Introduction

As we know, one of the future crises of modern humanity to survive on this planet is a shortage of fresh water for consumption [1]. More than 2/3 Earth is made up of water, but unfortunately, 94% of it is the ocean and ocean water that is non-drinkable saline water [2]. Only 3% of the total freshwater of world water can be used, which is often found in polar fridges and ground springs [3]. As we have seen, the high potential of salt water in the world has led humans to sweeten this water and turn it into drinkable water. The processes of desalinating work according to the principle of energy. Which are classified into two classes; First, Temperature processes involving phase change. Second, Membrane processes, including pressure energy. Thermal processes are classified into several categories such as; multi-stage evaporation (MEE), multi-stage flash (MSF) and Compressed vapor (VC). Also, Membrane processes are classified into several categories; Reverse Osmosis (RO) and Electro Dialysis (ED) [4]. To analyze the systems of desalination, Rautenbach examined general desalination system and made it possible to use it in different scales [5]. Morin compared the multi-effect desalination and multi-stage flash systems and found some impressive results. He concluded that the multi-effect desalination system has advantages such as lower initial cost and less cost-performance, and it has fewer problems than a multi-stage flash system [6].

Rashidi et al. performed the thermodynamic analysis of the COP cycle. Also, they used the first and second law to analyze system performance and observed that there is a linear relationship between the specific heat of the operating fluid and its temperature [7, 8].

Sheikholeslami et al. focus on the effects of a magnetic field and thermal energy on hydrothermal Fe3O4eH2O and the CuOeH2O nanofluid. The solution of final equations obtained by CVFEM for different values of Darcy numbers (Da), and Reynolds number (Re). Also, they worked on latent heat thermal energy storage systems (LHTESS) to save thermal energy. The results show that by adding CuO nanoparticles to pure PCM, the compression process increases [9, 10]. In the other researches, three-dimensional porous cavities with magnetic field effect were investigated. They used the Lattice Boltzmann method and observed that the degree of gradient had a direct relationship with Darcy Number and Reynolds number [11,12,13]. He also researched CuO nanoparticles and found that using nanoparticles are an excellent way to accelerate the process of charging and full energy increasing [12, 14, 15]. He also studied on the heat transfer of the nanosilver (cooled) under thermal effect radiation researched and total energy, average temperature, isotherm, and solids [16,17,18,19,20,21,22].

Javadi et al. studied a mathematical model with a nominal capacity of 500 MW. This study was carried out using three-way optimization method. They also simulated a conventional hybrid cycle unit in Iran using a mathematical approach. Sensitivity analysis was performed on environmental emissions and electricity prices, exergy efficiency, CO2 emissions, and production costs were assessed [23, 24].

Hoseinzadeh et al. [25] studied thermal energy and economic analysis of zero-energy buildings in the humid mountainous area. In this regard, a residential building was used as a typical condition. And the energy efficiency and cost parameters were investigated [26, 27]. The research method in this study is based on two principles and MATLAB software was used. According to the results, 80% of the amount of electrical energy used for air conditioning in the building and repelled from 34 to 7 MW. In the case of return on investment (R0I), the electricity needed to generate, and the cost can be about $ 15,000 a year [28,29,30,31,32].

The study conducted by Gonda et al. [33] was also useful to get the flat-plate flatwork. In their research, the empirical results of evaporation indicated the film of falling water on a galvanized sheet. This module has consisted of stainless steel, which has a total heat and a thermal area of 0.267 m2 which has been tested.

Elsafi et al. [33] studied the humidification-dehumidification desalination and concentrated photovoltaic-thermal collectors and analyzed them in terms of energy and exergy-costing. Elsayed et al. [34] investigated the exergo-economic study of the MED system operating on a steam-compressor unit MED-MVC. The results showed that the production amount is 1500 m3/day, and the efficiency of the second law is 2.8%.

Olatayo et al. [35] studied wind systems in South Africa and concluded that although much energy is wasted and cannot be used by wind turbines, small-scale wind technologies can be used alongside government programs. It is considered economical and should, therefore be evaluated for its potential use in energy and economics. The possibility of using these cysts has also been evaluated in various parts of the country, and the low efficiency and low energy produced by this technology are the reason why it has not been used and developed.

