Comparative Analysis of Energy Recovery Configurations for Solar Vacuum Membrane Distillation

Abstract

Vacuum membrane distillation (VMD) is a promising desalination technology, which is likely to be integrated with solar energy, and offers a sustainable solution to freshwater scarcity. However, its industrial application remains limited due to high specific energy consumption and water production costs. The key to improving VMD performance lies in enhancing the recovery of the latent heat of condensation. In this investigation, four different configurations are proposed; each differs in the method of condensation and energy recovery. The first is applied by using a basic condenser, preheating seawater with latent heat from vapor. The second is implemented by incorporating a liquid ring vacuum pump (LRVP), enabling both condensation and vacuum generation. The third is performed by coupling VMD with a heat pump, which operates by using a refrigerant fluid. Lastly, the fourth is employed by using mechanical vapor compression (MVC), where the vapor is compressed to recover heat efficiently. The results show that the VMD-MVC is the most efficient configuration, offering the lowest specific energy consumption (154.6 kWh/m³), the highest energy recovery rate (54.64%), the highest gained output ratio (GOR) of 5.52, and the lowest water production cost (4.6 USD/m³). In contrast, the VMD system coupled with a heat pump presented the highest water production cost (36.4 USD/m³) among all the evaluated configurations.

1. Introduction

The demand for pure water is constantly increasing. This will reach critical levels in reference to population growth, industrialization, and global warming [1]. Currently, the global demand for water is approximately 4 trillion cubic meters per year. However, this consumption is projected to rise to 5 trillion cubic meters or more in 2025 [2]. In fact, water shortage is a critical issue that poses a significant threat to humanity’s survival. The United Nations predicts that by 2040, the world could experience global water scarcity of up to 40% [2]. To address the critical issue of water scarcity, two solutions have been proposed: water conservation and desalination [3]. Desalination has been used for over 50 years through two main types of technologies, notably thermal and membrane-based processes [4]. Thermal methods rely on evaporation and condensation [5]. Reverse osmosis (RO) is the most common membrane-based method. It is energy-efficient and space-saving. However, it has two main drawbacks: membrane fouling, which requires costly pre-treatment [6], and the production of brine, which can harm marine environments due to issues like eutrophication, pH changes, and heavy metal accumulation [7].

Membrane distillation (MD) is a hybrid desalination technique [3]. It is an evaporative thermal process using a microporous hydrophobic membrane [4]. This membrane separates saline or brackish water from freshwater by utilizing a temperature difference between two sides: a hot feed side and a cold permeate one [5]. The MD process depends on a temperature gradient to establish a vapor pressure difference, which drives the water molecules through the membrane. As a result, MD operates at lower pressures, unlike the RO, which functions under high pressure. It offers greater energy efficiency compared to traditional thermal distillation methods [8]. MD has emerged as a cost-effective and innovative solution for extracting pure drinking water from briny sources [9]. This separation process can effectively handle highly saline solutions, including saturated brines. It can be powered by renewable energy sources such as solar energy and waste heat, enhancing its sustainability and efficiency [10]. There are four common MD configurations.

Each one varies in the way it collects or condenses water. They are, notably, direct contact membrane distillation (DCMD), air gap membrane distillation (AGMD), sweeping gas membrane distillation (SGMD), and vacuum membrane distillation (VMD) [11]. Among these designs, VMD offers the highest system efficiency, thanks to its low conduction heat loss and significantly greater water productivity compared to the other configurations [8]. In VMD, a vacuum or a low pressure is created on the permeate side, which enhances the transport of vapor through the membrane. It reduces evaporation temperature and lessens the heating requirement as well [5]. However, VMD is characterized by high energy consumption, which limits its use in industrial levels. This limitation stems from the recovery of the latent heat of condensation difficulty and hence its lower efficiency because of the low temperature of vapor permeate [12].

Recently, VMD has been considered to be a vast area of research. Some developments have been carried out in relation to this technology. Ahmadi et al. [13] introduce in their work an innovative compact solar water heater (CSWHT) system in which heat recovery is integrated. The goal was to develop an efficient desalination technique that would lower water production costs while maximizing output. The results were shown on a 6 m² solar collector area of Mediterranean seawater. The system exhibited a daily production capacity of 92.5 kg of water while achieving a production cost of 12.2 USD/m³ and a gain output ratio (GOR) of 1.6. Mañas et al. [14] evaluated a multi-effect vacuum membrane distillation unit for desalting seawater. They proved that by preheating the feed flow in the condenser using seawater, GOR could reach 3.2. Alawad et al. [15] investigated the integration of vapor compression in multistage vacuum membrane distillation. They demonstrated that both productivity and energy efficiency were significantly improved with this configuration. This study investigates the impact of different compressor placements within the multi-stage vacuum membrane distillation (MSVMD) setup on productivity and GOR, considering a range of operational parameters. Su et al. [16] conducted an energy, exergy, and environmental analysis of VMD driven by solar energy coupled with a heat pump. Multi-objective optimization was used to assess the optimum operating conditions of the process. The results exhibited an optimal solution, which could be reached with a COP of 19.92, leading to a specific electrical energy consumption (SEEC) of 142.89 kWh/m³. Huang et al. [17] proved that the implementation of a multi-stage heat recovery system significantly enhanced the performance of the MD process by reutilizing the thermal energy released during condensation. Si et al. [18] conducted an experimental study of VMD with mechanical compression. The results demonstrated that the system exhibited excellent airtightness, ensuring proper evaporation conditions, along with a high separation efficiency of 99.9% and reduced evaporation energy consumption.

In this paper, our interest is essentially based on solar VMD. As is known, the key to VMD performance is the recovery of the latent heat of evaporation. With reference to this fact, the goal of this work is to optimize the heat recovery system of solar-powered VMD. Despite its importance, few studies have addressed the optimization of heat recovery in solar VMD systems. This highlights the relevance of this work and the need for further investigation in this area. Therefore, this study represents a critical contribution in this field, offering a novel approach that has not been extensively explored in the current literature. To achieve this, four solutions were considered. The first one was to use a condenser. The second consists of the use of a liquid ring vacuum pump (LRVP), which ensures condensation and vacuum creation at the same time. The third configuration proposed the use of a heat pump (HP). Lastly, the fourth solution involved the use of mechanical vapor compression (MVC). These four proposals were simultaneously evaluated with respect to heat recovery, specific energy consumption, energy efficiency, and water production cost.

