**1. Introduction**

With the reinforcement of environmental legislation, emission mitigation continues to be an essential problem at the industrial level, and heat recovery in manufacturing procedures is becoming standard practice because of progressively stringent policies on energy efficiency [1]. Therefore, waste heat recovery systems play an essential role in saving energy by considering existing energy generation technologies that are geared towards reducing fuel consumption, greenhouse emissions, and electricity production cost [1]. For this reason, the volume of power and temperature, as well as the form and the prices of technologies for the recovering of waste resources, are the key factors determining the feasibility of energy consumed. Accordingly, to reach a maximum recovery capacity, it is of particular significance that the temperature and the residual heat correlate with the energy recovery periods for the remaining electricity [1].

For alternative energy generation, the concept of the simple regeneration process has been suggested, considering CO2 as a working solvent due to its properties [2], including low critical strain, high thermal tolerance at interest temperature, inertia, well known thermal properties, as well as being nontoxic and economical. Angelino et al. [3] published research related to various cycle designs. They demonstrated that the recompression cycle is better at high temperatures, and it is particularly interesting in high-temperature gas-cooled reactors. Subsequently, Dostal et al. [4] in his thesis evaluated the Brayton S-CO2 cycle for advanced nuclear power generation reactors.

Nowadays, many organic Rankine cycle (ORC) applications have been used as a waste heat recovery system to convert waste heat into mechanical energy. However, the ORC has efficiency limitations when working with waste heat at high temperatures because of the physical and thermal properties usually presented by organic fluids. Abrosimov et al. [5] investigated the combination of a Brayton cycle and an ORC cycle by designing both ORC and combined cycle models using Aspen Hysys® version 9' (Aspen Technology, Inc., Bedford, MA, USA. Thermodynamic and economic optimizations of the models were made to conduct a comparative analysis between the solutions. The results have demonstrated the 10% advantage of the combined scheme over the ORC cycle in terms of generated power and system efficiency. Optimization based on the leveled energy cost for variable capacity factors has revealed an advantage of more than 6% of the solution investigated.

Zhangpeng Guo et al. [6] conducted a sensitivity analysis comparing the recompression cycle, the double-expansion recompression cycle, and the modified recompression cycle applied to fourth-generation nuclear reactors, which have high operating temperatures and pressures that would increase plant efficiency and hydrogen production. Vasquez Padilla et al. [7] conducted a detailed energy and exergy analysis of four Brayton S-CO2 cycle configurations (single Brayton cycle, recompression Brayton cycle, partial cooling recompression, and main compression with intercooling) with and without reheating to investigate the effect of replacing the reheater and heater by a solar receiver. In the same year, Ricardo Vásquez et al. [8] also performed the energy and exergy analysis of a supercritical Brayton cycle with recompression CO2, but a bottoming cycle was not proposed.

In recent decades, the Brayton S-CO2 cycle has attracted the attention of many academics and industries because of its significant advantages [3,9], such as a better thermal efficiency [10]. Brayton S-CO2 is less caustic relative to steam with the same operating speed, the turbomachine used is lightweight, almost ten times smaller than the steam turbine, and dry cooled easily in comparison with the steam engine [11]. Therefore, based on each of these benefits, the Brayton S-CO2 cycle has been tested for various uses as an energy conversion device, including nuclear, geothermal, solar, and thermal power plants. So, the device presents higher thermal performance and a smaller process size than the traditional Rankine steam device based on these advantages, and therefore the Brayton S-CO2 cycle is considered an efficient alternative to the steam process at Rankine [12].

The thermal performance of the heat exchanger plays an important role in the cycle efficiency, as shown in these previously described studies [13]. Thus, when a significant amount of heat is extracted in the recuperator to improve thermal performance, the high energy output is expected and thus the capital cost decreases by utilizing traditional shell and tube heat exchangers (STHE); nonetheless, some high-compact heat exchangers (up to ten times relative to STHE) and printed circuit heat exchangers (PCHE) have been sold and can be added directly to waste heat recovery from gas [14]. However, this type of heat exchanger can be multi-objective optimized, attending to exergy and energy objective function [15]. Yuan Jiang et al. [16] published a paper detailing the core architecture and optimization methodology built into the Aspen Custom Modeler for microtube shell and tube exchangers. They also sized a PCHE and then compared it among the various heat exchangers used for S-CO2 and indicated that the PCHE is a promising candidate due to its concentration, quick dynamic response, and mature construction state. Optimum configuration findings suggest that there is less metal mass in a system of two hot plates per cold plate and high angle channels; therefore, a safer option for broad-scale applications [17].

