Performance Improvement of the LNG Regasification Process Based on Geothermal Energy Using a Thermoelectric Generator and Energy and Exergy Analyses

Abstract

In this paper, a new approach is proposed to improve the performance of the LNG regasification process in a geothermal-transcritical CO₂–LNG cycle by using thermoelectric generators. Energy and exergy analyses were applied to the proposed system and the plant’s performance is compared with the conventional CO₂–LNG cycle. To achieve the optimal solution for the system, a multi-objective optimization technique based on a genetic algorithm is used. This study’s findings revealed that in the conventional CO₂–LNG cycle, the highest exergy destruction occurs in the preheater. However, integrating a thermoelectric generator allows a portion of this destroyed exergy to be converted into power. The proposed system demonstrated 2% less exergy destruction compared to the conventional system. Moreover, the TEG contributes additional power, increasing the net output power of the system by 24%. This improvement ultimately enhances the overall exergy efficiency of the system. The analysis also concluded that, although a lower LNG mass flow rate reduces the system’s net power output, it improves the exergy efficiency. Overall, the proposed system exhibits an 8.37% higher exergy efficiency and a 24.22% greater net output power compared to the conventional CO₂–LNG cycle.

1. Introduction

LNG (Liquefied Natural Gas) is natural gas that has been cooled to −162 °C and condensed into a liquid state. This liquefaction process significantly reduces its volume, facilitating easier and safer transportation. Upon reaching its destination, LNG must undergo a regasification process to convert it back into natural gas, which requires thermal energy. One proposed method is to use seawater as the heat source for regasification [1,2]. This approach does not produce greenhouse gases, and since seawater is abundant and free, it is economically viable. However, the main drawback of this method is that it does not utilize the cold energy stored in LNG. At −162 °C, LNG has a temperature far below ambient conditions, giving it a high exergy content. This exergy could be harnessed for more beneficial purposes. Using seawater in the regasification process leads to significant exergy loss due to the large temperature difference between seawater and LNG.

Many researchers have explored ways to utilize the cold energy of LNG. Dhameliya et al. [3] focused on the potential for the cryogenic energy utilization of LNG in India. Kanbur et al. [4] reviewed different methods for harnessing LNG cold energy across multiple applications, including gas separation, desalination, incineration, CO₂ capture, energy storage, and power generation. For power generation, they evaluated four system types: Rankine, Brayton, Stirling, and combined cycles. Similarly, He et al. [5] investigated additional innovative applications, such as data center cooling and cold chain systems for food transportation.

LNG has considerable potential as a heat sink in thermal power plants, particularly as a cooling agent in condensers. Lower condensation pressures result in higher thermal power plant efficiencies, and the low temperature of LNG enables cycles to achieve these lower pressures. Arcuri et al. [6] proposed utilizing LNG as a heat sink in ocean thermal energy conversion (OTEC) systems. OTEC systems typically suffer from low energy efficiency due to the minimal temperature difference between their heat sink and the heat source. Incorporating LNG as the heat sink increases this temperature difference, thereby improving the system efficiency. In another study [7], a techno-economic analysis was conducted on an integrated system combining an organic Rankine cycle (ORC) and LNG to generate electricity from geothermal resources. The study evaluated four types of ORC configurations: simple cycles, systems equipped with internal heat exchangers, regenerative cycles, and dual-fluid cycles. Mehrpooya et al. [8] investigated a two-stage ORC system designed to produce power using LNG and solar energy. Their exergoeconomic analysis identified solar collectors, thermal storage systems, and condensers as key components requiring optimization to enhance the performance of the plant. Similarly, Soffiato et al. [9] studied the performance of an ORC system employing LNG as a heat sink. They analyzed various configurations and working fluids, concluding that the choice of the working fluid depends on the system’s configuration. The fluid that achieves the best thermal match delivers the highest efficiency.

Although using LNG in an ORC increases the efficiency of the regasification process, the exergy destruction in the condenser remains significantly high. This is primarily because the lowest condensation temperature of most organic fluids is much higher than the temperature of LNG. This large temperature difference between the LNG in the condenser and the organic fluid leads to substantial exergy loss. To address this issue, some researchers have explored the use of cascade ORC systems to reduce the temperature difference. Lee [10] implemented a cascade ORC system to better exploit the exergy of LNG and optimized its performance using a genetic algorithm. While the optimization improved the efficiency, the exergy destruction in the condenser remained significant.

