A Comprehensive Study on Hydrogen Production via Waste Heat Recovery of a Natural Gas-Fueled Internal Combustion Engine in Cogeneration Power-Hydrogen Layouts: 4E Study and Optimization

Abstract

Internal combustion engines (ICEs) are one of the significant sources of wasted energy, with approximately 65% of their input energy being wasted and dissipated into the environment. Given their wide usage globally, it is necessary to find ways to recover their waste energies, addressing this inefficiency and reducing environmental pollution. While previous studies have explored various aspects of waste energy recovery, a comparative analysis of different bottoming configurations has been lacking. In this research, an extensive review of the existing literature was conducted by an exploration of four key bottoming cycles: the steam Rankine cycle (SRC), CO₂ supercritical Brayton cycle, inverse Brayton cycle (IBC), and air bottoming cycle. In addition, these four main bottoming systems are utilized for the waste energy recovery of natural gas-fired ICE with a capacity of 584 kW and an exhausted gas temperature of 493 °C. For the efficient waste heat recovery of residual exhausted gas and heat rejection stage of the main bottoming system, two thermoelectric generators are utilized. Then, the produced power in bottoming systems is sent to a proton exchange membrane electrolyzer for hydrogen production. A comprehensive 4E (energy, exergy, exergy-economic, and environmental) optimization is conducted to find the best main bottoming system for hydrogen production. Results showed that the SRC-based system has the highest exergy efficiency (21.93%), while the IBC-based system results in the lowest efficiency (13.72%), total cost rate (25.58 $/h), and unit cost of hydrogen production (59.91 $/GJ). This combined literature review and research article underscore the importance of finding an economically efficient bottoming cycle in the context of waste energy recovery and hydrogen production.

1. Introduction

In the present day, the issues of energy scarcity and environmental pollution have become increasingly important [1,2]. Consequently, the value of energy conservation cannot be overstated. In a country with a thriving industrial sector, a significant portion of the total fossil fuel consumption—roughly 60–70%—is attributed to internal combustion engines (ICEs), with automotive ICEs accounting for 40–50% of this figure [3,4]. However, a considerable amount of the total heat generated by the combustion of fuel in ICEs—approximately 65%—is squandered through exhaust and engine coolant, resulting in energy waste and emission-related predicaments [5,6,7]. If this waste heat can be recuperated, there could be a substantial improvement in engine fuel efficiency and a marked reduction in environmental pollution [8]. Thus, waste heat recovery has gained paramount importance. In this regard, various bottoming systems have been proposed for the purpose of utilizing the waste heat generated by ICEs [9,10]. Rankine cycle (RC), CO₂ supercritical Brayton cycle (SBC), and inverse Brayton cycle (IBC) are common proposed configurations for the waste energy recovery of ICEs. Although the above-mentioned systems were investigated in previous studies as bottoming systems of ICEs, there is a need in the literature for a comprehensive review and comparison of different systems for waste heat utilization of ICE. Hence, in the present study, these three cycles—steam RC (SRC), CO₂ SBC, and IBC—in addition to the air bottoming cycle (ABC) are investigated and compared as bottoming systems for a natural gas ICE from 4E (energy, exergy, exergy-economic, and environmental) perspectives. It should be mentioned that ABC has not been used for the waste heat recovery of an ICE, and it is used here as bottoming system for ICE for the first time.

One of the primary challenges is to address the increasing global energy demand and ascertain sustainable and environmentally sound energy solutions to meet this demand. Currently, the predominant portion of the energy demand is met by fossil fuel supplies, but these materials are limited by geography. Fossil fuels possess the disadvantage of faster depletion and greenhouse gas emissions. Due to the restricted supplies, fossil fuels are not expected to meet the cumulative demand, and further research is being conducted on renewable energy systems [11,12]. Hydrogen is widely recognized as a potential fuel due to its ability to function as both an energy carrier and storage medium, in addition to offering carbon-free solutions [13,14]. In comparison to electricity, hydrogen possesses several advantages, including high energy conversion effectiveness, ample sources, the capability to be produced with zero emissions from water, long-distance transportability, availability of storage options, conversion into fuels, the potential to be generated through renewable energies, and the elimination of environmental damage [15,16]. Hydrogen also offers superior heating values in comparison to traditional fossil fuels. Conversely, electricity carries the disadvantages of transmission and heat losses caused by high voltages and electrical resistance. Hence, in the present research, the produced power in the waste recovery bottoming systems is sent to an efficient type of hydrogen production unit named proton exchange membrane electrolyzer (PEME). Therefore, the complete system is converted to an efficient power-hydrogen production unit.

This paper is structured in a way that it first conducts a thorough review of the papers related to combined ICE with Rankine cycle (RC), SBC, IBC, and ABC (Section 1.1, Section 1.2, Section 1.3 and Section 1.4) and related to hydrogen production using PEME (Section 1.5). Section 2 introduces the considered systems. Section 3 presents the basic assumptions and mathematical modeling of the systems. In the Result section, Section 4, after validation (Section 4.1) and base case inputs (Section 4.2), a thorough parametric study is conducted to investigate the effect of influential parameters on the systems (Section 4.3), and the results of the multi-objective optimization for choosing the best configuration are presented in Section 4.4. Finally, the conclusion and recommendations are presented in Section 5.

1.1. The Waste Heat Recovery of Engines by Rankine Cycles

Rankine cycles are favorable choices for the unused energy utilization of ICEs that has been used in many studies and different configurations. Some review papers are available about the waste energy recovery of engines by organic Rankine cycles (ORCs). In this regard, Tian et al. [17] examined the use of 20 various organic fluids in ORC for efficient waste heat utilization of a diesel engine (235 kW power with an exhaust temperature of 519). Using R141b, R123, and R245fa led to the highest efficiency between 13.3% and16.6%. The electricity production cost was estimated as 0.3–0.35 $/kWh. Yu et al. [18] used R245fa as a passing flow stream for ORC in an ICE unused energy recovery system. A thermal oil circuit was used between ICE exhausted gas and ORC to prevent the decomposition of ORC fluid in a high temperature of exhausted gas. Energy efficiency (${\eta }_{en}$) and exergy efficiency (${\eta }_{ex}$) were 9.2% and 21.7%, respectively. Shu et al. [19] embedded a dual-loop Rankine cycle for unused energy utilization of a diesel engine with a capacity from 58.8 kW to 235.8 kW. Water was used in the high-temperature (HT) loop and six different organic fluids were used in the low-temperature (LT) loop and in subcritical or trans-critical mode. The HT loop heat source was exhausted gas, while the residual exhaust gas, engine coolant, and the heat rejection of the HT cycle were sources of energy for the LT loop. R134a was the best fluid in the LT loop with net electricity of 39.91 kW and ${\eta }_{ex}$ of 48.42%. Zhang et al. [20] introduced a novel dual-loop ORC with R245fa and R134a as working fluids in HT and LT loops. The exhausted gas of a 105 kW engine was the heat source of the HT loop, while intake air, heat rejection of the HT loop, and cooling water of engine were the sources of energy for the LT loop. The output electricity improvement was from 14% to 16% due to the waste heat recovery. Yang [21] investigated a dual-loop ORC with R245fa as a passing stream in both loops. The waste energy of exhausted gas, intake air path, and jacket cooling water of a 247 kW engine were used as energy sources of the dual-loop layout. The net output electricity of the bottoming system was 27.85 kW, and efficiency improvement was reported at 13%. Shu et al. [22] introduced a dual-loop Rankine system for the unused energy utilization of an engine with a maximum power of 235.8 KW and an exhausted temperature of 519. The HT loop fluid was water, and six organic fluids were used in the LT loop. R1234yf led to the highest output with a generated electricity of 36.77 kW and a ${\eta }_{ex}$ of 55.05%. Song and Gu [23] used a bottoming ORC for unused energy elimination of exhausted gas and jacket cooling water of a 996 kW engine. They used pure and zeotropic mixtures as working fluids of ORC. Using cyclohexane/R141b resulted in 13.3% more output power in comparison with pure cyclohexane.

Yue et al. [24] compared using ORC and Kalina cycle for the unused heat elimination of a 200–2000 kW diesel engine. The ORC passing fluids worked in trans-critical mode. N-nonane led to the highest efficiency at 64.1%. Song et al. [25] used exhausted gas and jacket cooling water of a diesel engine (996 kW power) as energy sources for HT ORC and LT ORC. The exhausted gas and cooling water were at 573.15 K and 363.15 K. Five and seven different working fluids were used for HT and LT loops. The highest generated power of the bottoming system was 101.1 kW. This led to the whole system’s efficiency improvement by 10.2%. Song and Gu [26] surveyed the energy–exergy outputs of a cascade partial evaporation Rankine cycle (PERC) (water) and ORC for the unused heat elimination of a 996 kW diesel engine. They used exhausted gas and cooling water from the engine as energy sources. Bottoming system power production was 115.1 kW.

Daghigh and Shafieian [27] used exhaust gas and jacket cooling water of a diesel engine as the heat source of an ORC, a hot water unit (HWU), and an absorption chiller (ACH) in a complex configuration. The bottoming system could produce 53 kW of power and 176.8 kW of cooling. Salek [28] et al. recovered the exhaust heat of a 250 kW engine in bottoming ORC and ACH. The exhaust gas of the engine was sent to the ORC evaporator and ACH generator in a series configuration. The output power and cooling were obtained as 6.73 kW and 14.2 kW, respectively. Habibi et al. [29] suggested using a cascade PERC/ORC/LNG subsystem for unused energy elimination of a 200 kW diesel engine. The exhausted gas acted as the energy source for the PERC evaporator and a HWU. Using isopentane led to the highest output. In this case, ${\eta }_{ex}$ and total cost rate (${\dot{C}}_{tot}$) were 38.74% and 19.3 $/h, respectively. Mohammadkhani et al. [30] used the exhausted energy of a 98.9 kW diesel engine as an energy source for an HT Kalian cycle. Jacket cooling water exhausted gas was used for preheating and evaporation of the NH₃–H₂O mixture of the Kalina cycle. The bottoming layout could generate 21.74 kW of power. This contributed to ${\eta }_{ex}$ and unit cost ($c_p$) of 55.52% and 15.51 cent/kWh. Jafarzad et al. [31] proposed a new configuration comprising an ORC, a steam generator, a hot water unit, and a reverse osmosis desalination unit (RODU) for efficient unused energy elimination of a 603 kW capacity diesel engine. ${\eta }_{en}$ and ${\eta }_{ex}$ were obtained as 82.82% and 54.1%.

A comprehensive review of papers based on the combination of ICE and RC is provided in

Table 1. ICE as the topping system and Rankine cycle as the main bottoming system.