2. Materials and Methods

VMD has not yet reached the industrial stage. This is due to its high energy consumption [19,20]. Although it has several advantages, this promising technology is in the development stage. Therefore, there is an urgent and clear need to minimize its energy demand. In fact, the enthalpy of water vaporization is approximately 2400 kJ/kg at 45 °C, whereas the Gibbs free energy of separation for seawater, which determines the energy required for processes like RO or electrolysis, is merely 2.7 kJ/kg [21]. By recovering latent heat in thermal desalination and considering the lower exergy content of heat compared to the work needed in reverse osmosis and electrolysis, this significant disparity can be substantially reduced [22]. Thus, the key to minimizing energy consumption is the recovery of the latent heat of vaporization. In order to identify the optimal configuration, which allows for high energy recovery, minimal energy consumption, and reduced water production cost, four configurations were proposed.

2.1. Principle of Operation of the Four Configurations

2.1.1. Configuration 1: VMD Using a Condenser

Figure 1 describes the composition of a solar VMD unit with regard to the first configuration. In the implementation of this configuration, distilled seawater (#3) is heated in a plate exchanger by heat transfer with the fluid circulating (#2) in the solar collectors. The temperature at the membrane inlet should not exceed 80 °C in order to protect the membrane structure. The membrane module has two outlets: the retentate outlet (#6) and permeate one (#5). The steam (#5) is then directed to the condenser to undergo condensation. During condensation, part of the latent heat is recovered by preheating extra seawater (#8). Condensation is carried out using cold seawater (#11). Its flow rate is chosen so that condensation can occur completely. A portion of the flow (#11) is recycled to cover the flows of #12 and #7, leaving the installation in such a way that the flow circulating in the installation is constant. In fact, discharge at point (#7) is carried out in order to avoid the increase in salinity during installation and to protect the membrane from clogging.

The vacuum is equipped with a vacuum pump mounted downstream of the condenser. A photovoltaic system is installed to provide electricity for the vacuum and the recirculation pumps.

2.1.2. Configuration 2: VMD Using an LRVP

Figure 2 visualizes the principle of the vacuum membrane distillation unit using LRVP. This is a type of rotary pump used for creating a partial vacuum or sucking in gases where permeate condensation takes place. It works by using a liquid, usually water, as the working fluid to create a vacuum inside the pump. This pump mainly consists of two elements: a rotor (often eccentric in shape) and a chamber-like cavity in which a liquid ring (#12) circulates. Due to the eccentricity of the rotor, the volume of these compartments changes as it rotates. As the cavity expands, it draws in the gas or air to be sucked in. This gas is then transported into the pump and displaced outwards, creating the vacuum. Process vapor (#5) enters through the suction port. By contacting the liquid ring, the steam is condensed and compressed. Subsequently, it is exhausted through the discharge port, along with a quantity of service liquid (#9). A continuous supply of service liquid is necessary to limit the temperature rise in the pump caused by condensation. Flow (#9) enters in a plate heat exchanger to make additional seawater hot (#8), which enters the installation as a kind of energy recovery.

A photovoltaic system has to be installed so as to provide electricity for the liquid ring vacuum pump, as well as the recirculation one.

2.1.3. Configuration 3: VMD Using a Heat Pump

A schematic diagram of the entire VMD system using a heat pump for the condensation and heat recovery is shown in Figure 3.

A heat pump consists of two heat exchangers (evaporator and condenser), a compressor, and an expansion valve, forming a thermodynamic cycle through which a refrigerant circulates. They allow energy to be drawn from a cold source in order for later use in heating a hot source. For this configuration, the vapor permeate (#5), known as a cold source, is condensed in the evaporator by exchanging heat with the refrigerant, identified by orange lines, which evaporates in the evaporator (#11) using the heat given off by the vapor permeate. The refrigerant in the gaseous state passes through the compressor (#12) to increase its pressure and therefore its temperature. Consecutively, it is condensed in the condenser (#13) to heat additional seawater (#9), forming a hot source by recovering the latent heat of condensation. And subsequently, the liquid refrigerant passes through the expansion valve (#14) in order to lower its pressure and undergo a new thermodynamic cycle, allowing for both the condensation of the permeate and the recovery of energy.

A photovoltaic (PV) system with an appropriate capacity has to be installed to provide electricity for the vacuum pump, the recirculation pump, and the compressor.

2.1.4. Configuration 4: VMD with MVC

Figure 4 displays the VMD process integrated with mechanical vapor compression (MVC). MVC is used to improve heat recovery in the unit.

Vacuum membrane distillation combined with mechanical vapor compression (VMD-MVC) is an innovative energy-saving approach based on the self-heat recuperation theory [23,24]. This method efficiently utilizes the latent heat from the vapor compressed by the compressor to preheat the feed solution, resulting in high thermodynamic efficiency.

The water vapor leaving the membrane module (#5) is highly superheated after being compressed in the compressor (#11). The heat exchange takes place between the compressed vapor (#11) and the brine (#10). As a result, the VMD does not depend on a solar collector field to heat the treated solution. In this case, the vapor compression is sufficient to heat the feed solution. Solely, a preheater is required in order to start the cycle. The vapor condensation then takes place by releasing the latent heat of condensation. The distillate (#12) is recuperated in a pure water tank.

A photovoltaic system has to be installed to provide electricity for the vacuum pump, recirculation pumps, and the compressor.

2.2. Energy Analysis of the Four Configurations

Table 1. Key equations used in the energy analysis.