The combination of a transcritical CO₂ cycle and LNG demonstrates superior performance compared to other thermal power plant systems. The saturation temperature of CO₂ at 6 bar is approximately −53 °C, which is significantly lower than the condensation temperature of most organic fluids. This reduces the temperature difference between the operating fluid and the LNG in the condenser, thereby improving the exergy efficiency. Wang et al. [11] conducted thermodynamic and economic analyses of a combined transcritical CO₂ cycle and LNG system, revealing the optimal turbine inlet temperature at which the minimum capital cost per net output power (NOP) is achieved. Their analysis indicated a total exergy efficiency of 8%. Ahmadi et al. [12] similarly analyzed a comparable system from an exergetic perspective, reporting an exergy efficiency of 12%. Sun et al. [13] proposed a system combining a solar collector, a CO₂ cycle, and LNG to produce power, which was subsequently used in an electrolyzer for hydrogen production. Their exergy analysis highlighted that the highest exergy destruction rate (EDR) occurred in the condenser. While the transcritical CO₂ cycle integrates effectively with LNG, its low critical temperature and pressure limit its compatibility with high-temperature heat sources. As such, it is better suited for integration with low-temperature heat sources, such as low-temperature geothermal water and solar collectors. To address this limitation, Sadreddini et al. [14] proposed a series configuration combining an ORC and a transcritical CO₂ cycle. This cascade scheme leverages the strengths of both medium-temperature heat sources and LNG, showing an improved performance compared to standalone ORC or CO₂ cycles.

Thermoelectric generators (TEGs) present another viable option to harness the cold energy of LNG. A TEG consists of semiconductor materials that are electrically connected in series and thermally connected in parallel [15]. These devices directly convert temperature differences into electricity, based on the Seebeck effect. TEGs offer several notable advantages, such as being environmentally friendly. An environmental analysis of TEGs [16] was performed, concluding that the primary energy consumption and carbon dioxide emissions associated with the production and use of TEGs show significant specific savings in applications such as cars, combined heat and power (CHP) systems, and wood-burning stoves. Since TEGs do not rely on combustion, they contribute to a cleaner environment by avoiding harmful emissions and helping to reduce the carbon footprint. Iyer et al. [17] conducted a life cycle analysis of TEGs and demonstrated that they have positive beneficial effects across different environmental impact categories, including global warming, human toxicity, and carcinogenicity. The analysis also revealed that the eco-friendly potential of TEGs is comparable to that of two widely used renewable energy sources, namely wind and solar. Lan et al. [18] compared the performance of TEGs with ORCs in terms of CO₂ emissions using the Life Cycle Climate Performance (LCCP) method. The results showed that the CO₂ emissions from TEGs are two to five hundred and ninety times lower than those from ORCs, highlighting the potential of TEGs in significantly reducing carbon footprints. In addition to being environmentally friendly, TEGs have no moving parts, produce no noise, require minimal maintenance, and are compact in design. However, their primary drawback is their low efficiency. Nevertheless, the power output increases as the temperature difference between the hot and cold junctions of the TEG rises, making LNG’s extremely low temperature an attractive resource for TEG applications.

TEGs have recently garnered significant attention for various waste heat recovery applications [19,20,21]. Faddouli et al. [22] and Cai et al. [23] integrated TEGs with solar collectors to generate electricity. These systems can also be combined with photovoltaic (PV) panels to convert part of the thermal energy into electricity, thereby enhancing the overall system performance [24,25]. Mahmoudinezhad et al. [26] investigated different materials for TEGs designed for solar collector applications. Cheng et al. [27] examined the performance of Bi₂Te₃ as a thermoelectric material for TEGs. Wu et al. [28] and Zhang et al. [29] explored the use of TEGs for power generation from fuel cell waste heat. Hsiao et al. [30] applied TEGs in automobiles for waste heat recovery, analyzing their performance when placed on the radiator and the exhaust pipe. Wang et al. [31] coupled a TEG with an ORC to improve system efficiency, while Qiu et al. [32] used a combination of a TEG and an ORC for micro combined heat and power (CHP) systems. Additionally, Yazawa et al. [33] and Meng et al. [34] studied TEGs for recovering heat and generating electricity from industrial exhaust gases, demonstrating their potential in factory settings.

As previously discussed, TEGs achieve a higher efficiency with greater temperature differences. In the studies mentioned earlier, a hot stream is typically used as the heat source, with ambient conditions serving as the heat sink. However, since LNG has an extremely low temperature, it can serve as an effective heat sink, significantly increasing the temperature gradient in a TEG system. Karabetoglu et al. [35] investigated the temperature dependency of the Seebeck coefficient and the electrical conductivity of Bi₂Te₃ at temperatures near that of LNG. Sun et al. [36] utilized the cold energy of LNG in a thermoelectric device for power generation, using ambient air as the heat source. Zhao et al. [37] explored a thermoelectric generator system with LNG as the heat sink and flue gas from a combustion process as the heat source. Their findings showed that the power output in this configuration was three times higher than that of a simple air-heated vaporizer regasification process.

