Exploring the Potential of Silicon Tetrachloride as an Additive in CO₂-Based Binary Mixtures in Transcritical Organic Rankine Cycle—A Comparative Study with Traditional Hydrocarbons

Abstract

Carbon dioxide (CO₂) has been recognized as one of the potential working fluids to operate power generation cycles, either in supercritical or transcritical configuration. However, a small concentration of some of the additives to CO₂ have shown promising improvements in the overall performance of the cycle. The current study is motivated by the newly proposed additive silicon tetrachloride (SiCl₄), and so we perform a detailed investigation of SiCl₄ along with a few well-known additives to CO₂-based binary mixtures as a working fluid in transcritical organic Rankine cycle setup with internal heat regeneration. The additives selected for the study are pentane, cyclopentane, cyclohexane, and silicon tetrachloride (SiCl₄). A comprehensive study on the energy and exergy performance of the cycle for warm regions is conducted at a turbine inlet temperature of 250 °C. The performance of the heat recovery unit is also assessed to highlight its importance in comparison to a simple configuration of the cycle. This study shows that the cycle operating with binary mixtures performs significantly better than with pure CO₂, which is mainly due to its better heat recovery in the heat recovery unit. The results show that the optimal molar concentration of the additives is in between 20% and 25%. Besides having better thermal stability, SiCl₄ shows an improvement in the cycle thermal efficiency by 6% points which is comparable to cyclopentane (7.3% points) and cyclohexane (7.8% points). The optimal cycle pressure ratio for SiCl₄ is also relatively lower than for other additives. The energy efficiency of the cycle with pure CO₂ is around 45% which is also increased to 58%, 63%, 64%, 60% with pentane, cyclopentane, cyclohexane, and SiCl₄, respectively. These results suggest that additives like SiCl₄ could make CO₂-based cycles more viable for power generation in warm regions.

1. Introduction

Organic Rankine cycles (ORCs) are an attractive option among power generation systems. This is due to their capability of utilizing low- to medium-grade heat, typically with an operating temperature range of 150 °C to 450 °C [1,2]. This heat is either available in the form of industrial waste heat or geothermal heat [3,4,5,6]. Due to the low operating temperatures, energy conversion is limited and relatively inferior compared to conventional steam Rankine cycles [7,8,9]. On the other hand, ORCs are quite reliable in operation, relatively cost effective due to their simple modular design, and have a low impact on the environment.

Organic Rankine cycles are intrinsically less efficient as they generally operate in low-temperature applications [7,10,11,12,13]. A review by Park et al. [14] examined over 200 scientific publications. They reported experimental results for ORC systems utilized in various applications. Their work demonstrates that practical ORC systems typically operate at relatively low efficiencies, with the average thermal efficiency being below 12% and the average exergy efficiency being 44%. The published literature indicates that the low heat to work conversion efficiency of ORCs is mainly linked with the thermo-physical properties of the organic fluid used in the cycle [7,10,11,13], and so recent work conducted in this area is mostly dedicated to finding an optimal working fluid for a certain operating condition. The selection of an optimal working fluid for a given operating condition is not a straightforward task. In addition to the cycle configuration, multiple factors play an important role in its selection, such as the source and ambient (sink) temperature, and the objective performance parameter (first and second law efficiency, power output capacity, allowable operating pressures, and many more) the cycle is optimized for. Therefore, the selection of the working fluid is one of the most crucial design parameters, and determining the optimal fluid is a highly intricate task. Moreover, the selection of organic fluid for the cycle also impacts the overall design of the cycle components [15]. One of the big concerns with most of organic fluids is their stability at high temperatures; in other words, most organic fluids have a potential to lose their physical and thermal properties over time when exposed to high temperatures, which happens due to chemical decomposition [16].

The literature published in the past decade indicates a radical increase in efforts towards the utilization of binary mixtures in ORCs, as they are found to have potential in improving the overall performance of the cycle, including energy conversion efficiency and operation [6,17,18,19,20,21,22]. A few studies also suggest that utilizing binary mixtures may require a slightly larger component size, which ultimately reflects in an increased overall plant cost [23,24]. Research has been conducted on a range of environmentally friendly organic fluids, such as hydrocarbons, hydrofluorocarbons, and hydrofluoroolefins, for their application in ORCs [20,21,22]. The literature provides valuable insights and comprehensive analyses of the criteria involved in choosing suitable organic fluids for ORC application [4,10,11]. Some papers provide basic guidelines for their selection for geothermal heat sources, some of which are related to fluid selection for the utilization of waste heat [15,25,26,27], some of which highlight economic and environmental advantages [28].

