Theoretical Study of a Closed-Cycle Evaporation System for Seawater Desalination

Abstract

This paper presents a numerical study of a closed-cycle evaporation system for the desalination of seawater. The system couples the condensing end of a heat pump with a humidifier, where the air is dehumidified in the heat pump evaporator. First, the mechanism of action of the closed-cycle evaporation system was analyzed from the perspective of heat transfer, and the control equations for the heat and mass transfer of the system were investigated. In addition, a mathematical model of the system was developed and validated. The influence of several important parameters of the air and seawater entering the system on the system’s performance under the design conditions was investigated numerically. The parametric analysis showed that the effect of the seawater mass flow rate on the system’s productivity was not significant. As the air mass flow rate increases, the freshwater production rate increases and then decreases. The output ratio (GOR) of the system was estimated and found to be competitive with other reported HDH systems.

1. Introduction

Socio-economic development and increases in population size have led to an increasing shortage of available freshwater [1,2]. As a cost-effective desalination method, seawater desalination is considered as a sustainable freshwater production technology [3,4].

HDH (humidification–dehumidification) systems mainly consist of a heat source, a humidification unit, and a dehumidification unit [5,6]. Conventional HDH systems which use solar energy are limited by solar radiation [7,8]. Heat pump units are increasingly being used in HDH systems. Heat pump units have the ability to function as both a heating source, providing warmth, and a cooling source, providing coolness [9,10,11].

Dul et al. [12] applied a heat pump to an HDH system and a pilot study was carried out which showed a productivity rate of 287.8 L per day. Faegh et al. [13] integrated a heat pump into a humidification–dehumidification system and evaluated the system’s performance, showing that the application of heat pumps to HDH systems is feasible.

Lawal et al. [14] developed a mathematical model of an HDH system coupled with a heat pump in terms of mass and energy balance and performed a theoretical analysis. Saeed et al. [15] developed a numerical model of an HDH system in order to analyze the influence of the main parameters on the production costs of the system. This provides some theoretical reference for the study of the performance of this type of system under different operating conditions. Zhang et al. [16] first developed an HDH system coupled with a heat pump, which was shown to have a GOR of 2.05 and a freshwater production efficiency of 22.26 kg per hour. Based on this, Zhang et al. [17] developed a mathematical analysis model of the system by analyzing the heat and mass transfer of the various components and used the MOPSO algorithm to optimize the hybrid system. Xu et al. [18] coupled solar energy as an auxiliary heat source with a heat-pump-driven HDH system for drinking water desalination. The pilot study found the maximum production efficiency of the system to be 3.45 kg per kWh. In addition, the study found that how the heat pump is connected to the HDH system affects the performance of the coupled system. Lawal [19] et al. analyzed three different HDH cycle layouts from a cost perspective. The results show that the lowest cost for desalinated water is for the HP-HDH air-to-heat system, followed by the HP-HDH water heating cycle, and finally the E-HDH.

The experimental analysis may be limited by the test conditions, thus preventing the analysis of the system performance under various operating conditions and scenarios. Due to cost and time constraints, experiments cannot provide a comprehensive prediction of the system operation law. Mathematical models replace some of the experiments and allow for a practical analysis of the system’s performance. In order to analyze the performance of HDH systems more accurately and to follow the changes in the operating state of the system, a number of scholars have developed different theoretical models of HDH systems from a thermodynamic perspective. He et al. [20] introduced an HDH desalination system featuring a heat pump unit and conducted a performance analysis of the system’s heat and mass transfer under the design conditions. In the system, the refrigerant mainly transfers heat with the seawater, the heated seawater creates heat and mass transfer with the air in the humidifier, and the remaining heat from the seawater is transferred to the refrigerant in the evaporator. In this system, additional dehumidifiers and cooling water are used, and a certain amount of energy is wasted. Kaunga et al. [21] developed a non-linear model for HDH systems, addressing the limitations of conventional models by proposing a non-linear mechanistic model for the humidification–dehumidification–desalination process with higher predictive accuracy. Their analysis showed that an increase in the inlet water temperature had a positive effect on the productivity of the system, while an increase in the inlet water-to-air-flow ratio had a negative effect.