As well as Zheng et al. [36] explored the feasibility of using the wind system in New Zealand and tracked environmental risk and cost factors.

Tovar et al. [37] also examined how the food–water–and energy cycles are connected, and proposed a new policy for connecting and evaluating this cycle.

For the thermodynamic analysis of wind energy systems, Hu et al. [38] conducted an exergy and energy analysis of wind systems and investigated the effect of factors such as wind speed, pressure, temperature and humidity rate on the efficiency of the system and the results showed Although the amplitude of the wind speed affects the performance of the system, the other factors mentioned have a high impact on the performance of the system and provided the effect of these factors. Asensio1 et al. [39] Study was carried out to achieve the equations of desalination systems operating on wind energy. In this study, they investigated the economic analysis of the reverse osmosis desalination plant system, which, by adding wind energy to the system, reduced the cost of fresh water production to 0.022 EUR m−3.

In order to obtain information on the use of solar and wind energy in the reverse osmosis Desalination work with Mitoa et al. [40], In this study, they examined the system’s strategic, functional and control settings, and ways to demonstrate system adaptability for renewable energies.

Agha et al. [41] consider the optimization of pool size and the number of steps for three different storage area temperatures. One consequence is that excessive quantity will lead to the rejection of some heat accumulated during the summer. The sensitivity analysis of the various factors affecting water costs shows that capital costs account for about 80% of total expenses and costs of the SP/MSF will be around 13–10% [42].

Kaldellis et al. [43] investigate the economic viability of desalination. The proposed analysis of all cost parameters is considered. These costs include the initial cost of the desalination plant, the annual cost of maintenance and operation, the cost of energy consumption, the capital cost index, and the associated inflation rate. The results show that the RES-based desalination system is the most promising and sustainable method for supplying fresh water and drinking water.

Then Kavvadias et al. [44] present a method for maintaining the high standards and reliability of some economic models. Sensitivity analysis was used to identify the most critical parameters in the DEEP model. This review proves that the DEEP economic model is entirely appropriate. Nisan et al. [45] a detailed analysis of the cost and cost of water for several nuclear reactors operating in one operation is presented. It has been presented and shown in particular, how to reduce desiccant costs by the use of micro-heat.

Ejli et al. [46] presents a comparative study of water cost for three cities in southern Morocco using two desalination processes: reverse osmosis and steam compression. Sources provide energy requirements: grid and wind energy and therefore, four combinations of desalination processes are considered in the assessment of desalination cost. An economic analysis of the main effects of the parameters related to the cost of produced water level is also presented.

Choi et al. [47] presented the new economic feasibility study for several methods and the feasibility and costs of chemical treatment. In the other same work, zou et al. [48] presented Economic effects analysis of seawater desalination in China with input–output technology. In this paper, five different configurations of a seawater desalination system using photovoltaic are studied. Plus a case study of an island in Greece was investigated. The present study shows that seawater reverse osmosis with photovoltaic energy and desalination unit, which includes water storage, is a low capacity battery. Filippini et al. [49] presented Design and economic evaluation of solar-powered hybrid multi effect and reverse osmosis system for seawater desalination. In this study, the feasibility of connecting a desalination plant to a solar photovoltaic (PV) field to produce electricity at a low cost and in a sustainable manner was investigated. And a detailed mathematical model for the PV system is presented. Information on four locations, namely Isola di Pantelleria (IT), Las Palmas (ES), Abu Dhabi (United Arab Emirates) and Perth (AUS) have seen used economically. It has examined the feasibility of installing the proposed plant, especially the solar PV farm at these four locations.

In this research, after studying different types of desalination systems and governing their equations, the energy consumption evaporative vacuum easy desalination system is modeled. After modeling, the energy consumption of new subsets such as the evaporator, condenser, vacuum pump, and other new pumps are presented. Since this system is home-sized, it is instrumental. And it can be used in any part of the world that has problems with access to unsafe water. On the other hand, the economic issues governing desalination systems are studied. Especially, desalination with brain thank system that the economy of this system and It is based on the cost of water production is analyzed. In the end, the economic analysis is obtained with three important cities (Abu Dhabi, Las Palmas, and Perth) in the world, and we compared them.