Ref. and Year	Systems Description		Analyses
	Topping System Description	Bottoming System(s) Description	Optimization	Energy Outputs	Exergy Outputs	Economic and Environmental Outputs
[17] in 2012	235 kW diesel engine with an exhaust temperature of 519 °C	ORC with 20 different working fluids	×	R141b, R123, R245fa $13.3<{\mathsf{\eta }}_{\mathrm{en}}<16.6\%$	–	0.3 < Electricity production cost < 0.35 $/kWh
[18] in 2013	117.7 < Diesel engine power < 258.3 KW, 693.15 < Exhaust gas temperature < 808.15 K, 363.75 < Jacket cooling water temperature < 366.15 K	Thermal oil circuit/ORC with R245fa working fluid	×	${\mathsf{\eta }}_{\mathrm{en}}=9.2\%$	${\mathsf{\eta }}_{\mathrm{ex}}=21.7\%$	–
[19] in 2013	58.8 < Diesel engine power < 235.8 KW, 326 < Exhaust gas temperature < 519 °C, 80.7 < Jacket cooling water temperature < 83.3 °C	SRC + Subcritical and trans-critical ORC with 6 working fluids	×	R134a is the best fluid ${\dot{W}}_{net}=39.91\mathrm{kW}$	${\mathsf{\eta }}_{\mathrm{ex}}=48.42\%$	–
[20] in 2013	light-duty diesel engine power = 105 kW with exhausted gas, intake air, and coolant water waste heat recovery	HT ORC (R245fa) + LT ORC (R134a)	×	The output power improved by 14–16%	–	–
[32] in 2013	Diesel engine power = 235.8 kW, Exhaust gas temperature = 792.2 K, Jacket cooling water temperature = 356.5 K	SRC or siloxane ORC at topping system + R134a trans-critical ORC bottoming system	×	${\dot{W}}_{net}=39.67 \mathrm{kW}$	${\mathsf{\eta }}_{\mathrm{ex}}=42.98\%$	–
[21] in 2014	Diesel engine power of 247 kW, With recovery of exhaust gas energy, waste heat from the coolant system, and released heat from turbocharged air in the intercooler	HT ORC (R245fa) + LT ORC (R245fa)	×	${\dot{W}}_{net}=27.85 \mathrm{kW}$, Thermal efficiency improvement =13%.	–	–
[22] in 2014	58.8 < Diesel engine power < 235.8 KW, 326 < Exhaust gas temperature < 519 °C, 80.7 < Jacket cooling water temperature < 83.3 °C	SRC + Subcritical ORC with six working fluids	×	R1234yf was the best fluid, ${\dot{W}}_{net}=36.77\mathrm{kW}$	${\mathsf{\eta }}_{\mathrm{ex}}=55.05\%$	–
[23] in 2015	Diesel engine power = 996 kW, Exhaust gas temperature = 573.15 K, Jacket cooling water temperature = 363.15 K	ORC with zeotropic mixtures cyclohexane/R141b (0.5/0.5)	×	Increasing the net power output of the system by 13.3% compared to pure cyclohexane	–	–
[24] in 2015	200 < Diesel engine power < 2000 KW, 419 < Exhaust gas temperature < 712 K	ORC (6 working fluids) or Kalina cycle	×	N-nonane was the best, ${\mathsf{\eta }}_{\mathrm{en}}=64.1\%$	–	–
[25] in 2015	Diesel engine power = 996 kW, Exhaust gas temperature = 573.15 K, Jacket cooling water temperature = 363.15 K	HT ORC (5 working fluids) + LT ORC (7 working fluids)	×	${\dot{W}}_{net}=101.1 \mathrm{kW}$, Efficiency improvement of ICE = 10.2%	–	–
[26] in 2015	Diesel engine power = 996 kW, Exhaust gas temperature = 573.15 K, Jacket cooling water temperature = 363.15 K	Cascade partial evaporation Rankine cycle (PERC) (water)/ORC (3 working fluids)	×	${\dot{W}}_{net}=115.1 \mathrm{kW}$, Efficiency improvement of ICE = 11.6%	–	–
[33] in 2015 (Experimental)	12.9 < Gasoline engine power < 44.8 kW, 429 < Exhaust gas temperature < 673 °C	ORC (ethanol)	×	${\mathsf{\eta }}_{\mathrm{en}}=6\%$	–	–
[34] in 2015	Diesel engine power = 247 kW, Exhaust gas temperature = 667 K	ORC (R245fa)	✓	${\dot{W}}_{net}=13.84 \mathrm{kW}$, Net power output per unit heat transfer area = 0.74 $\mathrm{kW}/{\mathrm{m}}^2$	–	–
[35] in 2015	Diesel and gasoline engine	ORC (R245fa)	×	An increase of the overall system efficiency up to 9%	–	–
[36] in 2016 (Experimental)	Diesel engine power = 243 kW, Exhaust gas temperature = 480 °C	Cascade SRC/ORC (R123)	×	${\dot{W}}_{net}=12.7 \mathrm{kW}$, Power enhancement = 5.6%	–	–
[37] in 2016	Diesel engine power = 243 kW, 200 < Exhaust gas temperature < 450 °C 74 < Jacket cooling water temperature < 84 °C	Cascade HT ORC (4 working fluids)/LT ORC (4 working fluids)	×	Toluene and R134a were best fluids for HT and LT cycles, ${\dot{W}}_{net}=33.9 \mathrm{kW}$, ${\mathsf{\eta }}_{\mathrm{en}}=9.9\%$	${\mathsf{\eta }}_{\mathrm{ex}}=39.1\%$	–
[27] in 2016	Diesel engine	ORC (R245fa) + HWU + ACH	×	${\dot{W}}_{net}=53 \mathrm{kW}$, ${\dot{Q}}_{chiller}=176.8 \mathrm{kW}$	–	–
[38] in 2017	Diesel engine power = 258 kW redundant break	ORC (R245fa)	×	Increase in power = 4.13 kW, Increase in efficiency = 0.66%	–	–
[39] in 2017	Truck diesel engine power = 258.9 kW, Exhaust gas temperature = 405 °C, Jacket cooling water temperature = 88 °C	Simple ORC, dual-loop ORC or cascade expansion ORC (Cyclopentane as working fluid)	×	dual-loop ORC power = 26.8 kW, cascade expansion ORC power = 29 kW	–	–
[40] in 2017	CNG (compressed natural gas) engine power = 210 kW	Cascade HT ORC (R245fa)/LT ORC (R245fa)	✓	${\dot{W}}_{net}=23.62 kW$, $8.79\%<{\mathsf{\eta }}_{\mathrm{en}}<10.17\%$	–	–
[28] in 2017	180 < Diesel engine power < 250 kW, 698 < Exhaust gas temperature < 758 K	ORC (R245fa) + ACH	×	${\dot{W}}_{net}=6.73\mathrm{kW}$, ${\dot{Q}}_{chiller}=14.2\mathrm{kW}$	–	–
[41] in 2017	Natural gas fired engine power of 2928 kW Exhaust gas temperature = 470 °C, Jacket cooling water temperature = 79.7 °C	RC (Water, R123, R134a)	×	–	${\mathsf{\eta }}_{\mathrm{ex},\mathrm{R}123}=21.01$, ${\mathsf{\eta }}_{\mathrm{ex},\mathrm{water}}=13.16$, ${\mathsf{\eta }}_{\mathrm{ex},\mathrm{R}134\mathrm{a}}=8.7$	–
[42] in 2017 (Experimental)	Diesel engine power = 200 kW, Exhaust gas temperature = 400 °C	ORC (4 working fluids)	×	MDM is the best fluid, ${\dot{W}}_{net}=8.1-9.8 \mathrm{kW}$	–	–
[43] in 2017	Diesel engine power = 80,080 kW, Exhaust gas temperature = 308 °C	ORC (R123) + Solid oxide electrolyzer	×	${\mathsf{\eta }}_{\mathrm{en}}=53.56\%$	–	–
[44] in 2018	Diesel engine power = 80 kW	ORC	✓	3.24% improvement in the output power	–	–
[45] in 2018	Two different diesel engines, 245 < Exhaust gas temperature < 354 °C	ORC (23 working fluids)	×	$22.7\%<{\mathsf{\eta }}_{\mathrm{en}}<23.76\%$	–	–
[29] in 2018	Diesel engine power = 200 kW, Exhaust gas temperature = 400 °C	Cascade PERC/ORC (6 working fluids)/LNG subsystem + HWU	✓	Iso-pentane as ORC working fluid, ${\dot{W}}_{net}=178.6 \mathrm{kW}$	${\mathsf{\eta }}_{\mathrm{ex}}=38.74$	${\dot{C}}_{tot}=19.3{\displaystyle \frac{\$}{h}}$
[46] in 2018	300 MW turbo-aspirated compression ignition	RC (7 working fluids)	×	R123 in super-critical mode was the best fluid, ${\dot{W}}_{net}=715.2 \mathrm{kW}$	–	–
[47] in 2018	Diesel engine	ORC (7 working fluids)	×	R141b was the best fluid, ${\dot{W}}_{net}=97\mathrm{kW}$	–	–
[48] in 2019	Diesel engine power = 243 kW	Optimal practical ORC, Basic ORC, trans-critical ORC, regenerative ORC, split regenerative ORC, cascade ORC, Dual pressure ORC	×	Cyclo-pentane working fluid, Dual pressure ORC efficiency was the highest at 14.23	–	–
[49] in 2019	117.7 < Automotive internal combustion engine power < 258.3 kW, 693.15 < Exhaust gas temperature < 808.15 K, 363.75 < Jacket cooling water temperature < 366.15 K	Basic ORC, Basic ORC with oil storage for higher stability	×	Dynamic behavior was analyzed for two systems, ${\dot{W}}_{net}=28.61 \mathrm{kW},$ ${\dot{W}}_{net, with OS}=23.34 \mathrm{kW}$	–	–
[50] in 2019	Diesel engine power = 98.9 kW Exhaust gas temperature = 524.9 °C, Jacket cooling water temperature = 86.8 °C	Cascade HT trans-critical ORC (Toluene or cyclohexane)/LT trans-critical ORC (CO2 or R134a)	×	Using toluene and R134a was the best, ${\dot{W}}_{net}=24.93 \mathrm{kW}$	–	PP = 9.24 years, Specific cost = 4361 $/kW
[51] in 2019	Diesel engine power = 247 kW Exhaust gas temperature = 635.15 K	ORC with zeotropic mixtures working fluids	×	0.9 toluene/0.1 decane was the best, ${\dot{W}}_{net}=26.9 \mathrm{kW}$	–	Electricity production cost = 0.5975 $/kWh
[30] in 2019	Diesel engine power = 98.9 kW Exhaust gas temperature = 524.9 °C, Jacket cooling water temperature = 86.8 °C	High-temperature Kalina cycle	×	${\dot{W}}_{net}=21.74 \mathrm{kW}$, ${\mathsf{\eta }}_{\mathrm{en}}=25.55\%$	${\mathsf{\eta }}_{\mathrm{ex}}=55.52\%$	Unit cost of electricity = 15.52 cent/kWh
[52] in 2020	Diesel engine power = 235.8 kW Exhaust gas temperature = 519 °C, Jacket cooling water temperature = 83.5 °C	Cascade HT ORC/LT ORC with 24 candidate working fluid pairs	✓	toluene/R124 was the best pair, ${\mathsf{\eta }}_{\mathrm{en}}=39\%$	–	PP = 1.26 years
[53] in 2020	Natural gas engine power = 85 Kw, Exhaust gas temperature = 850 °C, Jacket cooling water temperature = 95 °C	ORC + RODU	✓	Freshwater mass flow rate =2.926 kg/s	${\mathsf{\eta }}_{\mathrm{ex}}=30.7\%$	–
[54] in 2021 (Experimental)	Diesel engine power = 1000 kW Exhaust gas temperature = 530 °C, Jacket cooling water temperature = 84 °C	Cascade HT ORC (R245fa)/LT ORC (R134a)	×	${\dot{W}}_{net}=310 \mathrm{kW}$, ${\mathsf{\eta }}_{\mathrm{en}}=9.5\%$	${\mathsf{\eta }}_{\mathrm{ex}}=43\%$	–
[31] in 2021	Diesel engine power = 603 kW Exhaust gas temperature = 659.3 °C, Jacket cooling water temperature = 78.6 °C	ORC + HWU + HRSG + RODU	✓	${\mathsf{\eta }}_{\mathrm{en}}=82.82\%$	${\mathsf{\eta }}_{\mathrm{ex}}=54.1\%$	–
[55] in 2022	Biogas fueled internal combustion engine, Exhaust gas temperature = 587.08 °C	Trans-critical ORC (9 working fluids)	✓	n-decane was the best fluid, ${\dot{W}}_{net}=156.4 \mathrm{kW}$	–	PP=5.537 years
[56] in 2023	Vehicle engine under road condition	ORC (R245fa)	✓	${\mathsf{\eta }}_{\mathrm{en}}=82.82\%$, power output per unit heat transfer area = 0.55 $\mathrm{kW}/{\mathrm{m}}^2$	–	–
The present study	NG fueled ICE (${\dot{W}}_{ICE}=0.584\mathrm{MW}$)	SRC (Single pressure level HRSG)/TEG 2 + TEG 1 + PEME	✓	–	${\mathsf{\eta }}_{\mathrm{ex}}=21.93\%$	${\dot{C}}_{tot}=31.82{\displaystyle \frac{\$}{\mathrm{h}}},$ Unit cost of outputs = 101.3 $/GJ

. As was described in the literature review, dual-loop RCs were mostly used for waste heat elimination in ICEs. A few studies have been done about tri-generation systems using HWU, ACH, and RODU as bottoming systems for ICE. There is no study about the full waste heat recovery of ICE for hydrogen production, and the present study tries to fill this gap by introducing a new configuration.