The excellent research work of the aforementioned authors has promoted the development of heat-pump-driven HDH system technology, especially the theoretical research undertaken.

In this paper, a new, compact, closed-cycle HDH desalination system is theoretically investigated by developing a mathematical model. In this system, the humidifier is combined with the condenser of the heat pump, while the dehumidifier is combined with the evaporator of the heat pump, and the system is more compact. In this study, the goal is to examine a new heat-pump-operated HDH system using a mathematical model and assess its theoretical efficiency. To explain the system’s operation, the mass and energy balance equations of each component are applied. The air mass flow and seawater mass flow are the primary factors that affect the system’s effectiveness once the structural parameters are established. The paper analyzes how these parameters impact the system’s performance as well as its internal state. This research is useful for estimating and evaluating the operating conditions of various sorts of heat-pump-operated HDH systems. In addition, the research provides a better way to popularize desalination technology in remote areas where energy and freshwater resources are scarce.

2. Description

The closed-cycle evaporation system presented in this study was established in Hefei, China [22]. The system consists of humidifiers, two dehumidifiers, and a heat pump unit. The process flow of the system is shown in Figure 1. Figure 2 shows a photograph of the system.The closed-cycle evaporation system contains three media circulations during operation.

There are three media circulations:

• Seawater: Seawater is circulated in the circulation tank and the humidifier. The seawater is sprayed by a circulation pump onto a heat exchange coil inside the humidifier. The water molecules in the seawater absorb heat to form steam, and the remaining seawater participates in the next circulation.
• Air: The circulation fan is installed between the first dehumidifier and the second dehumidifier. Through the suction of the circulation fan, a large amount of air enters from the bottom of the humidifier and is heated and humidified. The nearly saturated air leaves the top of the humidifier and enters the two dehumidifiers where it is cooled and dehumidified, resulting in a large amount of freshwater.
• Refrigerant: The refrigerant is circulated through the humidifier, the second dehumidifier, and the compressor. The heat pump’s condensing end is represented by the heat exchanger coil of the humidifier, where the refrigerant is condensed and gives off heat. Meanwhile, the dehumidifier functions as the evaporating end of the heat pump, wherein the refrigerant gathers heat from the air.

3. Numerical Model

3.1. Sub-Model of the Humidifier

In the sub-model of the humidifier, the heat exchanger coil is simplified. The flow direction of refrigerant is assumed to be vertically downward, parallel to the direction of seawater movement, and the circulating air flows vertically upward. Figure 3 shows the heat and mass transfer analysis unit.

The following assumptions were considered:

(1)

Humidifiers are not affected by external temperature and humidity;

(2)

The nature of seawater is stable;

(3)

The model is in a stable process.

The mass conservation equation for the control body is expressed as:

$$\begin{array}{cc}{m}_k+m_c+m_w+m_a(1+\omega )\hfill & =m_k+d{m}_k+m_c+d{m}_c+m_w+d{m}_w\hfill \\ & +m_a(1+\omega +d\omega )\hfill \end{array}$$

(1)

The conservation of energy equation of the control body is expressed as:

$$\begin{array}{cc}\hfill m_k{i}_k+m_c{i}_c+m_w{c}_{pw}{T}_w+m_a{i}_a& =(m_k+d{m}_k)i_k+(m_c+d{m}_c)i_c\hfill \\ & +(m_w+d{m}_w)c_{pw}(T_w+d{T}_w)\hfill \\ & +m_a(i_a+d{i}_a)\hfill \end{array}$$

(2)

The change in the mass of the refrigerant in the humidifier can be expressed as:

$$d{m}_c=-d{m}_k$$

(3)

The energy change process of the refrigerant in the humidifier can be expressed by the following equation:

$$d{m}_c\left(i_k-i_c\right)=d{Q}_c$$

(4)

$$d{Q}_c=K_o\left(T_k-T_w\right)d{A}_w$$

(5)

