Reverse electrodialysis heat engine with helium-gap diffusion distillation: Energy efficiency analysis

Abstract

The depletion of energy resources poses a significant threat to the development of human society. Specifically, a considerable amount of low-grade heat (LGH), typically below 100 °C, is currently being wasted. However, efficient utilization of this LGH can relieve energy shortages and reduce carbon dioxide emissions. To address this challenge, reverse electrodialysis heat engine (REDHE) which can efficiently convert LGH into electricity has emerged as a promising technology in recent years. Extensive efforts have been dedicated to exploring more suitable thermal distillation technologies for enhancing the performance of REDHE. This paper introduces a novel REDHE that incorporates helium-gap diffusion distillation (HGDD) as the thermal separation (TS) unit. The HGDD device is highly compact and efficient, operating at a normal atmospheric pressure, which aligns with the operational conditions of the reverse electrodialysis (RED) unit. A validated mathematical model is employed to analyze the impacts of various operating and structural parameters on the REDHE performance. The results indicate that maintaining a moderate molality of the cold stream, elevating the inlet temperatures of hot and cold streams, lengthening hot- and cold-stream channels, and minimizing the thickness of helium gaps contribute to improving the REDHE performance. Especially, a maximum energy conversion efficiency of 2.96% is achieved by the REDHE when decreasing the thickness of helium gaps to 3 mm and increasing the length of stream channels to 5 m.

Key words： helium-gap diffusion distillation (HGDD); reverse electrodialysis (RED); heat engine; low-grade heat (LGH)

1 Introduction

The challenges posed by energy scarcity and the greenhouse effect necessitate a reevaluation of the current energy utilization pattern in order to address them effectively. One specific area of concern pertains to the abundant amount of low-grade heat (LGH) generated at temperatures below 100 °C (accounting for 63% of the total global waste heat [1], and 66% of the total waste heat in China [2], which is often disregarded due to its relatively low energy grade. However, if efficiently utilized, it has the potential to enhance overall energy utilization efficiency of human beings and subsequently reduce carbon dioxide emissions. In recent years, reverse electrodialysis (RED) heat engine (REDHE) has emerged as a promising and increasingly popular technology for harnessing LGH and converting it into electricity. The operational principle of REDHE involves two key components, the thermal separation (TS) unit and the RED unit [3], as illustrated in Fig.1. Initially, a brackish solution is introduced into the TS unit where it undergoes a separation process driven by the LGH [4]. This process results in the formation of a high-concentration (HC) solution and a low-concentration (LC) solution. Subsequently, these two solutions are pumped into the RED unit where they are used to generate electricity.

Fig.1 Schematic diagram of REDHE.

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The TS unit of REDHE exhibits a high level of flexibility. Luo et al. [5] proposed a REDHE, i.e., thermal-driven electrochemical generator (TDEG), which adopted a distillation column as the TS unit. They primarily focused on investigating the potential of ammonium bicarbonate (NH₄HCO₃) solutions for electricity generation in TDEG. The results indicated that the ionic flux and energy efficiency of the RED stack employing NH₄HCO₃ solutions could respectively reach 88% and 31% under the optimal condition. Regrettably, relevant studies concerning the whole performance of the REDHE were not conducted in their work. Giacalone et al. [6] constructed the first world laboratory-scale REDHE which consisted of a stripping column as the TS unit and a RED unit. They operated the REDHE for up to 55 h to demonstrate its feasibility and stability, and the highest exergy efficiency of it was equal to 1.1% for the case of 0.05−1.9 mol/L NH₄HCO₃ solutions. Long et al. [7] adopted membrane distillation (MD) as the TS unit which was combined with a RED stack to form a REDHE, and the whole performance of it was investigated. The results showed that a larger MD feed sodium chloride (NaCl) concentration induces a greater electrical efficiency which reaches 1.15% operating between 20 and 60 °C with the MD feed NaCl concentration of 5 mol/kg. Micari et al. [8] provided a perspective analysis for MD-RED heat engine, and the energetic efficiency of the REDHE could reach to 2.8% (corresponding to the exergy efficiency of about 16.5%) when highly performance RED membranes and future MD module were employed. Tamburini et al. [9] integrated a multi-effect distillation (MED) system with the RED stack to create a MED-RED heat engine. They employed a simplified model to analyze the performance of the REDHE and determined that the current state-of-the-art performances of RED and MED could achieve a maximum energetic efficiency of 5%. Hu et al. [10] presented a comprehensive thermodynamic analysis of a MED-RED heat engine, revealing that the system could achieve an energy conversion efficiency of 1.01% when the effect number of MED was set to 10. Palenzuela et al. [11] conducted a performance analysis on a MED-RED heat engine, obtaining a maximum thermal efficiency of 1.4% for the case of current membranes and up to about 6.6% thermal efficiency assuming ideal membrane properties. Ortega-Delgado et al. [12] performed an extensive exergy analysis on a REDHE with MED and identified the MED unit as the primary source of exergy destruction, resulting in an overall exergy efficiency of 24% for the REDHE when high-performance membranes were utilized. They also boosted the performance of the MED-RED heat engine, and the maximum thermal efficiency of the REDHE reached 9.4% by employing potassium acetate solution and adopting high-performing ion-exchange membranes (IEMs) [13]. Olkis et al. [14] integrated adsorption desalination (AD) with RED stack in REDHE and investigated the efficiencies of 277 salts and 10 adsorption materials, achieving an exergy efficiency of up to 30% for the REDHE. After that, they [15] implemented simulation analyses on different heat integration scenarios for the REDHE using validated models for both RED and dynamic AD based on experimental data, demonstrating that the exergy efficiency could reach up to 15%, while its energy efficiency could reach up to 0.55%. Liu et al. [16] employed a generator as the TS unit of REDHE, and simulated the REDHE system adopting lithium bromide (LiBr) solution as working fluid by Aspen Plus® 11. They found that under respective conditions, the maximum energy efficiency achievable by this particular configuration was determined to be around 6.05%. Afterwards, they experimentally investigated its performance through a laboratory-scale REDHE [17]. However, the results showed that the actual energy efficiency of the REDHE approached to 0%, which extremely deviated from the theoretical result mentioned above. Besides, they conducted a prospect analysis, which indicated that the energy efficiency of the REDHE had a capacity to reach 2.6% by employing IEMs with high permselectivity under high concentration conditions.