1.2. The Waste Heat Recovery of Engine by CO₂ SBC

As a promising alternative power block, the employment of SBCs has recently been proposed to replace the conventional water/steam Rankine cycle, as well as the ideal gas (air or helium) Brayton cycles, in waste heat recovery systems [57]. One of the key benefits of SBCs is their lower level of corrosiveness when compared to water, as well as the decreased compression work required in comparison to ideal gas Brayton cycles, ultimately leading to improved efficiency. Additionally, operating SBCs beyond the critical point (7.38 MPa, 31 °C) results in a smaller size of both turbo-machinery and heat exchangers when compared to that in conventional power cycles [58,59]. Hence, some studies have been done about the waste energy recovery of ICEs by CO₂ SBCs.

For example, Liang et al. [60] proposed using a cascade regenerative CO₂ SBC/ORC for the unused energy elimination of a diesel–natural gas engine (power between 126.8 kW and 251.1 kW). They used seven working fluids in the ORC. The output power of the bottoming system was 40.88 kW, leading to a 6.78% improvement in the whole system’s efficiency. Wu et al. [61] used the exhausted gas of a 2928 kW diesel engine as an energy source of a regenerative CO₂ SBC. Then, the waste heat of SBC was recovered by an ACH. ${\eta }_{en}$ and ${\eta }_{ex}$ were 39.85% and 53.54%. Furthermore, $c_p$ was calculated as 3.41 $/GJ. Feng et al. [62] used the exhausted gas of a 41,840 kW diesel engine as an energy source for a recompression CO₂ SBC and Kalia cycle in a series configuration. The bottoming system’s output power was 1976.1 kW. Pan et al. [63] used regenerative CO₂ SBC for unused energy elimination of a diesel engine. The generated electricity of SBC was fed to the compressor of an ejector refrigeration cycle for cooling production. Output cooling and coefficient of performance were 225.5 kW and 2.05. Almohana et al. [64] used a regenerative CO₂ SBC and a modified Kalina cycle for the unused energy utilization of an ICE. Furthermore, an ORC and thermoelectric generator 1 (TEG 1) were used as bottoming systems for SBC, and TEG 2 was used to recuperate the unused energy of the Kalina cycle. The net output power was 2657 kW. This resulted in ${\eta }_{en}$ and ${\eta }_{ex}$ of 26.33% and 51.69%. Wang et al. [65] used the waste gas of a 235.8 kW diesel engine (with a temperature of 519) in a cascade partial heating CO₂ SBC and trans-critical CO₂ Rankine cycle. ${\eta }_{en}$ and electricity production cost were calculated as 29.25% and 7.43 cent/kWh. Wang et al. [66] recovered the exhausted waste heat of a 1323.1 kW engine by CO₂ regenerative SBC and an ORC with a mixture of Benzene/R365mfc as a working fluid. Then, the unused heat of SBC was recuperated by an ejector refrigeration cycle. ${\eta }_{ex}$ and $c_p$ were estimated as 61.93% and 5.34 cent/kWh. Dadpour et al. [67] sent the exhausted gas of a ship engine to a new regenerative CO₂ SBC for power and cooling and trans-critical CO₂ ORC systems. Moreover, the ORC heat sink medium was a LNG subsystem. The proposed system could generate 9.06 kW power and 19.52 kW cooling, bringing about a ${\eta }_{ex}$ and total price of 42.3% and 2.5 M$.

A comprehensive review of papers based on the combination of ICE and SBC is provided in

Table 2. ICE as the topping system and SBC as the main bottoming system.

Ref. and Year	Systems Description		Analyses
	Topping System Description	Bottoming System(s) Description	Optimization	Energy Outputs	Exergy Outputs	Economic and Environmental Outputs
[68] in 2018	Diesel engine power = 996 kW Exhaust gas temperature = 300 °C, Jacket cooling water temperature = 90 °C	Regenerative CO2 SBC or Improved regenerative CO2 SBC	×	${\dot{W}}_{net}=68.4 \mathrm{kW}$	–	–
[60] in 2019	Diesel/natural gas dual-fuel engine, 126.8 < engine power < 251.1 kW 423.2 < Exhaust gas temperature < 488.3 °C	Cascade Regenerative CO2 SBC/ORC (7 working fluids)	×	${\dot{W}}_{net}=40.88 \mathrm{kW}$, improved the dual-fuel engine power output by 6.78%	–	–
[61] in 2020	Diesel engine power = 2928 kW Exhaust gas temperature = 470 °C	Cascade Regenerative CO2 SBC/ACH	✓	$248.1<{\dot{W}}_{net}<253.9,$ 70.5 < Cooling capacity < 168.8, ${\mathsf{\eta }}_{\mathrm{en}}=39.85\%$	${\mathsf{\eta }}_{\mathrm{ex}}=53.54\%$	Unit cost of outputs = 3.41 $/GJ
[62] in 2020	Diesel engine power = 41,840 kW	Recompression CO2 SBC + Kalina cycle	✓	${\dot{W}}_{net}=1976.1 \mathrm{kW}$, reduced the annual fuel consumption by 16.62%	–	–
[69] in 2020	Diesel engine	Regenerative CO2 SBC coupled with trans-critical CO2 refrigeration cycle	×	${\dot{W}}_{net}=20.88 \mathrm{k}\mathrm{W}$, Cooling capacity = 59.47 kW	${\mathsf{\eta }}_{\mathrm{ex}}=12.52\%$	–
[70] in 2020	184.8 < Diesel/natural gas dual-fuel engine power < 197 kW, Exhaust gas temperature = 557.6 K	Four configurations of CO2 SBC/ORC	×	${\dot{W}}_{net}=33.77 \mathrm{kW}$, ${\mathsf{\eta }}_{\mathrm{en}}=32.92\%$	${\mathsf{\eta }}_{\mathrm{ex}}=65.81\%$	–
[63] in 2020	Diesel/natural gas dual-fuel engine power = 197 kW, Exhaust gas temperature = 557.5 °C	Regenerative CO2 SBC couple with ejector expansion refrigeration cycle (zeotropic mixtures)	×	Cooling capacity = 225.5 kW, COP = 2.05	–	–
[71] in 2020	Diesel engine power = 1170 kW Exhaust gas temperature = 457 °C, Jacket cooling water temperature = 89 °C	Cascade Regenerative CO2 SBC/ORC (R245fa)	×	${\dot{W}}_{net}=215 \mathrm{kW}$	–	–
[72] in 2020	Diesel engine power = 235.8 kW Exhaust gas temperature = 519 °C	Novel CO2 SBC	✓	${\dot{W}}_{net}=39.49 \mathrm{kW}$, ${\mathsf{\eta }}_{\mathrm{en}}=35.86\%$,	${\mathsf{\eta }}_{\mathrm{ex}}=67.9\%$	–
[73] in 2021	Automobile engine	Regenerative CO2 SBC	×	Transient characteristic evaluation of the system, ${\dot{W}}_{net}=2.97 \mathrm{kW}$	–	Electricity production cost = 0.38 $/kWh
[74] in 2021	1071 < Natural gas engine power < 2108 kW, 590 < Exhaust gas temperature < 690 °C	Vortex Tube (VT) heat booster coupled with Regenerative CO2 SBC and Recompression CO2 SBC	×	Implementing VT boosts energy and exergy efficiencies by up to 1.85%	Implementing VT decreases exergy destruction by around 8–12%	Electricity price = 0.3 $/kWh, 8 < PP < 12 years, Adding VT contributed to reducing LCOE by 10–15% and the payback period by around 3–5 years
[75] in 2021	Marine Diesel engine	Different Confs. of CO2 SBC	×	The best CO2 cycle improved the efficiency by 6.6–7.25%	–	–
[64] in 2022	Internal combustion engine, Exhaust gas temperature = 519 °C	Cascade Regenerative CO2 SBC/TEG 1/ORC + Modified Kalina cycle/TEG 2	✓	${\dot{W}}_{net}=2657\mathrm{kW}$, ${\mathsf{\eta }}_{\mathrm{en}}=26.33\%$	${\mathsf{\eta }}_{\mathrm{ex}}=51.69\%$	–
[65] in 2022	Diesel engine power = 235.8 kW Exhaust gas temperature = 519 °C,	Cascade partial heating CO2 SBC/Trans-critical CO2 ORC	✓	${\dot{W}}_{net}=841.84 \mathrm{kW}$, ${\mathsf{\eta }}_{\mathrm{en}}=29.25\%$	–	Electricity production cost = 7.43 cent/kWh
[66] in 2022	Engine power = 1323.1 kW Exhaust gas temperature = 633.1 °C	Cascade Regenerative CO2 SBC/Ejector refrigeration cycle + ORC (Benzene/R365mfc)	✓	${\mathsf{\eta }}_{\mathrm{en}}=33.17\%$,	${\mathsf{\eta }}_{\mathrm{ex}}=61.93\%$	Electricity production cost = 5.34 cent/kWh
[76] in 2023	Gas engine power = 45 kW Exhaust gas temperature = 350 °C, Jacket cooling water temperature = 90 °C	Gas engine coupled with heat pump and HWU + Regenerative CO2 SBC	×	${\dot{W}}_{net,SBC}=2.14 \mathrm{kW}$	${\mathsf{\eta }}_{\mathrm{ex},\mathrm{SBC}}=36.61\%$	–
[67] in 2023	Ship engine, Exhaust gas temperature = 572 °C	New Regenerative CO2 SBC for power and cooling + Trans-critical CO2 ORC + LNG subsystem	✓	${\mathsf{\eta }}_{\mathrm{en}}=69.6\%$, ${\dot{W}}_{net}=9.06 \mathrm{kW}$, Cooling capacity = 19.52 kW	${\mathsf{\eta }}_{\mathrm{ex}}=42.3\%$	Total cost= 2.5 M$
[77] in 2023	584 < Natural gas (NG) engine power < 1167 kW, 445 < Exhaust gas temperature < 493 °C	Partial heating CO2 SBC	✓	${\mathsf{\eta }}_{\mathrm{en}}=48.94\%$,	${\mathsf{\eta }}_{\mathrm{ex}}=52.01\%$	Unit cost of electricity = 13.19 euro/kWh
Present study	NG fueled ICE (${\dot{W}}_{ICE}=0.584 \mathrm{M}\mathrm{W}$)	Regenerative SBC (CO2)/TEG 2 + TEG 1 + PEME	✓	–	${\mathsf{\eta }}_{\mathrm{ex}}=18.05\%$	${\dot{C}}_{tot}=30.75{\displaystyle \frac{\$}{\mathrm{h}}},$ Unit cost of outputs = 93.38 $/GJ

. In this case, the waste heat elimination of ICE was mainly conducted by SBC and ORC in series and cascade configurations. In some studies, other systems such as the ACH and Kalina cycles were used for utilization of the heat rejection stage in the SBC, and in the present research, the whole waste heat of bottoming systems is recovered by two TEG and the output power is directed to a PEME for hydrogen production.

1.3. The Waste Heat Recovery of Engines by IBC

IBC is another bottoming cycle that although it has a good potential for recovery of high-temperature exhausted gas, less attention is devoted to it in comparison with other bottoming cycles. The basic IBC has three main components: a gas turbine that expands the hot gas to sub-atmospheric pressure, a cooling heat exchanger to cool down gas before entering the compressor, and a compressor for increasing the pressure of gas to atmosphere pressure [78,79].