The use of carbon dioxide (CO₂) as a working fluid in subcritical, transcritical, and supercritical conditions has received significant interest in the past decades due to its versatility and high performance, particularly for waste heat recovery and renewable energy resource applications [29,30,31,32,33,34]. Using CO₂ along with suitable additives such as working fluid for ORCs has demonstrated a notable enhancement in the overall cycle efficiency (energy and exergy) compared to utilizing pure CO₂ [22,35,36]. The literature suggests that while using a CO₂-based mixture as the working fluid requires larger heat exchangers compared to pure CO₂, the cost per unit of power generated by a transcritical ORC can be significantly reduced, by up to 41% [35]. Sánchez and da Silva studied eight various organic fluids for CO₂-based binary mixtures [37]. They investigated the effect of the molar concentration of the additives in the mixture on the cycle’s thermal performance. Propane as an additive in CO₂ was investigated by Niu et al. and Ma et al. for solar concentrated power plants [38,39]. Their work reveals promising results for this mixture when operating at a temperature of 550 °C.

Most recently (April 2024), silicon tetrachloride (SiCl₄) was proposed by Doninelli et al. for operation in high temperature ORCs due to its excellent thermal stability, as found in their experiments [40,41]. They performed energy analysis along with exploring the thermal stability and material compatibility of SiCl₄. Their work showed promising findings, demonstrating nearly a 10% points improvement in the energy conversion efficiency of high-temperature organic Rankine cycle (ORC) systems beyond what is achievable with currently available organic fluids [40]. Moreover, they also investigated the performance of SiCl₄ in CO₂ as a binary mixture for the recompression supercritical Brayton cycle. They found over 50% improvement in the thermal efficiency of the cycle and a significant increase in net power output when compared to pure CO₂.

The objective of the current work is to investigate the performance of SiCl₄ in CO₂-based binary mixture for transcritical ORC with heat regeneration configuration. The transcritical cycle is selected because subcritical ORCs inherently exhibit lower efficiency, primarily due to significant irreversibility losses associated with the isothermal phase change in the working fluid [23,24]. The transcritical cycle operates within the transitional range between the subcritical and supercritical regions. The cycle is studied for warm regions with a relatively high condenser temperature (35 °C) because most work found in the literature was primarily carried out for relatively low sink temperatures. This study is presented in an organized manner, starting with discussion on the selected additives for the study, the cycle configuration and simulation environment, a mathematical model for energy and exergy analysis, the performance of heat recovery systems, and finally a discussion of the results.

2. Additive Selection for CO₂-Based Binary Mixtures

The organic Rankine cycle (ORC) provides a flexible and adaptable platform to produce power from various heat sources. As seen from the literature review [1,4,10,11,16,19,42], numerous organic fluids are available, so naturally one ends up with a situation where the selection of an ideal and optimal additive for a given source temperature and ambient conditions becomes challenging. The current investigation focuses on identifying the potential of silicon tetrachloride in comparison to other commonly studied additives for CO₂-based binary mixtures in transcritical ORC, and so determining the optimal molar fraction when blended with CO₂ for improved overall thermodynamic performance of the cycle.

The thermodynamic properties of CO₂ and the additives investigated in the current work are presented in

Table 1. Thermodynamic properties of working fluids examined in this study [16,40,47,48,49,50].

