Performance Analysis of a Floating Seawater Desalination Structure Based on Heat Pipes

Abstract

This study presents a comprehensive numerical simulation and thermal performance analysis of a novel modular floating solar still system, featuring integrated heat-pipe vacuum tube collectors, designed for seawater desalination. This innovative system—subject of International Patent Application WO 2023/062261 A1—not only aims to enhance efficiency and scalability beyond traditional solar stills, but also addresses the significant environmental challenge of concentrated brine discharge inherent in conventional desalination methods. The study evolved from an initial theoretical model to a rigorous dynamic thermal model, validated using real hourly meteorological data from Málaga, Andalusia, Spain. This modelling approach was developed to quantify heat transfer mechanisms and accurately predict system performance. The refined hourly simulation forecasts an annual freshwater production of approximately 174 L per unit. Notably, a preliminary economic assessment estimates the Cost of Produced Water per Litre (CPL) at 0.7509 EUR/litre, establishing a valuable baseline for future optimisation. These findings underscore the critical importance of dynamic hourly simulations for realistic performance prediction and validate the technical and preliminary economic feasibility of this novel approach. The system’s projected output, modular floating design, and significant environmental advantages position it as a promising and sustainable solution for freshwater production, particularly in coastal regions and sensitive marine ecosystems. This work provides a solid foundation for future experimental validation, cost optimisation, and scalable implementation of renewable energy-driven desalination.

1. Introduction

The escalating global demand for freshwater resources, coupled with increasing scarcity driven by climate change and environmental concerns, highlights an urgent need for scalable and sustainable water production technologies [1,2]. In this context, desalination and water reuse have become indispensable complements to hydrological planning worldwide, particularly in regions facing recurrent droughts and structural water deficits, such as Spain [3,4]. Currently, global desalinated water production capacity exceeds 100 million ${\mathrm{m}}^3/\mathrm{day}$ [5]. Furthermore, the burgeoning demand for renewable hydrogen as a clean energy vector, with projections exceeding 100 million tons per year by 2050 [6], underscores the need for vast quantities of fresh water (approximately 10–12 L per kg of hydrogen) [7]. This growing water demand intensifies the pressure on existing freshwater resources, making sustainable desalination solutions paramount. Current desalination technologies primarily fall into two categories: thermal-based and membrane-based processes [8]. Thermal technologies, such as multi-stage flash distillation (MSF), multi-effect distillation (MED), and vapour compression distillation (VCD), rely on supplying thermal energy to seawater for evaporation and subsequent condensation to produce desalinated water [9]. While effective, these methods are often characterised by high energy consumption and a significant environmental footprint [10]. Membrane-based technologies, predominantly reverse osmosis (RO), have gained widespread adoption due to their lower energy consumption, reduced environmental impact, and greater operational flexibility [11]. RO, which accounts for 61% of the global desalination market, forces seawater through semi-permeable membranes under high pressure to separate water from salt [12,13]. Despite their prevalence, both thermal and membrane technologies still face significant challenges regarding economic viability, sustainability, and environmental impact, particularly concerning their considerable energy demands and the intensive generation of high-concentration brine [14]. Current research efforts are focused on developing hybrid systems that integrate solar, wind, or hydroelectric energy to enhance efficiency and reliability, along with improving energy efficiency through concentrated solar power and energy storage [15]. However, the management of highly concentrated brine remains a persistent challenge in traditional desalination, incurring significant environmental impact and waste management costs. While solutions like brine valorisation for chemical industries or various treatment methods exist [16,17], conventional desalination systems still necessitate the transport and treatment of large volumes of brine for reintegration into the environment. This often results in localised high concentrations and even dead zones if discharged improperly.

It is important to acknowledge that the broader desalination landscape is continuously evolving, with significant advancements being made across various technologies to enhance efficiency, reduce costs, and improve overall sustainability at a system scale. For instance, substantial research efforts are dedicated to optimising membrane-based processes, including electrodialysis for cost-efficiency improvements [18] and bipolar membrane electrodialysis for value extraction from brine [19]. While these developments are crucial for global water security, our study specifically focuses on a distinct pathway: offshore, solar-driven thermal desalination. This approach offers a unique combination of direct solar energy utilisation, inherent advantages in passive brine management within the marine environment, and modular scalability, presenting a novel solution for sustainable freshwater production.

Despite advancements in large-scale desalination technologies, the simplicity and low energy consumption of traditional passive solar stills have maintained their relevance, particularly for small-scale applications and in rural or isolated areas. These systems operate based on the natural principle of evaporation and condensation: water is heated directly by solar radiation in a basin, evaporates, and the vapour then condenses on a cooler surface (typically the glass cover), flowing down and collecting as fresh water. While they offer a decentralized and environmentally friendly solution, requiring no external energy input and producing no concentrated brine discharge, their widespread adoption has been severely limited by their notably low thermal efficiency (typically between 20% and 50%) and their low water production rates per unit area (generally in the range of 1 to 4 L per square meter per day) [20,21]. These limitations render conventional designs impractical for meeting significant water demands, highlighting the need for innovations that substantially improve their performance without compromising their inherent sustainability [22].

To overcome these inherent limitations and explore new frontiers in sustainable water production, various innovative approaches and patented solutions have emerged, focusing on enhanced thermal efficiency, continuous operation, and integration with renewable energy sources. For instance, systems have been proposed that utilise low-temperature continuous evaporation–condensation with enthalpy recovery within a closed circuit, employing cylindrical evaporators and concentric condensers to optimise heat and mass transfer [23].

Furthermore, the concept of autonomous floating platforms for freshwater production has gained attention as a means of addressing land constraints and improving brine management. Patented designs for non-propelled floating devices integrate renewable energy systems on deck to power desalination plants and incorporate onboard storage tanks for freshwater, aiming to obtain water directly at sea without the need for fixed land installations [24].

Among these broader developments, the specific area of floating solar desalination systems has emerged as a particularly promising avenue, addressing challenges such as land constraints for large-scale deployment and facilitating the direct management of brine discharge into large water bodies. A range of experimental and numerical studies have explored different designs and approaches for such floating structures.

Table 1. Summary of Diverse Studies on Floating Solar Still Technologies.

Study/ Reference	Type	Floating System Type/Focus	Key Findings/Approach	Advantages/Limitations
Kaviti et al. (2024) [25]	Experimental	Nanocoated floating absorber in solar still	MSS with Cr-Mn-Fe oxide nanocoating improved output by up to 87% over CSS; 15.6% more cost-effective.	Advantage:Up to 87% more output than CSS; cost-effective vs. bottled water; nanocoated steel and stable flotation. Limitation: Modest total yield (390 mL/day); durability and scalability not addressed.
Ni et al. (2018) [26]	Experimental	Salt-rejecting floating evaporator	Produced 2.5 L/m2/day at 3$/m2 using floating solar system.	Advantage: Ultra-low cost; salt-rejection enables long-term use; off-grid suitable. Limitation: Limited to individual use; no durability data from field use.
Li et al. (2018) [27]	Experimental	Graphene membrane solar evaporator	Laser-scribed graphene evaporates 1.37 kg/m2/h with high water purity.	Advantage: Waste-free process; scalable; self-righting; purer than domestic water. Limitation: No field tests; marine durability unverified.
Nafey et al. (2002) [28]	Experimental + Numerical	Perforated black plate for solar still	Showed up to 40% productivity gain; validated thermal model.	Advantage: Simple design upgrade; proven by theory and experiment. Limitation: Small test scale (0.25 m2); not aimed at harsh or large-scale settings.
Chen et al. (2021) [29]	Experimental + CFD	Bionic floating solar still (plant-inspired)	Reached 1.5 kg/m2/day; outdoor-tested; airflow modeled via CFD.	Advantage: High yield; reduced heat loss; CFD model addresses motion. Limitation: Scalability and cost not assessed; wave motion remains a challenge.

summarises five key recent advancements in floating solar still technologies.

These studies collectively highlight the potential of floating designs to enhance solar still performance and address space constraints. They demonstrate various approaches to improving evaporation efficiency and distillate yield through material innovation, structural modifications, and heat management strategies. However, the existing literature primarily focuses on small-scale applications, specific material improvements, or isolated components. A significant research gap remains in the comprehensive numerical modelling and performance analysis of fully integrated, modular offshore solar desalination units that incorporate advanced solar collection technologies—such as heat-pipe vacuum tube collectors—and offer a holistic solution for sustainable freshwater production combined with environmentally sound brine management at sea. Importantly, the economic viability and scalability of such novel integrated offshore systems remain largely unexplored beyond laboratory-scale proof-of-concept studies, representing a critical area for further investigation in pursuit of real-world applications.

To address these limitations, this paper introduces a novel desalination device based on a natural condensation process, specifically designed for complete sustainability. This innovation, protected by national and international patents as a result of technology transfer at the University of Málaga [30], fundamentally diverges from existing market technologies. It is deployed on an offshore floating platform and powered exclusively by solar energy via a system of heat-pipe solar collectors. These collectors absorb solar radiation, raising the water temperature to vapour, which then condenses upon contact with the cooler structural body enclosing the condenser, producing desalinated water.

The proposed device offers a dual sustainability advantage. Firstly, its exclusive reliance on solar energy aligns with global efforts to decarbonise economies and achieve net-zero emissions, as outlined in frameworks such as the European Green Deal [2,31]. Secondly, its offshore positioning enables the natural dilution of resulting salts. This approach mitigates the environmental impact inherent in conventional desalination methods by avoiding intensive brine generation and localised high-salinity discharges, thereby also eliminating related waste management costs [16,17].