	Configuration 1	Configuration 2	Configuration 3	Configuration 4
Total energy (kW)	${\mathcal{P}}_{\mathrm{t}\mathrm{o}\mathrm{t}}={\mathcal{P}}_{\mathrm{t}\mathrm{h}}+{\mathcal{P}}_{\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}}$ (1) [25]
Thermal energy (kW)	${\mathcal{P}}_{\mathrm{t}\mathrm{h}}={\dot{\mathrm{m}}}_3·{\mathrm{C}\mathrm{p}}_{\mathrm{f}\mathrm{e}\mathrm{e}\mathrm{d}}·({\mathrm{T}}_3-{\mathrm{T}}_4)$ (2) [25]			${\mathcal{P}}_{\mathrm{t}\mathrm{h}}={\dot{\mathrm{m}}}_1·{\mathrm{C}\mathrm{p}}_{\mathrm{f}\mathrm{e}\mathrm{e}\mathrm{d}}·({\mathrm{T}}_2-{\mathrm{T}}_1)$ (3) [25]
Electrical energy (kW)	${\mathcal{P}}_{\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}}={\dot{\mathrm{W}}}_{\mathrm{c}\mathrm{i}\mathrm{r}}+{\dot{\mathrm{W}}}_{\mathrm{v}\mathrm{a}\mathrm{c}}$ (4) [12]		${\mathcal{P}}_{\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}}={\dot{\mathrm{W}}}_{\mathrm{c}\mathrm{i}\mathrm{r}}+{\dot{\mathrm{W}}}_{\mathrm{v}\mathrm{a}\mathrm{c}}+{\dot{\mathrm{W}}}_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}}$ (5) [26]	${\mathcal{P}}_{\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}}={\dot{\mathrm{W}}}_{\mathrm{c}\mathrm{i}\mathrm{r}}+{\dot{\mathrm{W}}}_{\mathrm{v}\mathrm{a}\mathrm{c}}+{\dot{\mathrm{W}}}_{\mathrm{M}\mathrm{V}\mathrm{C}}$ (6) [23]
Circulation pump power (kW)	${\dot{\mathrm{W}}}_{\mathrm{c}\mathrm{i}\mathrm{r}}={\displaystyle \frac{{\dot{\mathrm{V}}}_{\mathrm{f}\mathrm{e}\mathrm{e}\mathrm{d}}·∆\mathrm{P}}{{\mathsf{\eta }}_{\mathrm{c}\mathrm{i}\mathrm{r}}}}$ (7) [27]
Vacuum pump power (kW)	${\dot{\mathrm{W}}}_{\mathrm{v}\mathrm{a}\mathrm{c}}={\displaystyle \frac{2.85{10}^{-4}}{{\mathsf{\eta }}_{\mathrm{v}\mathrm{p}}}}·{\mathrm{T}}_{\mathrm{p}}·{\mathrm{Q}}_0·ln\left({\displaystyle \frac{{\mathrm{P}}_{\mathrm{a}\mathrm{t}\mathrm{m}}}{{\mathrm{P}}_{\mathrm{v}}}}\right)$ (8) [27]	${\dot{\mathrm{W}}}_{\mathrm{L}\mathrm{R}\mathrm{V}\mathrm{P}}={\displaystyle \frac{{\mathrm{P}}_{\mathrm{i}\mathrm{n}}\times {\dot{\mathrm{V}}}_{\mathrm{g}\mathrm{a}\mathrm{s}}\times \mathrm{l}\mathrm{n}\left(\frac{{\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t}}}{{\mathrm{P}}_{\mathrm{i}\mathrm{n}}}\right)}{3.6·{10}^6\times {\mathsf{\eta }}_{\mathrm{L}\mathrm{R}\mathrm{V}\mathrm{P}}}}$ (9) [25]	Calculated using Equation (8)
Heat pump power (kW) and Mechanical vapor compressor power (kW)			${\dot{\mathrm{W}}}_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}}={\displaystyle \frac{{\mathcal{P}}_{\mathrm{e}\mathrm{f}\mathrm{f}}}{{\mathsf{\eta }}_{\mathrm{M}\mathrm{e}\mathrm{l}}·{\mathsf{\eta }}_{\mathrm{t}\mathrm{r}}}}$ (10) ${\mathcal{P}}_{\mathrm{e}\mathrm{f}\mathrm{f}}={\displaystyle \frac{{\mathcal{P}}_{\mathrm{a}\mathrm{b}\mathrm{s}}}{{\mathsf{\eta }}_{\mathrm{e}\mathrm{f}\mathrm{f}}}}$ (11) ${\mathcal{P}}_{\mathrm{a}\mathrm{b}\mathrm{s}}={\dot{\mathrm{m}}}_{\mathrm{r}\mathrm{e}\mathrm{f}\mathrm{r}\mathrm{i}}·({\mathrm{h}}_{12}-{\mathrm{h}}_{11})$ (12) [26]	${\dot{\mathrm{W}}}_{\mathrm{M}\mathrm{V}\mathrm{C}}={\displaystyle \frac{{\dot{\mathrm{m}}}_5·({\mathrm{h}}_{11}-{\mathrm{h}}_5)}{{\mathsf{\eta }}_{\mathrm{M}\mathrm{V}\mathrm{C}}}}$ (13) ${\mathrm{T}}_{11}={\mathrm{T}}_5·{\left({\displaystyle \frac{{\mathrm{P}}_{11}}{{\mathrm{P}}_5}}\right)}^{{\displaystyle \frac{\mathsf{\gamma }-1}{\mathsf{\gamma }}}}$ (14) [23]

summarizes the key equations used in the energy analysis of the four proposed configurations.

The total energy flow rate consumed, ${\mathcal{P}}_{\mathrm{t}\mathrm{o}\mathrm{t}}$, for the four configurations consists of the thermal energy flow rate, ${\mathcal{P}}_{\mathrm{t}\mathrm{h}}$, which is required to heat the seawater at the inlet of the membrane module provided by the thermal sensor field. The electrical energy flow rate, ${\mathcal{P}}_{\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}}$, is required to operate the circulation and the vacuum pumps. These are calculated using Equation (1). The thermal energy flow rate for configurations 1–3 is determined by Equation (2), where ${\dot{\mathrm{m}}}_3$ is the feed flow at the inlet of the membrane (kg/s), while ${\mathrm{C}\mathrm{p}}_{\mathrm{f}\mathrm{e}\mathrm{e}\mathrm{d}}$ is the specific heat of the feed solution (kJ/kg·K). In contrast, Configuration 4 does not require a solar thermal collector field; the energy flow is given by Equation (3) since only a one-time preheating of the saline solution is needed to initiate the cycle. For Configurations 1 and 2, the electrical energy corresponds to the combined consumption of the circulation pumps and the vacuum one, as shown in Equation (4).