	Name	Chemical Formula	Critical Pressure (MPa)	Critical Temperature (°C)	Standard Boiling Point (°C)	GWP (ASHRAE Safety Group)	Thermal Stability Threshold (°C)
1	Carbon dioxide	CO2	7.4	31	−78.5	1 (A1)
2	Pentane	C5H12	3.4	197	36.1	5 (A3)	280–320
3	Cyclopentane	C5H10	4.5	239	49.2	6 (A3)	350
4	Cyclohexane	C6H12	4.1	281	80.8	- (A3)	-
5	Silicon Tetrachloride	SiCl4	3.6	235	57.7	0 (-)	>650

. The literature showed us that the choice of organic fluid plays a key role in overall cycle performance, including energy and exergy efficiency [4,43,44,45,46]. This is mainly due to the inherent variations in thermophysical properties among organic fluids, such as critical temperature, specific heat capacity, latent heat of vaporization, and standard (normal) boiling temperature. In this study, we select organic fluids which possess critical temperatures spanning around the turbine inlet temperature of 250 °C to assess their compatibility with the heat source temperature of 300 °C.

3. Organic Rankine Cycle: System Configuration and Operating Conditions

An organic Rankine cycle (ORC) integrating a heat recovery unit (HRU) was used to assess the performance of CO₂-based binary mixtures as a working fluid. Figure 1a illustrates the composition of the cycle, which comprises a pump, evaporator, expander, condenser, and the HRU. The working fluid is pressurized and pumped to the evaporator, where it absorbs heat from the hot air stream and transforms into super-heated vapors. These super-heated vapors then expand through the expander. In most cases, at the exit of the expander, the working fluid is still hot enough to heat the fluid leaving the pump, so a heat recovery unit (HRU) is installed in the cycle configuration. The HRU recovers the residual heat from the expander exhaust before the fluid is condensed in the condenser and rejects heat to the cooling medium used.

The temperature–entropy (T-s) diagram in Figure 1b depicts the cycle’s operation at a given source temperature. This diagram was produced for a transcritical organic Rankine cycle operating at a turbine inlet temperature of 250 °C, using CO₂ (95%) and cyclopentane (5%) binary mixture as the working fluid. In general, the T-s diagram is an essential tool for visualizing the overall operating states of the cycle and its components. It may also be helpful in identifying potential areas of improvement in the cycle by revealing opportunities to minimize a component’s irreversibility in the cycle. The power is produced by the expander during the expansion process between states 1 and 2. It can be seen from the T-s diagram that the working fluid temperature at the exit of the expander (state 2) is still significantly higher than the ambient temperature. Therefore, without the heat recovery unit (HRU), this residual heat would be wasted and be rejected to the environment in the condenser. The HRU recuperates heat between states 2 and 3, preheating the fluid from state 5 to 6. Subsequently, the stream between states 6 and 1 receives heat in the evaporator, which is provided with hot air as a heating medium, reaching the desired cycle operating temperature.

We simulated the cycle, shown in Figure 1a, using Aspen V11, a commercial software developed by Aspen Technology, Inc., located in Bedford, MA, USA. To determine the thermophysical properties of the working fluids, we employed the Peng–Robinson model. Table 1 outlines the specific working fluid under investigation. Throughout our analysis, we assumed that the cycle operates under steady-state conditions, disregarding pressure and heat losses within the interconnecting pipelines. Additionally, we neglected pressure drops in the evaporator, condenser, and heat recuperator for both the cold and hot streams.

Table 2. Parameters and their corresponding values employed in modeling the ORC system [51,52].

Cycle Components/Parameters	Operating Conditions
Source	Air at 300 °C and 101 kPa with mass flow rate of 1 kg/s.
Sink	Water at 30 °C and 101 kPa.
Turbine	The inlet temperature is 250 °C and pressure is optimized for maximum thermal efficiency. Adiabatic efficiency is 80%.
Pump	Saturated liquid with inlet temperature fixed at 35 °C. Adiabatic efficiency is 90%.
Dead State (Ambient Condition)	101 kPa; 35 °C.
Evaporator	The minimum pinch temperature is 10 °C.
Condenser and HRU	The minimum pinch temperature is 5 °C.

provides a summary of the designed and operating parameters of the cycle.

4. Quantitative Framework: A Mathematical Model for the System

4.1. Energy Model

To assess the performance of the cycle, shown in Figure 1, basic essential parameters, like thermal efficiency, specific net power output, specific heat input requirement, and cycle pressure ratio are calculated.

The first law efficiency of the cycle (${\eta }_{th}$) is obtained as:

$${\eta }_{th}=\left({\dot{W}}_T-{\dot{W}}_P\right)/{\dot{Q}}_i$$

(1)

Here, ${\dot{Q}}_i$ denotes the rate at which the heat is provided to the cycle. ${\dot{W}}_T$ and ${\dot{W}}_P$ represent the turbine’s power output and the pump’s work input, respectively.