The heat transfer coefficient for a coil within the heat exchanger can be determined by utilizing the subsequent formula:

$$K_o=\frac{1}{\frac{1}{{\alpha }_c}\frac{d_w}{d_c}+\frac{\delta }{\lambda }\frac{d_w}{d_m}+\frac{1}{{\alpha }_w}}$$

(6)

The following equation can be used to compute the mass exchange of air within the humidifier:

$$d{m}_a=d{m}_w={\beta }_{aw}\left[{\omega }_{ws}-{\omega }_a\right]d{A}_a$$

(7)

Expressing the relationship between heat transfer and mass transfer, the Lewis factor plays a crucial role as a parameter in the heat–mass transfer process. The empirical equation of the Lewis factor is:

$$L{e}_f={0.865}^{0.667}\left(\frac{{\omega }_{ws}+0.622}{{\omega }_a+0.622}-1\right)/\ln \left(\frac{{\omega }_{ws}+0.622}{{\omega }_a+0.622}\right)$$

(8)

By organizing the above equations, the control equation for the mathematical model of the humidifier is:

$$d{m}_w={\beta }_{aw}\left[{\omega }_{ws}-{\omega }_a\right]d{A}_a$$

(9)

$$\begin{array}{cc}\hfill \frac{d{T}_w}{d{A}_a}& =\frac{-{\beta }_{aw}\left[L{e}_f\left(i_{as }-i_{a }\right)+\left(1-L{e}_f\right)\left({\omega }_{ws}-{\omega }_a\right)i_v\right]}{m_w{c}_{pw}}\hfill \\ & +\frac{K_o\left(T_k-T_w\right)+c_{pw}{T}_w{\beta }_{aw}\left[{\omega }_{ws}-{\omega }_a\right]}{m_w{c}_{pw}}\hfill \end{array}$$

(10)

$$\frac{d{\omega }_a}{d{A}_a}=-\frac{{\beta }_{aw}\left[{\omega }_{ws}-{\omega }_a\right]}{m_a}$$

(11)

$$\frac{d{i}_a}{d{A}_a}=-\frac{{\beta }_{aw}\left[L{e}_f\left(i_{as }-i_{a }\right)+\left(1-L{e}_f\right)\left({\omega }_{ws}-{\omega }_a\right)i_v\right]}{m_a}$$

(12)

$$\begin{array}{cc}\hfill \frac{d{T}_a}{d{A}_a}& =-\frac{{\beta }_{aw}\left[L{e}_f\left(i_{as }-i_{a }\right)+\left(1-L{e}_f\right)\left({\omega }_{ws}-{\omega }_a\right)i_v\right]}{m_a{c}_{pma}}\hfill \\ & +\frac{\left(i_{fgwo}+c_{pv}{T}_a\right)\left[{\beta }_{aw}\left({\omega }_{ws}-{\omega }_a\right)\right]}{m_a{c}_{pma}}\hfill \end{array}$$

(13)

3.2. Sub-Model of the Heat Pump Unit

In this study, the heat pump unit heats the water and cools the air directly. Its energy balance equation is given by:

$$Q_c=Q_e+P$$

(14)

$$Q_c=m_c(i_{c1}-i_{c2})$$

(15)

$$Q_e=m_c(i_{c4}-i_{c3})$$

(16)

When the evaporating and condensing temperatures are determined, the compressor capacity and the required input power can be estimated using a polynomial function provided by the manufacturer. In the equation fitting method, the compressor cooling capacity and heating capacity can be calculated by the following equations:

$$\begin{array}{cc}\hfill Q_e& =c_{e,1}+c_{e,2}{T}_k+c_{e,3}{T}_e+c_{e,4}{T}_k{}^2+c_{e,5}{T}_k{T}_e\hfill \\ & +c_{e,6}{T}_e{}^2+c_{e,7}{T}_k{}^3+c_{e,8}{T}_e{T}_k{}^2+c_{e,9}{T}_k{T}_e{}^2+c_{e,10}{T}_e{}^3\hfill \end{array}$$