In this regard, Zhu et al. [80] recovered the waste energy of an asymmetric twin-scroll turbocharged diesel engine by an IBC. Output power was increased by about 5% due to using the IBC bottoming system. Battista et al. [81] used IBC for the unused energy recovery of a turbocharged diesel engine. The effect of important parameters such as turbine and compressor efficiencies and pressure drops were investigated on the combined system. The waste heat recovery leads to the production of an extra 1.5–2% of engine output power. Chagnon-Lessard et al. [82] proposed using different configurations of IBC as bottoming systems for a methane-fueled engine. Inverted Brayton cycle with liquid water drainage, steam turbine, and refrigeration cycle had the highest amount of specific work among different configurations. The highest thermal indicator of 25% was obtained for the considered layout. Abrosimov et al. [83] used the IBC cycle as the bottoming system for a methane engine with a capacity between 500 and 1400 kW. An ORC and a regenerative ORC were coupled with the IBC heat rejection heat exchanger through a thermal oil loop. Using pentane in regenerative ORC led to the output power of 152.9 kW for the IBC/ORC system. ${\eta }_{en}$ and LCOE were obtained as 11.09% and 159.5 $/MWh. Salek et al. [84] used cascade IBC/ORC for unused energy elimination of a turbo-charged industrial diesel engine. They used R245fa as a passing stream in the ORC. The bottoming IBC/ORC enhanced the generated electricity of the layout by 18%.

A comprehensive review of papers based on the combination of ICE and IBC is provided in

Table 3. ICE as the topping system and IBC as the main bottoming system.

Ref. and Year	Systems Description		Analyses
	Topping System Description	Bottoming System(s) Description	Optimization	Energy Outputs	Exergy Outputs	Economic and Environmental Outputs
[80] in 2019	Diesel engine power = 351 kW	IBC	×	Power improvement due to IBC = 5%	–	–
[81] in 2019	63.6 < Diesel engine power < 91.1 kW, 200 < Exhaust gas temperature < 500 °C	IBC	×	Waste heat recovery of 1.5–2% of engine power by IBC	–	–
[85] in 2020	Diesel engine power = 130 kW	IBC	×	Efficiency improvement due to IBC = 3.4%	–	–
[82] in 2020	Engine with CH2 fuel, Exhaust gas temperature = 1140 K,	Five different configurations of IBC (with liquid water drainage, steam turbine, and refrigeration cycle)	×	${\mathsf{\eta }}_{\mathrm{en}}=25\%$	–	–
[86] in 2020	Methane engine power = 1.4 MW, 470 < Exhaust gas temperature < 570 °C	IBC/Thermal oil loop/Regenerative ORC	✓	${\mathsf{\eta }}_{\mathrm{en}}=13.3\%$	–	LCOE = 146.1 $/MWh
[83] in 2020	500 < Methane engine power < 1400 kW, 400 < Exhaust gas temperature < 600 °C	IBC/Thermal oil loop/Basic ORC or regenerative ORC (3 different working fluids)	✓	Pentane was the best fluid, ${\dot{W}}_{net}=152.9 \mathrm{k}\mathrm{W}$, ${\mathsf{\eta }}_{\mathrm{en}}=11.09\%$	–	LCOE = 159.5 $/MWh
[84] in 2022	Diesel engine maximum power = 257 kW 1056.9 < Exhaust gas temperature < 1071.5 K	IBC/ORC (R245fa)	×	IBC/ORC system leads to enhancement of the system power by about 18%	–	–
Present study	NG fueled ICE (${\dot{W}}_{ICE}=0.584 \mathrm{M}\mathrm{W}$)	IBC/TEG 1 + TEG 2 + PEME	✓	–	${\mathsf{\eta }}_{\mathrm{ex}}=13.72\%$	${\dot{C}}_{tot}=25.58{\displaystyle \frac{\$}{h}},$ Unit cost of outputs = 59.91 $/GJ

. As clarified in the literature review, limited studies have been conducted on the waste energy recovery of ICE by IBC. In some studies, an ORC was used for waste heat elimination in the heat rejection stage of ICE, while the exhaust gas was not recovered for extra power generation. In the present research, the energy of both heat rejection and exhausted gas in IBC was recovered by two TEGs for the first time. Then, the output power of bottoming systems was sent to a PEME for hydrogen output.

1.4. The Waste Heat Recovery of Engines by ABC

ABC is composed of three main components: air compressor, heating air heat exchanger, and air turbine. Some studies have been done on the combination of the gas turbine cycle (GTC) and ABC [87,88]. These studies showed that ABC can be an economically competitive option to a conventional system (GTC-SRC), especially in small-scale power generation [89]. On the other hand, despite the high potential of ABC for exhausted gas recovery, there is no study in the literature on using ABC for engine waste heat recovery. Therefore, this is the first study that compares using ABC with other common unused heat elimination bottoming systems for an NG-fueled engine.

1.5. Hydrogen Production by PEME

PEMEs possess a multitude of advantages in comparison to alternative electrolysis technologies [90,91]. Said benefits encompass superior energy efficacy, heightened hydrogen production velocity, a more condensed configuration, augmented hydrogen purity, and diminished power utilization [92,93].

Emadi et al. [94] utilized geothermal energy as the primary source of heat, while the LNG subsystem functioned as the heat sink in a cascade Kalina cycle/Stirling engine. The system’s output power was subsequently consumed in a PEME. The hydrogen produced by the system amounted to a rate of 204.77 kg/h, and ${\eta }_{ex}$ was 43.46%. Nami et al. [95] successfully recuperated the residual energy from a gas turbine modular helium reactor setup by means of two ORCs. The resultant residual energy from the ORC was then conveyed to a PEME for hydrogen production. The optimal conditions resulted in an ${\eta }_{ex}$ of 49.21% and an output of hydrogen totaling 56.2 kg/h. Akrami et al. [96] employed a cascade ORC/absorption cooling and heating system coupled with a heat pump-driven geothermal heat source. The resultant power generated by the ORC was subsequently directed to a PEME to facilitate the production of hydrogen. ${\eta }_{en}$ and ${\eta }_{ex}$ were determined to be 34.98% and 49.18%, respectively. The minimum $c_p$ was computed to be 22.73 $/GJ. Habibollahzade et al. [97] employed the residual energy generated by a solid oxide fuel cell to power a bottoming Stirling engine. The resulting power output of the Stirling engine was directed toward a PEME unit. The most favorable ${\eta }_{ex}$ and $c_p$ were computed to be 38.03% and 24.93 $/GJ, respectively. Ishaq and Dincer [98] conducted a comparative analysis of three renewable energy-based systems, namely biomass, solar, and geothermal, for the purpose of hydrogen production using PEME. The exergy of the aforementioned systems, specifically the biomass gasification system, geothermal power system, and solar photovoltaic system, were determined to be 49.8%, 10.2%, and 16.95%, respectively.

Akrami et al. [99] employed the thermal and electrical properties of photovoltaic/thermal cells to operate an air conditioning system and PEME. The suggested system underwent scrutiny from both an energy and exergy-economic standpoint. The system’s all-encompassing ${\eta }_{ex}$ came to 11.28%. Additionally, photovoltaic/thermal cells constituted ~80% of the total exergy depletion. Habibollahzade et al. [100] employed PTSC as an energy source for an SRC. The recovery of waste energy from the SRC was accomplished through a TEG. Thereafter, the resultant electricity output from the SRC was transmitted to a PEME unit. The utilization of multi-objective optimization yielded a ${\eta }_{ex}$ and $c_p$ of 12.76% and 61.69 $/GJ, respectively, for the system. Ahmadi et al. [101] used an ORC in a hybrid combination of solar and ocean thermal energy conversion systems. The resultant power output of the ORC was then transmitted to a PEME unit for the purpose of hydrogen production. The integrated system’s ${\eta }_{en}$ and ${\eta }_{ex}$ were calculated to be 3.6% and 22.7%, respectively. Moharramian et al. [102] employed a combined ORC/PEME system as a bottoming cycle in a GTC fueled by natural gas and hydrogen, with a post-combustion chamber fed by biomass. The hydrogen produced was subsequently introduced into the combustion chamber of the GTC. The integration of hydrogen injection resulted in a noteworthy decrease of 37% and 27% in the exergy and CO₂ emissions, respectively.

2. Systems Description

Figure 1, Figure 2, Figure 3 and Figure 4 show the schematic diagrams of the suggested setups. An NG-fired ICE with a 584 kW capacity and a 493 °C exhaust gas temperature serve as a topping system in all versions. SRC, regenerated CO₂ SBC, IBC, and ABC play the primary bottoming system roles in Configurations 1–4. Two TEGs are used in bottoming systems to recover all waste energy. The remaining heat of exhausted gas is converted by a TEG to 70 °C, which is the lowest temperature of exhausted gas. For the recovery of heat rejection stages in main bottoming systems, another TEG is employed. A generator uses the output power of the topping GTCs to generate electricity, while a PEME makes hydrogen using the output power of the main bottoming systems plus TEG 1 and TEG 2. The Appendix has more information on the calculations and formulas for each point, and a point-to-point explanation of systems is provided below.

In Figure 1, exhaust gas (Point 1) exits the ICE at high temperature, entering the HRSG. The exhaust gas transfers heat to the working fluid (water) in the HRSG, generating high-pressure steam (Point 6). The high-pressure steam flows to the steam turbine. The steam expands through the turbine, generating mechanical work and converting it to electrical power. The low-pressure steam exits the turbine (Point 7) and moves to TEG 2. In TEG 2, the steam releases heat and condenses back into water (Point 8). The condensate water is pumped to increase its pressure before returning to the HRSG (Points 8 to 9). Then, any remaining heat from the exhaust gas (Point 2) is transferred to TEG 1, converting temperature differences directly into electrical energy, enhancing overall energy recovery efficiency.

In this study, the focus was on the SRC due to its superior performance for high-temperature waste heat recovery (above 400 °C). The SRC is particularly effective in utilizing the high-temperature exhaust gases from the ICE, allowing for more efficient energy recovery compared to ORCs, which are generally more suitable for lower temperature ranges. It is believed that the SRC offers a better match for the temperature conditions in this application, providing an optimized solution for maximizing energy recovery.

Throughout the electrolysis process, the PEME is supplied with the heat and electricity required to fuel the electrochemical operations. Liquid H₂O is supplied to the system at the reference environment parameters of 25 °C and 1 atm (Point 10). Before H₂O enters, the TEG (Points 10 to 11) and a counter-flow heat exchanger (Points 11 to 12) boost its temperature to that of the PEME. As the H₂ exits the cathode (Point 14), heat is released into the surrounding air, where it cools to the temperature of the reference environment. The O₂ gas produced at the anode is cooled to the temperature of the reference environment (Point 16) following its isolation from the H₂O/O₂ mixture (Point 15). The residual hot H₂O (Point 17) is recycled into the H₂O supply stream (Point 12) for the subsequent cycle of H₂ production. Throughout the entire PEME reaction, H₂O is transformed into H₂ and O₂, along with energy and heat. PEME has a surface area of 1 m².

In Figure 2, the process begins with the hot exhaust gases exiting the ICE at Point 1, carrying high temperature and pressure from the combustion process. As these gases flow through the HRHX at Point 2, they transfer heat to the supercritical CO₂ working fluid, causing the exhaust gases to cool down. The supercritical CO₂ enters the cycle at Point 6, absorbing heat from the exhaust gases and expanding through the turbine (Points 6 to 7), where it undergoes adiabatic expansion, converting thermal energy into mechanical work that drives a turbine generator. The CO₂ exits the turbine at Point 7, now at a lower pressure and temperature, but still in the supercritical state. In the recuperator, the high-temperature CO₂ (Points 7 to 8) transfers heat to low-temperature CO₂ (Points 10 to 11), improving overall cycle efficiency by preheating the incoming CO₂. Exiting the recuperator at Point 8, CO₂ is at a lower temperature and ready for compression in the compressor, where it is recompressed to high pressure, requiring mechanical work input. Before that, the temperature of CO₂ is reduced in TEG 2 (Points 8 to 9), converting the waste energy to useful power. At point 10 and after compressor, CO₂ enters the high-pressure side of the cycle again, now at a higher temperature and pressure, prepared to absorb heat from the heat exchangers in the recuperator and HRHX. Finally, at Point 2, TEG 1, located at the exhaust system exit, converts part of the waste heat directly into electricity through the Seebeck effect, utilizing the temperature difference between the exhaust gases and the ambient water to generate additional electrical power, thereby maximizing energy recovery efficiency.