Numerous endeavors have been dedicated to exploring more suitable TS technologies for enhancing the performance of REDHE. However, the aforementioned TS technologies exhibit either limited efficiency or necessitate operation under negative pressure, thereby impeding further advancements in the energy conversion efficiency of REDHE. In the study described in this paper, a novel distillation technique named helium-gap diffusion distillation (HGDD) was employed in combination with multi-stage RED (MSRED) to create the HGDD-MSRED heat engine, as illustrated in Fig.2. The principle of the HGDD can be found in Hu et al. [18].

Fig.2 Schematic diagram of HGDD-MSRED heat engine. AEM, anion-exchange membrane; CEM, cation-exchange membrane.

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The suitability of the HGDD as the TS unit of REDHE is further supported by the fact that HGDD operates under normal atmospheric pressure, which aligns with the operation condition of the RED unit. Consequently, unlike MED [12–13,19], AD [14], and vacuum-assisted air-gap membrane distillation (V-AGMD) [8], the HGDD system does not require pressurization of the LC and HC solutions to atmospheric pressure using a booster pump, resulting in significant energy savings. The HGDD device is highly compact and efficient, developed based on the principle of air-gap membrane distillation (AGMD) [20–22]. The main structural feature of HGDD compared to AGMD lies in the elimination of hydrophobic membranes, thereby eliminating the resistance to water vapor transfer across the membranes. Additionally, filling the gaps of HGDD with helium gas (which has a higher thermal conductivity and water diffusion coefficient compared to air) enhances the heat and mass transfers within the system [18], replacing the need for a vacuum pump [23] or rotating fans [24] as used in AGMD. Additionally, the incorporation of MSRED into the REDHE was implemented to augment its performance. It is well known that MSRED exhibits a superior capacity in capturing salinity gradient energy (SGE) compared to a single RED stack due to its adeptness in circumventing the electrodialysis phenomena [25–28].

In this paper, a comprehensive analysis is presented on the performance of the HGDD-MSRED heat engine. To ensure credibility, both mathematical models for HGDD and MSRED are validated through relevant experiments. The analysis commences by examining the REDHE performance under fundamental operating conditions, followed by an investigation into the impact of operational and design parameters on its efficiency. These parameters encompass the molality of the cold stream, inlet temperatures of hot and cold streams, and structural characteristics of HGDD. This exploration aims to uncover potential capabilities of REDHE and provide valuable guidance for improving its performance.

2 Mathematical model of heat engine

The system description, previously presented in Section 1, has been omitted here. It is worth noting that MSRED, as depicted inFig.2, employs a series-control strategy where each RED stack is interconnected in series and ultimately linked to an external load. This strategic approach offers the advantage of facilitating easy regulation and control over the output power of RED stacks within MSRED, making it highly suitable for practical operational scenarios [28].

2.1 Modeling assumption

The working fluid for the HGDD-MSRED heat engine in this study is the NaCl solution. When modeling the heat engine, it is assumed that the system works under the steady condition and heat exchange with the surrounding environment is ignored. The water vapor is film condensation on the cold plate of HGDD. In the gaps of HGDD, heat and mass transfers only in the direction of perpendicular to the y axis (shown inFig.2) in HGDD model and the heat transfers of natural convection and radiation are ignored. The cold and hot streams and condensate water only flow along the y axis in the HGDD model. The LC and HC solutions only flow along the x axis (shown inFig.2) in MSRED model. The salt in LC solution derives from the brackish solution (not shown in Fig.2). However, it is assumed that the mass flowrate of LC solution is equal to the mass flowrate of condensate water generated by HGDD, as the amount of the brackish solution mixed in LC solution is too small to be considered. In MSRED, the parasitic current and polarization phenomenon are both ignored [28]. The energy consumption for pumping solution into HGDD is ignored since HGDD works at a normal atmospheric pressure, which is small compared to the pump power for MSRED and the amount of input LGH.

2.2 Model establishment

The HGDD-MSRED heat engine mainly consists of a TS unit (HGDD) and a RED unit (MSRED). For the independent models of HGDD and MSRED, they can be respectively seen in Hu et al. [18,28], which are no longer presented here.

As shown inFig.2, according to the law of mass conservation, the mass flowrate of HC solution flowing into MSRED can be calculated by

(1){\dot{m}}_{\text{HC}}={\dot{m}}_{\text{b}} -{\dot{m}}_{\text{LC}},

where ṁ_LC is the mass flowrate of LC solution, and ṁ_b the mass flowrate of brackish solution leaving from MSRED, which equals to the mass flowrate of salt solution flowing into hot-stream channels of HGDD and the mass flowrate of solution in cold-stream channels of HGDD, expressed as

(2){\dot{m}}_{\text{b}} ={\dot{m}}_{\text{h}}={\dot{m}}_{\text{c}}.

The molality of the three solutions mentioned above is the same, expressed as

(3)m_{\text{b}} =m_{\text{h}}=m_{\text{c}}.