The electrical consumption of the circulation pumps is evaluated using Equation (7), where ${\dot{\mathrm{W}}}_{\mathrm{c}\mathrm{i}\mathrm{r}}$ is the pump work needed to pressurize the fluid (kW), and ${\dot{\mathrm{V}}}_{\mathrm{f}\mathrm{e}\mathrm{e}\mathrm{d}}$ is the volumetric flow rate of the feed flow (m³/s). $∆\mathrm{P}$ is the pressure difference between the pump inlet and outlet. In Configuration 3, the electrical energy is supplied by the photovoltaic (PV) field. It covers the operation of the circulation pumps, the vacuum pump, and the heat pump compressor, as given in Equation (5). In Configuration 4, the electrical energy corresponds to the sum of the power required by the circulation pumps, the vacuum pump, and the mechanical vapor compressor, as expressed in Equation (6). The power consumption of the vacuum pump in Configurations 1, 2, and 4 is calculated using Equation (8), which represents a conventional vacuum pump. Here, ${\mathsf{\eta }}_{\mathrm{c}\mathrm{i}\mathrm{r}}$ and ${\mathsf{\eta }}_{\mathrm{v}\mathrm{p}}$ denote the mechanical efficiencies of the circulation and vacuum pumps, respectively (assumed to be 0.8). ${\mathrm{T}}_{\mathrm{p}}$ is the permeate temperature (K), ${\mathrm{Q}}_0$ is the flow rate of air evacuated from the permeate line (std ft³/min), and ${\mathrm{P}}_{\mathrm{a}\mathrm{t}\mathrm{m}}$ and ${\mathrm{P}}_{\mathrm{v}}$ are the atmospheric and vacuum pressures (Pa). In Configuration 3, the vacuum pump consumption is obtained from Equation (9) since the LRVP has a different operating principle; ${\dot{\mathrm{W}}}_{\mathrm{L}\mathrm{R}\mathrm{V}\mathrm{P}}$ is the power consumed (kW), ${\mathrm{P}}_{\mathrm{i}\mathrm{n}}$ and ${\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$ are the suction and discharge pressures (Pa), ${\dot{\mathrm{V}}}_{\mathrm{g}\mathrm{a}\mathrm{s}}$ is the volumetric flow rate of pumped gas (m³/h), and ${\mathsf{\eta }}_{\mathrm{L}\mathrm{R}\mathrm{V}\mathrm{P}}$ is the electromechanical efficiency.

The electrical power required by heat pump compressor is given using Equation (10). The effective power absorbed by the compressor ${\mathcal{P}}_{\mathrm{e}\mathrm{f}\mathrm{f}}$ is calculated with Equation (11), where ${\mathsf{\eta }}_{\mathrm{M}\mathrm{e}\mathrm{l}}$ and ${\mathsf{\eta }}_{\mathrm{t}\mathrm{r}}$ are motor and transmission efficiencies (manufacturer data) and ${\mathsf{\eta }}_{\mathrm{e}\mathrm{f}\mathrm{f}}$ is the compressor efficiency. Several correlations exist for estimating compressor efficiency, depending on the type of compressor. For piston compressors, selected in this study, the effective efficiency can be determined from the compression ratio, defined as the outlet-to-inlet pressure ratio. The theoretical power absorbed by the compressor is evaluated using Equation (12), where ${\dot{\mathrm{m}}}_{\mathrm{r}\mathrm{e}\mathrm{f}\mathrm{r}\mathrm{i}}$ is the refrigerant mass flow (kg/s), while ${\mathrm{h}}_{11}$ and ${\mathrm{h}}_{12}$ are the specific enthalpies of the refrigerant at the compressor inlet and outlet, respectively (kJ/kg), obtained from refrigerant enthalpy charts. To determine the required refrigerant mass flow rate ${\dot{\mathrm{m}}}_{\mathrm{r}\mathrm{e}\mathrm{f}\mathrm{r}\mathrm{i}}$, a heat balance is performed in the evaporator. The cooling capacity of the heat pump, ${\mathrm{Q}}_{\mathrm{C}}$, corresponds to the capacity exchanged between the inlet and outlet of the evaporator, which represents the actual cooling effect on the vapor leaving the membrane module, as given by Equation (15) [25].

$${\mathrm{Q}}_{\mathrm{C}}={\dot{\mathrm{m}}}_{\mathrm{r}\mathrm{e}\mathrm{f}\mathrm{r}\mathrm{i}}·\left({\mathrm{h}}_{11}-{\mathrm{h}}_{14}\right)={\dot{\mathrm{m}}}_5·[{\mathrm{C}}_{\mathrm{p}\mathrm{v}}\left({\mathrm{T}}_5-{\mathrm{T}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}}\right)+{\mathrm{L}}_{\mathrm{v}}+{\mathrm{C}}_{\mathrm{p}\mathrm{l}}·\left({\mathrm{T}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}}-{\mathrm{T}}_{10}\right)]$$

(15)

where ${\mathrm{C}}_{\mathrm{p}\mathrm{v}}$ and ${\mathrm{C}}_{\mathrm{p}\mathrm{l}}$ are the heat capacities of the vapor and liquid permeates, respectively (kJ/kg·K), ${\mathrm{L}}_{\mathrm{v}}$ is the latent heat of vaporization (kJ/kg), and ${\mathrm{T}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}}$ is the condensation temperature (K). It is worth noting the temperature at which the vapor permeate is condensed into liquid.

The latent heat of vaporization, heat capacities, and the condensation temperature are calculated using equations, depending on the vacuum pressure created in the membrane, temperature, and the salinity of seawater.

The heat capacity, ${\mathrm{Q}}_{\mathrm{h}}$, of the heat pump represents the amount of heat transferred from the cold source to heat the hot source. It corresponds to the heat power available between the inlet and the outlet of the condenser. According to the first law of thermodynamics, it is equal to the sum of the refrigerating capacity and the work of the compressor as expressed in Equations (16) and (17) [26] below:

$${\mathrm{Q}}_{\mathrm{h}}={\mathrm{Q}}_{\mathrm{c}}+{\mathrm{P}}_{\mathrm{a}\mathrm{b}\mathrm{s}}$$

(16)

The heat balance in the condenser is expressed as [26]

$${\mathrm{Q}}_{\mathrm{h}}={\dot{\mathrm{m}}}_{\mathrm{r}\mathrm{e}\mathrm{f}\mathrm{r}\mathrm{i}}·\left({\mathrm{h}}_{13}-{\mathrm{h}}_{12}\right)={\dot{\mathrm{m}}}_9·{\mathrm{C}}_{\mathrm{p}\mathrm{l}}·\left({\mathrm{T}}_8-{\mathrm{T}}_9\right)$$

(17)

To calculate the electrical energy consumed by the mechanical vapor compressor, there are several equations. The most used among them is Equation (13). Here, ${\mathrm{h}}_5$ and ${\mathrm{h}}_{11}$ are the specific enthalpy at the inlet and the outlet of the compressor, respectively, while ${\mathsf{\eta }}_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}}$ signifies the efficiency of the compressor. The isentropic efficiency of the MVC is assumed to be 70%.

To determine the outlet temperature of the compressor, the adiabatic (isentropic) Equation (14) can be used, assuming that there is no heat transfer, where γ is the ratio of the heat capacities (${\mathrm{C}}_{\mathrm{p}}/{\mathrm{C}}_{\mathrm{v}})$ of the gas, for water vapor γ ≈ 1.33 [23].