Desalination system modeling

The system consists of two heat exchanger and the type of heat exchangers are plate. The amount of heat transfer of them are 0.72 m2 and each one can be divided into two sub-sections. The first part is the heating and steam section, which consists of two heating and evaporator sections. In the cooling section, the cooling unit is consisted of two sub-sections of cooling and condenser.

The heating cell, the evaporating cell, the cooling cell and the brine tank are known as an evaporative desalination system. Also, the condenser cell and vacuum pump and the heater unit and the other pumps are each introduced separately as a system and examined in economic analysis. The schematic form of this evaporative desalination system with the vacuum brine tank is given in Fig. 1.

Fig. 1
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Schematic of the evaporative vacuum domestic desalination system with Brine tank

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Each of the system subsets are described as following.

Heating system

In the heating section, the heating cell has an environmental pressure, and the hot water entering into the temperature of 70 °C has a warming effect. The required amount of heating to evaporate the water by rotating this hot water is provided

In the evaporator section, the pressure is reduced by a vacuum pump and reaches to 12 mbar that causes the evaporation temperature of the water to decrease and reaches an approximate 49.6 °C. In this section, the feeding water is entered into the brine tank at first and after mining, it is pumped into the set, the top-of-the-range distribution system supplies this entry. A portion of the water is evaporated, and it is entered into the condenser. And pump removes the amount of water that does not evaporate as brine from the set and enters into the brine tank and needs its heat into the feeding water.

Brine tank of system

In the tank, the concentration of feed water is measured in each stage after mixing with brine water by concentration gauge. This concentration gauge is connected to the brine tank next to the sewage valve. If the concentration of feed water were higher than the permitted limit, it would be removed from the system as wastewater, and if it had low salt concentration, it would re-enter into the system and run the cycle.

Cooling system

In the cooling section, the cooling unit consists of two sub-sections of cooling and condenser. The cooling system is provided by the tap water supply, which causes the surface temperature of the metal between two parts equal to the tap water temperature. The amount of the evaporated water in evaporator section is introduced the condenser by holes. And it is condensed on this flat metallic surface and is removed from the cell by a pump.

Vacuum pump of system

The vacuum pump is used to reduce gas pressure in a given volume, in other words, to minimize gas density. Therefore, it is necessary to remove gas particles such as air from the volume to be vacuumed. In this system, the vacuum pump reduces the pressure in the evaporator and condenser cells and the brine tank to 12 mbar. Of all types of vacuum pumps, Oily rim pumps are selected because they are suitable for water vapor and water vapor and can supply the required pressure [50, 51].

Other pumps of system

The other pumps in the system are conventional pumps that we use for such things as rotating the heating water, draining the fresh water and entering and rotating the feed water.

The values of fluid discharge in rotation within the system are presented in Table 1. Plus, the amount of fresh water produced by the system is approximately 21 L h−1.

Table 1 Fluid flow values in system rotation
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Energy and economic analysis

In order to achieve the economic modeling of this system, we first obtain the energy consumption equations for each of the subsets, then present the economic equations governing the system. The energy equations governing each subset of the system are presented in Tables 2, 3, and 4.

Table 2 The energy equations governing of heater and evaporator
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Table 3 The energy equations governing of Brine tank and condenser
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Table 4 The energy equations governing of vacuum pump and other pump
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The decision parameters for modeling of the system are presented in Table 5.

Table 5 The decision parameters for modeling this system
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After obtaining the energy consumption of each of the system subsystems, we perform a system economic analysis and obtain the governing equations of the system. The economic equations of the system are presented in Table 6. These equations are taken from paper [49].

Table 6 Economic equations of the system
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The decision parameters for economic modeling of the system are presented in Table 7. Some of these values are taken from the paper [49].

Table 7 The decision parameters for economic modeling of the system
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After economic simulation and achieving the economic equations of the evaporative vacuum domestic desalination system, it is concluded that one of the most important pillars in economic analysis is the electricity price system since it has a vacuum pump to supply the vacuum governing the system. However, other factors such as the incoming feed water temperature and the salt concentration are also unaffected.