Therefore, the molality of the HC solution generated by HGDD is

(4)m_{\text{HC}}=\frac{{\dot{m}}_{\text{b}}{m}_{\text{b}}}{{\dot{m}}_{\text{HC}}-0.01m_{\text{b}}{M}_{\text{NaCl}}{\dot{m}}_{\text{LC}}},

where M_NaCl is the relative molecular mass of NaCl.

The total LGH consumption by HGDD to regenerate salt solution is expressed as

(5)Q={\dot{m}}_{\text{c}}{C}_{\text{p}}(T_{\text{h}}^{\text{in}}- T_{\text{c}}^{\text{out}}),

where C_p is the specific heat of the salt solution, and T_{\text{h}}^{\text{in}} and T_{\text{c}}^{\text{out}} are the inlet temperature of hot-stream channels and outlet temperature of cold-stream channels, respectively.

For the HGDD-MSRED heat engine, the energy conversion efficiency of it is

(6)\eta =\frac{P_{\text{MSRED}}}{Q+P_{\text{pump}}}\times 100\mathrm{\%},

where P_{\text{MSRED}} is the output power of MSRED, and P_{\text{pump}} the required pump power which can be calculated by

(7)P_{\text{pump}}=\frac{\mathrm{\Delta }{P}_{\text{HC}}{\Phi }_{\text{HC}}+\mathrm{\Delta }{P}_{\text{LC}}{\Phi }_{\text{LC}}}{{\eta }_{\text{pump}}},

where η_pump is the efficiency of pump set by default to 75% [10], and \mathrm{\Delta }{P}_{\text{HC}} and \mathrm{\Delta }{P}_{\text{LC}} are pressure drops of HC and LC solutions through the compartments of MSRED respectively, which can be expressed by [29]

(8)\mathrm{\Delta }P=\frac{12\mu L_{\text{RED}}\Phi }{B_{\text{RED}}{\delta }^3},

where μ and Φ are respectively the viscosity and flowrate of the solution, and L_RED, B_RED and δ are respectively the length, width and thickness of solution compartments of the RED stack.

2.3 Model validation

The mathematical model of the HGDD-MSRED heat engine was implemented by the MATLAB (R2017a) software, comprising a HGDD model and a MSRED model. The detailed calculation program flowchart for the HGDD model, which is essentially similar to the air-gap diffusion distillation model, was provided in Xu et al. [30]. Similarly, the calculation program flowchart for the series-control MSRED model can be found in Hu et al. [28]. Therefore, the program flowchart of the heat engine is no longer shown in this paper. The model validations for HDGG and MSRED are respectively presented in Fig.3. It is noted that the experimental data shown in Fig.3(a) and Fig.3(b) was obtained by the HGDD experimental device shown in Hu et al. [18], and the relevant conditions can be found in Tab.1. The experimental data shown in Fig.3(c) was derived from Hu et al. [27] and the RED stack was equipped with Selemion AMV/CMV IEMs (Asahi Glass Company, Japan) [26]. The maximum relative deviations between experiment and simulation for T_h and T_c are respectively 6.92% and 12.65%; the relative deviation between experiment and simulation for ṁ_LC is 5.66%; the maximum relative deviations between experiment and simulation for P_{\text{MSRED}}^{\text{net}} are respectively: 5 mol/kg-7.51%, 4 mol/kg-5.13%, and 3 mol/kg-8.51%.

Tab.1 Input parameters of HGDD-MSRED heat engine for model validation

Item	Parameter	Symbol	Value
HGDD	Cold-stream channel thickness	δcold	2 mm
	Helium-gap thickness	δc	12 mm
	Number of helium gaps	N	1
	Temperature of solutions	T	25 ± 1 °C
	Mass flowrate of cold stream	ṁc	6 kg/h
	Molality of cold stream	mc	1 mol/g
	Molality of LC solution	mLC	0.05 mol/kg
MSRED	Thickness of HC solution compartments	δHC	108 μm
	Thickness of LC solution compartments	δLC	108 μm
	Number of cells in a RED stack	Ncell	5
	Velocities of HC and LC solutions	vHC and vLC	1 cm/s

Fig.3 Model validations for HGDD and series-control MSRED.

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3 Simulation and results discussion

3.1 Basic working conditions

In this paper, a HGDD-MSRED heat engine was designed, the relevant design parameters of which are shown inTab.2.

Tab.2 Design parameters of the HGDD-MSRED heat engine

Item	Parameter	Symbol	Value
HGDD	Hot-stream channel	L × B × δh	3 m× 2 m × 0.005 m
	Cold-stream channel	L × B × δc	3 m × 2 m × 0.002 m
	Cold-plate thickness	δp	1 mm
	Helium-gap thickness	δc	5 mm
	Number of helium gaps	N	100
	Inlet temperature of cold stream	T_{\text{c}}^{\text{in}}	20 °C
	Inlet temperature of hot stream	T_{\text{h}}^{\text{in}}	80 °C
	Mass flowrate of cold stream	ṁc	6000 kg/h
	Molality of cold stream	mc	2 mol/kg
	Productivity of LC solution	ṁLC	340.56 kg/h
	Productivity of HC solution	ṁHC	5659.44 kg/h
MSRED	Solution compartment of a RED stack	LRED × BRED	0.1 m × 1 m
	Thickness of HC solution compartments	δHC	1 mm
	Thickness of LC solution compartments	δLC	0.1 mm
	Number of cells in a RED stack	Ncell	400
	Number of RED stacks	NRED	15

In the design condition, Selemion AMV/CMV IEMs were still employed in RED stacks. As shown in Tab.2, the productivity of the LC solution is 340.56 kg/h, which is far less than the HC solution. Therefore, the HC solution compartments in RED stacks are thicker than LC solution compartments, in order to decrease the required pump power while obtaining the output power of MSRED as large as possible [27]. Since MSRED adopts the series-control strategy, the output power of MSRED can be controlled expediently by adjusting the electrical resistance of the external load to change its output current. Therefore, the Nelder-Mead simplex method [31] was adopted to search the maximum output power of MSRED in the process of the simulation. In the future practical application of MSRED, achieving optimal output power remains a desirable objective, despite variations in the relevant operating and structural parameters among different REDHEs. Therefore, for practical purposes, the Nelder-Mead simplex method was still adopted to optimize the output power of MSRED in the next analysis concerning the influence of these parameters on the REDHE performance.