The device operates by industrialising and optimising the natural evaporation and condensation cycle that occurs in the marine environment, specifically through the use of vacuum tube solar collectors with a heat-pipe system—a technology previously investigated for desalination by institutions such as the University of Málaga and Edith Cowan University [32].

This paper presents the fundamental design and operational principles of an innovative offshore solar desalination unit. Specifically, the objectives of this project are twofold:

• Objective A: Harnessing Solar Energy for Desalination. This work demonstrates how the patented solution optimises natural condensation by leveraging solar energy captured through heat-pipe vacuum tube solar collectors. These collectors efficiently transfer solar radiation as heat to the water, taking into account the absorptivity and emissivity of the aluminium nitrate absorber plate, as well as the transmissivity and emissivity of the borosilicate glass tubes.
• Objective B: Minimising the Environmental Impact of Brine. This study details how the offshore installation, combined with the system’s condensation process, enables the gradual release of lower-salinity waste liquids into a larger volume of seawater, thereby facilitating rapid dilution and significantly reducing the environmental burden associated with conventional brine discharge.

This innovative approach seeks to overcome the limitations of traditional solar stills, offering a more efficient and scalable solution for freshwater production. By thoroughly analysing the system’s design, performance, and initial economic feasibility, this work lays the foundation for future developments in sustainable offshore desalination. The technology presented herein is protected under International Patent Application WO 2023/062261-A1 [30], underscoring its novel contribution to the field of solar desalination.

2. Materials and Methods

This section details the design, main components, operational principles, and modular architecture of the proposed sustainable solar desalination system.

2.1. Description of Solar Distiller

2.1.1. System Components

The core of the system is the water condensation and desalination structure, primarily designed with an inverted conical or pyramidal geometry, the upper section of which extends outwards. This structure is preferably fabricated from a material with high mechanical and thermal resistance, low thermal conductivity, and a low coefficient of thermal expansion, effectively functioning as a cold body for condensation. The inner surface incorporates a series of channels or grooves distributed along its entire perimeter. These channels facilitate the collection and downward flow of the condensed desalinated water, which forms upon contact between water vapour and the cooler structural body. The collected water is then directed to a pipe located at the base of the condensation structure, from where it is transported by a pumping system.

Integrated within this condensation structure are vacuum tube solar collectors with a heat-pipe system. These collectors are arranged radially and inclined along the inner wall of the structure to maximise solar radiation absorption. Their evaporative elements are positioned or connected at their lower ends, oriented towards the centre of the structure, ensuring direct contact with seawater for efficient evaporation. The vacuum tubes are 1.8 m in height, allowing them to extend beyond the condensation structure for optimal solar capture. Internally, each tube contains a two-phase thermosiphon, which enables highly efficient heat transfer through the evaporator by combining thermal conductivity with a liquid-to-vapour phase change. The system is designed to operate at a maximum temperature below 140 °C to prevent the formation of superheated steam and ensure efficient vapour production.

The primary material selected for the condensation structure is borosilicate glass, owing to its excellent thermal shock resistance, high mechanical strength, good ultraviolet radiation resistance, and, crucially, its low thermal conductivity and low coefficient of thermal expansion, enabling it to act as an effective cold body.

The lower section of the condensation and desalination structure is hollow and designed with a specific depth. When the system is deployed on water, this cavity allows a small volume of seawater to enter, contributing to the flotation of the system. Additionally, this design reduces thermal contact with the surrounding water, thereby maintaining a more stable temperature gradient within the condensation structure. A perforated membrane or permeable surface delimits the bottom base, acting as a filter. This filter prevents external debris from entering the condenser cavity, protects the system’s operation, and importantly, preserves marine biodiversity by preventing marine organisms from entering and being exposed to potentially harmful internal temperatures.

2.1.2. System Operation

The proposed desalination plant concept is based on modular floating platforms that support the solar collection and condensation systems. Each modular floating unit consists of high-density polyethylene (HDPE) cubes, interconnected by specific joints. A fundamental sub-assembly forms a square floating base, with a central opening intentionally left free of modules to accommodate the condenser. Each unit comprises 48 HDPE cubes and occupies a surface area of 16 ${\mathrm{m}}^2$. The condenser is attached to this central opening using the same joining mechanism as the cubes, facilitating assembly and enhancing structural rigidity. The system is also designed to collect and treat rainwater.

The condensation structure is optimally designed for maximum performance and solar radiation capture. It is affixed to the floating platform using the same HDPE connection joints. The lower, hollow part of the condenser has a trapezoidal sheet form with a thickness of 4 cm, an internal extrusion angle of 50°, and a depth that permits a small volume of seawater to enter its cavity upon submersion. This internal void increases the buoyancy of the system, thereby reducing stress on the floating base. The water retained within the lower walls of the condenser helps maintain a stable temperature gradient by limiting contact with the cooler surrounding seawater. A perforated sheet covers the submerged base, acting as a filter to prevent foreign matter from entering and to safeguard marine biodiversity.

The upper part of the structure mirrors the lower portion but features an outward extrusion angle of 45° and a height of 70 cm, allowing the solar collectors to protrude and optimise solar capture. The upper base lid contains an inverted cone-shaped recess that ensures the correct inclination of the solar collectors for maximum solar radiation absorption throughout the day. The diameter of the upper base is 2.6 m, while the lower base measures 0.8 m. The depth of the cone ensures the evaporator remains in direct contact with the seawater.

A key innovation distinguishing this system from conventional solar stills is the strategic positioning of the solar collector evaporators at the lower base of the inverted cone, set at a 50° inclination. This configuration addresses a common limitation of traditional designs, where rising water vapour can accumulate and obstruct solar radiation, thus reducing efficiency (typically limited to 1–4 L/${\mathrm{m}}^2$). In the present system, solar radiation directly reaches the collectors, which maintain continuous contact with the water surface, preventing vapour clouds from interfering with energy absorption. This distinct operating principle, combined with its modular architecture, is expected to result in significantly higher water production rates. The condensed water flows through internal channels within the condenser body, collecting in a main pipe for subsequent pumping.

A rendered 3D view of the solar desalination unit is provided in Figure 1, offering a comprehensive visual representation of the design. This visualisation illustrates the spatial arrangement of components, including the solar collection area, heat pipes, condensation surfaces, and HDPE cubes within the system.

An adjacent modular floating unit can be integrated to support photovoltaic solar panels. This auxiliary unit may harvest solar radiation to generate the electrical power required for auxiliary systems, such as the pumping mechanism used to transport desalinated water.

Figure 2 presents an elevation and cross-sectional view of the system. Identified elements include: 1. polyethylene cube, 2. connecting joints, 3. vacuum tube, 4. filter, 5. heat pipe, and 6. condensation wall.

2.1.3. Modular Design

The system is conceived as a highly modular and scalable solution. The floating platform is constructed from multiple interconnected HDPE cubes, forming modular floating structures designed to facilitate ease of assembly and maintenance, thereby allowing for various configurations. A preferred embodiment situates the condensation and desalination structure within a central void created by these floating modules. Connections between adjacent floating modules, as well as between the modules and the condensation structure, are achieved via specific joining elements. This design enables the aggregation of multiple units, potentially forming an “infinite network” of floating desalination plants. Each individual HDPE cube has a mass of 7 kg, contributing to the system’s overall lightweight construction.

2.1.4. Key Design Specifications

The main design specifications were developed based on a detailed study of the operational requirements. Key aspects include:

• Size: Each modular floating system covers 16 ${\mathrm{m}}^2$. The condensation structure has a base measuring of 2 × 2 m and a height of 1.15 m.
• Weight: The design prioritises minimising weight to reduce manufacturing, distribution, and transportation costs. The condensation system weighs 250 kg.
• Materials: HDPE is selected for the flotation system, and borosilicate glass for the condensation structure. These materials were selected for their resistance to environmental stressors—including temperature fluctuations, direct solar radiation, saline environments, and wind gusts—as well as their low thermal conductivity and thermal expansion coefficients. Particular emphasis is placed on using recyclable, environmentally friendly materials that do not degrade or release toxic substances.

Table 2. Key Design Specifications of the Offshore Solar Desalination Unit.

Parameter	Value	Unit	Justification/Basis
Solar Collector Design
Number of Heat-Pipe Tubes	17	-	Geometric limitations.
Inner Tube Diameter	0.37	cm	Standard heat-pipe dimension.
Outer Tube Diameter	0.47	cm	Standard heat-pipe dimension.
Tube Length	150	cm	Selected to match the collector length and maximize absorption.
Collector Area ($A_c$)	1.3832	${\mathrm{m}}^2$	Determined by the number and dimensions of heat-pipes and collector design.
Mass of Water ($m_w$)	60	kg	Determined by dimensions.
Material Properties
Glass Transmissivity	0.74	-	Borosilicate glass (clear conditions).
Absorber Plate Absorptivity	0.99	-	Aluminium nitrate.
Absorber Plate Emissivity	0.1	-	Aluminium nitrate.
Glass Emissivity	0.88	-	Borosilicate glass.
Water Emissivity	0.96	-	Typical.
Operating Conditions
Average Ambient Temp.	297.15	°K	Representative for location and season.
Average Relative Humidity	66.15	%	Representative for location and season.
Average Wind Speed	3	m/s	Representative for offshore conditions.
Operational Hours per Day	13	h	Represents daylight hours with sufficient solar irradiation for distillation.
Average Solar Irradiance	312.70	${\mathrm{W}/\mathrm{m}}^2$	From Average Solar irradiance per day and 13 h of operational hours.

provides key design specifications, material properties and operating conditions.