The PCHE is a type of micro-channel heat exchanger residing in various carve sheets composed of many micro-waved channels in each layer [18]. Thus, Devesh Ranjan et al. [19] in 2019 developed experimental research in which the characteristics of heat flow and pressure drop decrease for the PCHE with a different configuration, which is a promising result increasing the thermal performance of the S-CO2 integrated with ORC.

All this research involves a substantial economic investment; however, there is an effective way with a high degree of reliability to perform these tests without the need for tuning, and that is through dynamic modeling. In engineering, dynamic modeling and simulation are increasingly relevant, as there is a growing need to study the chaotic function of complex structures made up of components from different domains. The models may be used to conduct danger and operability tests. Automated emergency response protocols were validated in [20], as in the case of Xiaoyan Ji et al. [18] also, who performed the heat exchanger design for the suspensions in biogas plants, which was analyzed numerically based on the rheological properties and further coupled with full thermal cycles to demonstrate waste heat recovery and high heating capacity for heat exchangers design. Dynamic models may help design heat-sharing facilities [21]. For example, Oh Jong-Taek et al. [22] demonstrated employing computational fluid dynamics to study the heat transfer and flow characteristics, as well as the effect of mass flow on temperature and pressure distribution in PCHE.

On the other hand, the Brayton S-CO2 cycles help to predict the advantages of compact equipment within the moderate temperature range (450–750 ◦C), as well as finding the disadvantages of materials due to high temperatures and pressure, studied in various applications [23,24]. Craig S. Turchi et al. [25] using simulations of the Brayton S-CO2 cycle, observed favorable characteristics such as the capacity to adapt dry cooling and produce the desired efficiency in the area of solar energy concentration. Yann Le Moullec [26] proposed a closed Brayton S-CO2 loop based on combining carbon capture and storage facilities to mitigate CO2 pollution as electricity production from coal-fired power plants is a significant source of ambient CO2 pollution, as Olumide Olumayegun et al. [27] where the thermodynamic performance of Brayton S-CO2 cycles coupled to a coal furnace and integrated with 90% post-combustion CO2 capture was evaluated, investigating three background s-CO2 cycle designs, including a new recompression cycle with a single recuperator, showing as a result, that the configuration with a recompression cycle and a single recuperator has the highest net plant efficiency. Without CO2 capture, the effectiveness of the coal-fired plants was higher than that of steam. Youcan Liang et al. [28], shows the application of the method on a dual-fuel engine, which reveals that the maximum net power of the system is up to 40.88 kW, improving by 6.78%, leading to greater energy efficiency and reduced fuel consumption of the engine. Complementarily, Shih-Ping Kao et al. [29] released the results of a complex simulation code based on actual gas and integral momentum models, which was developed at the Massachusetts Institute of Technology to test control strategies for a small light-water reactor fitted with a compact Brayton S-CO2 cycle.

Based on the significant energy loss presented in the industrial generation engine, some waste heat recovery systems based on the Brayton S-CO2 cycle have been studied. Therefore, in 2018 Antti Uusitalo et al. [30] examined the use of supercritical Brayton cycles to recover power from the exhaust gases of large-scale engines. The objective of this study was to examine electricity generation through varying operating conditions and organic fluids and thus define the key design parameters influencing the cycle's energy output. In 2018 Piero Danieli et al. [31] measured the economic and thermodynamic efficiency of four separate waste heat recovery systems implemented through simulation to two hollow glass furnaces producing around 4 MWt of heat loss at 450 ◦C. Also, Subhash Lahane et al. [32] planned a heat exchanger design to collect the excess heat from the exhaust gases of a diesel engine to preheat the air entering the combustion chamber; this should be situated between the engine's inlet and outlet ducts.

However, it is also possible to determine optimal operating conditions of the combined Brayton-ORC system through advanced exergetic analysis, as in the case of Valencia et al. [33], where the fluid is selected to perform an advanced exergetic analysis in a combined thermal system using the ORC as bottoming cycle of an internal combustion engine, finding improvements of up to 80% in the components of the process. The thermo-economic analyses had been used to optimize the components of a trigeneration system, constituted by a gas microturbine and a heat recovery steam

generation sub-system [34]. In addition, the ORC as a bottoming cycle of an internal combustion engine was proposed, identifying the heat transfer equipment with the highest exergy destruction costs, representing 81.25% of the total system cost, and acetone as the working fluid with the best impact on reducing these costs [35]. Another approach to determining optimal operating conditions is to conduct mathematical modeling of the physical phenomena. So, a phenomenologically based semi-physical model for a 2 MW internal combustion engine was obtained as a function of average thermodynamic value, validated by real operating data, to predict the thermodynamic performance parameters of the bottoming cycle as waste heat recovery systems [36].