In the waste heat recovery system using an IBC (Figure 3), the process begins at point 1, where hot exhaust gases exit the ICE at high temperature and pressure. The exhaust gases then enter the turbine at Point 1, still retaining substantial thermal energy. As the gases expand to sub-atmospheric pressure through the turbine, they produce mechanical work by driving the turbine. The gases exit the turbine at Point 2, now at a lower pressure and temperature due to the energy extracted. In TEG 1, the exhaust gases are further cooled, producing extra electricity. Finally, at point 3, the cooled, low-pressure gases are drawn into the compressor, where they are pressurized to ambient pressure. Furthermore, at Point 4, these gases transfer their heat to TEG 2, which completely converts this waste heat into electricity via the Seebeck effect. This system efficiently recovers waste heat from the engine, converting it into useful electrical energy.

In the waste heat recovery system utilizing an ABC (Figure 4), the process begins at point 1, where hot exhaust gases exit the ICE. At this stage, the hot gases enter the AHX, transferring heat to the working fluid (air) of the bottoming ABC. In the ABC, ambient air is compressed by the ABC compressor, moving from points 6 to 7. The hot, high-pressure air at point 7 then absorbs energy from the exhaust gases, becoming sufficiently hot to enter the ABC turbine at point 8 and produce bottoming cycle output power. The remaining exhaust gas at point 2 and exhaust air at point 9 enter thermoelectric generators (TEG 1 and TEG 2, respectively) to fully utilize the system’s residual energy, thereby generating additional power.

3. Modeling with Mathematics

The simulations of energy, exergy, exergy-economic, and environment related to the previously specified configurations have been carried out by means of suitable correlations included in the Engineering Equation Solver (EES). Following that, the EES software’s (Version 11.644) outputs have been coupled to the MATLAB NSGA-II toolbox through the use of artificial neural network (ANN) modeling. The following list of simplifying assumptions has been taken into consideration when the simulation process was started [29,77,103,104,105]:

1.

The equations for conversion have been inscribed while adhering to the conditions of a constant state.

2.

In heat exchangers, the gas streams have a 3% pressure drop.

3.

The energy and exergy equations’ kinetic and potential components have been ignored.

4.

It is assumed that the isentropic efficiencies do not change for any turbo-machines.

5.

Correlations pertaining to the mixture of ideal gases are utilized to compute the characteristics of gas and air mixtures.

6.

All components are fully insulated and have adiabatic performance.

7.

The mole fraction of ICE exhausted gas is N₂: 72.5%, O₂: 9.5%, H₂O: 9.8%, CO₂: 8.2%.

8.

The minimum temperature of the exhaust gas that is exiting the TEGs is regarded as being equivalent to 70 °C.

9.

In the bottoming SRC, the pump inlet fluid is saturated liquid.

10.

The values of ambient pressure and temperature are deemed as the reference standards for any analysis involving exergy.

Table 4. Fundamental correlations for a few configuration components.

Correlation	Note	Number
Thermoelectric generator [106,107]
${\dot{W}}_{TEG}={\eta }_{TEG}·{\dot{Q}}_{coldside}$	Output power	(1)
${\dot{Q}}_{coldside}={\dot{m}}_{cold}\left(h_{out}-h_{in}\right)$	Cold side energy rate	(2)
${\eta }_{TEG}={\eta }_{Carnot}{\displaystyle \frac{\sqrt{1+Z{T}_M}-1}{\sqrt{1+Z{T}_M}+\frac{T_L}{T_H}}}$	Efficiency of TEG	(3)
${\eta }_{Carnot}=1-{\displaystyle \frac{T_L}{T_H}}$	Carnot efficiency	(4)
Proton exchange membrane electrolyzer [108,109]
${\dot{n}}_{H_2,out}={\displaystyle \frac{J}{\mathbf{2}F}}$	Molar rate of hydrogen	(5)
$E{n}_i=J.V={\dot{W}}_{bottoming,main}+{\dot{W}}_{TEG,1}+{\dot{W}}_{TEG,2}$	The energy provided to the PEME	(6)
$V=V_0+V_{act,an}+V_{act,ca}+V_{ohm}$	Electric potential in PEME	(7)
$V_0\mathbf{=}\mathbf{1.229}-\mathbf{0.00085}\mathbf{\left(}{T}_{PEM}-\mathbf{298}\mathbf{\right)}$	Nernst equation	(8)
$V_{act,i}={\displaystyle \frac{R{T}_{PEM}}{F}}sin{h}^{-1}\left({\displaystyle \frac{J}{2.J_{0,i}}}\right)$	Activation over potential	(9)
$J_{0,i}=J_i^{ref}exp\left({\displaystyle \frac{-E_{act,i}}{R{T}_{PEM}}}\right)$	Exchange current density	(10)
$V_{ohm}=J.R_{PEM}$	Ohmic over potential	(11)
$R_{PEM}={{\displaystyle \int }}_0^D{\displaystyle \frac{dx}{{\omega }_{PEM}.{\theta }_x}}$	Overall resistance of the PEME	(12)
$\theta \left(x\right)={\displaystyle \frac{{\theta }_a-{\theta }_c}{D}}.x+{\theta }_c$	Membrane surface water	(13)
${\omega }_{PEM}=\left(0.5139 \theta \left(x\right)-0.326\right)·exp\left(1268\left({\displaystyle \frac{1}{303}}-{\displaystyle \frac{1}{T_{PEM}}}\right)\right)$	Local ionic conductivity	(14)

shows the essential equations for the TEG and PEME simulation.

3.1. Thermodynamic and Exergy-Economic Analyses

The formulas pertaining to mass, energy, exergy, and exergy-economic simulations of entire configurations are delineated below [110,111,112]:

$${\displaystyle \sum }{\dot{m}}_{\mathrm{i}}={\displaystyle \sum }{\dot{m}}_{\mathrm{e}}$$

(15)

$$\dot{Q}+{\displaystyle \sum }{\dot{m}}_{\mathrm{i}}{h}_{\mathrm{i}}=\dot{W}+{\displaystyle \sum }{\dot{m}}_{\mathrm{e}}{h}_{\mathrm{e}}$$

(16)

$${\dot{Ex}}_{\mathrm{Q}}+{\displaystyle \sum }{\dot{m}}_{\mathrm{i}}e{x}_{\mathrm{i}}={\dot{Ex}}_w+{\displaystyle \sum }{\dot{m}}_{\mathrm{e}}e{x}_{\mathrm{e}}+{\dot{Ex}}_{\mathrm{dest}}$$

(17)

$$c_{\mathrm{Q}}{\dot{Ex}}_{\mathrm{Q}}+{\displaystyle \sum }{c}_i{\dot{Ex}}_i+\dot{Z}={\displaystyle \sum }{c}_e{\dot{Ex}}_e+c_{\mathrm{w}}\dot{W}$$

(18)

According to the Refs. [111,113], Appendix A contains the fuel and product exergies as well as the energy balance equations for each of the various devices in the arrangements. Furthermore, Appendix B presents the exergy-economic and associated complimentary relationships in a tabular style for each of the configurations’ devices. Moreover, Appendix C provides an exact demonstration of the principal expenses required for the procurement of the component parts. The variables related to the cost of procurement for each component are then listed in Appendix D.

3.2. Output Parameters

The exergy efficiency is computed by means of the following equation:

$${\eta }_{ex}={\displaystyle \frac{{\dot{Ex}}_{hydrogen}}{{\dot{Ex}}_1}}$$

(19)

Then, for the purposes of exergy-economic evaluation, the total cost rate is calculated in the following manner:

$${\dot{C}}_{tot}={\displaystyle \sum }{\dot{Z}}_{\mathrm{k}}+{\displaystyle \sum }{\dot{C}}_{dest,k}+{\dot{\mathrm{C}}}_{\mathrm{env}}$$

(20)

Finally, the environmental cost rate is determined as below [114]:

$${\dot{\mathrm{C}}}_{\mathrm{env}}=0.024 {\dot{m}}_{{CO}_2}$$

(21)

3.3. Optimization

It should be remembered that energy conversion systems frequently face competing goals that need to be resolved at the same time. Building an efficient system usually costs more than building a less efficient one. It is possible to obtain a group of optimal solutions while working with several goals. The NSGA-II sub-program in MATLAB software (R2023b) has been used in the current study to identify a set of optimal spots. The parametric study in Section 4.3 reveals that three output parameters, ${\eta }_{ex}$, ${\dot{\mathrm{C}}}_{\mathrm{tot}}$, and ${\mathrm{c}}_{\mathrm{hydrogen}}$, have opposite trends. Therefore, they are convenient for a three-objective optimization problem. It is worth mentioning that ${\eta }_{ex}$ should be maximized and ${\dot{\mathrm{C}}}_{\mathrm{tot}}$ and ${\mathrm{c}}_{\mathrm{hydrogen}}$ should be minimized:

$${Objfun}_1=\max \left({\eta }_{ex}\right)$$

(22)

$${Objfun}_2=\min \left({\dot{C}}_{tot}\right)$$

(23)

$${Objfun}_3=\min \left(c_{hydrogen}\right)$$

(24)

The proper input parameters and their considered range in the optimization problem are tabulated in

Table 5. The parameters in the optimization process, together with their range.

Parameter	Value/Description
SRC (Configuration 1)
$T_{HRSG} (°C)$	170–300
$\mathbf{\Delta }{T}_{pinch,HRSG} \mathbf{\left(}°C\mathbf{\right)}$	5–50
$\mathbf{\Delta }{T}_{supeheat,HRSG }\mathbf{\left(}°C\mathbf{\right)}$	50–150
$T_{con}\mathbf{\left(}°C\mathbf{\right)}$	30–50
SBC (Configuration 2)
$T_{in,com}\mathbf{\left(}°C\mathbf{\right)}$	30–50
$P_{in,com }\mathbf{\left(}kPa\mathbf{\right)}$	7400–11,000
$P{R}_{com}$	1.2–3
$\mathbf{\Delta }{T}_{HS,HRHX }\mathbf{\left(}°C\mathbf{\right)}$	10–50
IBC (Configuration 3)
$IBTBP \mathbf{\left(}\mathbf{kPa}\mathbf{\right)}$	30–80
$T_{in,com }\mathbf{\left(}°C\mathbf{\right)}$	30–100
ABC (Configuration 4)
${PR}_{com}$	3–7
$\mathbf{\Delta }{T}_{HS,AHX} \mathbf{\left(}°C\mathbf{\right)}$	10–50

.

The process of transferring data from the EES stage to the optimization stage involves several steps. First, numerical data are extracted from EES, which includes the necessary parameters and performance metrics of the systems under study. These data are then imported into MATLAB, where it is used to train an ANN. The ANN is trained to establish a relationship between the design parameters and the objective functions. Once the ANN is trained, it produces m-files that encapsulate this relationship. These m-files are used in the optimization stage, where the NSGA-II algorithm in MATLAB optimizes the design parameters based on the ANN’s predictions. The optimization process is performed entirely in MATLAB, utilizing the ANN’s output to efficiently navigate the design space and identify optimal solutions. This approach ensures that the complex, nonlinear relationships captured by the ANN are accurately reflected in the optimization process.

4. Results and Discussion

Section 4.1 of this part contains the systems’ validation reports. Section 4.2 shows the simulation’s input values as well as the entire work flowchart. Section 4.3 reports on a thorough parametric investigation of four configurations, and Section 4.4 presents the optimization results.

4.1. Validation

The entire investigation is simulated using the EES. Table 6 first presents a comparison of the outcomes of regenerative SBC with those of earlier research. Furthermore, Figure 5 compares the cell potential–current density of PEME to a related study. The fact that the output parameters only differ slightly suggests that the simulation is correct.

Table 6. Regenerative SBC results validation using the same input data *.

State Point	Temperature (°C)	Temperature (°C) [115]	$\mathbf{Pressure}\left(\mathbf{kPa}\right)$	$\mathbf{Pressure}\left(\mathbf{kPa}\right)$ [115]
14	32	32	7360	7360
15	62.69	65.9	20,000	20,000
16	323.7	323.9	20,000	20,000
17	550	550	20,000	20,000
18	435.4	434.7	20,000	20,000
19	72.19	75.4	7360	7360

* Isentropic efficiency of compressor = 0.86, Isentropic efficiency of gas turbine = 0.93, Inlet temperature to compressor = 32 °C, Inlet temperature to turbine = 500 °C, Recuperator effectiveness = 0.86.