2.2. Thermal Performance Modelling

The theoretical thermal performance of the proposed solar desalination system was evaluated through a series of energy balance calculations—a robust and efficient method specifically employed to quantify the system-level heat transfer mechanisms and the fundamental operational principles of the novel modular floating solar still. This methodology aligns strategically with the primary objectives of this paper.

While advanced computational fluid dynamics (CFD) methods provide detailed insights into localised fluid dynamics and heat transfer within specific components, their substantial computational requirements and the need for detailed input data render them less suitable for the overall performance assessment central to this study. In contrast, the energy balance approach offers an ideal framework for efficiently analysing the macroscopic energy transformations that govern the unit’s performance, enabling accurate assessment of how solar radiation is absorbed, transferred as heat, and utilised in the natural condensation process.

This approach proved particularly effective in progressing from theoretical modelling to rigorous hourly simulations based on actual meteorological data from Málaga, Andalusia, Spain, thereby facilitating a realistic and comprehensive understanding of the system’s performance under dynamic conditions.

2.2.1. Solar Collector Thermal Modelling

The operation of the vacuum tube heat-pipe solar collectors, integral to the system, was analysed under steady-state conditions using a comprehensive energy balance equation. This balance considers the total incident solar heat absorbed by the collector ($Q_u$) and the heat losses to the surroundings ($Q_L$), while the rate of change in internal energy stored within the collector is assumed negligible.

A key characteristic of vacuum tube collectors is their significant reduction of heat losses. The vacuum between the absorber plate and the glass tubes effectively eliminates conduction and convection losses, making radiative heat loss the predominant mechanism.

The actual incident heat ($q_{abs}$) absorbed by the collector plate was determined using the following equation:

$$q_{abs}=I_t·{\alpha }_{absorber}$$

(1)

where $q_{abs}$ is the actual solar heat flux absorbed by the collector plate in (${\mathrm{W}/\mathrm{m}}^2$); $I_t$ represents the average solar irradiance incident on the collector ($312.70{\mathrm{W}/\mathrm{m}}^2$), obtained from the given average solar irradiation for the Málaga region ($4065.1{\mathrm{Wh}/(\mathrm{m}}^2·\mathrm{day}$) considering 13 effective hours of solar operation) and adjusted for the tilted surface; and ${\alpha }_{absorber}$ is the absorptivity of the absorber plate ($0.95$ for aluminum nitrate).

The total incident heat absorbed by the collectors ($Q_{inc}$) in (W), considering the useful collection surface area ($A_c=1.3832{\mathrm{m}}^2$), was calculated as:

$$Q_{inc}=q_{abs}·A_c$$

(2)

The optical efficiency factor ${\alpha }_s$, which determines the percentage of incident radiation that effectively reaches and is absorbed by the collector plate, is calculated using the following equation:

$${\alpha }_s={\displaystyle \frac{{\tau }_g·{\alpha }_p}{1-(1-{\alpha }_p)·{\rho }_d}}$$

(3)

where ${\tau }_g$ is the transmissivity of the vacuum tube glass (0.74 for borosilicate glass tubes); ${\alpha }_p$ is the absorptivity of the absorber plate (0.99 for aluminum nitrate); and ${\rho }_d$ is the diffuse reflectance (0.16, same as for vacuum tubes, representing internal reflections).

2.2.2. Solar Distiller Heat Transfer Analysis

For the design and performance evaluation of the solar condenser and the overall distiller unit, a detailed analysis of heat transfer mechanisms was conducted. This analysis considers the solar energy absorbed and its subsequent distribution, accounting for useful energy transfer and various heat loss pathways.

Heat Loss by Conduction:Heat loss due to conduction, specifically at the interface where the heat-pipe evaporator of the vacuum tube contacts the seawater, was calculated using the following formula:

$$q_{cond}=U_b·(T_w-T_{hp})$$

(4)

where $q_{cond}$ is the heat lost by conduction (${\mathrm{W}/\mathrm{m}}^2$); $U_b$ represents the equivalent global heat transfer coefficient of the water ($0.58{\mathrm{W}/(\mathrm{m}}^2·\mathrm{K})$); $T_w$ is the mean temperature of the water ($333\mathrm{K}$); and $T_{hp}$ is the temperature of the heat-pipe ($297\mathrm{K}$).

Heat Loss by Radiation from the Glass Surface: Radiative heat loss from the walls of the condensation structure (glass) was determined using the Stefan-Boltzmann law, adapted for transparent surfaces radiating to the sky:

$$q_{rg}={\epsilon }_g·\sigma ·(T_g^4-T_{sky}^4)$$

(5)

where $q_{rg}$ is the heat lost by radiation from the glass (${\mathrm{W}/\mathrm{m}}^2$); ${\epsilon }_g$ is the emissivity of the glass ($0.88$); $\sigma$ is the Stefan-Boltzmann constant ($5.6697\times {10}^{-8}{\mathrm{W}/(\mathrm{m}}^2·{\mathrm{K}}^4$)); $T_g$ is the temperature of the glass (assumed as $308.65\mathrm{K}$); and $T_{sky}$ is the sky temperature ($285.34\mathrm{K}$), calculated as:

$$T_{sky}=T_a·{(0.711+0.0056·T_{dp}+0.000013·T_{dp}^2+0.012·v)}^{0.25}$$

(6)

where $T_{dp}$ is the dew point temperature (17.232 °C), calculated as:

$$T_{dp}=T_a-\left({\displaystyle \frac{100-RH}{5}}\right)$$

(7)

where $T_a$ is the ambient temperature (24 °C) or $297.15\mathrm{K}$); $RH$ is the ambient relative humidity (considered as $66.16\%$); and v is the wind speed ($3\mathrm{m}/\mathrm{s}$). The term involving v assumes $cos(\Phi )$ to be unity for simplification in this average sky temperature correlation.

Heat Loss by Convection from the Glass Surface: Heat loss from the glass surface due to combined conduction and convection (influenced by wind speed and temperature difference between glass and air) was calculated as:

$$q_{cg}=h_{cg}·(T_g-T_a)$$

(8)

where $q_{cg}$ is the heat lost by convection from the glass (${\mathrm{W}/\mathrm{m}}^2$); $h_{cg}$ is the convective heat transfer coefficient of the glass (${\mathrm{W}/(\mathrm{m}}^2·\mathrm{K}$)), determined by the empirical relation $h_{cg}=5.7+3.8v$; $T_g$ is the temperature of the glass ($308.65\mathrm{K}$); and $T_a$ is the ambient temperature ($297.15\mathrm{K}$). The assumed wind speed (v) is $3\mathrm{m}/\mathrm{s}$.

Heat Loss by Radiation from Water to Glass: Radiative heat transfer from the water surface to the glass plate was calculated considering them as parallel flat plates, using a modified Stefan-Boltzmann equation:

$$q_{rw}={\displaystyle \frac{\sigma ·(T_w^4-T_g^4)}{\frac{1}{{\epsilon }_w}+\frac{1}{{\epsilon }_g}-1}}$$

(9)

where $q_{rw}$ is the heat lost by radiation from water to glass (W/m²); $\sigma$ is the Stefan-Boltzmann constant ($5.6697\times {10}^{-8}{\mathrm{W}/(\mathrm{m}}^2·{\mathrm{K}}^4)$); $T_w$ is the mean temperature of water ($333\mathrm{K}$); $T_g$ is the mean temperature of glass ($308.65\mathrm{K}$); ${\epsilon }_w$ is the emissivity of water ($0.96$); and ${\epsilon }_g$ is the emissivity of the glass ($0.88$).

Heat Loss by Natural Convection from Water to Glass: Natural convection heat loss occurs between the water surface and the glass, driven by temperature differences and air currents in the enclosed space. The heat loss ($q_{cw}$) was calculated using:

$$q_{cw}=h_{cw}·(T_w-T_g)$$

(10)

where $q_{cw}$ is the heat lost by natural convection from water to glass (${\mathrm{W}/\mathrm{m}}^2$); $h_{cw}$ is the total convective heat transfer coefficient of water (${\mathrm{W}/(\mathrm{m}}^2·\mathrm{K})$); $T_w$ is the water temperature ($333\mathrm{K}$); and $T_g$ is the glass temperature ($308.65\mathrm{K}$). The $h_{cw}$ coefficient is determined using the following correlation:

$$h_{cw}=0.884·{\left[{\displaystyle \frac{T_w-T_g}{T_{avg}+273.15}}\right]}^{0.333}$$

(11)

where $T_{avg}$ is the mean temperature inside the distiller ($320.825\mathrm{K}$). It is assumed that the temperature difference $(T_w-T_g)$ can be in Kelvin (or Celsius, as the difference is the same), while the $T_{avg}$ within the correlation’s denominator should be in Celsius and then converted to Kelvin for consistency with the formula’s constants.

Heat Loss by Evaporation: The heat loss due to evaporation ($q_e$) of water within the distiller was calculated using an evaporative heat transfer coefficient ($h_e$):

$$q_e=h_e·(P_w-P_g)$$

(12)

where $q_e$ is the heat lost by evaporation (${\mathrm{W}/\mathrm{m}}^2$); $h_e$ is the evaporative heat transfer coefficient (${\mathrm{W}/(\mathrm{m}}^2·\mathrm{Pa})$), determined to be $0.0008209{\mathrm{W}/(\mathrm{m}}^2·\mathrm{Pa})$; $P_w$ is the saturated vapor pressure of water at the water temperature ($148.21\mathrm{kPa}$ at $333\mathrm{K}$); and $P_g$ is the saturated vapor pressure of water at the glass temperature ($43.25\mathrm{kPa}$ at $308.65\mathrm{K}$). These vapor pressures were calculated using the Antoine equation. The coefficient $h_e$ was related to the total convective heat transfer coefficient of water ($h_c$) by the empirical correlation: $h_e=0.01627·h_c$, where $h_c$ for the given conditions takes a value of $0.0504{\mathrm{W}/(\mathrm{m}}^2·\mathrm{Pa})$.