3. Performance Indicators

3.1. Gained Output Ratio (GOR)

The GOR is a key indicator of the process efficiency in the thermal desalination systems. This parameter is defined as the ratio of the latent heat of the produced distillate and the thermal energy introduced into the unit considering energy recovery. GOR is a dimensionless parameter. It reflects the degree of energy recovery in the system. As long as the GOR is greater than 1, energy recovery occurs. Conversely, once GOR is less than 1, it explicitly means that there is no energy recovery in the unit. The GOR can be calculated mathematically as follows [5,28]:

$$\mathrm{G}\mathrm{O}\mathrm{R}={\displaystyle \frac{{\dot{\mathrm{m}}}_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}}·{\mathrm{L}}_{\mathrm{v}}}{{\mathcal{P}}_{\mathrm{t}\mathrm{h}}}}$$

(18)

3.2. Specific Energy Consumption (SEC)

Specific energy consumption (SEC) is a widely used parameter that quantifies the total energy consumed in order to produce one cubic meter of distilled water. It is expressed in kWh/m³ and is calculated as follows [27]:

$$\mathrm{S}\mathrm{E}\mathrm{C}={\displaystyle \frac{{\mathcal{P}}_{\mathrm{t}\mathrm{o}\mathrm{t}}}{{\dot{\mathrm{m}}}_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}}}}$$

(19)

As is known, vacuum membrane distillation has two types of energy requirements: thermal and electrical. Thus, specific energy consumption can be divided into the terms specific thermal energy consumption (STEC) and specific electrical energy consumption (SEEC), as follows:

$$\mathrm{S}\mathrm{E}\mathrm{C}=\mathrm{S}\mathrm{T}\mathrm{E}\mathrm{C}+\mathrm{S}\mathrm{E}\mathrm{E}\mathrm{C}$$

(20)

The specific thermal energy consumption is a measure of the amount of thermal energy needed to generate a unit of freshwater. This performance criterion strongly depends on the feed temperature, which is defined as follows:

$$\mathrm{S}\mathrm{T}\mathrm{E}\mathrm{C}={\displaystyle \frac{{\mathcal{P}}_{\mathrm{t}\mathrm{h}}}{{\dot{\mathrm{m}}}_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}}}}$$

(21)

where ${\mathcal{P}}_{\mathrm{t}\mathrm{h}}$ is the total thermal energy flow rate input (kW).

Specific electrical energy consumption (SEEC) is defined as the amount of electrical energy consumed to produce a unit mass of pure water. It is expressed in kWh/m³ and is determined as follows:

$$\mathrm{S}\mathrm{E}\mathrm{E}\mathrm{C}={\displaystyle \frac{{\mathcal{P}}_{\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}}}{{\dot{\mathrm{m}}}_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}}}}$$

(22)

where ${\mathcal{P}}_{\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}}$ is the total electrical energy flow rate input (kW).

3.3. Water Product Cost (WPC)

To examine the economic feasibility of the four configurations, it is necessary to calculate the water product cost for each one. WPC is an important parameter frequently used in the literature to assess the economic performance of the desalination processes. It represents the ratio of the total capital cost, which includes capital and operational expenditures, to the unit’s production [29]. Figure 5 illustrates the elements necessary for determining the cost of water production by membrane distillation process [30,31,32].

WPC is expressed in USD/m³ and can be established using this following equation [33]:

$$\mathrm{W}\mathrm{P}\mathrm{C}={\displaystyle \frac{{\mathrm{C}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}}{\mathrm{ƒ}·{\mathrm{D}}_{\mathrm{c}\mathrm{a}\mathrm{p}}·365}}$$

(23)

where ${\mathrm{C}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$ is the total annual cost, ƒ is the availability of the unit, and ${\mathrm{D}}_{\mathrm{c}\mathrm{a}\mathrm{p}}$ is the daily capacity of the installation expressed in (m³/day).

The total annual cost is the sum of the fixed cost ${\mathrm{C}}_{\mathrm{f}\mathrm{i}\mathrm{x}\mathrm{e}\mathrm{d}}$ and the variable operation and the maintenance cost ${\mathrm{C}}_{\mathrm{O}\&\mathrm{M}}$ as follows:

$${\mathrm{C}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}={\mathrm{C}}_{\mathrm{f}\mathrm{i}\mathrm{x}\mathrm{e}\mathrm{d}}+{\mathrm{C}}_{\mathrm{O}\&\mathrm{M}}$$

(24)

Operating costs are the expenses incurred once the plant is operational. They are generally divided into fixed and variable costs throughout its operation costs [34]. Fixed operation and maintenance cost obviously include amortization and insurance. Variable operation and maintenance cost consist of equipment replacement cost and other costs, notably labor, chemicals, brine disposal, and operation (energy consumption) [35].

The fixed operation and maintenance costs can be estimated using the following equation [4,12]:

$${\mathrm{C}}_{\mathrm{f}\mathrm{i}\mathrm{x}\mathrm{e}\mathrm{d}}=\mathrm{a}·\mathrm{C}\mathrm{C}$$

(25)

where $\mathrm{C}\mathrm{C}$ is the capital cost, and $a$ is the amortization factor, calculated as follows [36]:

$$\mathrm{a}={\displaystyle \frac{\mathrm{i}{(1+\mathrm{i})}^{\mathrm{n}}}{{(1+\mathrm{i})}^{\mathrm{n}}-1}}$$

(26)

where $\mathrm{n}$ denotes the installation lifetime, and $\mathrm{i}$ is the annual interest rate, expressed as the percentage of the total equipment cost paid yearly.

The capital cost is composed of the direct capital one, abbreviated as $\mathrm{D}\mathrm{C}\mathrm{C}$, and indirect capital cost, $\mathrm{I}\mathrm{C}\mathrm{C}$. $\mathrm{D}\mathrm{C}\mathrm{C}$ includes the cost of process equipment (membrane module, heat exchangers, compressors, pumps, etc.), the cost of energy production systems (solar thermal collectors, PV panels, batteries, etc.), the cost of construction and installation, the cost of land, and the like. Of note, the $\mathrm{I}\mathrm{C}\mathrm{C}$ involves insurance, freight, construction overhead, engineering and supervision, and contingencies.

$$\mathrm{C}\mathrm{C}=\mathrm{D}\mathrm{C}\mathrm{C}+\mathrm{I}\mathrm{C}\mathrm{C}$$

(27)

With reference to the literature, indirect costs in an MD plant are often estimated to be 10% of the direct cost [30].

$$\mathrm{I}\mathrm{C}\mathrm{C}=0.01·\mathrm{D}\mathrm{C}\mathrm{C}$$

(28)

Table 2. Data and assumptions considered in the economic study.