Table 6. Regenerative SBC results validation using the same input data *.

State Point	Temperature (°C)	Temperature (°C) [115]	$\mathbf{Pressure}\left(\mathbf{kPa}\right)$	$\mathbf{Pressure}\left(\mathbf{kPa}\right)$ [115]
14	32	32	7360	7360
15	62.69	65.9	20,000	20,000
16	323.7	323.9	20,000	20,000
17	550	550	20,000	20,000
18	435.4	434.7	20,000	20,000
19	72.19	75.4	7360	7360

* Isentropic efficiency of compressor = 0.86, Isentropic efficiency of gas turbine = 0.93, Inlet temperature to compressor = 32 °C, Inlet temperature to turbine = 500 °C, Recuperator effectiveness = 0.86.

Figure 5. PEME’s cell potential–current density in comparison with [116].

Figure 5. PEME’s cell potential–current density in comparison with [116].

4.2. Baseline Condition Inputs

Table 7. Input data for the baseline condition.

Parameter	Value
Reference temperature ($T_0$)	20 °C
Reference pressure ($P_0$)	101.3 kPa
NG ICE (All Configurations) [77]
Mass flow rate of exhausted gas (${\dot{m}}_{gas}$)	3303 ${\mathrm{kg}\mathrm{h}}^{-1}$
Temperature of the exhaust gas ($T_1$)	493 °C
Pressure of the exhaust gas $\left(P_1\right)$	105 kPa
TEG (All Configurations) [117,118]
Temperature of TEGs water inlet	25 °C
Temperature of TEGs water outlet	35 °C
${ZT}_M$	0.9
PEME (All Configurations) [119,120]
$T_{PEME}$	80 °C
$E_{act,an}$	76 $\mathrm{kJ}/\mathrm{mol}$
$E_{act,ca}$	18 $\mathrm{kJ}/\mathrm{mol}$
${\theta }_{an}$	14
${\theta }_{ca}$	10
$D$	100 $\mathsf{\mu }\mathrm{m}$
$F$	96,486 $\mathrm{C}/\mathrm{mol}$
$J_{an}^{ref}$	$1.7\times {10}^5$ $\mathrm{A}/{\mathrm{m}}^2$
$J_{ca}^{ref}$	$4.6\times {10}^3$ $\mathrm{A}/{\mathrm{m}}^2$
SRC (Configuration 1) [121,122]
HRSG evaporation temperature $(T_{HRSG}$)	250 °C
HRSG pinch temperature difference $(\mathbf{\Delta }{T}_{pp,HRSG})$	30 °C
HRSG degree of superheating $(\mathbf{\Delta }{T}_{sup,HRSG})$	100 °C
SRC condensation temperature ($T_{con}$)	40 °C
SRC pump’s isentropic efficiency	0.8
SRC turbine’s isentropic efficiency	0.85
SBC (Configuration 2) [123,124]
Compressor inlet temperature ($T_9$)	40 °C
Compressor inlet pressure ($P_9$)	8000 kPa
Pressure ratio related to compressor (${PR}_{SBC}$)	2.5
Hot side temperature difference of HRHX $(\mathbf{\Delta }{T}_{HS,HRHX})$	25 °C
The isentropic efficiency of SBC compressor	0.86
The isentropic efficiency of SBC turbine	0.86
IBC (Configuration 3) [125,126]
Inverse Brayton turbine back pressure (IBTBP) ($P_2$)	50 kPa
Compressor inlet temperature ($T_3$)	65 °C
The isentropic efficiency of IBC compressor	0.86
The isentropic efficiency of IBC turbine	0.86
ABC (Configuration 4) [87,127]
Pressure ratio related to compressor (${PR}_{ABC}$)	5
Hot side temperature difference of AHX $(\mathbf{\Delta }{T}_{HS,AHX})$	25 °C
Minimum temperature of air ($T_{10}$)	30 °C
The isentropic efficiency of ABC compressor	0.86
The isentropic efficiency of ABC turbine	0.86

displays the fundamental requirements for conducting the simulation, while Figure 6 outlines the complete process of simulation and optimization using EES and MATLAB software.

4.3. Parametric Study

In this part, the impact of changes in influential parameters in four bottoming systems is investigated on ${\eta }_{ex}$, ${\dot{\mathrm{Ex}}}_{\mathrm{dest},\mathrm{tot}}$, ${\dot{\mathrm{C}}}_{\mathrm{tot}}$, and ${\mathrm{c}}_{\mathrm{hydrogen}}$. It is of great importance to note that solely the parameter under consideration experiences alterations within the desired range, while the remaining parameters remain unaltered, as demonstrated in Table 7.

4.3.1. SRC Parametric Analysis

The influence of fluctuation in the evaporation temperature of the HRSG, spanning from 170 °C to 300 °C, on the overall performance of the system (Configuration 1) is demonstrated in Figure 7. An increase in evaporation temperature, with the consideration of the energy balance equation in HRSG, results in a decrease in ${\dot{m}}_{SRC}$. Conversely, an increase in enthalpy difference in the SRC turbine leads to a rise in SRC output power. In TEG 2, a decrease in passing flow stream reduces power output, whereas in TEG 1, an increase in T₂ contributes to an enhancement in power. An increase in the power of SRC and TEG 1 has a positive impact on ${\dot{W}}_{PEME}$, ${\dot{m}}_{hydrogen}$, and ${\eta }_{ex}$. This leads to a notable rise in ${\eta }_{ex}$ from 18.89 to 20.82% (Figure 7a). Additionally, a reduction in ${\dot{Ex}}_{dest}$ of HRSG leads to a decrease in ${\dot{\mathrm{Ex}}}_{\mathrm{dest},\mathrm{tot}}$ from 144.1 to 139.6 kW. Despite an increase in investment cost rate, $\dot{Z}$, of SRC turbine and PEME, a decrease in ${\dot{\mathrm{C}}}_{\mathrm{dest}}$ of HRSG results in a drop in ${\dot{\mathrm{C}}}_{\mathrm{tot}}$ from 32.97 $/h to 31.43 $/h. Subsequently, ${\mathrm{c}}_{\mathrm{hydrogen}}$ is reduced from 117 to 101.7 $/GJ (Figure 7b).

The illustration of the system’s performance (Configuration 1) is shown in Figure 8, with regard to the temperature at the pinch point, which spans from 5 to 50. A rise in the pinch point temperature leads to a decrease in ${\dot{m}}_{SRC}$, resulting in a decline in ${\dot{W}}_{SRC}$ and ${\dot{W}}_{TEG 2}$. Conversely, an increase in T₂ results in a surge in ${\dot{W}}_{TEG 1}$. The former holds more power and causes a decrease in ${\dot{W}}_{PEME}$ and ${\dot{m}}_{hydrogen}$. Therefore, ${\eta }_{ex}$ decreases from 22.67% to 19.82%. The primary reason for the increase in ${\dot{\mathrm{Ex}}}_{\mathrm{dest},\mathrm{tot}}$ from 135.3 kW to 141.9 kW (Figure 8a) is the rise in ${\dot{Ex}}_{dest}$ of TEG 1. Furthermore, a reduction in ${\dot{\mathrm{C}}}_{\mathrm{dest}}$ of the PEME and a decrease in $\dot{Z}$ of HRSG are the critical factors contributing to a decline in ${\dot{\mathrm{C}}}_{\mathrm{tot}}$, from 32.67 $/h to 31.62 $/h. It is worth noting that ${\mathrm{c}}_{\mathrm{hydrogen}}$ has experienced an increase from 104.5 $/GJ to 105.9 $/GJ, as illustrated in Figure 8b.

Figure 9 illustrates the impact of varying the superheating temperature of the HRSG within the range of 50 °C to 150 °C on the system’s performance, as noted in Configuration 1. An increase in the superheating temperature results in a decline in ${\dot{m}}_{SRC}$, which subsequently causes a reduction in ${\dot{W}}_{SRC}$ and ${\dot{W}}_{TEG 2}$. Conversely,${\dot{W}}_{TEG 1}$ increases due to the expansion of T₂. This trend, however, results in a minimum for ${\dot{m}}_{hydrogen}$ and ${\eta }_{ex}$ at a superheating temperature of 88 °C. Additionally, a maximum for ${\dot{\mathrm{Ex}}}_{\mathrm{dest},\mathrm{tot}}$ occurs at this point, as depicted in Figure 9a. Furthermore, according to Figure 9b, ${\dot{\mathrm{C}}}_{\mathrm{tot}}$ decreases from 32 $/h to 31.81 $/h, and ${\mathrm{c}}_{\mathrm{hydrogen}}$ drops from 105.4 to 104.1 $/GJ.

Figure 10 illustrates the impact of alterations in the condenser temperature difference, ranging from 30 to 50, on the system’s performance in accordance with Configuration 1. In this instance, ${\dot{m}}_{SRC}$ remains constant, while a decrease in the enthalpy difference of the turbine leads to a decline in the SRC output power. Conversely, the output power of TEG 1 and TEG2 increases, with the former exhibiting greater power, resulting in a reduction in ${\dot{W}}_{PEME}$ and ${\dot{m}}_{hydrogen}$. Consequently, ${\eta }_{ex}$ experiences a drop from 21.82% to 20.34% (as indicated in Figure 10a). The primary factor contributing to the increase in ${\dot{\mathrm{Ex}}}_{\mathrm{dest},\mathrm{tot}}$ from 137.3 kW to 140.7 kW is the rise in TEG 2 exergy destruction. Then, a reduction in $\dot{Z}$ and ${\dot{\mathrm{C}}}_{\mathrm{dest}}$ of SRC turbine and PEME is the main reason for a fall in ${\dot{\mathrm{C}}}_{\mathrm{tot}}$ from 32.05 $/h to 21.77 $/h. Ultimately, ${\mathrm{c}}_{\mathrm{hydrogen}}$ goes down from 106.2 $/GJ to 103.5 $/GJ (Figure 10b).

4.3.2. SBC Parametric Analysis

Figure 11 illustrates the impact of varying inlet temperature of the compressor on the system’s performance (Configuration 2). An elevation in temperature results in an increase in ${\dot{m}}_{SBC}$. Consequently, the power of the SBC turbine, TEG 1, TEG 2, and SBC compressor also increases. The SBC compressor’s effect is dominant, leading to a decline in ${\dot{W}}_{PEME}$ and ${\dot{m}}_{hydrogen}$. As a result, ${\eta }_{ex}$ experiences a reduction from 16.53% to 13.96% (Figure 11a). An increase in ${\dot{Ex}}_{dest}$ of TEG 1 and TEG 2 contributes to a rise in ${\dot{\mathrm{Ex}}}_{\mathrm{dest},\mathrm{tot}}$ from 149.6 kW to 155.6 kW. The primary cause for the decrease in ${\dot{\mathrm{C}}}_{\mathrm{tot}}$ from 32.93 $/h to 30.07 $/h can be attributed to the decline in ${\dot{\mathrm{C}}}_{\mathrm{dest}}$ of the SBC recuperator and PEME, as well as $\dot{Z}$ of PEME. It is worth noting that ${\mathrm{c}}_{\mathrm{hydrogen}}$ has also experienced a decline, decreasing from 102.5 $/GJ to 87.74 $/GJ (Figure 11b).

The effects of fluctuation in the inlet temperature of the compressor, ranging from 7400 kPa to 11,000 kPa, on the system’s performance (Configuration 2) are illustrated in Figure 12. In this particular scenario, a decline in ${\dot{m}}_{SBC}$ results in a decrease in the power of SBC turbine, TEG 2, and SBC compressor. Additionally, a reduction in T₂ leads to a decline in TEG 1 output power. The aforementioned trends, however, lead to a maximum ${\eta }_{ex}$ of 15.98% in P_in,com = 9400 kPa (Figure 12a). Furthermore, a decrease in TEG 1 and an increase in recuperator exergy destruction results in a minimum value for ${\dot{\mathrm{Ex}}}_{\mathrm{dest},\mathrm{tot}}$ at this juncture. Furthermore, an increase in ${\dot{\mathrm{C}}}_{\mathrm{dest}}$ of both PEME and SBC recuperator, along with a surge in $\dot{Z}$ of PEME, contributes to the escalation of ${\dot{\mathrm{C}}}_{\mathrm{tot}}$ from 30.3 $/h to 31.39 $/h. Additionally, it is noteworthy that ${\mathrm{c}}_{\mathrm{hydrogen}}$ attains its maximum value of 95.14 $/GJ at P_in,com = 10,200 kPa, as illustrated in Figure 12b.