(17)

$$\begin{array}{cc}\hfill Q_c& =c_{c,1}+c_{c,2}{T}_k+c_{c,3}{T}_e+c_{c,4}{T}_k{}^2+c_{c,5}{T}_k{T}_e\hfill \\ & +c_{c,6}{T}_e{}^2+c_{c,7}{T}_k{}^3+c_{c,8}{T}_e{T}_k{}^2+c_{c,9}{T}_k{T}_e{}^2+c_{c,10}{T}_e{}^3\hfill \end{array}$$

(18)

$$\begin{array}{cc}\hfill P& =c_{p,1}+c_{p,2}{T}_k+c_{p,3}{T}_e+c_{p,4}{T}_k{}^2+c_{p,5}{T}_k{T}_e\hfill \\ & +c_{p,6}{T}_e{}^2+c_{p,7}{T}_k{}^3+c_{p,8}{T}_c{T}_k{}^2+c_{p,9}{T}_k{T}_e{}^2+c_{p,10}{T}_e{}^3\hfill \end{array}$$

(19)

3.3. Sub-Model of the First Dehumidifier

The calculations of the model take into account the following assumptions:

• Heat radiation losses have been ignored;
• Heat transfer occurs under steady-state conditions;
• The thermal resistance due to fins is neglected;
• The efficiency of the fins under humid conditions is the same as the efficiency of the dry fins;

• The following equation can be used to represent the heat transfer that occurs within the internal heat exchange channels of the first dehumidifier:

$$Q_{1d,n}^{}=K_{1d,n}^{}{A}_{1d,n}^{}\mathsf{\Delta }{T}_{1d,n}^{}$$

(20)

$$Q_{1d,n}^{}=m_a\left(i_{a2}-i_{a7}\right)=m_a\left(i_{a1}-i_{a4}\right)+m_{1d,n}^{}{i}_{1d,n}^{}$$

(21)

$${\omega }_{a1}={\omega }_{a4}$$

(22)

b

The heat exchange in the external heat exchange channels of the first-stage dehumidifier can be expressed as:

$$Q_{1d,w}^{}=K_{1d,w}^{}{A}_{1d,w}^{}\mathsf{\Delta }{T}_{1d,w}^{}$$

(23)

$$Q_{1d,w}^{}=m_a\left(i_{a3}-i_{a7}\right)=m_a\left(i_{a6}-i_{a5}\right)+m_{1d,w}^{}{i}_{1d,w}^{}$$

(24)

$${\omega }_{a5}={\omega }_{a6}$$

(25)

To simulate the first dehumidifier, the ε-NTU approach was employed, which brought forth the ideas of the effectiveness of heat exchange and NTU, a measurement for the number of heat transfer units. The effectiveness of a heat exchanger is defined as the proportion of heat transferred by the exchanger to the total heat that could potentially be extracted from the thermal fluid operating at a given starting temperature.

ε can be expressed as:

$$\epsilon =\frac{Q}{Q_{\max }}=1-\exp \left[{\left(NTU\right)}^{0.2}\left\{\exp \left[-{\left(NTU\right)}^{0.78}\right]-1\right\}\right]$$

(26)

NTU can be expressed as:

$$NTU=\frac{KA}{W_{\min }}=\frac{KA}{m_a{C}_a}$$

(27)

The individual coefficients within the above equation are calculated as:

$$K=\frac{1}{\frac{1}{{\alpha }_l^{}{\eta }_l^{}}\frac{A}{A_l^{}}+\frac{1}{{\alpha }_r^{}{\eta }_r^{}}}$$

(28)

$$\alpha =St{c}_{p}G$$

(29)

$$St=j{\mathrm{Pr}}^{-2/3}$$

(30)

$$\mathrm{Pr}=\frac{c_p\mu }{{\lambda }_{1d}}$$

(31)

$$\ln j=0.103109{(\ln \mathrm{Re})}^2-1.91091(\ln \mathrm{Re})+3.211$$

(32)

3.4. Sub-Model of the Second Dehumidifier

The calculations of the model take into account the following assumptions:

(1)

Heat radiation losses have been ignored;

(2)

The thermal resistance of the fins is ignored;

(3)

The efficiency of the fins under humid conditions is the same as that of the dry fins;

(4)

The evaporation temperature of the refrigerant is constant.