	Value	References
Data and assumptions
Plant life	20 years	[31,35,36,37]
Availability of the unit	90%	[23,36]
Annual interest rate (i)	5%	[31,35,36,37]
Equipment costs
Membrane	PVDF 300 $/m2	[38]
Solar thermal collector	$150\times {{\mathrm{A}}_{\mathrm{s}\mathrm{c}}}^{0.95}$; ${\mathrm{A}}_{\mathrm{s}\mathrm{c}}$: Solar collector area (m2)	[36]
Solar PV collector	Panel: 144 $/m2 Inverter DC-AC: 432$ Regulator, support and cables, etc.: 450$	Supplier: WS.Energy photovoltaïque, Sousse, Tunisia
Heat exchanger	$300\times {\mathrm{A}}_{\mathrm{H}\mathrm{X}}\times {10.77}^{0.6907}$ (Plate heat exchanger)	[19]
Condenser/Evaporator	$2467.2\times {\left({\displaystyle \frac{{\mathrm{A}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}}}{0.51}}\right)}^{0.024}$ (Shell and tube)	[12,31]
Pump	$3540\times {\mathrm{W}}_{\mathrm{p}}^{0.71}$	[36,38]
Compressor	Supplier: Shandong Huadong Blower Co., Ltd., Jinan, China
Preheater	Supplier: ELEDIS, Sfax, Tunisia

summarizes the equations used to calculate the equipment costs of the installations, along with the data and assumptions considered in the economic study.

4. Results and Discussions

4.1. Solar Radiation

One of the major advantages of membrane distillation is its operation at low temperatures, ranging from 50 °C to 80 °C, which makes it particularly suitable for coupling with solar energy) [25]. Autonomous membrane distillation, operating entirely with solar thermal or photovoltaic energy, constitutes a sustainable and promising solution for producing drinking water. In fact, for solar-powered desalination systems, the intensity of solar radiation significantly affects the production of pure water [27]. For this reason, the first step is to study the solar deposit available in the area where the unit is installed. Solar irradiation in Tunisia is one of the highest in the Mediterranean basin, which makes it a very favorable country for the exploitation of solar energy. The Tunisian territory benefits averagely from 2800 to 3200 h of sunshine per year [39].

Figure 6a represents the variation in the maximum radiation value reached for each month. In Tunisia, solar irradiation varies significantly throughout the year due to seasonal changes in the sun’s position. During the month of June, which includes the summer solstice, the solar irradiation can reach nearly 1000 W/m² at noon, making it the peak period for solar energy potential. This month also benefits from the longest duration of sunlight, averaging about 14 h and 29 min. In contrast, December experiences the lowest levels of solar irradiation, with peak values below 600 W/m² and a shorter daylight duration of approximately 9 h and 36 min, which includes the winter solstice. The equinox months, such as March and September, have moderate irradiation levels and a balanced sunlight duration of around 12 h and 9 min. Furthermore, Figure 6b gives an example of the variation in solar irradiation during the day of 24 June 2024. With regard to the figure, it is noticeable that the sunshine increases exponentially during the day and reaches its peak at 12:15 (985 W/m²). However, it decreases in the same way to reach zero at the time of sunset. These data were obtained from TuTiempo.net as it is a particular website specializing in meteorology. It provides detailed climate data for thousands of countries around the world, including in Tunisia.

4.2. Design of Equipment for the Four Configurations

One of the primary objectives of this study is to determine the appropriate design of the equipment for the four configurations, including the required surface areas of the thermal and photovoltaic (PV) panels, the capacities of the heat exchangers, pumps, compressors, preheaters, and other components of a system associated with each configuration. The four configurations were sized to achieve a temperature of 80 °C at the membrane module inlet under maximum sunlight conditions during the year (985 W/m²), corresponding to the day 21 June at 12:15 p.m. This design choice guarantees optimal thermal performance and high pure water production under the most favorable sunlight conditions for the four configurations.

Table 3. Design of equipment for the four configurations.

	Configuration 1: Solar VMD Using Condenser	Configuration 2: Solar VMD Using LRVP	Configuration 3: Solar VMD Using HP	Configuration 4: Solar VMD Using MVC
Membrane	Type: Hollow fiber PVDF Total area: 4 m2
Solar thermal collector field	Type: Flat solar collector
	Total area: 70 m2	Total area: 85 m2	Total area: 27 m2	-
Heat exchangers	Type: Plate heat exchanger with titanium coating
	Power: 29 kW Total area: 1.07 m	(1) Power: 35 kW Total area: 1.23 m2 (2) Power: 2.28 kW Total area: 0.1 m2	Power: 11 kW Total area: 0.54 m2	-
Condenser	Type: Shell and tube with titanium coating
	Power: 50 kW Total area: 2.91 m2	-	-	(1) Power: 38 kW Total area: 0.6 m (2) Power: 12 kW Total area: 0.4 m2
Heat pump	-	-	𝓟eff = 12 kW	-
Compressor	-	-	-	Power: 0.7 kW
Circulating pump	Power: 0.3 kW			Power: 0.45 kW
Vacuum pump	Type: dry screw Power: 1 kW	Type: Liquid ring vacuum pump Power: 0.5 kW	Type: dry screw Power: 1 kW	Type: dry screw Power: 1 kW
Photovoltaic sensor field	6 PV panel 330 Wc Total power: 2 kWc Total panel area: 6 × 1.6 = 9.6 m2	3 PV panel 330 Wc Total power: 0.73 kWc Total panel area: 3 × 1.6 = 4.8 m2	108 PV panel 330 Wc Total power: 35.5 kWc Total panel area: 108 × 1.6 = 172.8 m2	34 PV panel 330 Wc Total power: 11 kWc Total panel area: 34 × 1.6 = 54.4 m2

summarizes the design results of the four configurations. For each configuration, the dimensions, materials, and power requirements of the necessary equipment are indicated. The design was carried out by respecting the energy and mass balances within each component, as well as the entire system.