The simulation results of the heat engine operating under the basic conditions are presented in Tab.3. HGDD generates 0.79 kW SGE at a cost of 32.17 kW LGH consumption. For MSRED, its maximum output power achieves 0.54 kW when the output current is 1.56 A. Ultimately, the energy conversion efficiency of the REDHE reaches 1.68%.

Tab.3 Simulation results of the heat engine under the basic working conditions

Item	Parameter	Symbol	Value
HGDD	Total LGH consumption	Q	32.17 kW
	SGE between HC and LC solutions	PSGE	0.79 kW
MSRED	Maximum output power	PMSRED	0.54 kW
	Output current	I	1.56 A
HGDD-MSRED heat engine	Energy conversion efficiency	η	1.68%

3.2 Influence of the molality of cold stream

The influence of the molality of cold stream m_c on the REDHE performance is shown in Fig.4. As depicted in Fig.4(a), there is a linear increase in the total LGH consumption Q with an augmentation of m_c. The rise in m_c signifies an increased amount of salt ions within the solution, resulting in a reduction of water-vapor evaporation from the surface of hot stream due to the enhanced ion binding effects. Consequently, less heat carried by water vapor can be transferred to the cold stream, leading to a decrease in the outlet temperature. To achieve the desired inlet temperature for the hot stream, additional LGH input is required into HGDD, thereby causing an increase in Q. Conversely, as shown in Fig.4(a), reduced water-vapor evaporation implies a decline in LC solution productivity ṁ_LC, and hence ṁ_LC decreases as m_c increases.

Fig.4 Influence of molality of cold stream m_c.

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However, the decrease in ṁ_LC does not initially result in a drop in the output power of MSRED P_MSRED. As shown in Fig.4(b), P_MSRED climbs as m_c increases from 1 to 2.6 mol/kg. The reason for this is that the increase in m_c also leads to an increase in the concentration of HC solution, which is helpful for boosting the output voltage and reducing the internal resistance of RED stacks [28]. However, P_MSRED drops as m_c continues increasing since ṁ_LC is so deficient that MSRED cannot capture more SGE. The peak value of P_MSRED is 0.57 kW as m_c equals 2.6 mol/kg. The variation of the energy conversion efficiency of the heat engine η is similar to P_MSRED, which rises first and then drops with m_c. As shown in Fig.4(b), the maximum of η reaches 1.68% when m_c equals 2 mol/kg. Compared to AGDD-MSRED heat engine under the same operating conditions, as shown in Fig. S1 (Electronic Supplementary Material), the maximum P_MSRED of the HGDD-MSRED heat engine is slightly larger than that of the AGDD-MSRED heat engine. However, due to the distinct augmentation in Q, the maximum η of the HGDD-MSRED heat engine surpasses that of the AGDD-MSRED heat engine by 1.87 times.

Based on the aforementioned analysis, it is evident that an increase in m_c does not always yield benefits for enhancing the performance of the HGDD-MSRED heat engine, despite the potential for obtaining a higher concentration of HC solution. Hence, maintaining a moderate concentration of the cold stream (the optimal range of m_c is presented in Tab.4) becomes indispensable to ensure optimal performance of it.

Tab.4 Optimal molality range of cold stream m_c

mc/(mol·kg−1)	Q/kW	PMSRED/kW	η/%
1.5	30.04	0.45	1.59
2	32.17	0.51	1.68
2.5	34.26	0.54	1.65

3.3 Influence of inlet temperatures of hot and cold streams

The influence of inlet temperatures of hot and cold streams on the performance of the heat engine can be seen from Fig.5 to Fig.6.

Fig.5 Influence of inlet temperatures of hot and cold streams.

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Fig.6 Influence of inlet temperatures of hot and cold streams.

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As shown in Fig.5(a), the total LGH consumption Q decreases with the increasement of the inlet temperature of cold stream T_{\text{c}}^{\text{in}} at arbitrary inlet temperature of hot stream T_{\text{h}}^{\text{in}}. The reason for this is that the increase of T_{\text{c}}^{\text{in}} results in less heat being needed to heat the cold stream to T_{\text{h}}^{\text{in}}, and therefore, the cold stream can be preheated to a higher temperature at the outlet of cold-stream channels (i.e., T_{\text{c}}^{\text{out}}), as shown in Fig.7(a). As a consequence, the difference between T_{\text{h}}^{\text{in}} and T_{\text{c}}^{\text{out}} becomes smaller when T_{\text{c}}^{\text{in}} increases, which means that less LGH is needed to heat the outlet-cold stream to reach T_{\text{h}}^{\text{in}}.

Fig.7 Temperature variations of streams in HGDD.

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Conversely, the impact of T_{\text{h}}^{\text{in}} on Q is negligible when T_{\text{c}}^{\text{in}} remains constant. This can be attributed to the fact that an increase in T_{\text{h}}^{\text{in}} amplifies the temperature gradient between the hot and cold streams, resulting in an enhanced heat transfer from the former to the latter, thereby causing a corresponding rise in T_{\text{c}}^{\text{out}}. Consequently, there is only a marginal change observed in the disparity T_{\text{h}}^{\text{in}} and T_{\text{c}}^{\text{out}}, as depicted in Fig.7(b), which illustrates a slight increment in this difference with an elevation of T_{\text{h}}^{\text{in}}, leading to an inconspicuous enhancement of Q.