The heat balance equation for a two-stage dehumidifier is:

$$Q_e=m_c(i_{co}^{2d}-i_{ci}^{2d})+m_{2d}{i}_{2d}=m_a(i_{a3}-i_{a4})$$

(33)

3.5. Validation

In order to verify the mathematical model of the closed-cycle evaporation system, the working conditions in the test were selected and calculated by the mathematical model.

Table 1. Comparison of the mathematical model simulation results and the experimental results of the closed cycle evaporation system.

Parameters	Unit		Condition 1	Condition 2	Condition 3	Condition 4
Ta2	°C		51.70	51.30	51.50	51.90
ωa2	g/kg		86.48	79.39	87.00	85.51
mw	kg/s		8.89	8.89	9.45	7.78
Ma	kg/s		3.50	3.80	3.50	3.50
Ta1	°C	Exp.	43.40	42.30	44.00	42.50
	°C	Num.	42.90	41.05	44.10	42.30
	%	Deviation	1.15	2.96	0.23	0.47
ωa1	g/kg	Exp.	15.25	14.30	15.30	14.70
	g/kg	Num.	14.80	14.20	14.80	14.20
	%	Deviation	2.95	0.70	3.27	3.40
ia1	kJ/kg	Exp.	83.75	80.10	84.60	81.46
	kJ/kg	Num.	82.10	78.60	83.40	79.19
	%	Deviation	2.01	1.91	1.44	2.87
Ta4	°C	Exp.	20.60	20.20	20.70	20.10
	°C	Num.	20.27	19.27	20.67	19.90
	%	Deviation	1.60	4.61	0.16	1.00
mf	g/s	Exp.	249.30	245.18	250.81	247.84
	g/s	Num.	250.88	247.72	252.70	249.59
	%	Deviation	0.63	1.03	0.75	0.70

displays a comparison between the mathematical model calculations and the experimental data. By analyzing the table, it can be seen that the maximum deviation of temperature is 4.61%, the maximum deviation of moisture content is 3.27%, the maximum error of total productivity is 1.03%, the errors are within 5%, and the errors of the model results and test data are acceptable. Therefore, the calculation platform of the closed-cycle evaporation system is reliable and can be used for theoretical analysis.

3.6. Calculation Process

A balance exists between the evaporation of seawater in the humidifier, the freshwater discharge from the first dehumidifier, and the freshwater discharge from the second dehumidifier. The extent of the evaporation of seawater in the humidifier impacts the heat exchange at the condensing end of the heat pump unit. This, in turn, affects the cooling capability at the evaporating end of the heat pump unit, as well as the freshwater discharge and GOR of the entire system. Therefore, when analyzing the system’s performance using a mathematical model, the first step is to analyze and calculate the humidifier model as the core component.

Only one parameter was changed under any working condition, and the other parameters were kept at their reference values. The reference values and variation range of each key parameter are shown in

Table 2. Parameters under the condition of a fixed structure and variable working conditions.

	mw (kg/s)	ma (kg/s)	Ta5 (°C)	φa5 (%)	φa2 (%)
Reference values	9	3.6	20	65	95
Interval	7.5~10.5	2.8~4.2

. The refrigerant is R134a, whose physical parameters can be found through REFPROP 7.0. In the mathematical model calculation, the characteristics of the seawater are assumed to be the same as those of pure water. In comparison to the power consumed by the heat pump unit, the power utilized by the pump and fan is relatively insignificant. As per the recorded data from the tests, the power consumption of the pump and the fan is approximately 10% of the power consumed by the heat pump unit, and this consumption is considered in the mathematical model.