For the four proposed approaches, a membrane surface of 4 m², in (PVDF), was configured in a hollow fiber geometry. As a result of the design analysis, the total area of solar thermal collectors required for the four configurations was estimated to be 70 m² for the first configuration, 85 m² for the second, and 27 m² for the third. It is clear that the third configuration required a smaller collector area due to the high capacity of the heat pump to recover the latent heat of condensation from the vapor permeate, and it was reused to heat the feed solution, thereby reducing the need for solar collector heating. Regarding Configuration 4, which involves the use of mechanical vapor compression, calculations showed that from a compression ratio of 1.15, the unit no longer requires heating by solar thermal collectors. The heat exchange between the compressed vapor (#10) and the retentate mixed with the additional flow (#10) is sufficient to heat the seawater stream undergoing distillation. The surfaces and capacities of heat exchangers and condensers required for each configuration are also delineated in Table 3. The heat exchangers were selected with a titanium coat since seawater is highly corrosive due to its high salt content while titanium is one of the most corrosion-resistant materials, even at high temperatures. This significantly extends the service life of the heat exchangers. Moreover, titanium offers convenient thermal conductivity, maintaining noticeable mechanical strength. Regarding the second configuration, there is no need for a condenser, as the LRVP ensures both condensation and vacuum generation at the same time. The heat pump for Configuration 3 was also dimensioned to recover the latent heat of condensation from the vapor permeate for heating the retentate. The required compressor power was 12 kW after calculation, indicating a significant energy demand, unlike Configuration 4 where the compressor power is only 0.7 kW. This is due to the fact that compression is applied to water vapor, which typically has a much lower volumetric flow rate than the refrigerant flow needed in a heat pump to transfer an equivalent amount of thermal energy. For the heat pump, the selected refrigerant was R1234ze. Initially, four refrigerants are suitable. They offer appropriate evaporation and condensation temperatures, which in turn were selected; notably, they are R134a, R22, R1234yf, and R1234ze. If R134a and R22 refrigerants are taken into consideration, although they are thermally efficient, they pose major environmental issues that have led to their gradual phase-out or strict regulation in many countries. Therefore, the choice was between R1234yf and R1234ze, both of which have a very low global warming potential (GWP), with no impact on the ozone layer. Furthermore, they offer evaporation and condensation temperatures compatible with solar vacuum membrane distillation. An analysis of the compressor power consumption for both refrigerants revealed that R1234ze requires up to 20% less compression power compared to R1234yf. The circulation pumps were sized based on the flow rates within the systems. Regarding the vacuum pumps, peristaltic pumps with a power rating of 1 kW were selected for Configurations 1, 2, and 4 while a liquid ring vacuum pump with a power rating of 0.5 kW was chosen for Configuration 3. In fact, peristaltic pumps have a strong capacity for gas handling and are characterized by simple and quick maintenance. Using Equations (5) and (6), it was found that liquid ring vacuum pumps exhibit lower energy consumption compared to other types of vacuum pumps. To ensure that all configurations operate autonomously and rely entirely on solar energy (thermal and photovoltaic), the electricity requirements for the operation of circulation pumps, vacuum pumps, compressors, and the electric preheater in Configuration 4 were covered by a photovoltaic panel field. Following the design process, it was determined that Configuration 1 requires a photovoltaic power of 2 kWp (9.6 m²), Configuration 2 requires a photovoltaic power of 0.73 kWp (4.8 m²), Configuration 3 requires a photovoltaic power of 35.5 kWp (172.8 m²), and Configuration 4 requires a photovoltaic power of 11 kWp (54.4 m²). Configuration 3 is characterized by a very high photovoltaic power demand due to the significant electricity consumption of the heat pump compressor. Similarly, the photovoltaic power demand of Configuration 4 is slightly higher due to the electrical consumption of the preheater for the cycle start-up.

4.3. Energetic Evaluation of the Four Configurations

The four configurations presented in the second section will be compared in terms of the specific energy consumption, the gained output ration, and the heat recovery rate. For a fair comparison, the four configurations are considered under the same operating conditions (feed temperature, feed flow, salinity of seawater, vacuum pressure created in the permeate side of membrane, surface and characteristics of the membrane module).

Table 4. Common operating conditions adopted for the energy comparison of the four configurations.

Operational Parameters	Values and Specifications
Solar radiation (W/m2)	985
Feed temperature (°C)	80
Feed flow (kg/h)	2000
Salinity (g/kg)	35 (seawater)
Vacuum pressure (Pa)	7000
Membrane	Type: Hollow fibers Material: PVDF Number of fibers: 806 Module length: 1.129 m Inner diameter: 1.4 mm Thickness of the membrane: 0.4 mm Pore radius: 0.1 μm Permeability at 20 °C: 6.6·10−6 s·mol0.5/m·kg0.5 Tortuosity: 2.1 Total area: 4 m2

presents the common conditions adopted for the four configurations. In fact, a polyvinylidene fluoride (PVDF) membrane was selected for several reasons. PVDF membranes are commonly chosen due to their high liquid entry pressure (LEP), which results from their low surface energy. They also offer good permeability, making them well-suited for vacuum membrane distillation, especially when compared to other commercially available membranes such as PTFE and PP. In addition, PVDF membranes exhibit favorable mechanical strength. However, mitigation strategies are necessary to protect the membrane from fouling, scaling, and wetting, including feedwater pretreatment, chemical cleaning, and control of operating conditions. The membrane used in this study is a commercial membrane purchased as part of a research project, along with the other components that enabled the experimental study carried out in previous years (PALL UMP 3247 R).

A MATLAB R2015a program was established for each configuration, allowing for the prediction of temperature, flow rate, salinity, and pressure at each point of the installation. The modeling of the solar thermal collector field, as well as the hollow fiber membrane module was described meticulously in a previous study [25]. The four configurations were modeled based on the methodology sketched out in Figure 7. An experimental validation of this model was carried out in Figure 8. Both the experimental and theoretical permeate flux profiles exhibit a bell-shaped trend, corresponding to the variation in solar irradiation. The graphical comparison underscores the model’s effectiveness in accurately representing the experimental data. The relative standard deviation was employed to assess the degree of uncertainty between the predicted and observed flux values. Notably, the maximum discrepancy observed did not exceed 10.32%. This deviation is primarily attributed to the inherent challenge of maintaining a stable vacuum pressure throughout the experimental process. Consequently, these pressure fluctuations led to a non-uniform productivity profile within the system. The modeling results, obtained under the conditions specified in Table 4, are illustrated in Figure 9, Figure 10, Figure 11 and Figure 12, corresponding, respectively, to Configurations 1, 2, 3, and 4.

In fact, the design of the components for the four approaches was carried out so that all systems would achieve the same water production under identical operating conditions. However, they differ in solar collector areas, heat exchanger sizes, and pump power requirements. Under the selected conditions (Table 4), all the four configurations ensured the same permeate flux of 0.02 kg/s (72 kg/h) (Figure 7, Figure 8, Figure 9 and Figure 10).

For the first three configurations, water production varies significantly with the saline water temperature, which is directly influenced by solar irradiation. Production follows the typical daily solar profile—gradually increasing in the morning, peaking at noon, and declining toward sunset, eventually reaching zero at night. Consequently, daily water production is higher in summer and lower in winter.

In contrast, for the fourth configuration, the membrane feed temperature is kept constant and does not depend on solar irradiation. This allows the system to achieve higher water production compared to the other configurations.