The mass flow rate ratio of the power cycle to the heating medium working fluids, also referred to as the “flow ratio”, is an important parameter in the design and operation of power plants. This ratio defines the relationship between the mass flow rates of the working fluid in the power cycle (organic fluids in this study) and the heating medium (hot air in this study) used to transfer heat to the power cycle. Increasing the flow ratio generally comes with trade-offs in terms of increased size, cost, and potentially reduced efficiency. Mathematically, the flow ratio can be defined as follows:

$${\psi }_{flow}={\dot{m}}_{cycle}/{\dot{m}}_{air}$$

(2)

where ${\dot{m}}_{cycle}$ is the mass flow rate of the working fluid of ORC and ${\dot{m}}_{air}$ denotes the mass flow rate of the hot air supplied to heat the working fluid in the evaporator. The specific net power output, SNPO, of the cycle is a measure of net power output produced per unit mass flow rate of working fluid. It is calculated as follows:

$$\mathrm{S}\mathrm{N}\mathrm{P}\mathrm{O}=\left({\dot{W}}_T-{\dot{W}}_P\right)/{\dot{m}}_{cycle}$$

(3)

4.2. Exergy Model

Exergy analysis is an effective method for evaluating and enhancing the efficiency of energy conversion. It represents the potential of the system to convert available energy into useful work. Energy of a higher quality, such as high-temperature heat, has a higher exergy content and can potentially be converted into more useful work. This analysis aids in pinpointing energy losses in the system due to irreversibility, inefficiencies, and opportunities for optimization of the process.

Mathematically, the exergy at any given state point in the system (${\dot{E}}_{x\_i}$) is defined as follows:

$${\dot{E}}_{x\_i}=\dot{m}\left(h-T_{a}s\right)$$

(4)

Here, $\dot{m}$, $h$, $s$, and $T_a$ denote mass flow rate, specific enthalpy, specific entropy, and ambient temperature in absolute scale, respectively. Calculating the difference in exergy between two state points in the system represents a loss, so component-wise exergy loss (${\dot{E}}_{xl\_i}$) for the cycle shown in Figure 1 can be estimated as follows:

$${\dot{E}}_{xl\_T}=\left({\dot{E}}_{x1}-{\dot{E}}_{x2}\right)-{\dot{W}}_T$$

(5)

$${\dot{E}}_{xl\_P}={\dot{W}}_p-\left({\dot{E}}_{x5}-{\dot{E}}_{x4}\right)$$

(6)

$${\dot{E}}_{xl\_Eva}=({\dot{E}}_{x7}-{\dot{E}}_{x8})-\left({\dot{E}}_{x1}-{\dot{E}}_{x6}\right)$$

(7)

$${\dot{E}}_{xl\_HRU}=\left({\dot{E}}_{x2}-{\dot{E}}_{x3}\right)-\left({\dot{E}}_{x6}-{\dot{E}}_{x5}\right)$$

(8)

$${\dot{E}}_{xl\_Con}=\left({\dot{E}}_{x3}-{\dot{E}}_{x4}\right)-\left({\dot{E}}_{x10}-{\dot{E}}_{x9}\right)$$

(9)

where ${\dot{E}}_{xl\_T}$, ${\dot{E}}_{xl\_P}$, ${\dot{E}}_{xl\_Eva}$, ${\dot{E}}_{xl\_HRU}$, and ${\dot{E}}_{xl\_Con}$ represent exergy losses occurring in the turbine, pump, evaporator, heat recovery unit, and condenser, respectively. The determination of net exergy loss within a cycle leads to the computation of exergy efficiency (${\eta }_{Ex})$, which represents how effectively the available energy is converted into useful work and is defined as follows:

$${\eta }_{Ex}=\left(1-{\dot{E}}_{xl\_net}/{\dot{E}}_{in}\right)\times 100$$

(10)