2.2.3. Overall Energy and Mass Balance

The overall thermal performance of the solar desalination system was evaluated by establishing a comprehensive energy balance. Solar radiation incident on the tilted surface was obtained from the Andalusian Energy Agency, considering an average value for August for a surface inclined at 45°. The system was analysed by considering its main components as isolated sub-systems and then integrating them into an overall balance, adhering to the principle of energy conservation: Energy In – Energy Out = Energy Stored. The most representative heat loss mechanisms were considered in this analysis.

Energy Balance on the Structural Cover: The heat stored by the structural cover ($q_c$) was calculated by balancing the heat flows across its surfaces:

$$q_c={\alpha }_{g,s}·I_T+q_{rw}+q_{cw}+q_e-q_{rg}-q_{cg}$$

(13)

where $q_c$ is the heat stored by the structural cover (${\mathrm{W}/\mathrm{m}}^2$); ${\alpha }_{g,s}$ is the solar absorptivity of the glass cover; $I_T$ is the total incident solar radiation on the tilted surface (${\mathrm{W}/\mathrm{m}}^2$); $q_{rw}$ is the heat transferred by radiation from the water to the glass (${\mathrm{W}/\mathrm{m}}^2$); $q_{cw}$ is the heat transferred by convection from the water to the glass (${\mathrm{W}/\mathrm{m}}^2$); $q_e$ is the heat lost by evaporation from the water and condensed on the glass (${\mathrm{W}/\mathrm{m}}^2$); $q_{rg}$ is the heat lost by long-wave radiation from the glass to the environment (${\mathrm{W}/\mathrm{m}}^2$); and $q_{cg}$ is the heat lost by convection from the glass to the environment (${\mathrm{W}/\mathrm{m}}^2$).

Energy Balance on the Water Mass: The heat stored within the water mass ($q_w$) was determined by considering the absorbed solar radiation and heat losses from the water surface:

$$q_w=I_T·{\tau }_{g,s}·{\alpha }_w-(q_{rw}+q_{cw}+q_e+q_{cond})$$

(14)

where $q_w$ is the heat stored internally by the water per unit area (${\mathrm{W}/\mathrm{m}}^2$); $I_T$ is the total incident solar radiation ($312.70{\mathrm{W}/\mathrm{m}}^2$); ${\tau }_{g,s}$ is the solar transmissivity of the glass cover ($0.90$); ${\alpha }_w$ is the effective absorptivity coefficient accounting for the absorption of solar radiation by the water and the distiller’s bottom (approximated as $0.3$); $q_{rw}$ is the heat lost by radiation from water to glass; $q_{cw}$ is the heat lost by convection from water to glass; $q_e$ is the heat lost by evaporation; and $q_{cond}$ is the heat lost by conduction from the water to the base of the distiller.

The total heat stored per unit area ($q_t$) by the system is the sum of the heat stored in the cover and the water:

$$q_t=q_c+q_w$$

(15)

where $q_t$ is the total heat stored per unit area (W/m²).

Finally, the total heat absorbed by the entire device ($Q_T$) was calculated by scaling the stored heat per unit area by the solar energy collection area ($A_c$), and adding the total incident heat absorbed by the collector ($Q_{inc}$):

$$Q_T=q_t·A_c+Q_{inc}$$

(16)

where $Q_T$ is the total heat absorbed by the system (W); $q_t$ is the total heat stored per unit area (W/m²); $A_c$ is the area for solar energy capture ($1.3832{\mathrm{m}}^2$); and $Q_{inc}$ is the total incident heat absorbed by the collector, as defined in Section 2.2.1.

2.2.4. Required Heat for System Operation

To characterize the system’s energy demands, the total heat required for its operation was calculated considering the sensible heat needed to raise the temperature of the glass cover and the contained water, as well as the latent heat for water evaporation. These calculations assume an operation time of 13 h per day.

Heat Required to Heat the Glass ($Q_g$): The heat absorbed by the glass cover to increase its temperature from ambient ($T_a$) to an equilibrium temperature ($T_g$) was calculated as:

$$Q_g=m_g·C_{pv}·(T_g-T_a)$$

(17)

where $Q_g$ is the quantity of heat required to heat the glass; $m_g$ is the mass of the glass ($64.887\mathrm{kg}$), determined by its density (${\rho }_v=2230{\mathrm{kg}/\mathrm{m}}^3$), thickness ($E_v=0.003\mathrm{m}$), and area ($A_{glass}=9.7{\mathrm{m}}^2$); $C_{pv}$ is the specific heat capacity of glass ($750\mathrm{J}/(\mathrm{kg}·$°C)); $T_g$ is the equilibrium temperature of the glass (35.5 °C or $308.65\mathrm{K}$); and $T_a$ is the ambient temperature (24 °C or $297.15\mathrm{K}$).

Heat Required to Heat the Water ($Q_{ca}$): The sensible heat required to raise the temperature of the water contained in the base of the structural system from ambient ($T_a$) to its equilibrium temperature ($T_w$) was estimated. The mass of water ($m_s$) was determined from the volume defined by the condenser base dimensions:

$$Q_{ca}=m_s·C_p·(T_w-T_a)$$

(18)

where $Q_{ca}$ is the quantity of heat needed to heat the water; $m_s$ is the mass of water in the condenser ($60\mathrm{kg}$); $C_p$ is the specific heat capacity of water ($4186\mathrm{J}/(\mathrm{kg}·$°C)); $T_w$ is the equilibrium temperature of the water (59.85 °C or $333\mathrm{K}$); and $T_a$ is the ambient temperature (24 °C or $297.15\mathrm{K}$).

Heat Required for Water Evaporation ($Q_{ev}$): To achieve water evaporation, the system must supply the latent heat required for the phase change. This energy, needed to evaporate a certain percentage (x) of the water mass, was calculated as:

$$Q_{ev}=x·m_v·\lambda$$

(19)

where $Q_{ev}$ is the quantity of heat required to evaporate x percentage of water; x is the percentage of mass evaporated (1, representing $100\%$); $m_v$ is the mass evaporated or collected condensate ($11.15\mathrm{kg}$); and $\lambda$ is the enthalpy of vaporization at the water temperature ($2,357,700\mathrm{J}/\mathrm{kg}$ at 59.85 °C).

Total Heat Absorbed by the System ($Q_N$): The total heat required for the system’s operation, encompassing the heating of the glass and water, and the complete ($100\%$) evaporation of the water, is given by the sum of these heat components:

$$Q_N=Q_g+Q_{ca}+Q_{ev}$$

(20)

where $Q_N$ represents the total necessary heat for the process. This value comprises the heat required to heat the glass ($Q_g=\mathrm{559,590.375}\mathrm{J}$), the heat required to heat the water ($Q_{ca}$), and the heat required for the evaporation of water ($Q_{ev}$).

2.2.5. System Efficiency and Theoretical Water Production

The overall performance of the solar desalination system was further characterized by calculating its thermal efficiency and theoretical daily water production.

System Efficiency (${\eta }_{sys}$): The thermal efficiency of the solar distiller system (${\eta }_{sys}$) is a critical parameter, defined as the ratio of the energy effectively used for water vaporization (useful energy) to the total incident solar energy on the distiller. This reflects how effectively the system converts solar radiation into desalinated water. The intensity of incident solar energy is the primary factor influencing production. The efficiency was calculated as:

$${\eta }_{sys}={\displaystyle \frac{Q_{evap}}{Q_{incident}}}$$

(21)

where ${\eta }_{sys}$ is the overall system efficiency; $Q_{evap}$ represents the useful energy utilized for water vaporization, derived from the total evaporative heat over 13 h of operation; and $Q_{incident}$ refers to the total solar energy incident on the glass cover of the distiller, calculated as $I_T·A_{glass}$ with $I_T=312.7{\mathrm{W}/\mathrm{m}}^2$ and $A_{glass}=9.7{\mathrm{m}}^2$.

Theoretical Water Production Rate ($M_e$): The theoretical quantity of desalinated water produced by the system ($M_e$) was estimated based on the total useful heat specifically employed for water vaporization and the latent heat of vaporization of water. This calculation provides an insight into the potential daily yield of fresh water.

$$M_e={\displaystyle \frac{Q_{ev}}{\lambda }}$$

(22)

where $M_e$ is the quantity of desalinated water produced by the system, which can be converted to litres assuming a water density of approximately $1\mathrm{kg}/\mathrm{L}$; $Q_{ev}$ is the heat required for water evaporation, representing the energy directly converted into vapor; and $\lambda$ is the latent heat of vaporization of water at the operating temperature (2,357,700 J/kg at 59.85 °C).

Figure 3 provides a graphical abstract of the operation of the novel offshore solar desalination unit, illustrating the solar-driven energy balance for efficient freshwater production and an eco-friendly brine management.