Figure 13 reveals the impact of variations in compressor pressure ratios between 1.2 and 3 on the performance of the system (Configuration 2). An increase in pressure ratio leads to a rise in the SBC turbine, TEG 2, and SBC compressor power. Conversely, a decrease in T₂ results in a reduction in TEG 1 power. In conclusion, an increase in turbine output power has a significant effect, resulting in an improvement in ${\dot{W}}_{PEME}$ and ${\dot{m}}_{hydrogen}$. As a result, ${\eta }_{ex}$ increases from 6.46% to 16.11%. ${\dot{\mathrm{Ex}}}_{\mathrm{dest},\mathrm{tot}}$ decreases from 173 kW to 150.6 kW due to a decrease in ${\dot{Ex}}_{dest}$ of the recuperator and TEG 1 (Figure 13a). Moreover, the primary cause for the decrease in ${\dot{\mathrm{C}}}_{\mathrm{tot}}$ from 47.86 $/h to 29.67 $/h can be attributed to a dip in $\dot{Z}$ and ${\dot{\mathrm{C}}}_{\mathrm{dest}}$ of these two components. Additionally, within the range of consideration, ${\mathrm{c}}_{\mathrm{hydrogen}}$ experiences a decline from 195.4 $/GJ to 86.41 $/GJ (Figure 13b).

Figure 14 depicts the ramifications of altering the outputs consequent to an increase in the hot side temperature differential of the heater, ranging from 10 °C to 50 °C. This escalation in temperature disparity leads to a surge in ${\dot{m}}_{SBC}$, which in turn leads to a rise in the power of turbine, compressor, and TEG 2. Subsequently, there is a decrease in the TEG 1 power due to a decline in T₂. The increase in the turbine of SBC and TEG 2 leads to an improvement in PEME power, thereby resulting in an advancement in ${\eta }_{ex}$ from 14.77% to 15.22% (as shown in Figure 14a). The pivotal factor for the decrement in ${\dot{\mathrm{Ex}}}_{\mathrm{dest},\mathrm{tot}}$ from 153.7 kW to 152.6 kW is the reduction in ${\dot{Ex}}_{dest}$ of TEG 1. Furthermore, it should be noted that an increase in SBC cost rates and a decrease in TEG 1 cost rate result in a minimum point of 30.36 $/h for ${\dot{\mathrm{C}}}_{\mathrm{tot}}$ at a temperature differential of 21.1 °C. It is interesting to observe that at this point, ${\mathrm{c}}_{\mathrm{hydrogen}}$ reaches its minimum value of 90.16 $/GJ (as depicted in Figure 14b).

4.3.3. IBC Parametric Analysis

The impact of alterations in inverse Brayton turbine back pressure (IBTBP) ranging from 30 kPa to 80 kPa on the output indicators is shown in Figure 15. An escalation in IBTBP results in a decline in IBC turbine power, TEG 2 power, and IBC compressor power. Consequently, the output power of TEG 1 surges owing to an increase in T₂. These aforementioned parameters collectively lead to a decrease in PEME input power, thereby causing a reduction in ${\eta }_{ex}$ from 13.02% to 11.39% (Figure 15a). Furthermore, ${\dot{Ex}}_{dest,tot}$ experiences an upsurge from 158.2 kW to 162 kW due to the amplification of TEG 1 exergy destruction. A decrease in ${\dot{\mathrm{C}}}_{\mathrm{dest}}$ of TEG 2 as well as a reduction in $\dot{Z}$ of IBC turbine, TEG 2, and PEME are the principal factors contributing to the diminution of ${\dot{\mathrm{C}}}_{\mathrm{tot}}$ from 26.81 $/h to 25.74 $/h. Subsequently, ${\mathrm{c}}_{\mathrm{hydrogen}}$ declines from 60.15 $/GJ to 58.33 $/GJ within the examined range (Figure 15b).

Figure 16 presents an analysis of the impact of varying the inlet temperature of the IBC compressor within the range of 30 °C to 100 °C on the system’s performance. Notably, this increase leads to a rise in the power of both the IBC compressor and TEG 2. However, the TEG 1 output power experiences a decrease. Consequently, the input electricity to PEME decreases, which results in a reduction in ${\eta }_{ex}$ from 14.89% to 12.11% (as shown in Figure 16a). Moreover, ${\dot{\mathrm{Ex}}}_{\mathrm{dest},\mathrm{tot}}$ increases from 153.8 kW to 160.3 kW due to the rise in TEG 2 exergy destruction. The upsurge in $\dot{Z}$ and ${\dot{\mathrm{C}}}_{\mathrm{dest}}$ of TEG 2 is the main contributing factor to the enhancement of ${\dot{\mathrm{C}}}_{\mathrm{tot}}$ from 25.55 $/h to 26.2 $/h (as illustrated in Figure 16b). Ultimately, ${\mathrm{c}}_{\mathrm{hydrogen}}$ decreases from 60.73 $/GJ to 59.14 $/GJ.

4.3.4. ABC Parametric Analysis

Figure 17 illustrates the impact of varying the pressure ratio of ABC from 3 to 7 on the system’s outputs. An increase in the pressure ratio results in a corresponding increase in the ABC compressor, ABC turbine, and TEG 1. Conversely, the output power of TEG 2 decreases. These aforementioned parameters collectively contribute to a reduction in ${\dot{W}}_{PEME}$ and ${\dot{m}}_{hydrogen}$. Consequently, ${\eta }_{ex}$ reduces from 13.68% to 8.46% (as shown in Figure 17a). The primary cause of the increase in ${\dot{\mathrm{Ex}}}_{\mathrm{dest},\mathrm{tot}}$ from 156.2 kW to 168.4 kW is due to the increase in ${\dot{Ex}}_{dest}$ of the ABC turbine and TEG 1. Moreover, an increase in ${\dot{\mathrm{C}}}_{\mathrm{dest}}$ of the ABC compressor, ABC turbine, and TEG 1 results in a rise in ${\dot{\mathrm{C}}}_{\mathrm{tot}}$ from 46.3 $/h to 55.64 $/h. Lastly, ${\mathrm{c}}_{\mathrm{hydrogen}}$ surges by 53.07% within the examined range (Figure 17b).

Figure 18 illustrates the impact of the variation in hot side temperature difference of the AHX, ranging from 10 °C to 50 °C, on the output indicators. An increase in temperature difference leads to an increase in the ABC passing stream, resulting in a rise in the ABC compressor and turbine work. Consequently, the output power of TEG 2 decreases due to a decline in T₉. Overall, the input power to the electrolyzer and hydrogen production decreases, leading to a dip in ${\eta }_{ex}$ from 12.35% to 10.52% (Figure 18a). ${\dot{\mathrm{Ex}}}_{\mathrm{dest},\mathrm{tot}}$ increases from 159.3 kW to 163.6 kW because of an increase in ${\dot{Ex}}_{dest}$ of AHX. A decrease in ${\dot{\mathrm{C}}}_{\mathrm{dest}}$ of TEG 2 and PEME, coupled with a reduction in $\dot{Z}$ of AHX, leads to a notable decrement of ${\dot{\mathrm{C}}}_{\mathrm{tot}}$ from 54.27 $/h to 47.44 $/h. As a result, ${\mathrm{c}}_{\mathrm{hydrogen}}$ experiences a decline from 145.5 $/GJ to 132.2 $/GJ, as illustrated in Figure 18b.

4.4. Optimization Results

The present section showcases the outcomes linked with the NSGA-II algorithm and the three-objective optimization. In view of the fact that the objectives in question, namely, ${\mathsf{\eta }}_{\mathrm{ex}}$, ${\dot{C}}_{tot}$, and ${\mathrm{c}}_{hydrogen}$, are in conflict with each other, the Pareto frontier and its associated numerical achievements are depicted in Figure 19, Figure 20, Figure 21 and Figure 22 and

Table 8. The four layouts’ optimal operating points.

Decision Variables	Values
SRC (Configuration 1)
$T_{HRSG,SRC}$	284 °C
$\mathbf{\Delta }{T}_{pinch,eva,SRC}$	42.46 °C
$\mathbf{\Delta }{T}_{sup,eva,SRC}$	14.6 °C
$T_{con,SRC}$	131.2 °C
SBC (Configuration 2)
$T_{in,com, SBC}$	34.47 °C
$P_{in,com, SBC}$	40.84 °C
${PR}_{com,SBC}$	8360 kPa
$\mathbf{\Delta }{T}_{HS,HRHX,SBC}$	2.992
IBC (Configuration 3)
$P_{in,tur, IBC}$	59.71 kPa
$T_{in,com, IBC}$	41.27 °C
ABC (Configuration 4)
${PR}_{com,ABC}$	3.018
$\mathbf{\Delta }{T}_{HS,AHX,ABC}$	40.48 °C

and

Table 9. Values of the objective functions for Configurations 1–4 at the optimal condition.

Parameters	SRC-Based System (Configuration 1)	SBC-Based System (Configuration 2)	IBC-Based System (Configuration 3)	ABC-Based System (Configuration 4)
${\eta }_{ex}\mathbf{(}\mathbf{\%}\mathbf{)}$	21.93	18.05	13.72	13.26
${\dot{C}}_{tot}\mathbf{\left(}\mathbf{\$} {\mathbf{h}}^{-1}\mathbf{\right)}$	31.82	30.75	25.58	43.94
$c_{hydrogen}\mathbf{\left(}\mathbf{\$} \mathbf{G}{\mathbf{J}}^{-1}\mathbf{\right)}$	101.3	93.38	59.91	108.6
$Specific cost of system={\displaystyle \frac{{\dot{C}}_{tot}}{{\dot{Ex}}_{product}}}\mathbf{\left(}\mathbf{\$}/\mathbf{k}\mathbf{W}\mathbf{h}\mathbf{\right)}$	0.6159	0.7235	0.7919	1.407

, respectively. Table 8 is related to design variables, and Table 9 is regarding objective functions. Then, all of the red circles within this frontier display the optimal points that are not dominated by any other points. Therefore, the results for the tradeoff point are reported in Table 9. Accordingly, the highest ${\eta }_{ex}$ is related to the SRC-based system (21.93%), while the lowest ${\dot{\mathrm{C}}}_{\mathrm{tot}}$ (25.58 $/h) and ${\mathrm{c}}_{\mathrm{hydrogen}}$ (59.91 $/GJ) are for the IBC-bases system. Furthermore, the specific cost of the system (=total cost rate/exergy of product), which is a tradeoff between exergy and economic parameters, is minimum for the SRC-based system (0.6159 $/kWh). Hence, the SRC-based and IBC-based systems have been chosen as the best configurations for the waste energy recovery of high-temperature exhaust heat of ICE.

Then, the main output parameters of each layout at the optimum point are tabulated in

Table 10. System performances at their optimal condition.