${\dot{E}}_{xl\_net}$ denotes net exergy loss in the system obtained by adding losses from Equation (5) to Equation (9). ${\dot{E}}_{in}$ represents the exergy supplied to the cycle. In this study, the cycle receives heat from hot air and, therefore, the exergy loss of the air between state points 7 and 8 is considered as the exergy input to the cycle. Hence,

$${\dot{E}}_{in}=\left({\dot{E}}_{x7}-{\dot{E}}_{x8}\right)$$

(11)

5. Energy Conversion Analysis

In this section, we present the simulation results and key factors affecting the performance of the cycle. Through first law analysis, we evaluate the cycle’s thermal efficiency, estimate the specific net power output (SNPO), the specific heat input requirement, and the pressure ratio of the cycle. A higher SNPO typically corresponds to smaller turbomachines and, consequently, a smaller overall plant size for a given net power output requirement. Therefore, it is an important key parameter along with the thermal efficiency of the cycle.

5.1. Thermal Efficiency and SNPO versus Turbine Inlet Pressure

To isolate the effect of additive concentration, the total mixture concentration is kept fixed at the start of the analysis. This approach ensures that any observed changes in performance are attributed solely to the cycle operating pressures, rather than variations in the overall mixture composition. Figure 2 depicts the thermal efficiency and net specific power output as functions of turbine inlet pressures spanning from 10 MPa to 25 MPa for various binary mixtures formed by adding a 5% mole fraction of pentane, cyclopentane, cyclohexane, and silicon tetrachloride to CO₂. Irrespective of the specific additive compound incorporated into the mixture, Figure 2a shows that the thermal efficiency curve exhibits a non-linear behavior, with a maximum value attained at different turbine inlet pressures for different mixture compositions.

At this stage of the analysis, we noted that the presence of any of these selected additives significantly enhances the cycle’s thermal efficiency when compared to pure CO₂ (see Figure 2a). Interestingly, the observation that the peak thermal efficiency occurs at different turbine inlet pressures for different mixtures implies that the presence and concentration of additives can influence the optimal operating conditions for the cycle. The improvement in cycle efficiency can be attributed to the superior thermodynamic properties exhibited by the mixture when compared to pure CO₂. These properties encompass, but are not confined to, factors such as better matching of the critical temperatures and pressures of the mixtures with the source temperature, the temperature glide during phase changes (which can facilitate more effective heat transfer during phase changes), and thermal conductivity (which led to better heat recovery). Figure 2b reveals that the specific net power output (SNPO) exhibits a non-linear increasing trend as the turbine inlet pressure rises. However, the pressure value at which SNPO reaches its peak does not coincide with the pressure that yields the maximum thermal efficiency.

By setting up case studies for each additive, we aim to systematically assess how varying the additive’s concentration alters the performance of the cycle. A comprehensive analysis is conducted by evaluating thermal efficiency and associated parameters across a wide spectrum of mixture compositions. The investigated range spans from pure CO₂ (0% additive concentration) to mixtures containing up to 50% additive concentration.

5.2. Thermal Efficiency versus Mixture Concentration

Figure 3 represents a box plot of thermal efficiency data for various mixture concentrations. It should be kept in mind that these are the maximum attainable thermal efficiencies for each mixture concentration, achieved through the optimization of the turbine inlet pressure. All the additives studied showed an exceptional ability to increase the cycle’s thermal efficiency. A cycle operating with pure CO₂ displays a thermal efficiency of around 17.5%. The additives are found to increase the cycle thermal efficiency from 17.5% to a minimum of 22.5% (with pentane at 20% concentration) to maximum of 25.5% (with cyclohexane at 20% concentration). The figure clearly demonstrates that a molar concentration of additive in CO₂ ranging from 15% to 25% holds significant promise for enhancing the energy efficiency of the cycle. The better thermal efficiency of the cycle with cyclohexane and cyclopentane is a result of the better heat recovery and relatively fewer irreversibility losses in the components with these additives compared to pentane and SiCl₄, and this is evident from the analyses performed in the following Section 6 and Section 7.