2.3. Meteorological Data Acquisition and Processing

A comprehensive dataset comprising 8760 hourly records of key environmental parameters was obtained to characterise the atmospheric and solar conditions at the study location (Málaga, Andalusia, Spain) over the analysed period. The precise geographical coordinates of the data acquisition point are: latitude 36.705° N, longitude 4.425° W, and an elevation of 0 m. The solar irradiance data specifically corresponds to a surface inclined at 37° with an azimuth of 0° (south-facing in the Northern Hemisphere).

These data provided detailed meteorological insights where the parameters directly utilized in this study include:

• Date and Time:Timestamp for each hourly record.
• Global irradiance on the inclined plane ($G\left(i\right)$): Measured in Watts per square meter (${\mathrm{W}/\mathrm{m}}^2$), representing the total solar radiation incident on the tilted surface of the solar array.
• Sun height ($H_{sun}$): Expressed in degrees (°), indicating the elevation angle of the sun above the horizon.
• 2-m air temperature($T_{2m}$): Measured in degrees Celsius (°C), representing the ambient air temperature at a height of two meters above the ground.
• 10-m total wind speed ($W{S}_{10m}$): Measured in meters per second (m/s), indicating the total wind speed at a height of ten meters above the ground.

These data were comprehensively sourced from [33], accessed via platforms such as the Photovoltaic Geographical Information System. SARAH3 (Satellite Application Facility on Climate Monitoring –Solar surfAce Radiation HEliosity), developed by EUMETSAT, is a satellite-derived dataset renowned for its high spatial resolution and accuracy in representing solar conditions across Europe. It provides robust estimates of solar radiation components and other related meteorological parameters through advanced atmospheric modelling based on satellite observations. Its high fidelity makes it particularly suitable for localised environmental assessments in solar energy applications.

Figure 4 displays global irradiance (a), sun height (b), and 10-metre total wind speed (c).

2.4. Sea Water Temperature Data Generation

To obtain a continuous and detailed time series of seawater temperature covering a full year with hourly resolution, a computational modelling process was implemented using code developed in MATLAB R2023b environment. This process resulted in a series of 8760 data points.

The generation methodology was based on an iterative approach combining climatological statistical data with real measurements, aiming to faithfully reproduce the thermal dynamics of seawater. This iterative refinement involved several key steps:

• Modelling Seasonal and Diurnal Variation:To ensure a realistic and continuous transition between monthly cycles, the generation algorithm was not limited to individual monthly values. Instead, it incorporated the influence of temperatures from the preceding and succeeding months, allowing for smoother and more coherent seasonalisation of the series. This seasonalisation process underwent several iterations to optimise the representation of the annual cycle.
• Integration of Real Variability and Noise: To simulate natural variability and inherent fluctuations in real measurements, a random noise component was introduced into the generated series. The magnitude and characteristics of this noise were adjusted iteratively to replicate the dispersion observed in empirical data and to provide the synthetic series with greater realism. The quality of the series was further enhanced by applying smoothing techniques, such as cubic splines, to ensure continuity of the temperature curve and eliminate non-physical abrupt changes, especially after noise injection or integration of real data points.
• Calibration with Real Field Measurements: The model was calibrated and validated using 192 real measurements of seawater temperature taken on different days throughout the year. These measurements were essential for anchoring the generated series to observed conditions, serving as key reference points for fine-tuning model parameters during iterations. The iterative calibration process concluded when the root mean square error (RMSE) between the generated series and real calibration points fell below 1%.

Through this combination of advanced seasonal modelling, controlled incorporation of noise, and calibration with real data—summarised in Algorithm 1—a seawater temperature time series was successfully constructed that is continuous, plausible, and representative of the environmental conditions. Figure 5 shows the computationally modelled seawater temperature time series alongside the actual air temperature time series at 2 m obtained from SARAH3.

Algorithm 1 Sea Water Temperature Data Generation.

1: INITIALIZE variables and data structures for the hourly series generation 2: GENERATE initial hourly temperature series by modeling seasonal and diurnal variations from monthly statistics, considering adjacent months for smooth transitions. 3: INITIALIZE variables for iterative refinement 4: for$t=1,2,\dots$do 5:     ADJUST the series by integrating real temperature measurements for calibration. 6:     ADD random noise to the series to simulate natural fluctuations. 7:     APPLY a spline smoothing technique to ensure continuity and refine the curve. 8:     if convergence based on RMSE < 1% then 9:         BREAK 10:     end if 11: end for 12: OUTPUT final generated sea water temperature time series.

3. Results

3.1. Solar Collector Performance

The thermal performance of the vacuum tube heat-pipe solar collectors, fundamental to the proposed system, was evaluated considering their specific geometric and material properties. Each collector comprises 17 tubes, each 150 cm long, with an outer diameter of 0.47 cm and an inner diameter of 0.37 cm. The effective collection area, calculated as $1.3832{\mathrm{m}}^2$, correspond to the periphery of the inner tube where water is heated, while the outer tube maintains a vacuum to minimise conduction and convection losses. The surface of the outer tube consistently remains below ambient temperature.

Key factors influencing the collector’s efficiency include the solar radiation available at the deployment site (Málaga region) and the physical properties of the vacuum tubes, such as the absorptivity and emissivity of the aluminium nitrate absorber plate (adhered to the inner tubes) and the solar transmissivity and emissivity of the borosilicate glass outer tubes. Based on these calculations (detailed in Section 2.2), the total incident heat absorbed by the solar collectors ($Q_{inc}$) was determined to be $1955.93\mathrm{W}$, with an absorbed heat flux ($q_{abs}$) of $977.965{\mathrm{W}/\mathrm{m}}^2$.

3.2. Overall System Thermal Performance and Water Production

A comprehensive thermal analysis of the solar distillation system was performed to quantify heat gains, losses, and overall performance. This involved detailed calculations of various heat transfer mechanisms, including:

• Heat loss by conduction from water to base ($q_{cond}$): $20.88{\mathrm{W}/\mathrm{m}}^2$
• Heat loss by radiation from glass to ambient ($q_{rg}$): $19.00{\mathrm{W}/\mathrm{m}}^2$
• Heat loss by convection from glass to ambient ($q_{cg}$): $2.20{\mathrm{W}/\mathrm{m}}^2$
• Heat loss by radiation from water to glass ($q_{rw}$): $152.82{\mathrm{W}/\mathrm{m}}^2$
• Heat loss by natural convection from water to glass ($q_{cw}$): $9.11{\mathrm{W}/\mathrm{m}}^2$
• Heat lost by evaporation ($q_e$): $86.14{\mathrm{W}/\mathrm{m}}^2$

An energy and mass balance was performed on the structural condensation system to determine the heat stored within the system and the total heat absorbed. The heat stored internally by the glass cover ($q_c$) was calculated as $-57.955{\mathrm{W}/\mathrm{m}}^2$, while the heat stored internally by the water ($q_w$) was $-184.521{\mathrm{W}/\mathrm{m}}^2$. Consequently, the total heat stored per unit area ($q_t$) by the system (cover and water) was $-242.476{\mathrm{W}/\mathrm{m}}^2$. The total heat absorbed by the entire device ($Q_T$), considering the solar energy collection area of $1.3832{\mathrm{W}/\mathrm{m}}^2$, was determined to be $75.24\mathrm{W}$.

This analysis also included calculating the sensible and latent heat required for the system’s operation over a 13-h period. The heat required to heat the glass ($Q_g$) was 559,590.375 J, the heat required to heat the water ($Q_{ca}$) was 9,004,506 J, and the latent heat required for water evaporation ($Q_{ev}$) was 26,300,455 J. Summing these components, the total heat necessary for the system’s operation ($Q_N$) was 35,864,551.375 J.

The theoretical water production rate ($M_e$) was derived from these thermal calculations. For an operational period of 13 h per day, the system is projected to produce $11.155\mathrm{kg}$ of desalinated water (equivalent to $11.155\mathrm{L}$), based on the useful heat effectively used for water vaporization. This highlights the system’s ability to efficiently convert solar energy into potable water.

The overall efficiency of the proposed desalination system (${\eta }_{sys}$) is a crucial indicator of its performance. Defined as the ratio of energy utilized for water vaporization to the total incident solar energy on the distiller, the system efficiency was calculated to be $0.1852$ or $18.52\%$. This efficiency underscores the effectiveness of the optimized natural condensation process leveraging solar energy.

3.3. Case 1: Hourly Simulation with Real Meteorological Data

To provide a more comprehensive and realistic assessment of the system’s performance, the theoretical model was extended to incorporate hourly meteorological data over a full year (8760 h) from the Málaga region. This advanced simulation accounted for the dynamic variations in solar irradiance, ambient temperature, and wind speed, which were previously treated as constant average values in the theoretical calculations.

The primary modification in this hourly simulation was the transition from constant heat loss coefficients and a fixed evaporative heat flux ($q_e$) to dynamically calculated values for each hour. Specifically:

• Hourly Environmental Parameters: The global irradiance on the inclined plane ($I_t$), 2-m air temperature ($T_a$), and 10-m total wind speed ($U_{wind}$) were read from the provided dataset for each time step.
• Dynamic Glass Temperature ($T_g$): Unlike the previous theoretical model where $T_g$ was implicitly assumed or constant, here $T_g$ was estimated hourly based on a simplified energy balance that considers solar input to the glass and heat exchanges with the ambient air and the water in the basin. This allowed for $T_g$ to vary realistically with ambient conditions and solar radiation.
• Variable Heat Losses and Evaporation: Consequently, all heat transfer rates, including conductive heat loss to the base ($q_{cond}$), radiative and convective losses from the glass to the ambient ($q_{rg}$, $q_{cg}$), and radiative and convective exchanges between the water and the glass ($q_{rw}$, $q_{cw}$), were recalculated hourly using the instantaneous $T_a$, $U_{wind}$, and the dynamically estimated $T_g$. Crucially, the useful heat for evaporation ($q_e$) was no longer a fixed value but was derived hourly using its dependence on the varying vapor pressure difference between the water and the glass.
• Constant Water Temperature ($T_w$): For this initial hourly simulation, the water temperature within the distiller ($T_w$) was maintained at a constant design value of 59.85 °C, mirroring the assumption made in the initial theoretical model.