This paper presents a transcritical carbon dioxide cycle for LNG regasification, utilizing low-temperature geothermal water as the heat source. To enhance the system performance, a thermoelectric device is integrated to recover LNG cold energy. The proposed scheme is evaluated using energy and exergy analyses and compared with a simple geothermal-transcritical CO₂-LNG system. To provide a deeper understanding of the system’s operational performance, a sensitivity analysis is conducted on key system parameters. Finally, a genetic algorithm is employed to optimize the system’s performance. The proposed system enhances the efficiency of LNG gasification, contributing to progress toward a sustainable future. The novelties of this paper are as follows:

• A novel method is proposed to mitigate the significant exergy losses observed in conventional CO₂-LNG systems by integrating a thermoelectric generator into the cycle.
• Comprehensive analysis of the proposed system using both the first and second laws of thermodynamics.
• Optimization of the system performance using evolutionary algorithms.

2. System Description

Figure 1 illustrates the conventional combination of a transcritical CO₂ cycle and LNG regasification. Geothermal water serves as the heat source, transferring energy to the CO₂ cycle in the vapor generator. The supercritical CO₂ then expands in the turbine, generating power. Following this, the CO₂ must release its heat to condense back into a liquid state, which is achieved in the condenser using LNG as the cooling agent. As LNG absorbs heat from the CO₂ cycle, its temperature increases. Given the high pressure of LNG, it can be utilized in a turbine to produce additional power. However, its temperature must be raised before entering the turbine to prevent icing. This temperature increase is achieved in a heat exchanger, referred to as the preheater, which uses water at ambient temperature. In this process, ambient water entering the preheater is converted into chilled water, while the LNG’s temperature rises. Due to the substantial temperature difference between the water and LNG, the EDR in the preheater is notably high.

Figure 2 presents a schematic diagram of the proposed system. In this enhanced scheme, a TEG is integrated before the preheater to harness a portion of the temperature difference for electricity generation. Low-temperature LNG serves as the heat sink, while ambient air acts as the heat source. As heat is transferred, the temperature of the LNG rises. However, additional heating is still required before the LNG can enter the turbine. This remaining thermal energy is supplied by water in the preheater. Subsequently, the high-pressure LNG is directed to the turbine, where it expands and generates additional power. The incorporation of the TEG not only improves the system’s energy utilization but also reduces exergy loss by partially recovering the temperature difference that would otherwise result in inefficiencies.

In [38], an experimental study was performed on a TEG under cryogenic conditions. Their results showed that using a liquid-phase cryogenic material in the cold junction of the TEG increases the temperature difference between the two junctions of the TEG and results in high power production. This design principle is applied in the proposed system by ensuring that LNG remains in its liquid phase in the thermoelectric device and the gasification occurs within the preheater.

3. Mathematical Modeling

The plant is analyzed using the first and second laws of thermodynamics. The mathematical modeling framework of the system is presented in this section.

3.1. Energy Modeling

Energy balance is applied to each control volume to determine the pressure, temperature, enthalpy, and entropy of each stream. To simplify the analysis, some assumptions are made, as follows:

• The plant works in steady-state conditions.
• The pressure drop is neglected in the pipes and all the equipment except for the turbines and pumps.
• The isentropic efficiencies in the turbines and pipes considered to be constant.
• All equipment is assumed to be adiabatic.
• LNG is assumed to consist only of methane.
• The electricity produced in the thermoelectric device flows along the arm of the TEG.

The plant could be divided into two sections. The first part includes the transcritical CO₂ cycle and the LNG section and the second part consists of the TEG. Each one of these sections are analyzed in detail in the following sections.

3.1.1. Transcritical CO₂ and LNG Cycles

By applying mass and energy balances to the vapor generator, the mass flow rate of CO₂ is calculated as follows:

$${\dot{m}}_{C{O}_2}={\displaystyle \frac{{\dot{m}}_w\left(h_{in}-h_{out}\right)}{\left(h_{out}-h_{in}\right)}}.$$

(1)

The power produced by the CO₂ turbine can be expressed as

$${\dot{W}}_{tur}={\dot{m}}_{in}\left(h_{in}-\left(h_{in}-{\eta }_{tur}\left(h_{in}-h_{out,s}\right)\right)\right),$$

(2)

where ${\eta }_{tur}$ is the isentropic efficiency of the turbine.

The condenser connects the CO₂ cycle to the LNG section. It should be mentioned that the lowest temperature difference between the cold and hot streams in the condenser should always be higher than a specified value (the pinch temperature). The amount of LNG required to condense the carbon dioxide in the condenser is calculated using the following equation:

$${\dot{m}}_{LNG}={\displaystyle \frac{{\dot{m}}_{C{O}_2}\left(h_{in}-h_{out}\right)}{\left(h_{in}-h_{out}\right)}}.$$

(3)

The power consumed by carbon dioxide pump is computed as follows:

$${\dot{W}}_{pump}={\dot{m}}_{in}\left(h_{in}-\left(h_{in}-{\displaystyle \frac{h_{in}-h_{out,s}}{{\eta }_{pump}}}\right)\right)$$

(4)

Similarly, the power produced and consumed by the LNG turbine and pump are computed using Equations (2) and (4), respectively.