5.3. SNPO and Flow Ratio versus Mixture Concentration

Figure 4 presents box plots of SNPO and flow ratio (as defined in Equations (2) and (3)) versus molar fraction of additives. At a first glance, it is observed from Figure 4a that the mixture composition that yields the highest thermal efficiency does not coincide with the composition that produces the maximum SNPO. For instance, in the case of cyclohexane (Figure 3), the peak thermal efficiency of approximately 25.5% is achieved at a 20% cyclohexane concentration in the mixture, corresponding to an SNPO of around 37.3 kW/kg. However, the maximum SNPO of nearly 45 kW/kg occurs at a lower mixture composition of 7% cyclohexane concentration. This indicates that there may be trade-offs to consider when optimizing the cycle’s performance. Flow ratio data are plotted in Figure 4b, which shows that when using pure CO₂ in the cycle, the flow ratio is nearly one, which means that 1 kg/s of CO₂ in the cycle needs 1 kg/s of hot air to be supplied to the evaporator. However, the flow ratio drops significantly when using additives in CO₂, expect for SiCl₄. For instance, with the best performing additives (cyclopentane and cyclohexane), in terms of thermal efficiency, the flow ratio drops to nearly 0.8, which signifies a 20% decrease in the cycle’s mass flow rate requirements and so may lead to a smaller heat exchanger and turbomachinery for the cycle. It is also observed that pentane, despite being the worst-performing additive in terms of improving the cycle’s thermal efficiency (Figure 3), exhibits the highest specific net power output (SNPO) among others, as depicted in Figure 4a.

5.4. Cycle’s Optimal Pressure Ratio versus Mixture Concentration

A cycle’s pressure ratio is one of the important parameters in designing and selecting materials for turbomachinery and heat exchangers. Figure 5 illustrates the optimal cycle’s pressure ratio versus mixture concentration. In the case of pure CO₂, the cycle operates at a pressure ratio of around 2. When considering the best-performing additive, cyclohexane at a 20% mixture concentration, the pressure ratio experiences a modest increase to 2.6. This relatively small increase in the cycle pressure ratio is compensated for by the substantial improvement in thermal efficiency. For the other additives, the cycle pressure ratio fluctuates within a range of 2 to 3, except for pentane which exhibits a considerably higher cycle pressure ratio compared to the others.

As observed from the data analyzed above, the cycle’s thermal efficiency is fundamentally influenced by two key factors: the turbine inlet pressure and the molar proportion of the additive compound within the binary CO₂-based mixture. Consequently, identifying the optimal operating condition necessitates determining the specific combination of turbine inlet pressure and additive concentration that yields the maximum attainable thermal efficiency. Therefore, the optimal operating condition of the cycle for each additive is obtained by finding the mixture composition and turbine inlet pressure combination that maximizes thermal efficiency.

Table 3. Critical temperature and pressure of the working fluids at optimal mixture composition.

Parameters	80% CO2/20% C5H12	75% CO2/25% SiCl4	75% CO2/25% C5H10	80% CO2/20% C6H12
Cricondentherm (°C)	105	148	142	168
Cricondenbar (MPa)	9.7	11.4	12.6	14.8

presents the optimal mixture compositions for each additive, along with their critical temperature and pressure properties. Figure 6 presents the optimal operating conditions of the cycle and highest achievable thermal efficiency and corresponding specific net power output for each additive examined in the current study. It is noteworthy that the condenser operates at a lower pressure when using binary mixtures compared to pure CO₂. This can be seen from the lower pump inlet pressures for the mixtures. When looking at the thermal efficiency of cycles using CO₂ mixed with additives like SiCl₄, cyclopentane, and cyclohexane, the thermal efficiencies exhibited by these mixtures are comparable; however, cyclohexane has an advantage because it produces a significantly higher specific net power output than the other additives.

6. Exergy Performance of the Cycle

This section is dedicated to the estimation of irreversibility in the system. The set of equations from Equation (4) to Equation (11) are used to calculate the exergy losses in the system. The exergy loss in each component of the cycle is calculated and presented as a bar chart in Figure 7. Based on the findings of a previous study, especially from Figure 6, the optimal mixture composition is in the range of 20% to 25%. Therefore, in this section, we will assess and compare the exergy performance of a cycle using pure CO₂ with a cycle operating at a mixture composition between 20% to 25%. In terms of exergy loss occurring in the pump, cycles operating with pure CO₂ have the highest value, reaching nearly 6%. However, this loss significantly declined to 1% to 2% when using a binary mixture composed of any of the additives. A similar pattern is observed for exergy loss in the heat recovery unit (HRU). The condenser exhibits an exergy loss of approximately 9% with pure CO₂, which significantly dropped to 4% for cyclopentane and cyclohexane, and to 6% for SiCl₄. Cyclopentane does not seem to cause improvement in condenser exergy loss compared to pure CO₂.