Case 1. Analysis of Results

The hourly simulation yielded a more nuanced and realistic representation of the system’s performance over an annual cycle. The total annual freshwater production was calculated to be approximately 102.633 L, resulting in an average daily production of 0.2812 L/day and an overall system efficiency of $2.3431\%$.

A significant observation from this hourly simulation is the noticeable decrease in daily average water production compared to the initial theoretical calculations. This reduction is directly attributable to the model’s ability to account for the dynamic and often suboptimal real-world operating conditions:

• Variable Solar Input:As illustrated in Figure 6, the system’s performance in Case 1 directly reflects the dynamic nature of solar input. This model accurately captures periods of zero water production during nighttime hours when solar irradiance is absent. More critically, it accounts for the fluctuating (and often suboptimal) irradiance levels during daylight hours, as well as the system’s dynamic thermal response to changing environmental conditions. This realistic hourly simulation approach significantly lowers the overall daily and annual averages compared to idealised theoretical models which, despite accounting for active daylight hours, often assume constant optimal irradiance and operational efficiency throughout those periods.
• Dynamic Heat Losses: Ambient conditions such as varying wind speeds and ambient temperatures directly influence heat loss mechanisms. For instance, higher wind speeds increase convective losses from the glass, reducing the net energy available for evaporation.
• Seasonal Variation: Figure 7 clearly demonstrates the seasonal dependency of water production. Higher production rates are observed during summer months due to increased solar irradiance and ambient temperatures, while winter months show significantly lower yields. This contrasts sharply with the constant production implied by the initial theoretical model.
• Efficiency Fluctuations: While the useful evaporative heat ($q_e$) now varies, the instantaneous efficiency of the system (ratio of evaporative heat to incident solar energy) also fluctuates, as shown in Figure 8. This is because both the numerator ($Q_{ev\_watts\_hourly}$) and the denominator ($I_t·A_{glass}$) are dynamic, reflecting the system’s varying performance under changing conditions.
• Diurnal Performance and Driving Forces: Figure 9 provides crucial insights into the daily performance of the system under Case 1 (fixed water temperature). Contrary to an assumption of direct proportionality, water production does not strictly follow the solar irradiance curve. Instead, peak production is observed in the morning and evening hours (approximately 6:00 a.m. and 7:00 p.m.), with a local minimum occurring around midday when solar irradiance is at its peak. This behaviour is attributed to the primary driving force of evaporation in a solar still: the vapour pressure difference between the basin water surface ($P_{vs,w}$) and the inner glass surface ($P_{vs,g}$). This pressure difference is directly influenced by the temperature gradient between the water ($T_w$) and the inner glass ($T_g$). In Case 1, $T_w$ is fixed at 59.85 °C, resulting in a constant and relatively high $P_{vs,w}$. During early morning and late evening, while solar irradiance is not at its maximum, the glass temperature ($T_g$) is relatively low due to cooler ambient conditions. This creates a significant $T_w-T_g$ difference, and consequently, a large $P_{vs,w}-P_{vs,g}$ difference, driving high rates of evaporation. Conversely, at midday, although irradiance is at its maximum, $T_g$ also rises significantly, reducing the $T_w-T_g$ gradient and thus leading to a local minimum in production.

In conclusion, although the average daily production may appear lower, this hourly simulation provides a far more accurate and robust estimation of the system’s real-world annual performance by fully integrating the temporal variations of meteorological parameters. The results underscore the importance of dynamic modelling for a realistic assessment of solar-driven desalination technologies.

3.4. Case 2: Hourly Simulation with Dynamic Water Temperature ($T_w$) and Refined Thermodynamic Properties

This section presents the refined hourly simulation, building upon the dynamic $T_w$ model introduced previously. The primary objective was to enhance the model’s accuracy by incorporating two additional key thermodynamic effects: the temperature-dependent latent heat of vaporisation of water ($\lambda$) and the impact of salinity on water vapour pressure. These refinements aim to provide a more comprehensive and precise assessment of the solar distiller’s performance under varying environmental conditions.

The hourly water temperature within the distiller ($T_w$) continued to be calculated dynamically, influenced by the sea water temperature ($T_{sea}$) and the instantaneous global solar irradiance ($I_t$). The core relationship used was:

$$T_{w,celsius}=T_{sea,celsius}+k_{tw\_solar}·I_{t,solar\_incident}$$

(23)

where $T_{sea,celsius}$ is the hourly sea water temperature, $I_{t,solar\_incident}$ is the hourly global irradiance on the inclined plane, and $k_{tw\_solar}$ is an empirical coefficient set to 0.1 to account for the solar energy absorption. To further refine the model, the following adjustments were implemented:

• Dynamic Latent Heat of Vaporization ($\lambda$): Instead of a fixed value, the latent heat of vaporization ($\lambda$) was calculated hourly as a function of the dynamic water temperature ($T_w$). This dependency was modeled using a common correlation:

  $$\lambda \left(T_w\right)=2.501\times {10}^6-2361.3·T_{w,celsius}\left(\mathrm{J}/\mathrm{kg}\right)$$
  This ensures that the energy required for evaporation accurately reflects the varying thermal conditions of the water.
• Effect of Salinity on Vapor Pressure: The presence of dissolved salts in the basin water slightly reduces the vapor pressure of water compared to pure water. This effect was incorporated by applying a correction factor to the saturated vapor pressure of water at $T_w$. Assuming an initial sea water salinity of 35 g/kg, the corrected vapor pressure $P_{vs,w,corrected}$ was calculated using an empirical factor:

  $$P_{vs,w,corrected}=P_{vs,w,pure}·(1-0.000537·S)$$

  (24)

  where S is the salinity in g/kg. This adjustment directly impacts the evaporative heat flux ($q_e$), as $q_e$ is proportional to the difference in vapour pressures between the water and the glass. For this annual simulation, the salinity of the water in the basin was considered constant, assuming continuous or periodic replenishment with seawater.

The calculated results are summarized in

Table 3. Summary of Calculated Performance Parameters.

Parameter	Value	Unit	Notes/Conditions
Incident Heat on Collectors
Total Incident Heat Absorbed by Collectors ($Q_{inc}$)	410.87	W	For the specified conditions ($A_c=1.3832{\mathrm{m}}^2$)
Absorbed Heat Flux by Collectors ($q_{abs}$)	297.065	W/m2
System Thermal Performance
Heat Loss by Conduction ($q_{cond}$)	20.88	W/m2	From water to base
Heat Loss by Glass Radiation ($q_{rg}$)	19.00	W/m2	From glass to ambient
Heat Loss by Glass Convection ($q_{cg}$)	2.20	W/m2	From glass to ambient
Heat Loss by Water Radiation ($q_{rw}$)	152.82	W/m2	From water to glass
Heat Loss by Water Natural Convection ($q_{cw}$)	9.11	W/m2	From water to glass
Heat Loss by Evaporation ($q_e$)	86.14	W/m2	Per unit area
Heat Stored by Glass Cover ($q_c$)	−57.955	W/m2	Per unit area
Heat Stored by Water Mass ($q_w$)	−184.521	W/m2	Per unit area
Total Heat Stored Per Unit Area ($q_t$)	−242.476	W/m2	Sum of $q_c$ and $q_w$
Total Heat Absorbed by Device ($Q_T$)	75.24	W	Considering $A_c=1.3832{\mathrm{m}}^2$
Total Heat Required for Operation ($Q_N$)	766.336	W	Over 13 h of operation
Heat Required for Evaporation ($Q_{ev}$)	561.975	W	Over 13 h of operation
Overall System Efficiency
System Efficiency (${\eta }_{sys}$)	18.52	%	Ratio of useful evaporation energy to total incident solar energy on $A_{glass}$
Desalinated Water Production
Daily Water Production	11.155	L	Over 13 h of operation
Annual Water Production	174	L/year	From Case 2 simulation (as used in economic analysis)

.

Case 2. Analysis of Results

The inclusion of these thermodynamic refinements in Case 2 yielded a highly robust and accurate representation of the solar distiller’s performance. The total annual freshwater production was calculated to be approximately 173.951 L, corresponding to an average daily production of 0.4766 L/day. The overall system efficiency, considering only hours with production, averaged $0.3063\%$.

Comparing these results with those from Case 1 (without these refinements), a significant improvement in total annual water production of approximately 71 L was observed. While these refinements substantially enhance total water production, their greater value lies in elevating the model’s scientific rigour and predictive accuracy. Specifically, these thermodynamic refinements involve a dynamic and comprehensive energy balance for the distiller water mass, continuously accounting for transient solar absorption, radiative and convective heat losses to the ambient, and the latent heat of vaporisation. Unlike the simplified fixed water temperature assumption in Case 1, this dynamic approach captures the complex interplay of energy flows that dictate real-world distiller performance. This enhanced physical realism inherently strengthens the model’s validity and robustness, as it is grounded in a more complete representation of fundamental thermodynamic principles. Consequently, the model’s predictive accuracy is significantly improved, as demonstrated by the evaporative production profile (Figure 10), which now follows the dynamic solar input, providing a far more reliable basis for forecasting the system’s output under variable environmental conditions and enabling more robust design optimisation.