The mass flow rate of the chilled water in the preheater is also determined by applying mass and energy balances as follows:

$${\dot{m}}_w={\displaystyle \frac{{\dot{m}}_{LNG}\left(h_{in}-h_{out}\right)}{\left(h_{in}-h_{out}\right)}}.$$

(5)

3.1.2. Thermoelectric Generator

Based on the Seebeck effect, if a temperature difference is applied to an electric conductor, electricity will be induced in it. The amount of heat delivered to the hot junction and the amount of heat rejected by the cold junction are calculated as follows [39,40]:

$${\dot{Q}}_H=\alpha I{T}_H+K\left(T_H-T_L\right)-{\displaystyle \frac{1}{2}}R{I}^2,$$

(6)

$${\dot{Q}}_L=\alpha I{T}_L+K\left(T_H-T_L\right)+{\displaystyle \frac{1}{2}}R{I}^2.$$

(7)

In the above equations, $\alpha$ is the Seebeck coefficient, K is the thermal conductance, and R is the internal electrical resistance of the thermoelectric elements. Since the TEG is using low temperature ranges, it was decided to use a Bi₂Te₃-Sb₂Te₃ alloy as the P-type semiconductor and a Bi₂Te₃-Bi₂Se₃ alloy as the N-type semiconductor of the TEG. Bi₂Te₃ alloys are widely used in thermoelectrics due to their high thermoelectric efficiency. Around 70% of the thermoelectric modules available on the market use Bi₂Te₃ [41], which makes them a practical choice. In terms of its environmental impact, Bi₂Te₃ outperforms other materials [42]. In addition, Bi₂Te₃ alloys offer good mechanical and thermal stability at cryogenic temperatures, contributing to the durability and long-term performance of the TEGs in harsh cryogenic environments [43]. The value of the abovementioned parameters for this type of material is calculated based on formulas given in [36].

After calculating the value for each leg, the total value for the whole TEG is calculated as [39]

$$\alpha ={\alpha }_P-{\alpha }_N$$

(8)

$$R={\displaystyle \frac{{\rho }_P{l}_P}{A_P}}+{\displaystyle \frac{{\rho }_N{l}_N}{A_N}}$$

(9)

$$K={\displaystyle \frac{k_P{A}_P}{l_P}}+{\displaystyle \frac{k_N{A}_N}{l_N}},$$

(10)

where A represents the cross-sectional area of each element and l represents their length.

The power produced by the TEG can be calculated using the following equation [44]:

$${\dot{W}}_{TEG}={\dot{Q}}_H-{\dot{Q}}_L=VI$$

(11)

The system efficiency of the TEG is defined as follows [28]:

$${\eta }_{TEG}=\left({\displaystyle \frac{T_H-T_L}{T_H}}\right)\left({\displaystyle \frac{\sqrt{1+ZT}-1}{\sqrt{1+ZT}+\frac{T_L}{T_H}}}\right).$$

(12)

In the above equation, T is the average temperature of the hot and cold junctions and Z is the figure of merit of the thermoelectric generator, which is defined as follows [28]:

$$Z={\displaystyle \frac{{\alpha }^2}{KR}}.$$

(13)

3.2. Exergy Modeling

Exergy represents the quality of energy. The first law of thermodynamics does not differentiate different kinds of energy, such as electrical and thermal. But the second law identifies which kind of energy is more valuable. Another difference between the first and second laws is in the conservation concept. While the first law of thermodynamics states that energy will never be destroyed, the second law expresses that exergy could be destroyed. Therefore, another term, named exergy destruction, should be added to the exergy balance of a control volume as follows:

$${\dot{Ex}}^Q+\sum {\dot{m}}_{in}{ex}_{in}={\dot{Ex}}^w+\sum {\dot{m}}_{out}{ex}_{out}+{\dot{Ex}}^D.$$

(14)

In the above equation, ${\dot{Ex}}^Q$ and ${\dot{Ex}}^w$ are the exergy transfer values due to heat transfer and power and ${\dot{Ex}}^D$ shows the EDR. More details about how to calculate each term in the above equation are presented in [45].

By applying Equation (14) to each control volume, the exergy destruction in all of the equipment can be computed.

Table 1. The set of equations to determine EDR in each unit of the system.

Component	Exergy Destruction
Vapor generator	${\dot{Ex}}_{VG}^D=\sum {\dot{Ex}}_{in}-\sum {\dot{Ex}}_{out}$
Turbine	${\dot{Ex}}_{tur}^D={\dot{Ex}}_{in}-{\dot{W}}_{tur}-{\dot{Ex}}_{out}$
Condenser	${\dot{Ex}}_{Cond}^D=\sum {\dot{Ex}}_{in}-\sum {\dot{Ex}}_{out}$
Pump	${\dot{Ex}}_{pump}^D={\dot{Ex}}_{in}+{\dot{W}}_{Pump}-{\dot{Ex}}_{out}$
Preheater	${\dot{Ex}}_{PH}^D=\sum {\dot{Ex}}_{in}-\sum {\dot{Ex}}_{out}$
TEG	${\dot{Ex}}_{TEG}^D={\dot{Ex}}_{in}-{\dot{W}}_{TEG}-{\dot{Ex}}_{out}-{\dot{Ex}}_{Q_H}$

presents the set of equations used to calculate the EDR in each unit of the system.