The productivity of LC solution ṁ_LC, as shown inFig.5(b), increases with the increasement of T_{\text{h}}^{\text{in}} at an arbitrary T_{\text{c}}^{\text{in}}. The reason for this is that the temperature difference between the hot stream and the cold stream increases when T_{\text{h}}^{\text{in}} rises while T_{\text{c}}^{\text{in}} keeps constant. Therefore, the difference between water-vapor-partial pressures at the gap and porous-medium interface (P_ha) and at the gap and condensate-film interface (P_af) enlarges with T_{\text{h}}^{\text{in}}. Under this condition, the mass flux of the vapor diffusion in the gap J_v augments with the increasing difference between P_ha and P_af , thus ṁ_LC rises with T_{\text{h}}^{\text{in}} [18]. On the other hand, ṁ_LC also rises with the decrease of T_{\text{c}}^{\text{in}} when T_{\text{h}}^{\text{in}} keeps constant. The reason for that also derives from the augmentation of the temperature difference between the hot and cold streams. As shown inFig.5(b), the maximum of ṁ_LC with a value of 525.53 kg/h can be obtained at a T_{\text{c}}^{\text{in}} of 5 °C and a T_{\text{h}}^{\text{in}} of 95 °C.

Since the increase of ṁ_LC means that the concentration of HC solution augments, the variation of P_MSRED with T_{\text{c}}^{\text{in}} and T_{\text{h}}^{\text{in}} is the same as that of ṁ_LC. As shown in Fig.6(a), the peak value of P_MSRED reaches 0.78 kW at a T_{\text{c}}^{\text{in}} of 5°C and a T_{\text{h}}^{\text{in}} of 95 °C. However, due to more Q being needed under this situation (Fig.5(a)), the energy conversion efficiency of the heat engine η is not maximum. As shown in Fig.6(b), the maximum value of η is 2.64% at a T_{\text{c}}^{\text{in}} of 35 °C and a T_{\text{h}}^{\text{in}} of 95°C. The reasons for this are that, first, Q is almost minimum at a T_{\text{c}}^{\text{in}} of 35°C and a T_{\text{h}}^{\text{in}} of 95 °C; Next, ṁ_LC is not low under this situation; Finally, the increase of T_{\text{c}}^{\text{in}} leads to the rise in the temperature of HC and LC solutions (i.e., the operating temperature of MSRED rises), which is positive for elevating P_MSRED [32,33]. The last two reasons lead MSRED to have a good performance. As shown in Fig.6(a), P_MSRED reaches 0.60 kW at a T_{\text{c}}^{\text{in}} of 35 °C and a T_{\text{h}}^{\text{in}} of 95 °C, which has exceeded three quarters of the maximum P_MSRED. From the above analysis, it can be realized that rising the inlet temperature of cold stream T_{\text{c}}^{\text{in}} or the inlet temperature of hot stream T_{\text{h}}^{\text{in}} can promote the energy conversion efficiency of the heat engine η. For increasing T_{\text{c}}^{\text{in}}, it is positive for reducing Q and rising the operating temperature of MSRED, while rising T_{\text{h}}^{\text{in}} is helpful for elevating ṁ_LC, which are all beneficial for enhancing η. Compared to the AGDD-MSRED heat engine under the same operating conditions, as shown in Fig. S3, the maximum P_MSRED of the HGDD-MSRED heat engine is slightly larger than that of the AGDD-MSRED heat engine. However, owing to a significant increase in Q (Fig. S2), the maximum η of the HGDD-MSRED heat engine is 1.76 times that of the AGDD-MSRED heat engine.

3.4 Influence of structure parameters of HGDD

In this section, the influence of relevant structure parameters of HGDD on the performance of the heat engine was analyzed. These parameters include the thickness of helium gaps δ_c and the length of stream channels L.

The influence of δ_c and L on the total LGH consumption Q can be seen in Fig.8(a). Since the heat-exchange area of the hot and cold streams increases with the augmentation of L at an arbitrary δ_c, more heat can be transferred from the hot stream to the cold stream, and thus the outlet temperature of the cold stream T_{\text{c}}^{\text{out}} rises. Therefore, less LGH is needed to heat the cold stream to reach the inlet temperature of the hot stream T_{\text{h}}^{\text{in}}, which means that Q decreases with the increase of L. On the other hand, Q increases with the augmentation of δ_c when L keeps unchanged. The reason for this is that the increasement of δ_c results in the increase of the thermal resistance of HGDD [18], which has a negative effect on the heat transfer between the hot stream and the cold stream. Therefore, the cold stream is not able to obtain more heat from the hot stream, which leads to more Q being input into HGDD to heat the outlet cold stream. Besides, the increase of δ_c means that the distance of water-vapor diffusing from the surface of the hot water to the cold plate lengthens. Therefore, the diffusing capacity of water vapor drops according to Fick’s law, which leads to the decrease of ṁ_LC, as shown in Fig.8(b). It can be seen in Fig.8(b) that the maximum ṁ_LC is 353.24 kg/h at an L of 2 m and a δ_c of 3 mm. The reason why ṁ_LC becomes maximum when the stream channels are the shortest is that the decrease of L results in the minimum heat-exchange area of hot and cold streams, and thus the temperature difference between the hot and cold streams enlarges. As analyzed in Section 3.3, the mass flux of the vapor diffusion in the gap J_v increases under this situation, and finally, ṁ_LC rises with the decrease of L.