In actual working conditions, it is difficult for the air state at the outlet of the humidifier to reach just a saturated state. However, if the condensing heat of the refrigerant is not ultimately released, the operational stability of the system will be significantly affected. The purpose of the simulation study is to explore the operation of the closed-cycle low temperature evaporation system under different operating parameters; therefore, in this simulation process, only the humidifier outlet air is not saturated (assuming that the relative humidity of the outlet air is 95%).

The system’s design was implemented by considering different values of the mass flow rate of seawater and air for certain operating conditions, as shown in Figure 4. The main reason for studying the influence of these values on the system’s design is that variations in these parameters can affect the heat transfer rate of the heat pump and therefore the heat transfer efficiency of the overall system.

3.7. Evaluation Indicators

The GOR (gained output ratio) was introduced to evaluate the energy consumption of the closed-cycle evaporation system.

$$GOR=\frac{m_f{h}_f}{W}$$

(34)

4. Discussion

The closed-cycle evaporation system has fixed parameters for its components, whereas the system’s performance is primarily influenced by the air mass flow rate and the seawater mass flow rate. In order to assess the system’s productivity and GOR, the impact of these parameters was studied. Moreover, changes in these parameters were analyzed with respect to their effect on the internal air state of the system.

4.1. Seawater Mass Flow

By varying the speed of the seawater pump, the seawater mass flow can be adjusted. Figure 5 shows the effect of seawater mass flow on freshwater production and the GOR. During this calculation, the ambient air condition at the inlet of the radiator fan was (T_a5 = 20 °C, RHa5 = 65%).

Figure 5 demonstrates the small effect of variation in the seawater mass flow on the performance of the closed-cycle evaporation system. The seawater film completely covers the heat exchanger coil during the simulation calculations. The variation in the seawater circulation flow rate has a negligible effect on the individual parameters within the mathematical model.

The charge of sparkling water waft in the closed-cycle evaporation system is extensively impacted by the water evaporation manner in the humidifier. Additionally, a detailed analysis was performed to recognize the alteration within the circumstance of the air gift inside the humidifier.

The change in the seawater mass flow mainly affects the state of the water film in the heat exchanger coil. As can be seen in Figure 6 and Figure 7, there is a slight increase in the temperature and enthalpy of the air inside the humidifier. The increase in seawater mass flow contributes, to a certain extent, to the rate at which the air absorbs heat inside the humidifier. As the seawater mass flow rate increases, the temperature and enthalpy of the air at the humidifier inlet increase by 0.8% and 4%, respectively, and the temperature and enthalpy at the humidifier outlet increase by 0.7% and 1.7%, respectively. The state of the air inside the system is stable during the change in the seawater mass flow rate.

4.2. Air Mass Flow

During this calculation, the ambient air condition on the inlet of the radiator fan is (T_a5 = 20 °C, RHa5 = 65%). Figure 8 illustrates the version of the device’s freshwater along with the flow and the GOR for the different air mass flow values. The effect of air mass flow on freshwater manufacturing rates is illustrated in Figure 8. The increase in air mass flow will increase the performance of the warmth and mass switch inside the humidifier. The increase in air mass flow will increase the humidity distinction and enthalpy difference between the circulating air and the floor of the warmth exchanger coil. As the air mass flow continues to increase, the temperature distinction between the seawater and the refrigerant and the temperature difference between the seawater and the circulating air continues to decrease, the warmth and the mass switch efficiency are affected, and the freshwater flow fee and the GOR generally tend to stabilize.