Parameter	SRC-Based System (Configuration 1)	SBC-Based System (Configuration 2)	IBC-Based System (Configuration 3)	ABC-Based System (Configuration 4)
${\dot{W}}_{ICE}\left(KW\right)$	584	584	584	584
${\dot{W}}_{main,bottoming}\left(KW\right)$	102.5	75.14	36.91	41.73
${\dot{W}}_{TEG,1}\left(KW\right)$	4.95	7.38	25.84	3.22
${\dot{W}}_{TEG,2}\left(KW\right)$	1.64	4.314	0.71	16.16
${\dot{W}}_{PEME}\left(KW\right)$	109.1	86.85	63.74	61.16
${\dot{m}}_{hydrogen}\left({\displaystyle \frac{kg}{h}}\right)$	1.587	1.306	0.992	0.959
${\dot{Ex}}_{fuel,tot}\left(kW\right)$	235.5	235.5	235.5	235.5
${\dot{Ex}}_{product,tot}\left(kW\right)$	51.66	42.51	32.31	31.24
${\dot{Ex}}_{dest,tot}\left(kW\right)$	137	146	156.6	157.2
${\dot{Ex}}_{loss,tot}\left(kW\right)$	46.86	46.98	46.67	47.11
${\eta }_{ex}(\%)$	21.93	18.05	13.72	13.26
${\dot{Z}}_{tot}\left(\$/h\right)$	5.52	2.732	1.98	9.348
${\dot{C}}_{dest\mathbf{,}tot}\left(\$/h\right)$	16.34	18.06	13.64	24.63
${\dot{C}}_{env}\left(\$/h\right)$	9.96	9.96	9.96	9.96
${\dot{C}}_{tot}\left(\$/h\right)$	31.82	30.75	25.58	43.94
$c_{el\mathbf{,}bottoming} \left(\$/GJ\right)$	43.1	40.83	25.61	50.63
$c_{hydrogen}\left(\$/GJ\right)$	101.3	93.39	59.91	108.6

. The lowest amount of hydrogen production and exergy efficiency is related to the ABC-based system. Then, the IBC-based system has the second stage. Despite the IBC-based system producing low hydrogen and having low ${\eta }_{ex}$, the lowest ${\dot{\mathrm{C}}}_{\mathrm{tot}}$ and ${\mathrm{c}}_{\mathrm{hydrogen}}$ are related to this configuration. As is clear from Table 10, the addition of TEGs to the systems considerably improves the output power, especially in cases of TEG 1 in the IBC-based system (25.84 kW output power) and TEG2 in the ABC-based system (16.16 kW output power). Therefore, the waste energy recovery of systems by TEGs is justifiable. Furthermore, in an IBC-based system, for example, the exergy of exhausted gas is 235.5 kW, of which 32.31 kW is converted to useful output productions, bringing about a ${\eta }_{ex}$ of 13.72%. Then, 66.49% (156.6 kW) of fuel exergy is turned out to exergy destruction and 19.81% (46.67 kW) is changed to exergy loss. In addition, ${\dot{\mathrm{Z}}}_{\mathrm{tot}}$, ${\dot{\mathrm{C}}}_{\mathrm{dest},\mathrm{tot}}$, and ${\dot{\mathrm{C}}}_{\mathrm{env}}$ rate make up 7.74%, 53.32%, and 38.93% of ${\dot{\mathrm{C}}}_{\mathrm{tot}}$ of IBC-based system (25.58 $/h). As is obvious, the IBC-based system has the lowest amounts of ${\dot{\mathrm{Z}}}_{\mathrm{tot}}$ (1.98 $/h) and ${\dot{\mathrm{C}}}_{\mathrm{dest},\mathrm{tot}}$ (13.64 $/h) among different configurations. This occurs because of the lowest number of components of IBC in comparison with other bottoming systems. Finally, the IBC-based system leads to the lowest ${\mathrm{c}}_{\mathrm{el}}$ in the bottoming cycles (25.61 $/GJ) and, consequently, the lowest ${\mathrm{c}}_{\mathrm{hydrogen}}$ (59.91 $/h).

The primary energy-exergy-economic parameters in the various system components at the optimal point are shown in

Table 11. Component performances at their optimal state.

System/Components	$\dot{\mathit{W}} \mathbf{or} \dot{\mathit{Q}}\left(\mathbf{kW}\right)$	${\dot{\mathit{E}\mathit{x}}}_{\mathit{f}}\left(\mathbf{kW}\right)$	${\dot{\mathit{E}\mathit{x}}}_{\mathit{p}}\left(\mathbf{kW}\right)$	${\dot{\mathit{E}\mathit{x}}}_{\mathit{D}}\left(\mathbf{kW}\right)$	${\mathit{\eta }}_{\mathit{e}\mathit{x}}\left(\mathit{\%}\right)$	$\dot{\mathit{Z}}\left(\mathbf{\$}/\mathbf{h}\right)$	${\dot{\mathit{C}}}_{\mathit{d}\mathit{e}\mathit{s}\mathit{t}}\left(\mathbf{\$}/\mathbf{h}\right)$
Bottoming systems Configuration 1
HRSG	317.2	162.6	131.8	30.8	81.06	0.826	2.61
SRC turbine	103.4	120.6	103.4	17.22	85.72	2.56	1.92
TEG 2	1.64	11.98	3.51	8.46	29.32	0.044	0.946
SRC pump	0.902	0.902	0.731	0.171	81.03	0.032	0.026
TEG 1	4.95	29.31	5.93	23.38	20.24	0.134	1.98
PEME	109.1	109.1	52.11	56.96	47.78	1.97	8.83
Bottoming systems Configuration 2
HRHX	281.3	149.1	139.7	9.44	93.67	0.332	0.801
SBC turbine	101.4	109.4	101.4	8.05	92.64	0.196	1.08
Recuperator	257.6	101.9	67.25	34.62	66.02	0.216	4.65
TEG 2	4.314	18.66	6.08	12.57	32.63	0.117	1.68
SBC compressor	26.24	26.24	23.04	3.20	87.8	0.142	0.47
TEG 1	7.38	42.84	8.65	34.18	20.21	0.2	2.90
PEME	86.85	85.85	42.88	43.97	49.37	1.52	6.46
Bottoming systems Configuration 3
IBC turbine	92.14	98.79	92.14	6.64	93.27	0.108	0.564
TEG 1	25.84	138	28.85	109.2	20.9	0.701	9.27
IBC compressor	55.23	55.23	48.96	6.27	88.64	0.038	0.578
TEG 2	0.719	4.52	0.953	3.57	21.06	0.019	0.376
PEME	63.47	63.47	32.59	30.88	51.35	1.11	2.84
Bottoming systems Configuration 4
ABC compressor	141.4	141.4	127.3	14.17	89.98	0.167	2.58
Air heat exchanger	347.2	172.6	160.8	11.8	93.16	7.33	1.00
ABC turbine	183.2	199.2	183.2	15.97	91.98	0.243	2.65
TEG 1	3.22	19.39	3.94	15.45	20.34	0.087	1.31
TEG 2	16.16	88.84	18.65	70.19	20.99	0.438	11.68
PEME	61.16	61.11	31.51	29.59	51.57	1.074	5.39

. As is clear from Table 11, important components in terms of exergy destruction are PEME (Configuration 1 and Configuration 2), TEG 1 (Configuration 3), and TEG 2 (Configuration 4). Hence, exergy efficiencies of all components are higher than 50% except for TEG 1, TEG 2, and PEME (in Configuration 1 and Configuration 2). Moreover, the biggest investment cost rate is related to SRC in Configuration 1 and PEME in Configurations 2 and 3, while in Configuration 4, the AHX has the highest investment cost rate. This is the main reason why Configuration 4 has the highest ${\dot{\mathrm{C}}}_{\mathrm{tot}}$ among the four considered configurations. Regarding the exergy destruction cost rate, in Configurations 1 and 2, the PEME has the highest values. Then, in Configurations 3 and 4, TEG 1 and TEG 2 are important components. This occurs because of the high values of TEG1 power in Configuration 3 and TEG 2 power in Configuration 4.

5. Practical Implementation, Limitations, and Future Research

The practical implementation of waste heat recovery systems, such as the SRC, SBC, IBC, and ABC, in ICEs presents a promising opportunity to enhance energy efficiency, reduce operational costs, and contribute to environmental sustainability. These systems can be scaled and adapted to various engine sizes, integrated into existing infrastructures with minimal disruption, and be economically viable with proper financial incentives. To ensure reliability and widespread adoption, it is essential to focus on robust designs, regular maintenance, and training for maintenance personnel. Additionally, supportive government policies and regulations will play a crucial role in facilitating the implementation of these technologies. Standardized interfaces and collaboration with engine manufacturers can further ease the integration process, ensuring compatibility and efficiency. By converting waste heat into useful energy forms, such as electricity and hydrogen, these technologies align with global sustainability goals, reducing greenhouse gas emissions and fossil fuel consumption while promoting the use of cleaner energy sources. Our study demonstrates the potential of these systems to make significant contributions to energy efficiency and environmental sustainability, providing a strong foundation for future research and practical applications.

It is acknowledged that simulations may not capture all real-world variables and challenges. However, the insights gained from theoretical models are crucial in the early stages of research, guiding future experimental studies to identify key parameters and potential issues before large-scale implementation. It is recognized that the systems presented, particularly the SBC, involve high implementation complexity and may entail significant costs. This feasibility analysis highlights these aspects and aims to provide an understanding of the potential benefits and challenges associated with these advanced systems. The high complexity is intrinsic to the innovative nature of the technologies explored. However, it is through detailed theoretical studies that can pave the way for more practical and cost-effective solutions in the future. While this study focuses on theoretical validation, it sets the stage for future experimental research. This study emphasizes the importance of experimental studies to further validate the findings and address real-world challenges. The current work provides a necessary first step, offering a detailed theoretical framework that can inform and guide experimental designs. It is anticipated that future research will build on these findings, incorporating experimental data to refine and enhance the models.

The advancement of waste energy recovery systems in ICEs holds significant potential for future research and practical applications. Future studies can focus on the integration of novel materials and advanced manufacturing techniques to enhance the efficiency and cost-effectiveness of bottoming cycles. Additionally, exploring hybrid systems that combine multiple waste heat recovery technologies could provide even greater efficiency gains. Experimental validations and real-world pilot projects will be crucial to demonstrating the viability and benefits of these systems. Furthermore, developing standardized protocols and fostering collaboration between industry stakeholders and policymakers will be essential to accelerate the adoption of waste energy recovery technologies. Ultimately, continued innovation and optimization in this field will contribute to achieving global sustainability goals, reducing greenhouse gas emissions, and promoting the transition to cleaner energy sources.

6. Conclusions

This study extensively reviewed the existing literature on four key bottoming cycles: SRC, CO₂ SBC, IBC, and ABC. In addition, these four main bottoming systems were utilized for the waste energy recovery of natural gas-fired ICE with a capacity of 584 kW and an exhausted gas temperature of 493 °C. This was undertaken with the objective of determining the optimal configuration for waste recovery from high-temperature exhausted gas produced by an ICE. Four distinct cycles—namely, SRC, SBC with CO₂ working fluid, IBC, and ABC—were selected as the primary bottoming systems. Furthermore, to ensure complete utilization of the waste heat generated by the bottoming systems, two TEGs were incorporated into the design. One TEG was utilized to harness residual heat from the exhausted gas, while the other was employed to recover unused energy from the main bottoming system. The power generated by the bottoming systems was subsequently directed toward a PEME for hydrogen production, thereby prompting the main inquiry: which main bottoming system yields the most cost-effective hydrogen production, as determined by a 4E optimization? The key findings of this study are presented below:

• At the optimum mode, the SRC-based system resulted in the highest exergy efficiency (21.93%), while it brought about the second worst total cost rate (31.82 $/h) and unit cost of hydrogen (101.3 $/GJ). On the other hand, the IBC-based system conduced to the lowest exergy efficiency (13.72%), total cost rate (25.58 $/h), and unit cost of hydrogen (59.91 $/GJ).
• Using TEGs for complete waste heat recovery of the topping and main bottoming system was a good choice, especially for TEG 1 in the IBC-based system (25.84 kW output power) and TEG 2 in the ABC-based system (16.16 kW output power). Although TEG 2 had a good performance in Configuration 4, it did not have a good performance overall in comparison with other configurations because of the low power generation of the main system and the high cost of AHX.
• PEME in Configurations 1 and 2, TEG 1 in Configuration 3, and TEG 2 in Configuration 4 had the highest amount of exergy destruction among the different components of the systems. Those led to the highest exergy destruction cost rate of the above-mentioned components. Regarding investment cost rate, SRC turbine in Configuration 1, PEME in Configurations 2 and 3, and AHX in Configuration 4 were important components. The high cost of AHX in Configuration 4 is the chief reason for the worst economic performance of this configuration.