The dynamic behaviour of the system, as illustrated in Figure 10, shows a highly responsive distiller water temperature ($T_w$, purple line) that closely tracks solar irradiance (red line) and significantly exceeds the seawater temperature ($T_{sea}$, green dashed line) during daylight hours. Unlike Case 1, where water production exhibited an indirect relationship with irradiance due to a fixed $T_w$, in Case 2 this enhanced and dynamically modelled $T_w$ directly drives the evaporative process, resulting in a production profile that more closely follows the solar curve. This robust thermal modelling ensures a more reliable and realistic prediction of the system’s output. Furthermore, Figure 11 visually confirms the sustained production over the annual cycle, showcasing the cumulative benefits of the dynamic and refined modelling approach. The figure clearly illustrates the significant increase in water production achieved with Case 2 (dynamic) — approximately 174 L (blue line) — compared to the 103 L produced under Case 1 (fixed, red line). This direct comparison provides a more confident basis for evaluating the real-world operational potential of the solar distiller.

4. Discussion

The simulation results provide comprehensive insight into the performance of the solar still, highlighting the significant differences between theoretical idealisations and more realistic, dynamic modelling approaches. This section discusses the implications of the methodologies employed and interprets the observed trends in freshwater production and system efficiency.

4.1. Comparison of Modelling Approaches

The initial theoretical model served as a baseline, providing an idealised estimate of the distiller’s maximum potential output under constant, optimal conditions. While valuable for establishing an upper performance bound, its underlying assumptions—such as constant water temperature and uninterrupted solar input—led to a substantial overestimation of daily and annual freshwater production compared to the subsequent hourly simulations. This discrepancy underscores a key limitation of static models: their inability to represent the complex, time-dependent interactions governing solar distillation systems. In particular, static models neglect the diurnal and seasonal fluctuations in solar irradiance, ambient temperature, and wind speed typical of real-world environments. More critically, they overlook the system’s thermal inertia, whereby the water temperature ($T_w$)—and thus the evaporation rate—varies continually in response to dynamic energy inputs and losses. This inability to capture transient heat accumulation and dissipation, as well as the resulting variations in vapour pressure, results in highly idealised and often unrealistic performance predictions. Consequently, relying solely on static models may lead to significant misestimations in system sizing, efficiency, and operational planning, often producing over-optimistic projections that fail to materialise in practice.

The transition to Case 1, which incorporated hourly meteorological data, marked a significant step towards realism. By dynamically accounting for variations in solar irradiance, ambient temperature, and wind speed throughout the year, the model revealed a marked reduction in annual water yield relative to the theoretical baseline. This drop is primarily due to the system’s inactivity at night and its reduced performance during unfavourable weather conditions (e.g., cloud cover, high winds). The hourly production profile in Figure 6 clearly shows a strict dependence on daylight hours, with output dropping to zero at night—substantially lowering daily averages. Similarly, the monthly average production in Figure 7 highlights seasonal variations driven by solar availability.

The final refined model, Case 2, extended Case 1 by introducing a dynamically evolving water temperature ($T_w$) influenced by both solar input and sea water temperature, as well as temperature-dependent latent heat of vaporisation and the effect of salinity on vapour pressure. Although the increase in total annual water production between Case 1 and Case 2—approximately 71 L—was quantitatively significant, the refinement represents a more substantial improvement in the model’s physical realism and predictive reliability. The ability of $T_w$ to respond dynamically to solar intensity (as illustrated in Figure 10) enabled the model to capture the distiller’s capacity to exploit solar energy more effectively during peak hours, thus increasing instantaneous evaporative rates. This enhanced fidelity ensures that performance predictions align more closely with the expected behaviour of a solar still under real operating conditions.

Furthermore, Figure 11 visually confirms the cumulative advantages of the refined dynamic modelling. The figure clearly shows the total annual water production achieved in Case 2 (174 L, blue line) compared to Case 1 (103 L, red line), highlighting the tangible impact of incorporating thermodynamic realism into the simulation. This direct comparison provides a more robust foundation for evaluating the distiller’s real-world operational potential.

As illustrated in Figure 12 (Efficiency and Solar Irradiance Profiles), a key insight emerges when comparing Cases 1 and 2. Case 1, which assumes a fixed water temperature, shows instances of markedly higher instantaneous efficiency, peaking at approximately 2.3%. However, Case 2, with a dynamic $T_w$, maintains a much lower peak efficiency (around 0.3%) yet demonstrates more consistent energy utilisation throughout the day. This is evidenced by the Case 2 efficiency curve (red line) tracking the solar irradiance pattern (green line) more steadily, even though its peaks are lower than those of Case 1 (blue line). The result is a counterintuitive but crucial outcome: a lower average operating efficiency in Case 2 leads to significantly greater total annual water production.

This analysis highlights a critical design insight for solar distillation systems: prioritising sustained energy conversion over the entire operational cycle is more effective than focusing solely on peak instantaneous efficiency. The dynamic modelling approach in Case 2 captures this long-term advantage, offering a more rigorous and realistic framework for evaluating the viability and optimising the performance of solar-driven desalination technologies.

4.2. Influence of Key Environmental Parameters

Solar irradiance emerges as the principal driving force behind freshwater production. The simulations consistently reveal a strong and direct correlation between instantaneous solar radiation and hourly water output (Figure 10). Periods of high irradiance invariably correspond to peak production rates, whereas its absence or low intensity drastically diminishes or halts the distillation process.

The dynamic interplay of temperatures ($T_w$, $T_g$, $T_a$, $T_{\mathrm{sea}}$) is equally critical. The evaporation mechanism is fundamentally governed by the vapour pressure gradient between the basin water and the inner surface of the glass cover, which is directly related to the temperature difference $T_w-T_g$. By allowing $T_w$ to vary dynamically in response to solar input and sea water temperature in Case 2, the model more accurately captures the system’s thermal potential for evaporation. The hourly efficiency profiles (Figure 10 and Figure 12) illustrate how system efficiency fluctuates, governed by these dynamic thermal interactions and associated heat loss mechanisms.

Although not the primary driver, wind speed plays a significant secondary role by affecting convective heat losses from the glass cover to the ambient environment. This in turn influences $T_g$, thereby altering the thermal balance of the system and indirectly impacting its overall efficiency.

4.3. Practical Implications and Model Limitations

The findings underscore the critical importance of dynamic, hourly simulations in accurately predicting the long-term performance of solar stills. While static theoretical models provide useful upper bounds, they fail to capture the diurnal and seasonal variations, as well as the inherent inefficiencies (e.g., non-productive nighttime hours), which significantly impact the annual yield. The refined Case 2 model, which predicts an annual output of 174 L, offers a far more realistic foundation for feasibility assessments and system sizing in specific geographical contexts such as Málaga. Such detailed modelling proves invaluable for engineers and planners seeking to optimise system design and reliably forecast freshwater availability from solar desalination technologies.

Despite the substantial improvements in realism, the current model remains subject to several assumptions and limitations, including:

• The use of a simplified estimation for the glass cover temperature ($T_g$), rather than a complete dynamic energy balance iteration.
• The omission of thermal inertia effects for both the basin water and the structural components of the distiller, implying a quasi-steady-state assumption across hourly intervals.
• The assumption of constant salinity in the basin water—justified either by continuous replenishment or negligible salt accumulation—rather than accounting for progressive salinity increases in a batch-operation scenario.
• The exclusion of real-world degradation factors such as dust accumulation on the glass surface, internal scaling, or material ageing, all of which can lead to a decline in actual performance over time.

These limitations highlight key areas for future refinement. Addressing them would enhance the predictive accuracy of the model and contribute to a more comprehensive understanding of the operational behaviour of solar distillation systems under real-world conditions.

4.4. Economic Feasibility Analysis

To assess the practical feasibility and potential competitiveness of the proposed offshore solar desalination unit, a basic economic study was conducted, building upon methodologies commonly employed in the evaluation of solar distillation systems [25,34]. The primary economic metric considered is the Cost of Produced Water per litre (CPL), which reflects the annualized cost of fresh water production.

4.4.1. Methodology and Assumptions

The economic analysis is based on a set of defined parameters, a series of established equations for calculation, and specific assumed values, as detailed in

Table 4. Definition of Economic Parameters.

Parameter	Definition
P	Capital Cost: Total initial investment for fabricating and installing one unit of the offshore solar desalination system.
y	System Lifetime: The expected operational life of the system in years.
i	Interest Rate: The annual discount rate or interest rate, expressed as a decimal.
CRF	Capital Recovery Factor: A factor used to convert the initial capital cost into an equivalent uniform annual cost over the system’s lifetime.
FAC	Fixed Annual Cost: The annual cost directly associated with the initial capital investment.
S	Salvage Value: The estimated residual value of the system at the end of its operational lifetime.
SFF	Sinking Fund Factor: A factor used to calculate the annual deposit needed to accumulate the salvage value over the system’s lifetime.
ASV	Annual Salvage Value: The annual equivalent value of the salvage obtained at the end of the system’s life.
AMC	Annual Maintenance & Operational Cost: The estimated annual expenses for system upkeep, repairs, and daily operations.
AC	Annual Cost: The total equivalent annual cost of owning and operating the system, considering fixed costs, maintenance, and salvage value.
M	Total Annual Distillate: The total volume of freshwater produced by one unit of the system per year (in litres), derived from simulation results.
CPL	Cost of Produced Water per litre: The final economic metric, representing the annualized cost of producing one litre of fresh water.