Finally, the total exergy efficiency of the plant can be determined by

$$\phi ={\displaystyle \frac{{\dot{W}}_{net}+\left({\dot{Ex}}_{14}-{\dot{Ex}}_{13}\right)}{{\dot{Ex}}_1+\left({\dot{Ex}}_7-{\dot{Ex}}_{12}\right)}}.$$

(15)

where ${\dot{W}}_{net}$ is defined as the summation of the power produced in the turbines and the TEG minus the power consumed by the pumps.

To define the plant’s total exergy efficiency, the fuel-product approach is used. In this technique, fuel is defined as the exergy consumed to produce the final product. In this plant, there are two sources of fuel. The first one is the hot geothermal water and the second one is the LNG. Since LNG is just used for its cold energy and it should be delivered to final customers in the form of natural gas, the amount of the total inlet exergy minus the total outlet exergy of LNG is considered in the denominator. In the numerator, the products of the plant should be considered. Here we have two different commodities as the product, namely NOP and the exergy of the chilled water produced in the preheater.

4. Genetic Algorithm

Different kinds of evolutionary optimization procedures can be utilized to optimize the performance of a plant, including genetic algorithms (GAs) [46,47], particle swarm optimization [48,49,50], control algorithms [51,52], ant colonies [53], robust optimization algorithms [54], etc., Feng et al. [55], Maleki [56], Maleki et al. [57]. Each method has unique advantages. Among them, GA is more popular, due to its robustness and simplicity. It uses Darwin’s theory to find the optimal solution. To do so, it first generates a random population. Each one of the random numbers is evaluated in the objective function and the best of them are selected and moved to the next step. Some new numbers will be produced in the second step using mating procedures (crossover and mutation). The objective function will be evaluated again for all numbers. This process will continue until it converges, and the final solution is found. More information is available in [58,59].

5. Results and Discussion

In this section, the simulation results are presented. MATLAB R2014a software was used to model the system, and the thermodynamic properties of the different fluids were determined by employing REFPROP [60]. Some design values were considered during the analysis, as shown in

Table 2. Design values for the analysis [36,61].

Parameter	Value	Unit
Ambient temperature	25	°C
Ambient pressure	1.01	bar
Geothermal water temperature	150	°C
Geothermal water pressure	10	bar
Geothermal water mass flow rate	10	kg/s
Transcritical CO2 cycle
Turbine inlet temperature	120	°C
Turbine inlet pressure	100	bar
Condenser pressure	6	bar
Pinch temperature in vapor generator	10	°C
Turbine isentropic efficiency	85	%
Pump isentropic efficiency	75	%
LNG section
Turbine outlet pressure	40	bar
Pinch temperature in condenser	50	°C
Pinch temperature in preheater	15	°C
Thermoelectric generator
LNG outlet temperature from TEG	−50	°C
Current	20	A
Cross-sectional area of P-type and N-type semiconductors	1	cm2
Length of P-type and N-type semiconductors	1	cm

.

Assuming the abovementioned values, the plant can be analyzed thermodynamically. The streams’ thermodynamic properties of the proposed plant (Figure 2) are presented in

Table 3. Thermodynamic properties of each stream.

Stream No.	P [bar]	T [°C]	h [kJ/kg]	s [kJ/kg K]	m [kg/s]
1	10	150	632.50	1.84	10
2	10	50	210.19	0.70	10
3	6	−53.12	86.80	0.55	9.71
4	100	−48.65	98.02	0.57	9.71
5	100	120	532.86	2.01	9.71
6	6	−53.12	425.51	2.09	9.71
7	1.01	−161.70	−0.76	−0.01	16.12
8	70	−158.33	21.01	0.04	16.12
9	70	−103.12	225.12	1.48	16.12
10	70	−50	592.28	3.33	16.12
11	70	10	798.30	4.16	16.12
12	40	−25.33	742.60	4.20	16.12
13	1.01	25	104.92	0.37	39.62
14	1.01	5	21.12	0.08	39.62

.

Table 4. The most important indicators of the system and their values.