The above studies propose heat recovery with bottoming cycles, using the different thermal power configurations, modeling the cycle components or making simulations of the same, including economic optimization in one of them; leaving with a wide uncertainty gap regarding the performance of this cycle integrated to ORC as bottoming cycle, which, despite not handling high temperatures, is a challenge in terms of designing a highly efficient heat exchanger so that high thermal performance of the combined power cycle can be obtained.

Therefore, the main contribution of this research is to present a thermodynamic, exergy, and environmental parametric study of a proposed combined S-CO2 and ORC as a bottoming cycle considering the toluene, cyclohexane, and acetone as the organic working fluids. The methodology of the life cycle analysis is applied to investigate the environmental impact of the components of the system during its lifetime, which allows for the evaluation of environmental impacts, and the determination of energetic and exergetic improvement potentials for the environmental sustainability of the system.

#### **2. Methodology**

#### *2.1. Description and Properties of the System*

The system shown in Figure 1 is an ORC configuration combined with a Brayton S-CO2 cycle. The Brayton cycle consists of the following components: the primary turbine (T1), a secondary turbine (T2), an axial compressor (C1), a reheater (RH), and a recuperator (HTR). The ORC cycle includes a shell and tube heat exchanger (ITC1), an evaporator (ITC2), a condenser (ITC3), a thermal oil circuit pump (P1), an organic fluid pump (P2), and a turbine (T1).

In the process, the carbon dioxide enters the primary turbine (T1) of the Brayton cycle at point 1, at a high temperature and pressure, then enters to the reheater (RH) at point 2 and is expanded to lower pressure in the secondary turbine (T2). Next, by means of the recuperator (HTR), the carbon dioxide (point 7) that leaves the compressor (C1) is reheated, which is conducted to the heater (RH) to obtain the thermodynamic state reported as (point 8). Meanwhile, the fluid in point 5 is cooled by yielding heat to the thermal oil, and then it is compressed by the compressor (C1) at point 6.

In the ORC, the thermal oil (Therminol 75) receives heat in the heat exchanger (ITC1) to be transferred to the evaporator (ITC2). During this process, there are three stages: preheating, evaporation, and overheating, with the purpose of heat the organic fluid (Cyclohexane, Toluene, Acetone), while the thermal oil flow through the cycle with the energy supply by the pump (P1). Then, the organic fluid enters the turbine (T3) at a high temperature and pressure through the 1ORC current and expands to decrease its pressure and temperature to enter the condenser (ITC3), where the water cools it at room temperature (point 1A), and then goes to the reservoir (2A). Subsequently, when the organic working fluid leaves the condenser (ITC3) at point 3ORC, it enters the pump (P2) as a saturated liquid and then completes the cycle entering the evaporator (ITC2).

**Figure 1.** Physical structure of the Brayton S-CO2 integrated into an organic Rankine cycle (ORC) as a bottoming cycle.

## *2.2. Working Fluids Properties*

To determine the thermodynamic properties in the ORC cycle, the types of fluids used in the system are determined through the T-s diagram (Figure 2). The working fluids are categorized in this diagram according to the slope of the saturation vapor line, and it is known that the dry fluid displays a positive slope in the diagram, a negative slope in the wet fluids, and an extremely broad slope in the isentropic fluids.

**Figure 2.** Entropy Temperature (T-s) diagram of organic fluids.

According to Equation (1), the fluid type is defined based on the slope of the saturation line. This slope classifies the working fluids by value of E = <sup>∂</sup><sup>s</sup> <sup>∂</sup><sup>T</sup> obtaining for dry fluids E > 0 isentropic fluids, E ≈ 0, and wet fluids E < 0 [37].

$$\mathbf{E} = \frac{\mathbf{C}\_p}{T\_H} - \frac{n \cdot T\_H - T\_{rH} + 1}{T\_H \mathbf{2} \cdot (\mathbf{1} - T\_{rH})} \Delta H\_H \tag{1}$$

where *TrH* = *TH TC* , and <sup>Δ</sup>*HH* is the enthalpy of evaporation.

#### *2.3. Thermodynamic Analysis*

The consideration adopted for carrying out the combined Brayton S-CO2 and ORC thermodynamic modeling are listed below [29]:


The energy balance in steady-state for the devices is presented in Equation (2)

$$
\dot{Q} - \dot{W} + \sum \dot{m}\_{in} \cdot h\_{in} - \sum \dot{m}\_{out} \cdot h\_{out} = 0 \tag{2}
$$

where . *<sup>Q</sup>* is the heat at the boundary in kW, . *W* is the conversion of energy by work in kW, *h* is the specific enthalpy value for the working fluid in kJ/kg·K, and . *m* is the mass flow rate in kg/s.