The developed models enabled the estimation of the average daily water production, which was found to be 539 L/day for Configurations 1, 2, and 3, and 1044 L/day for Configuration 4.

An energy consumption analysis, encompassing both thermal and electrical demands, was performed for the four configurations as shown in Figure 13. The results indicate that the VMD utilizing MVC exhibits the lowest overall energy consumption, purely electrical, at 154.6 kWh/m³. In contrast, the conventional solar VMD, employing a condenser, has a specific SEC of 413.3 kWh/m³, with STEC of 401.8 kWh/m³ and SEEC of 11.5 kWh/m³. The VMD employing the liquid ring vacuum pump shows the lowest electrical energy consumption at 3.5 kWh/m³. However, the highest thermal energy consumption reaches 485.7 kWh/m³. Finally, the VMD system coupled with a heat pump is identified as an energy-saving configuration, with a total energy consumption of 326.1 kWh/m³. Nevertheless, it exhibits high electrical energy demand primarily due to the operation of the heat pump. Considering the system’s reliance on photovoltaic energy and the significant electrical load imposed by the heat pump, it is essential to identify and analyze the main sources of irreversibility to further improve overall energy efficiency. In fact, upon examining Figure 11, it can be observed that stream (#17) represents a significant source of energy loss, which can be quantified through an exergy analysis. Recovering or valorizing this lost energy could substantially enhance the system’s energy performance by increasing productivity and reducing the specific energy consumption. Soumbati et al. [19] conducted a literature review on solar desalination systems using membrane distillation. The studies reported that SEC ranges from 59 to 801 kWh/m³, which is consistent with the values found in the present study. In comparison with the industrial desalination processes, membrane distillation exhibits a significantly higher SEC than multi-stage flash (MSF), multi-effect distillation (MED), and RO, whose SEC typically falls within the ranges of 50–80 kWh/m³, 25–35 kWh/m³, and 3–4 kWh/m³, respectively [30].

Similarly, the four configurations were compared in terms of gained output ratio and heat recovery (Figure 14). The GOR, a key indicator of energy performance in thermal desalination processes, directly reflects the efficiency of energy utilization. It is closely linked to the level of heat recovery. A higher heat recovery rate corresponds to a higher GOR. Conversely, a GOR value below 1 indicates the absence of energy recovery within the system. With reference to Figure 12, the VMD with MVC demonstrates the highest GOR, reaching 5.52, along with the highest heat recovery rate of 54.64%. In contrast, the VMD using a LRVP exhibits the lowest GOR at 1.34 and the lowest heat recovery rate of 4.7%.

4.4. Economic Evaluation of the Four Configurations

Figure 15 presents the results of the capital cost estimation for the four configurations. The calculation was carried out using the equations provided in Table 1 and the design data outlined in Table 2. The results show that for the first configuration, the total capital cost amounts to USD 18,435.5, with USD 8490.5 allocated to the solar thermal collectors (46%) and USD 3939 to the photovoltaic (PV) panels (21.4%). The configuration based on VMD using LRVP is characterized by a total capital cost of USD 15,893.3, including USD 10,210.3 for the solar thermal field and USD 2003.9 for the PV panel array. The VMD coupled with a heat pump presents the highest capital cost, reaching USD 61,202.8, primarily due to the photovoltaic field installation, which alone accounts for USD 44,004.8 (71.9%), and the heat pump unit at USD 11,160.1 (18.2%). Nevertheless, the VMD with mechanical vapor compression (MVC) represents the lowest-cost approach, with a capital cost of USD 14,882.6, owing to its simpler configuration and lower specific energy consumption compared to the other configurations.

As expected, Figure 16 shows that the VMD with mechanical vapor compression (MVC) is the configuration offering the lowest water production cost, at 4.6 USD/m³. The first and second approaches produce freshwater at unit costs of 11.03 USD/m³ and 9.63 USD/m³, respectively. Again, as anticipated, the VMD coupled with a heat pump operating entirely on solar energy exhibits the highest water production cost, reaching 36.4 USD/m³.

According to previous studies, the WPC of the solar membrane distillation systems ranges from 5 to 25 USD/m³. It can reach up to 85 USD/m³ in certain cases [19], depending on the system design and the type of thermal or photovoltaic solar panels used. In comparison, the WPC of solar RO systems typically ranges from 0.1 to 1.8 USD/m³, MSF from 2 to 8 USD/m³, and MED from 0.46 to 3.2 USD/m³. These comparisons indicate that the VMD-MVC system can be considered as a potentially competitive alternative to these mature desalination technologies [19,20,40,41].

While the proposed simulation provides valuable insights into the comparative performance of the four configurations, it is important to acknowledge that one of the main limitations of this study lies in the use of performance and efficiency data for key components such as the membrane distillation module, heat pump, photovoltaic panels, and compressors sourced from existing research. These data were obtained under specific experimental or operational conditions that may not fully reflect those of a fully integrated real-world system. Therefore, a comprehensive experimental validation of the proposed configurations, along with a sensitivity analysis on the performance of individual components (e.g., pumps, compressors), is essential to verify the predicted outcomes and to draw more robust and generalizable conclusions.

The proposed solar-based configuration is particularly adapted to regions with high solar irradiation, such as Mediterranean areas. In countries with lower irradiation, ensuring a stable and cost-effective operation, it would require the support of additional energy sources like wind, biomass, or grid electricity.

5. Conclusions

Vacuum membrane distillation (VMD) is a promising membrane-based desalination technology, although its practical application is limited by low energy efficiency and high energy consumption, primarily due to challenges in recovering the latent heat of vaporization. To address this, four solar-powered heat recovery configurations were designed and evaluated in terms of energy efficiency, specific energy consumption, and production cost. The first configuration utilizes a condenser to recover latent heat for preheating auxiliary seawater. The second employs a liquid ring vacuum pump (LRVP) that simultaneously provides vacuum and condensation. The third integrates a heat pump (HP) using a refrigerant to recover and reuse latent heat. The fourth configuration applies mechanical vapor compression (MVC), compressing the vapor to elevate its temperature for improved heat recovery. All systems operate entirely on solar energy, combining thermal input for feedwater heating and photovoltaic electricity for auxiliary equipment. The results showed that VMD coupled with mechanical vapor compression (VMD-MVC) achieved the lowest specific energy consumption (154.6 kWh/m³), the highest GOR of 5.52, the highest energy recovery rate (54.64%), and the lowest water production cost of 4.6 USD/m³. In contrast, VMD combined with a heat pump (VMD-HP) exhibited the highest WPC (36.4 USD/m³). Although the liquid ring vacuum Pump system was characterized by the lowest electrical power consumption, it suffered from a very low energy recovery rate (4%).