Parameter	Value	Unit
Power produced in the CO2 turbine	1042.6	kW
Power consumed in the CO2 pump	108.98	kW
Power produced in the LNG turbine	897.65	kW
Power consumed in the LNG pump	350.73	kW
Power produced in the TEG	358.65	kW
NOP	1839.2	kW
Mass flow rate of the chilled water	39.61	kg/s
Total exergy efficiency	21.45	%

shows the most important performance indicators of the proposed system. In this table, more than half of the NOP of the system is produced by the CO₂ cycle, while the power produced by LNG and the TEG is equal to almost 30 and 20 percent of the NOP of the system, respectively. Compared to the conventional CO₂–LNG cycle, the NOP of the plant increased by 24 percent by adding the TEG.

Adding the TEG to the system also lowers the mass flow rate of the chilled water. In the conventional CO₂–LNG cycle, the mass flow rate of chilled water was equal to 110.23 kg/s, while in the new, proposed plant, it was reduced to 39.61 kg/s. This is because in the new, proposed system, a part of the required heat is provided by the TEG and therefore a lower water mass flow rate is needed in the preheater. This reduces the EDR in the preheater and therefore the total exergy efficiency of the plant increases to 21.45%, while it was equal to 19.79% in the conventional CO₂–LNG cycle. As can be seen, due to adding the TEG, the exergy efficiency considerably increased.

Economic analysis is beyond the scope of this paper. However, to provide context for the reader, it is worth noting that, while the cost of ORC systems varies depending on multiple parameters, it is roughly estimated to range between $2000 and $4500 per kW [62]. In comparison, the cost of TEGs with a temperature difference of approximately 150 °C is around $14,000 per kW [63]. Nevertheless, it is important to emphasize that TEGs are still undergoing development, and advancements in their figure of merit are expected to significantly reduce their capital costs. Moreover, TEGs have nearly zero maintenance costs due to their lack of moving parts, which minimizes the risk of mechanical failures and the need for frequent maintenance [64].

To get more insight into the exergy performance of the proposed system, the EDR of different equipment for conventional systems and the proposed system is compared in Figure 3. As can be seen, the EDR remained unchanged after adding the TEG in all equipment except for the preheater. In the conventional CO₂–LNG cycle, the total EDR of the plant was 7534 kW. The highest EDR occurred in the preheater, where it amounted to 3301 kW, which constitutes approximately 44% of the total EDR of the plant. In the newly proposed system, the EDR in the preheater decreased significantly to only 534 kW, which now accounts for almost 7% of the total EDR of the plant. This improvement is due to the partial heat transfer being handled by the TEG, which recovers some of the energy from the LNG before it enters the preheater. However, the exergy destruction in the TEG is 2616 kW. Despite this, the overall total EDR in the new system is still 150 kW lower than that in the conventional CO₂–LNG cycle, demonstrating an improved system efficiency. Figure 4 compares the share of each equipment in the total EDR of conventional systems and the new proposed system, which allows us to compare the performance of each piece of equipment in both systems. Although adding a TEG to the plant reduces the plant’s total EDR, the TEG still has the highest EDR among all the equipment. This is due to its low efficiency. To reduce its exergy destruction, the figure of merit of the TEG should be improved. After the TEG, the maximum EDR existed in the condenser and the vapor generator, which is due to the noticeable difference between the temperatures of the cold and hot streams of the investigated equipment.

5.1. Sensitivity Analysis

To gain a deeper understanding of the system’s performance, a sensitivity analysis is performed on different parameters of the system. To do so, only the parameter under study is changed and all the other parameters are kept constant.

5.1.1. CO₂ Turbine Inlet Temperature

The effect of the CO₂ turbine inlet temperature (TIT) on the system is shown in Figure 5 and Figure 6. The total exergy efficiency of the plant increases with an increasing TIT, but there is an optimal value for TIT at which NOP reaches its maximum value. When the TIT in a CO₂ cycle increases, more energy is extracted from the geothermal water, but the increase in temperature results in a lower mass flow rate of the carbon dioxide. Despite this reduction in mass flow rate, the overall power produced by the carbon dioxide turbine increases, as shown in Figure 6.

Since the mass flow rate of CO₂ decreases with an increasing TIT, a lower mass flow rate of LNG is required in the condenser, resulting in reduced power production in the LNG turbine. However, as the TIT increases, the turbine outlet temperature rises, leading to an increase in the LNG temperature at the condenser outlet. Consequently, the temperature of the cold junction in the TEG increases slightly, which reduces the temperature difference between the two junctions of the TEG, ultimately causing lower power production in the TEG. This trend is shown in Figure 6.

Figure 5 shows that, when the TIT is between 100 °C and 127 °C, the increase in power production by the CO₂ turbine dominates, leading to a rise in the NOP with an increasing TIT. However, when the TIT exceeds 127 °C, the reduction in power production by the LNG turbine and the TEG becomes more significant, resulting in a decline in the NOP. This creates an optimal TIT for power production of around 127 °C. On the other hand, for the plant’s total exergy efficiency, there is no optimal value, and it increases continuously with a rising TIT. Although the NOP decreases beyond a TIT of 127 °C, the simultaneous decrease in the LNG mass flow rate (as explained earlier) reduces the denominator in Equation (15). As a result, the total exergy efficiency of the plant increases with a higher TIT.