To calculate the working fluid exergy as a function of the ambient conditions, Equation (3) is used.

$$\mathbf{e}\_{i} = h\_{i} - h\_{0} + T\_{0}\mathbf{s}\_{0} - T\_{0}\mathbf{s}\_{i} \tag{3}$$

For each device of the cycle, the exergy destruction can be determined with the exergy balance described in Equation (4)

$$
\dot{E}D\_{di} = \dot{E}D\_{Q\_i} - \dot{E}D\_{W\_i} + \sum \dot{m}\_{in} \cdot \mathbf{c}\_{in} - \sum \dot{m}\_{out} \cdot \mathbf{c}\_{out} \tag{4}
$$

where . *EDdi* is the exergy destruction rate for components (*i*), the exergy rate by work and heat movement over the boundary is . *EDxWi* and . *EDxQi* , and the inlet and outlet related exergy rates are *exin* and *exout*.

The exergy rate by heat transfer is determined with Equation (5)

$$\dot{E}D\mathbf{x}\_{Q\_i} = \dot{Q}\_i \left( 1 - \frac{T\_0}{T\_s} \right) \tag{5}$$

where *T*<sup>0</sup> is the atmospheric temperature, and *Ts* is the source temperature if the heat is produced and the temperature decreases when the heat is lost in the system. Also, Equation (6) is often used to quantify the exergy destruction rate by component ( . *EDdi*)

$$
\dot{E}D\_{di} = \dot{T}\_0 \dot{s}\_{\text{gen},i} \tag{6}
$$

where . *sgen*.*<sup>i</sup>* is the rate of entropy production, which is calculated with the general entropy balance with Equation (7), as shown as follows:

$$\dot{\mathbf{s}}\_{\rm gcn.i} = \sum \dot{m}\_{\rm out} \cdot \mathbf{s}\_{\rm out} - \sum \dot{m}\_{\rm in} \cdot \mathbf{s}\_{\rm in} - \sum \frac{\dot{Q}}{T} \tag{7}$$

The net power of the Brayton cycle ( . *Wnet*,*Brayton S*−*CO*<sup>2</sup> ) is calculated based on Equation (8), from the power of the main turbine (T1), the secondary turbine (T2) and the compressor (C1).

$$
\dot{\mathcal{W}}\_{\text{net, Bruyton S-CO}\_2} = \dot{\mathcal{W}}\_{T1} + \dot{\mathcal{W}}\_{T2} - \dot{\mathcal{W}}\_{\text{C1}} \tag{8}
$$

Equation (9) determines the net power of the ORC cycle ( . *Wnet*,*ORC*), based on the power of the turbine (T3) and pumps (P1 and P2).

$$
\dot{W}\_{\text{net},\text{ORC}} = \dot{W}\_{\text{T3}} - \dot{W}\_{\text{P1}} - \dot{W}\_{\text{P2}} \tag{9}
$$

The ORC thermal efficiency (η*I*,*ORC*) can be written based on Equation (10).

$$
\eta\_{I, \text{ORC}} = \frac{\dot{W}\_{\text{net}, \text{ORC}}}{\dot{Q}\_{\text{ITC1}}} \tag{10}
$$

where . *Wnet*,*ORC* is the net power of the ORC, and . *QITC*<sup>1</sup> is the heat collected from the heat exchanger.

Equation (11) is used to calculate the thermal performance of the Brayton cycle as a function of the net power of the Brayton cycle and the heat received from the thermal source ( . *QRH*).

$$\dot{\eta}\_{I,Brayton\ S-CO\_2} = \frac{\dot{\mathcal{W}}\_{net,Brayton\ S-CO\_2}}{\dot{Q}\_{RH}} \tag{11}$$

Also, considering the second law of thermodynamics, the exergy efficiency (η*II*,*ORC*−*Brayton S*−*CO*<sup>2</sup> ) is calculated, as shown in Equation (12)

$$\dot{I}\_{\text{III,ORC}-\text{Brynton S}-\text{CO}\_2} = \frac{\dot{E}D\_{\text{prod}}}{\dot{E}D\_{\text{fuel}}} \tag{12}$$

where . *EDf uel* and . *EDprod* are the fuel and product exergy rate for the components, which are defined in Table 1.


**Table 1.** Fuel-Product definition for the ORC and Brayton S-CO2 components.

Thus, the overall thermal efficiency of the integrated system Brayton S-CO2-ORC is a function of net power and heat source, as shown in Equation (13).

$$
\eta\_{I, \text{overall}} = \frac{\dot{W}\_{\text{net,Brayton}} \, \text{S} - \text{CO}\_2 + \dot{W}\_{\text{net,ORC}}}{\dot{Q}\_{RH}} \tag{13}
$$