The following research examines the feasibility of using this system in three locations around the world. These three points include Las Palmas. Abu Dhabi, Perth. The input variables for economic analysis at these three points are presented in Table No 8. As mentioned earlier, this system is home-based and portable and can be provided anywhere in the world with freshwater scarcity problems if provided. If applicable, be used.

Result

Abu Dhabi

Abu Dhabi city is situated on an island in the Persian Gulf off the central western coast, while the majority of the city and Emirate reside on the mainland connected to the rest of the country. As of 2019, Abu Dhabi’s urban area has an estimated population of 1.45 million people.

Abu Dhabi is one of the cities facing water problems and also has good groundwater levels and therefore has high potential to use this evaporative vacuum domestic desalination system with Brine tank. The details of this city are presented in Table 8. The economic analysis results for this city show that the cost of freshwater is equal to 0.719,360 M€ yr−1. The price of other influential economic factors are reported in Table 9.

Table 8 The input variables for economic analysis
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Table 9 Result of economic analysis of Abu Dhabi
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Las Palmas

Las Palmas is located in the northeastern part of the island of Gran Canaria, about 150 km off the Moroccan coast in the Atlantic Ocean. Las Palmas experiences a hot desert climate. This city also suffers from a water problem. Also. This city has the potential to use evaporative vacuum domestic desalination system with brine tank. The details of this city are presented in Table 8.

The results of economic analysis for the city show that the cost of fresh water is equal to 0.1047674 M€ yr−1. Costs other effective economic factors are reported in Table 10.

Table 10 Result of economic analysis of Las Palmas
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Perth

Perth is part of the South West Land Division of Western Australia, with the majority of the metropolitan area located on the Swan Coastal Plain, a narrow strip between the Indian Ocean and the Darling Scarp. The first areas settled were on the Swan River at Guildford, with the city’s central business district and port (Fremantle) both later founded downriver. This city also suffers from a water problem and has the potential to use evaporative vacuum domestic desalination system. The details of this city are presented in Table 8.

The results of economic analysis for the city show that the cost of fresh water is equal to 0.670097 M€ yr−1. Costs other practical economic factors are reported in Table 11.

Table 11 Result of economic analysis of Perth
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Besides, to compare the cost of using this system in different cities, the following diagrams are presented. Figure 2 shows the annual operating cost amount used to generate electricity in pumps (conventional pumps and vacuum pumps). This figure is presented to compare these three cities. The cost of generating electricity at pumps covers a large proportion of annual operating expenses. This system has a vacuum pump which has to supply the vacuum of the system and therefore has high power consumption.

Fig. 2
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Annual cost of power & vacuum pump

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As can be seen in Fig. 2, Las Palmas has the highest electricity cost for pump use, which is due to the high cost of electricity in the city. Perth has the lowest cost of pumps because it has the lowest electricity cost. On the other hand, Fig. 3 compares the annual operating cost of the desalination system in these three cities. As can be seen in Fig. 3, Las Palmas has the highest annual operating cost. Also, Fig. 4 is presented to compare the final annual cost of fresh water production by this evaporative desalination system in these three cities

Fig. 3
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The annual operating cost

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Fig. 4
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The total annual cost

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As shown in Figs. 2–4, it can be recognized that Perth and Abu Dhabi are less costly to produce fresh water than the Las Palmas. This fact indicates that this new easy desalination system can be used and cost-effective because of the low cost of electricity in these cities.

Conclusions

In this study, complete modeling of the new evaporative vacuum easy desalination system with brine tank was introduced. All components and sub-systems such as pumps are modeled. In terms of energy consumption, the economic feasibility of the system is examined. So, the economic equations of this system and its components were presented. Three critical cities provided the following information from different parts of the world (Abu Dhabi, Las Palmas, and Perth) with different characteristics. The results have shown that the annual operating cost of the pumps was estimated to be 0.19 M€ yr−1, 0.51 M € yr−1 and 0.14 M€ yr−1 for Abu Dhabi and Las Palmas and Perth respectively.

Additionally, the annual cost of fresh water production is compared with each other in the three cities. The results is confirmed that Perth had the lowest cost of fresh water production at 0.67 M€ yr−1. Las Palmas has the highest cost of fresh water production at 0.104 M€ yr−1. The reason is the difference in electricity prices in these two cities.