5.1.2. CO₂ Turbine Inlet Pressure

Figure 7 shows the effect of the CO₂ turbine inlet pressure on the system performance. An optimal turbine inlet pressure exists, maximizing both the NOP and the total exergy efficiency of the plant. Changes in the CO₂ turbine inlet pressure have a minimal impact on the LNG cycle and the TEG, as variations in the power generation by the LNG turbine and the TEG remain below 1%. However, the CO₂ cycle is significantly affected by this parameter. Initially, as the CO₂ turbine inlet pressure increases, the rise in power production by the turbine outweighs the power consumed by the CO₂ pump, leading to an increase in the overall power produced by the CO₂ cycle. This trend continues until the NOP reaches its peak. Beyond the optimal inlet pressure, the rate of power consumption by the pump exceeds the rate of power generation by the turbine, causing a decline in the NOP. The total exergy efficiency of the plant follows a similar trend to the NOP, rising with an increased inlet pressure until the optimal point, and declining thereafter.

5.1.3. Condenser Pressure

The effect of condenser pressure on system performance is shown in Figure 8 and Figure 9. Lowering the condensation pressure increases the power production due to the increased pressure ratio in the CO₂ turbine. Conversely, as the condenser pressure rises, the pressure ratio decreases, leading to a reduced power generation in the CO₂ turbine, as shown in Figure 9. An increase in the condenser pressure influences the mass flow rate and temperature of LNG at the condenser outlet. This, in turn, negatively affects the power produced by both the TEG and the LNG turbine. Figure 9 shows a decline in the power production from both of these components, resulting in an overall decrease in the NOP of the plant.

The total exergy efficiency of the plant also decreases with a rising condenser pressure, albeit at a slower rate compared to the decrease in NOP. This slower reduction occurs because higher condenser pressures reduce the mass flow rate of LNG, which decreases the denominator in Equation (15). This mitigates the decline in the total exergy efficiency relative to the drop in the NOP.

5.1.4. Minimum Temperature Difference in the Condenser

The effect of the minimum temperature difference in the condenser on the system performance is shown in Figure 10 and Figure 11. Changes in this parameter do not affect the CO₂ cycle but significantly impact the LNG cycle and the TEG. When the minimum temperature difference in the condenser increases, the outlet temperature of the LNG stream decreases. Consequently, the mass flow rate of LNG must rise to provide sufficient cooling energy for the condensation process. This relationship is shown in Figure 11, where the LNG mass flow rate increases with a higher minimum temperature difference. The increased LNG mass flow rate, combined with its lower temperature, enhances power production in the TEG. Similarly, the higher mass flow rate of LNG boosts power generation in the LNG turbine. These combined effects result in an overall increase in the NOP of the plant, as shown in Figure 10.

However, while the NOP increases, the system’s total exergy efficiency decreases with increasing minimum temperature differences. This decline is due to the increased mass flow rate of LNG, which negatively impacts the exergy efficiency by raising the denominator in Equation (15). Thus, even though a higher NOP has a positive influence, the increase in the LNG mass flow rate outweighs this benefit, leading to a reduction in the total exergy efficiency.

5.1.5. TEG Outlet Temperature

Figure 12 shows the impact of the TEG outlet temperature on the system’s performance. Changes in this parameter affect neither the CO₂ nor the LNG cycles; instead, they influence power production in the TEG and the cooling energy generated in the preheater.

When the TEG outlet temperature increases, power production in the TEG rises. This is because higher outlet temperatures indicate that more thermal energy is utilized by the TEG, allowing for greater electricity generation. However, the rate of this power production increment diminishes slightly as the outlet temperature increases. This trend occurs because the temperature difference between the hot and cold junctions in the TEG narrows at higher outlet temperatures.

A tradeoff exists between TEG power production and the cooling energy provided by the preheater. At lower TEG outlet temperatures, the preheater must compensate by transferring more thermal energy to the LNG, resulting in a higher chilled-water mass flow rate and greater exergy destruction in the preheater. This increased exergy destruction lowers the plant’s overall exergy efficiency. Conversely, as the TEG outlet temperature rises, power production by the thermoelectric device begins to decrease, due to the reduced temperature difference between the junctions. This reduction also diminishes the total exergy efficiency of the plant. Therefore, an optimal TEG outlet temperature exists that balances the power production and preheater performance to maximize the overall exergy efficiency of the proposed system.

5.1.6. Minimum Temperature Difference in the Preheater

Figure 13 shows the impact of the minimum temperature difference in the preheater on the system performance. This parameter primarily influences power generation in the LNG turbine and the cooling energy produced in the preheater. A smaller temperature difference in the preheater enhances the exergy efficiency of the system. This improvement is attributed to better thermal matching between the LNG and the heating fluid, reducing irreversibilities and exergy destruction in the heat exchange process.