Fig.8 Influence of thickness of helium gaps δ_c and length of stream channels L.

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The influence of L and δ_c on the output power of MSRED P_MSRED and the energy conversion efficiency of the heat engine η is presented in Fig.9.

Fig.9 Influence of thickness of helium gaps δ_c and length of stream channels L.

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As analyzed in Section 3.3, the variation of P_MSRED with L and δ_c is similar to ṁ_LC, as shown in Fig.9(a). The maximum P_MSRED is 0.56 kW at an L of 2 m and a δ_c of 3 mm. However, η does not reach the peak value under this situation, as shown in Fig.9(b). The optimal η is 2.69% at an L of 5 m and a δ_c of 3 mm. As presented in Fig.9(b), η rises with the augmentation of L. This is mainly caused by the fact that Q decreases with L due to more sufficient heat exchange between the hot and cold streams.

As shown in Fig. S5, the maximum P_MSRED of the HGDD-MSRED heat engine is still slightly larger than that of the AGDD-MSRED heat engine under the same operating conditions. However, due to a significant increase in Q (Fig. S4), the maximum η of the HGDD-MSRED heat engine exhibits a 44.6% improvement compared to that of the AGDD-MSRED heat engine.

The performance comparison of various recently proposed REDHEs is presented in Tab.5. As shown in Tab.5, the HGDD-MSRED heat engine in this work showcased exceptional energy conversion capabilities, which has a potential to be employed practically in the future.

Tab.5 Performance comparison of different REDHEs proposed in recent years

Item	Operating condition(a)	Maximum \eta	Year	Ref.
MD-RED heat engine	Tc = 20 °C, Th = 60 °C, mc = 5 mol/kg (NaCl aqueous solution)	1.15%	2017	Long et al. [7]
Stripping column-RED heat engine	Tc = 25 °C, Th = 60 °C, Cc = 2 mol/L (NH4HCO3 aqueous solution)	1.2%	2017	Bevacqua et al. [34]
MED-MSRED heat engine	Tc = 20 °C, Th = 90 °C, mc = 3.75 mol/kg (NaCl aqueous solution)	1.01%	2018	Hu et al. [10]
MED-RED heat engine	Tc = 20 °C, Th = 100 °C, CH = 3.5 mol/L, CL = 0.01 mol/L (NaCl aqueous solution)	1.4%	2018	Palenzuela et al. [11]
Stripping column-RED heat engine	Tc = 30 °C, Th = 80 °C, CH = 2 mol/L, CL = 0.01 mol/L (NH4HCO3 aqueous solution)	1.4%	2019	Giacalone et al. [35]
MD-RED heat engine	Tc = 20 °C, Th = 80 °C, CH = 2 mol/L, CL = 0.01 mol/L (NaCl aqueous solution)	2.8%	2019	Micari et al. [8]
Stripping column-RED heat engine	Tc = 25 °C, Th = 90 °C, CH = 1.9 mol/L, CL = 0.05 mol/L (NH4HCO3 aqueous solution)	0.20%(b)	2020	Giacalone et al. [6]
AD-RED heat engine	Tc = 25 °C, Th = 40 °C, mc = 0.6 mol/kg (NaCl aqueous solution)	0.55%	2021	Olkis et al. [15]
HGDD-MSRED heat engine	Tc = 35 °C, Th = 95 °C, mc = 2 mol/kg (NaCl aqueous solution)	2.96%	2023	This paper

Notes: (a) Tc and Th are temperatures of cold and hot sinks, respectively; mc, molality of cold stream; CH, concentration of HC solution flowing into RED; CL, concentration of LC solution flowing into RED; (b) Obtained through exergy efficiency multiplying by Carnot efficiency.

Based on the aforementioned analysis, it can be inferred that enhancing the energy conversion efficiency of the heat engine is facilitated by reducing helium gap thickness or extending stream channels. However, a continuous reduction in helium gap thickness may lead to an increased risk of hot and cold streams mixing in HGDD. Additionally, the performance analysis of the HGDD-MSRED heat engine in this study is conducted under the condition where a NaCl aqueous solution is employed as the working solution. However, in comparison to REDHEs that employ high-performing salts such as lithium chloride, potassium acetate, and LiBr [36], there still exists room for improvement for HGDD-MSRED heat engine. Therefore, the development of REDHE should not be limited to conventional working solutions like NaCl aqueous solutions and NH₄HCO₃ aqueous solutions. On the other hand, employing high performance IEMs is also important for improving the performance of REDHEs, which impels researchers to exploit novel IEMs with excellent performances [37].

4 Conclusions

In this paper, an HGDD-MSRED heat engine was proposed, and a validated mathematical model was employed to analyze the influences of relevant operation and design parameters on its performance. Based on the findings, the following conclusions can be reached:

1) The low molality of cold stream m_c leads to the poor performance of the RED unit due to the low concentration of the HC solution. However, increasing m_c results in the strengthened ion binding effect with the augmentation of input LGH consumption Q, while simultaneously decreasing the productivity of LC solution ṁ_LC. Therefore, modest m_c is the best for the heat engine to obtain the maximum energy conversion efficiency η. In addition, the peak value of η is 1.68% when m_c equals 2 mol/kg.