The heat generated by the condensation of the refrigerant in the humidifier is first transferred to the water film wrapped around the outer wall of the tube, and then the heat is transferred to the air. The increase in the air mass flow rate increases the humidity and enthalpy difference between the surface of the water film and the air, accelerating the efficiency of heat mass transfer between the water film and the air. Figure 9 demonstrates that an increase in the air mass flow rate leads to an increasing temperature and enthalpy of the air at the humidifier inlet. Figure 10 shows that the increase in the air mass flow rate reduces the temperature of the air at the humidifier outlet, but the enthalpy of the air increases. The increase in the air mass flow rate not only increases the efficiency of heat and mass transfer between the air inside the humidifier and the water film outside the heat transfer coil but also reduces the time for heat mass transfer between the air and the water film. The change in air enthalpy is mainly influenced by the latent heat exchange between the air and the water film. The increase in air mass flow promotes the evaporation of the water film, resulting in a higher enthalpy of air leaving the humidifier and a higher share occupied by latent heat transfer, which means that the share occupied by sensible heat transfer is reduced. The change in air temperature is mainly related to the sensible heat exchange between the air and the water film, with the sensible heat transfer occupying a lower share of the heat transfer, resulting in a lower temperature for the air leaving the humidifier. Although the air leaving the humidifier has a lower temperature, its enthalpy is higher, and the heat transfer within the first-level dehumidifier occupies only a smaller share of its heat. When the air with higher enthalpy enters the secondary dehumidifier and releases most of its heat, the air leaving the secondary dehumidifier is saturated. Based on the assumption that the cooling capacity of the compressor in the secondary dehumidifier is constant, the air with the higher enthalpy is relatively hot after it has released heat in the secondary dehumidifier. The main driver of heat transfer within the primary dehumidifier is the temperature difference, but the air leaving the humidifier only accounts for a smaller share of the heat released within the secondary dehumidifier; in addition, according to the control equations for the secondary dehumidifier, an increase in the air mass flow rate increases the heat transfer efficiency of the secondary dehumidifier, ultimately leading to an increase in the temperature and enthalpy of the air entering the humidifier.

4.3. Performance Comparison between the Current System and Other Systems

Following analysis, the maximum value of the GOR simulated for the system in this study was 4.1. Some of the reported performance parameters for other desalination systems are listed in

Table 3. Comparison of different systems.

Researchers	Heat Source	Maximum Productivity	GOR
Xu H. et al. [9]	Solar-assisted heat pump	20.54 kg/h	2.42
Wu G. et al. [11]	Solar	182 kg/h	2.65
Liu Z.H. et al. [23]	Solar	2.138 kg/(h∙m2)	2.5
Behnam P. et al. [24]	Solar	6.275 kg/(day·m2)	-
Rahimi-Ahar Z. et al. [25]	Solar	1.07 kg/(h·m2)	3.43
Zubair M.I. et al. [26]	Solar	19,445 kg/year	2.6
Lawal D.U. et al. [14]	Heat pump	287.8 kg/day	4.07
He W.F. et al. [19]	Heat pump	82.12 kg/h	5.14
Shafii M.B. et al. [27]	Heat pump	2.79 kg/h	2.08
Current study	Heat pump	852~867 kg/h	4.16~4.24

. The proposed system is ahead of most desalination systems in terms of freshwater productivity per unit of time and has very competitive production costs.

5. Study Limitations and Challenges

In this paper, the performance of a closed-cycle evaporation system consisting of a specific compressor and fixed-size humidifiers and dehumidifiers was investigated. In the operation of the model system, the study was limited mainly by considering the constant isentropic efficiency of the compressor and the constant saturation temperature of the refrigerant. In future research, variation in the system’s performance under operating conditions with non-fixed size components should be investigated.

6. Conclusions

This paper presents a numerical simulation study of a closed-cycle evaporation system driven by a heat pump. A mathematical model of the system was developed, and its effectiveness confirms that the mathematical model can be used for the theoretical evaluation of closed-cycle evaporation systems. In the context of the mathematical model, the influence of different parameters on the performance of the closed-cycle evaporation system was analyzed. The productivity and GOR of existing systems were evaluated and compared with other systems.

(1)

Variations in the seawater mass flow rate did not significantly improve system productivity, and there was no significant effect on system performance.

(2)

As the air mass flow rate increased, the overall heat and mass transfer efficiency of the system improved significantly, and the system’s productivity improved significantly.

(3)

The productivity of the system was 852~867 kg/h. The GOR of the system is estimated to be 4.16~4.24.

(4)

The system is competitive when compared with other systems.

(5)

The mathematical model developed in this paper provides theoretical support for the optimization of the system. The system is a closed system, and the field of application should not be limited to desalination. The system can be tested and applied in the field of wastewater treatment.