Additionally, power production in the LNG turbine increases as the minimum temperature difference decreases. A lower temperature difference raises the LNG turbine inlet temperature (TIT), allowing for more energy extraction during the expansion process and thereby boosting the turbine performance.

5.2. Optimization Results

To find the optimal result, a GA is employed. The optimization process takes into account six different decision variables, each with its own set of maximum and minimum bounds. These decision variables, along with their respective bounds, are presented in

Table 5. Decision variables with their lower and upper limits.

Decision Variables	Lower Limit	Upper Limit
CO2 TIT [°C]	100	140
CO2 turbine inlet pressure [bar]	80	180
Condenser pressure [bar]	6	10
Minimum temperature difference in condenser [°C]	40	60
TEG outlet temperature [°C]	−70	−20
Minimum temperature difference in preheater [°C]	10	20

. These parameters were chosen based on their significant impact on system performance, as demonstrated in the sensitivity analysis and corroborated by previous studies. Notably, all the decision variables are independent.

The optimization results, presented in

Table 6. Results of optimization using exergy efficiency as the objective function.

Parameter	Value
CO2 TIT [°C]	140
CO2 turbine inlet pressure [bar]	162.87
Condenser pressure [bar]	10
Minimum temperature difference in condenser [°C]	40
TEG outlet temperature [°C]	−47.06
Minimum temperature difference in preheater [°C]	10
Total exergy efficiency [%]	24.11

, are based on maximizing the total exergy efficiency as the objective function. As observed, the optimal values for most decision variables are either at their maximum or minimum limits, with the exception of the CO₂ turbine inlet pressure and the TEG outlet temperature. These parameters, as indicated in the sensitivity analysis section, have specific optimal values for achieving the best system performance. The maximum achievable total exergy efficiency of the proposed system is 24.11%, which represents a significant improvement compared to the exergy efficiency of the conventional CO₂–LNG cycle.

In the multi-objective optimization, where both total exergy efficiency and NOP are considered objective functions, a trade-off between these two parameters is observed. As shown in Figure 14, there is a clear conflict between maximizing the exergy efficiency and maximizing the NOP, specifically with regard to the following:

• If the goal is to maximize the exergy efficiency, the LNG mass flow rate tends to decrease. While this leads to a higher exergy efficiency, it also results in a decrease in the NOP, due to the reduced power output from both the TEG and the LNG turbine.
• Conversely, if the goal is to maximize the NOP, the LNG mass flow rate increases, leading to higher power production but a reduction in the exergy efficiency due to the increase in exergy destruction associated with higher LNG mass flow rates.

This trade-off highlights the inherent balance between achieving a high power output and maintaining high efficiency in the system. The optimization process allows for identifying the best compromise depending on the desired outcomes (exergy efficiency vs. power output).

6. Conclusions

In this paper, a TEG is used to improve the performance of a conventional CO₂–LNG cycle to regasify LNG. The addition of the TEG helps to increase power production and improve the exergy efficiency of the plant. The proposed system is analyzed energetically and exergetically and an evolutionary optimization technique is used to find the optimized performance of the system. The main outcomes of this study are summarized as follows:

• In the conventional CO₂–LNG cycle, before the introduction of the TEG, the highest rate of exergy destruction occurred in the preheater. This was due to the significant temperature difference required to heat LNG before it entered the turbine. This large temperature differential resulted in high exergy losses.
• The introduction of the TEG allowed part of the cold energy from LNG to be converted into electricity. This not only reduced the temperature difference in the preheater but also decreased the total exergy destruction. As a result, the overall exergy efficiency of the plant increased. Specifically, the NOP and total exergy efficiency saw improvements of 24% and 8.38%, respectively. Previous papers have reported a lower exergy efficiency for the system without a TEG. In comparison, previous studies reported lower exergy efficiencies for systems without TEGs; for instance, ref. [11] reported an exergy efficiency of 8%, and [12] reported an exergy efficiency of 12%, which is lower than the exergy efficiency of the proposed system in this paper.
• Sensitivity analysis revealed that the trend of total exergy efficiency diverges from that of the NOP. When the mass flow rate of LNG is reduced, lower power is produced by both the TEG and the LNG turbine. However, the total exergy efficiency increases, because the denominator in the exergy efficiency equation (Equation (15)) decreases, reducing the exergy destruction.
• Among all the parameters, the turbine inlet temperature (TIT) had the greatest effect on the system performance. Increasing the TIT influenced the performance of all sections of the system—the CO₂ cycle, the TEG, and the LNG cycle—because it directly impacted the mass flow rates and power production of these components.
• Adding the TEG allowed for the conversion of a portion of the temperature difference in the preheater into electricity. This not only increased the net output power but also reduced the exergy destruction in the preheater by lowering the mass flow rate of the chilled water, improving the overall efficiency of the system.