2) The increasement of the inlet temperature of cold stream T_{\text{c}}^{\text{in}} decreases the difference between T_{\text{c}}^{\text{in}} and T_{\text{h}}^{\text{in}}, which means that less LGH is needed to heat the outlet-cold stream to reach T_{\text{c}}^{\text{in}}. Moreover, a rising T_{\text{h}}^{\text{in}} is positive for the increase of ṁ_LC as more water vapor evaporates on the surface of the hot stream. However, the elevation of T_{\text{c}}^{\text{in}} is unfavorable for vapor condensation and thus negatively affects the augmentation in ṁ_LC. Furthermore, the output power of MSRED P_MSRED varying with T_{\text{c}}^{\text{in}} and T_{\text{h}}^{\text{in}} presents the same variation of ṁ_LC. For η, a superior value can be obtained as T_{\text{c}}^{\text{in}} and T_{\text{h}}^{\text{in}} rise simultaneously. The maximum η is 2.64% at a T_{\text{c}}^{\text{in}} of 35 °C and a T_{\text{h}}^{\text{in}} of 95 °C.

3) Decreasing the thickness of helium gaps δ_c or increasing the solution channels L positively influences the heat and mass transfers between the cold and hot streams, resulting in an increase in the temperature of the outlet cold stream and a reduced requirement of LGH. Additionally, ṁ_LC increases correspondingly with the reduction of δ_c and L. Moreover, P_MSRED has the same variation tendency with ṁ_LC when δ_c and L vary. Finally, decreasing δ_c and increasing L are both beneficial for enhancing η, and the maximum η is 2.96% at an L of 5 m and a δ_c of 3 mm.

The research in the future will primarily be focused on optimizing the relevant operating and structure parameters of the heat engine to a greater extent, and exploring multi-component salts with high performance to enhance the overall efficiency of the heat engine. Since the influence of relevant operating and structure parameters on the REDHE performance has been distinct through this work, guided by the conclusion in this work, an in-depth exergy analysis will be conducted for the HGDD-MSRED heat engine to identify effective measures that can minimize exergy destruction and improve its exergy efficiency. Additionally, it has been demonstrated that the HGDD-MSRED heat engine exhibits an excellent performance compared to other REDHEs through the performance analysis presented in this paper. To further enhance its performance, innovative working solutions that are more suitable for the heat engine than NaCl solution will be explored. The proposed technical route involves investigating bi-component salts by combining highly ionic active salt with high-conductivity salt to augment RED performance and identify optimal candidates, and conducting a thorough evaluation of the actual performance of the heat engine to refine the selection process for these candidates.

Acknowledgements

Financial support was sponsored by the Fundamental Research Program of Shanxi Province, China (No. 20210302123095) and China Postdoctoral Science Foundation (No. 2021M702418).

Electronic Supplementary Material

Supplementary material is available in the online version of this article at https:/doi.org/10.1007/s11708-024-0947-3 and is accessible for authorized users.

Competing Interests

The authors declare that they have no competing interests.

Notations

Abbreviations
AEM	Anion-exchange membrane
AGMD	Air-gap membrane distillation
CEM	Cation-exchange membrane
HC	High-concentration
HGDD	Helium-gap diffusion distillation
IEMs	Ion-exchange membranes
LC	Low-concentration
LGH	Low-grade heat
MD	Membrane distillation
MED	Multi-effect distillation
MSRED	Multi-stage reverse electrodialysis
RED	Reverse electrodialysis
REDHE	Reverse electrodialysis heat engine
SGE	Salinity gradient energy
TDEG	Thermal-driven electrochemical generator
TS	Thermal separation
Variables
B	Width, m
C	Concentration of solution, mol·m−3
Cp	Specific heat of salt solution, J·kg−1·K−1
I	Current, A
Jv	Mass flux of the vapor diffusion in the gap, kg·m−2·s−1
L	Length, m
ṁ	Mass flowrate, kg·s−1
m	Molality, mol·kg−1
MNaCl	The relative molecular mass of NaCl
N	Number of gaps in HGDD
Ncell	Number of cells in a RED stack
P	Output power, kW or pressure, Pa
Q	Total LGH consumption by HGDD, kW
α	Permselectivity of both ion-exchange membranes
γ	Water latent heat of evaporation, kJ·kg−1 or mean ion activity coefficient
δ	Thickness of solution compartments, m
δc	Thickness of gap, m
ΔP	Pressure drops, Pa
η	Energy conversion efficiency
ηpump	Efficiency of pump
Φ	Specific volume, m3·kg−1
Superscripts and subscripts
af	Water-vapor-partial pressure at the gap and condensate-water-film interface
b	Brackish solution
c/cold	Cold-stream channel or helium gaps
h	Hot-stream channel
ha	Water-vapor-partial pressure at the gap and porous-medium interface
in	Inlet flow
out	Outlet flow

References

1 Forman C, Muritala I K, Pardemann R. . Estimating the global waste heat potential. Renewable & Sustainable Energy Reviews, 2016, 57: 1568–1579

2 Lin Y, Chong C H, Ma L. . Quantification of waste heat potential in China: A top-down societal waste heat accounting model. energy, 2022, 261: 125194

3 Kang S, Li J, Wang Z. . Salinity gradient energy capture for power production by reverse electrodialysis experiment in thermal desalination plants. Journal of Power Sources, 2022, 519: 230806

4 Wu X, Zhang Y, Zhu X. . Experimental performance of a low-grade heat driven hydrogen production system by coupling the reverse electrodialysis and air gap diffusion distillation methods. Energy Conversion and Management, 2024, 301: 117994

5 Luo X, Cao X, Mo Y. . Power generation by coupling reverse electrodialysis and ammonium bicarbonate: Implication for recovery of waste heat. Electrochemistry Communications, 2012, 19: 25–28

6 Giacalone F, Vassallo F, Scargiali F. . The first operating thermolytic reverse electrodialysis heat engine. Journal of Membrane Science, 2020, 595: 117522

7 Long R, Li B, Liu Z. . Hybrid membrane distillation-reverse electrodialysis electricity generation system to harvest low-grade thermal energy. Journal of Membrane Science, 2017, 525: 107–115