,

Table 5. Equations Utilized in the Economic Analysis.

Parameter	Equation	No.
CRF	$CRF={\displaystyle \frac{i{(1+i)}^y}{{(1+i)}^y-1}}$	(25)
FAC	$FAC=P\times CRF$	(26)
S	$S=0.2\times P$	(27)
SFF	$SFF={\displaystyle \frac{i}{{(1+i)}^y-1}}$	(28)
ASV	$ASV=SFF\times S$	(29)
AMC	$AMC={AMC\_}_{\mathrm{percentage}}\times FAC$	(30)
AC	$AC=FAC+AMC-ASV$	(31)
CPL	$CPL={\displaystyle \frac{AC}{M}}$	(32)

, and

Table 6. Assumed Values for Economic Analysis.

Parameter	Value and Justification/Source
Capital Cost (P)	1248.34 Euros (This value is an initial estimate based on the prototype’s material costs and fabrication. It is subject to refinement with more precise data).
System Lifetime (y)	15 years (A typical expected operational life for solar desalination systems with durable components).
Interest Rate (i)	6% (0.06) (A standard interest rate reflecting a stable economic environment for investment).
Annual Maintenance & Operational Cost (AMC)	10% of the Fixed Annual Cost (FAC) (An assumption for annual upkeep, considering the system’s passive nature and robust materials).
Average Annual Distillate (M)	174 L/year (Directly derived from the Case 2 simulation results, representing the annual freshwater output of one unit).

, respectively.

4.4.2. Economic Analysis and Findings

Based on these inputs, the calculated economic parameters for the proposed offshore solar desalination unit are summarised in

Table 7. Calculated Economic Parameters for the Offshore Solar Desalination Unit.

Parameter	Value
Capital Recovery Factor (CRF)	0.1030
Fixed Annual Cost (FAC)	128.53 Euros/year
Salvage Value (S)	249.67 Euros
Sinking Fund Factor (SFF)	0.0430
Annual Salvage Value (ASV)	10.73 Euros/year
Annual Maintenance & Operational Cost (AMC)	12.85 Euros/year
Annual Cost (AC)	130.66 Euros/year
Cost of Produced Water per litre (CPL)	0.7509 Euros/L

.

The calculated cost per litre (CPL) of 0.7509 euros offers a preliminary indication of the system’s economic viability. In comparison to basic solar still designs—such as the Modified Solar Still (MSS) evaluated by [25], which reported a CPL of approximately 0.038 $/L —our proposed system exhibits a significantly higher unit cost. This discrepancy can be primarily attributed to several key factors:

• Novelty and Prototype Costs:The present economic analysis is based on a cost estimate for a novel, patented prototype. Initial unit costs for innovative technologies—especially those incorporating specialised components like heat-pipe vacuum tubes and engineered for offshore deployment—are inherently higher than those of simpler, low-cost solar stills, which are often mass-produced or designed with minimal capital requirements.
• Scale and Complexity: The proposed system is conceived as a modular unit specifically tailored for offshore use. It integrates advanced features not found in basic stills, including high-efficiency solar collectors, a durable floating platform suited for marine conditions, and mechanisms for sustainable brine management. While these elements raise the initial investment, they also enhance functionality, resilience, and adaptability to challenging operational contexts.
• Future Cost Reductions: With further development, design optimisation, and mass production, the capital cost per unit (P) is expected to decline considerably. These reductions would translate directly into a lower CPL. The current study thus serves as a reference point for targeted cost-reduction strategies.
• Environmental Benefits—Sustainable Brine Management: A critical, albeit non-quantified, advantage of the proposed system lies in its environmentally responsible approach to handling residual salts. Unlike conventional desalination plants that discharge concentrated liquid brine into the ocean—often disrupting marine ecosystems through alterations in salinity, temperature, and chemical composition—our system facilitates continuous, natural assimilation of salts into the surrounding seawater. This is achieved through minimal and highly diluted release, allowing rapid dispersion in the marine environment and avoiding the ecological damage typically associated with brine discharge. This feature enhances the system’s sustainability credentials, particularly in ecologically sensitive offshore zones where strict environmental regulations apply.

Although the current CPL is higher than that of traditional stills, this analysis provides a critical foundation for evaluating the economic implications of this novel offshore solar desalination approach. Future efforts focused on manufacturing efficiency and scaling will be essential to improve economic competitiveness and support broader adoption.

5. Conclusions

This study has presented a comprehensive numerical investigation into the performance of a solar still, advancing from theoretical idealisations to a refined hourly simulation based on real meteorological data from Málaga, Andalusia, Spain. The primary objective was to accurately predict freshwater production and system efficiency by accounting for the dynamic nature of environmental conditions and key thermodynamic parameters.

The main conclusions of this research are as follows:

• Significant Influence of Dynamic Environmental Conditions: While the initial theoretical model offered an idealised upper bound, it substantially overestimated annual freshwater production. In contrast, simulations incorporating hourly environmental data revealed that diurnal and seasonal variations in solar irradiance, ambient temperature, and wind speed are critical drivers of system performance. Ignoring these dynamic effects leads to unrealistic predictions and overoptimistic estimations.
• Improved Accuracy via Dynamic Water Temperature Modelling: Case 1, incorporating real hourly data, yielded more realistic results. Further refinement in Case 2—introducing a dynamic water temperature model ($T_w$) responsive to both sea water temperature and solar input—substantially enhanced the model’s thermodynamic consistency. This approach, together with a variable latent heat of vaporisation and consideration of salinity effects, led to a notable increase in annual output, reaching 173.95 L. This quantitative improvement reflects a more faithful representation of the distiller’s thermal behaviour and evaporative potential, making the model more reliable for practical deployment of this novel offshore concept.
• Necessity of Comprehensive Hourly Simulation: The results clearly demonstrate that detailed hourly simulations are essential for accurately assessing and designing solar stills. These simulations capture transient behaviours and operational inefficiencies—such as non-productive night-time periods—that static models inherently overlook. The proposed methodology thus offers a robust framework for feasibility assessments tailored to specific climatic contexts.
• Baseline for Economic Viability: The initial cost analysis, based on prototype estimations, yielded a Cost of Produced Water (CPL) of 0.7509 Euros/L. Although higher than that of basic, low-cost solar stills, this figure establishes a reference point for future improvements. It confirms the system’s potential for freshwater production even at the early stages of development and highlights key areas for economic optimisation through scaling and technological refinement.
• Environmentally Advantageous Brine Management: A particularly valuable feature of the proposed system—though not reflected in monetary terms—is its inherently sustainable brine management strategy. By allowing salts to be naturally and continuously assimilated into the surrounding seawater, the system avoids the harmful concentrated brine discharges typical of conventional desalination. This makes it especially well suited for deployment in environmentally sensitive marine areas, where conventional brine disposal is problematic or restricted.

Limitations and Future Work

While this study has substantially advanced the hourly modelling of solar stills, several limitations offer promising directions for future research:

• Experimental Validation: As the offshore solar desalination unit is a novel, patented concept (International Patent Application WO 2023/062261 A1) and has not yet been physically prototyped, this study has relied exclusively on numerical simulations. A crucial next step is the experimental validation of the system through prototype construction and field testing. This would confirm predicted performance metrics and further calibrate the model, supporting its future scalability.
• Advanced Thermal Modelling: Future research could introduce a full energy balance for the glass cover temperature ($T_g$) and account for the thermal inertia of both the water and structural components. This would allow for a more precise characterisation of thermal transients, especially during start-up and shut-down phases.
• Long-Term Operational Factors: Real-world deployment may be affected by issues such as dust accumulation, internal fouling, and material degradation. These aspects, which can reduce efficiency over time, merit investigation through long-duration simulations or empirical studies.
• Sensitivity Analysis: Although the influence of several empirical coefficients and environmental parameters on model performance has been observed, a systematic sensitivity analysis has not been undertaken. Future work could quantify the relative importance of these inputs, guiding model simplification or uncertainty reduction.
• Dynamic Salinity Effects: This study assumed constant basin water salinity due to continuous replenishment. Future work will investigate the system’s performance under dynamic and increasing salinity conditions, which naturally occur from continuous evaporation without full replenishment, to better understand long-term behaviour and optimize operational strategies.
• System Optimisation and Economic Viability: The refined hourly model developed here offers a valuable platform for future parametric studies aimed at optimising design geometry, material selection, and operational strategies for specific climates. Importantly, the economic analysis underscores the need for cost-reduction strategies, including improved manufacturing processes, mass production, and targeted deployment in niches where the system’s unique environmental advantages outweigh its current higher capital costs.
• Quantification of Environmental Benefits: While the system’s sustainable brine disposal is qualitatively advantageous, future studies should aim to quantify these benefits through life-cycle assessment or environmental impact modelling. Doing so would support a more holistic and monetised evaluation of the system’s sustainability, reinforcing its value proposition in regulatory and ecological contexts.

In summary, this research contributes meaningfully to the growing body of knowledge on sustainable desalination technologies. By providing robust and realistic modelling tools, it supports the development and deployment of solar stills as a viable and environmentally conscious solution to freshwater scarcity challenges.

6. Patents

The work reported in this manuscript has led to the following patent application: Solar-powered water condensation and desalination structure for floating desalination systems, invented by Vallejo Tejero, Juan José, and Rodríguea Gómez, Alejandro. The applicant and rights holder is Universidad de Málaga [ES/ES]. This patent was published internationally under number WO 2023/062261 A1 on 20 April 2023.