 5

Evolution of the outlet fluid temperatures of the solar collector (Toc), the feed temperature in the VMD (Tf), the average temperature in the storage tank (Tav), and variation of the permeation flux for the Bouzaréah (a) and Ghardaïa (b), respectively.

Close modal

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.

The plots of Figure 6(a) and 6(b) represent the variation of average hourly cycles of the outlet fluid temperatures of the solar collector, the feed temperature in the VMD, and the average temperature in the storage tank by month for the Bouzaréah (a) and Ghardaïa (b), respectively. However, at first glance, it looks like at the beginning and end of each month, the temperature is at its minimum before and after midday. The temperature is at its maximum in the middle of the month, recorded around midday. Figure 6(a) establishes that the maximum outlet fluid temperature of the solar collector in Bouzaréah was 132 °C at noon in October, while Figure 6(b) shows that the maximum temperature recorded in the Ghardaïa was 140 °C. Figure 6 also indicates that the average temperature in the storage tank was maintained at about 100 °C by circulating the salty hot water transferred from the heat exchanger. We also notice that the maximum feed temperature in the VMD module achieved 79 °C in October for Bouzaréah and 82 °C in July for Ghardaïa. Indeed, the feed temperature variations are associated with the temperature changes in the solar collector's output and the heat exchanger's thermal efficiency.
Figure 6

Average hourly of the outlet fluid temperatures of the solar collector (Toc), the feed temperature in the VMD (Tf), and the average temperature in the storage tank (Tav) by month for Bouzaréah (a) and Ghardaïa (b), respectively.

Figure 6

Average hourly of the outlet fluid temperatures of the solar collector (Toc), the feed temperature in the VMD (Tf), and the average temperature in the storage tank (Tav) by month for Bouzaréah (a) and Ghardaïa (b), respectively.

Close modal

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.

Chen et al. (2021a, 2021b) suggested a VMD process coupled with solar energy to provide a constant heat supply to operate at VMD with maximum efficiency. They used a storage tank to supply hot brine during night-time operations and returned it to the storage tank when the water temperature dropped below the set point. Figure 7(a) and 7(b) shows the average hourly permeation flux and energy consumption by month for Bouzaréah (a) and Ghardaïa (b), respectively. The findings also point out that the permeation flux in Bouzaréah would oscillate between 17 and 49 kg/h m2, and existing climatic conditions of each region could have contributed to this variation (Figure 7(a)). Figure 7(b) reveals that the maximum permeation flux through the VMD module is almost constant in Ghardaïa and equal to 47 kg/h m2 between May and November. While the reverse occurs during January and December, the flux is relatively lower, and its value does not exceed 35 kg/h m2. We notice that the permeation flux through the VMD module during February, March, April, May, June, July, and November is relatively higher in Ghardaïa than in Bouzaréah, with a flux exceeding 30 kg/h m2.
Figure 7

Average permeation flux and energy consumption hourly by month for Bouzaréah (a) and Ghardaïa (b), respectively.

Figure 7

Average permeation flux and energy consumption hourly by month for Bouzaréah (a) and Ghardaïa (b), respectively.

Close modal

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).

Figure 8(a) and 8(b) represents the findings of the temperature of condensing, the temperature of the coolant fluid, and Carnot COP by month for Bouzaréah (a) and Ghardaïa (b), respectively. The findings showed that the maximum condensing temperature is 45 and 48 °C for Bouzaréah (a) and Ghardaïa (b), respectively. The maximum temperature attained by the coolant fluid is 34 °C.
Figure 8

Variation of the condensing temperature, the temperature of the coolant, and Carnot coefficient of performance (COP) by month for Bouzaréah (a) and Ghardaïa (b), respectively.

Figure 8

Variation of the condensing temperature, the temperature of the coolant, and Carnot coefficient of performance (COP) by month for Bouzaréah (a) and Ghardaïa (b), respectively.

Close modal

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.

Table 4

Gained output ratio (GOR) and thermal recovery ratio (TRR) of solar desalination unit

GORTRR
Ghardaïa 10.9471 2.2076 
Bouzaréah 8.3389 1.9415 
GORTRR
Ghardaïa 10.9471 2.2076 
Bouzaréah 8.3389 1.9415 

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.

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