8 Micari M, Cipollina A, Giacalone F. . Towards the first proof of the concept of a reverse electrodialysis−membrane distillation heat engine. Desalination, 2019, 453: 77–88

9 Tamburini A, Tedesco M, Cipollina A. . Reverse electrodialysis heat engine for sustainable power production. Applied Energy, 2017, 206: 1334–1353

10 Hu J, Xu S, Wu X. . Theoretical simulation and evaluation for the performance of the hybrid multi-effect distillation—Reverse electrodialysis power generation system. Desalination, 2018, 443: 172–183

11 Palenzuela P, Micari M, Ortega-Delgado B. . Performance analysis of a RED-MED salinity gradient heat engine. Energies, 2018, 11(12): 3385

12 Ortega-Delgado B, Giacalone F, Catrini P. . Reverse electrodialysis heat engine with multi-effect distillation: Exergy analysis and perspectives. Energy Conversion and Management, 2019, 194: 140–159

13 Ortega-Delgado B, Giacalone F, Cipollina A. . Boosting the performance of a reverse electrodialysis—Multi-effect distillation heat engine by novel solutions and operating conditions. Applied Energy, 2019, 253: 113489

14 Olkis C, Santori G, Brandani S. An adsorption reverse electrodialysis system for the generation of electricity from low-grade heat. Applied Energy, 2018, 231: 222–234

15 Olkis C, Brandani S, Santori G. Adsorption reverse electrodialysis driven by power plant waste heat to generate electricity and provide cooling. International Journal of Energy Research, 2021, 45(2): 1971–1987

16 Liu Z, Lu D, Bai Y. . Energy and exergy analysis of heat to salinity gradient power conversion in reverse electrodialysis heat engine. Energy Conversion and Management, 2022, 252: 115068

17 Liu Z, Lu D, Guo H. . Experimental study and prospect analysis of LiBr-H₂O reverse electrodialysis heat engine. Applied Energy, 2023, 350: 121791

18 Hu J, Sun Y, Zhang J. . Experimental performance comparison of helium-gap diffusion distillation and air-gap diffusion distillation. Energy Conversion and Management, 2022, 273: 116427

19 Hu J, Xu S, Wu X. . Exergy analysis for the multi-effect distillation—Reverse electrodialysis heat engine. Desalination, 2019, 467: 158–169

20 Abu-Zeid M A E R, Zhang L, Jin W Y. . Improving the performance of the air gap membrane distillation process by using a supplementary vacuum pump. Desalination, 2016, 384: 31–42

21 Lawal D, Abdul Azeem M, Khalifa A. . Performance improvement of an air gap membrane distillation process with rotating fan. Applied Thermal Engineering, 2022, 204: 117964

22 Andrés-Mañas J A, Ruiz-Aguirre A, Acién F G. . Performance increase of membrane distillation pilot scale modules operating in vacuum-enhanced air-gap configuration. Desalination, 2020, 475: 114202

23 Shahu V T, Thombre S B. Air gap membrane distillation: A review. Journal of Renewable and Sustainable Energy, 2019, 11(4): 045901

24 Khalifa A, Lawal D, Antar M. . Experimental and theoretical investigation on water desalination using air gap membrane distillation. Desalination, 2015, 376: 94–108

25 Veerman J, Saakes M, Metz S J. . Reverse electrodialysis: Performance of a stack with 50 cells on the mixing of sea and river water. Journal of Membrane Science, 2009, 327(1–2): 136–144

26 Güler E, Elizen R, Vermaas D A. . Performance-determining membrane properties in reverse electrodialysis. Journal of Membrane Science, 2013, 446: 266–276

27 Hu J, Xu S, Wu X. . Experimental investigation on the performance of series control multi-stage reverse electrodialysis. Energy Conversion and Management, 2020, 204: 112284

28 Hu J, Xu S, Wu X. . Multi-stage reverse electrodialysis: Strategies to harvest salinity gradient energy. Energy Conversion and Management, 2019, 183: 803–815

29 BatchelorG K. An Introduction to Fluid Dynamics. New York: Cambridge University Press, 2000

30 Xu S, Xu L, Wu X. . Air-gap diffusion distillation: Theory and experiment. Desalination, 2019, 467: 64–78

31 Lagarias J C, Reeds J A, Wright M H. . Convergence properties of the Nelder–Mead simplex method in low dimensions. SIAM Journal on Optimization, 1998, 9(1): 112–147

32 Cui W Z, Ji Z Y, Tumba K. . Response of salinity gradient power generation to inflow mode and temperature difference by reverse electrodialysis. Journal of Environmental Management, 2022, 303: 114124

33 Zhang W, Yan H, Wang Q. . An extended Teorell-Meyer-Sievers theory for membrane potential under non-isothermal conditions. Journal of Membrane Science, 2022, 643: 120073

34 Bevacqua M, Tamburini A, Papapetrou M. . Reverse electrodialysis with NH₄HCO₃-water systems for heat-to-power conversion. Energy, 2017, 137: 1293–1307

35 Giacalone F, Vassallo F, Griffin L. . Thermolytic reverse electrodialysis heat engine: Model development, integration and performance analysis. Energy Conversion and Management, 2019, 189: 1–13

36 Liu Z, Lu D, Dong Y. . Performance improvement of LiBr-H₂O reverse electrodialysis unit for heat to power conversion with finite solution flowrate and large concentration change. Energy Conversion and Management, 2022, 270: 116263

37 Jiang D, Zhang N, He G. . Sandwich-structured covalent organic framework membranes for selective sodium ion transport. Desalination, 2023, 567: 116988