7. Heat Recovery Unit Performance in the Cycle

The heat recovery unit in the cycle is an additional component to the cycle which comes with an extra cost. To justify its presence in the cycle, one must estimate the effectiveness and potential energy savings due to its installation. To estimate it importance in the cycle, we defined its performance parameter as follows:

$$HR{U}_{eff}={\displaystyle \frac{{\dot{Q}}_{HRU}}{\left({\dot{Q}}_i+{\dot{Q}}_{HRU}\right)}}\times 100$$

(12)

where ${\dot{Q}}_{HRU}$ represents the amount of heat recovered by the HRU (in kW or MW). In principle, $HR{U}_{eff}$ represents the percentage of heat recovered by the HRU; therefore, in case the HRU is not present in the cycle, the same amount will be rejected in the condenser and therefore just wasted. Figure 8a presents the plot of heat recovery via the HRU in percentage versus a binary mixture of various compositions and molar fractions. It is observed that even if pure CO₂ is used, nearly 50% of the heat is recuperated by the HRU, which corresponds to a log mean temperature difference (LMTD) in the HRU of 20 °C (as seen from Figure 8b). The importance of the HRU in the cycle is very evident from Figure 8a, and it is even more significant when using binary mixtures formed by any of the additives to CO₂. Considering the optimal molar fractions of each additive and the heat recovery rate, pentane with a mole fraction of 20% achieves a recovery rate of 50%, which is comparable to pure CO₂. Cyclohexane, with a 20% mole fraction, achieves a recovery rate of nearly 70%, while cyclopentane and SiCl₄ with a 25% mole fraction, exhibit a heat recovery of 70%. The increasing trend of heat recovery with an increased molar fraction from 0 to 30% is due to a decreased LMTD between hot and cold fluids in the HRU and it is also evident from Figure 8b. This signifies that using a binary mixture in the cycle substantially improves the heat transfer characteristics of the working fluid and thus the overall energy and exergy performance of the cycle.

8. Conclusions

A detailed study was carried out to evaluate the performance of a recently proposed working fluid, silicon tetrachloride (SiCl₄), as an additive to make a binary mixture with CO₂ in the ORC. The energy and exergy conversion performance of the transcritical organic Rankine cycle were assessed for a turbine inlet temperature of 250 °C. A comparative assessment of cycle performance using SiCl₄ in a CO₂-based binary mixture was conducted against additives commonly found in the literature, namely, pentane, cyclopentane, and cyclohexane. The key outcomes of this study are summarized below:

• The cycle operating with binary mixtures performed significantly better than with pure CO₂. This was mainly due to better heat recovery in the heat recovery unit of the cycle (refer to Figure 7 and Figure 8).
• The optimal molar concentration of the additives in CO₂, which produced the maximum thermal efficiency, was between 20% to 25%.
• In comparison to pure CO₂, the thermal efficiency of the cycle saw significant improvements of 4.8, 7.3, 7.8, and 6.0 percentage points with the addition of pentane, cyclopentane, cyclohexane, and SiCl₄ as additives, respectively.
• Pentane, cyclopentane, cyclohexane, and SiCl₄ as additives also yielded considerable enhancements in the exergetic efficiency of the cycle, with respective improvements of 12.4, 17.3, 18.3, and 13.8 percentage points.
• In terms of SNPO, cyclohexane and cyclopentane produced similar results (disregarding pentane due to its low energy and exergy performance) and significantly higher results in comparison to SiCl₄ (refer to Figure 4).
• Silicon tetrachloride demonstrated comparable results in the thermal and exergy efficiency of the cycle compared to cyclopentane and cyclohexane. Furthermore, SiCl4 offers advantages over these additives as it is non-flammable and possesses superior thermal and chemical stability. The heat recovery from the cycle via the heat recovery unit (HRU) using SiCl₄ was nearly equivalent to that of cyclopentane and cyclohexane. Notably, the required turbine inlet pressure and the corresponding cycle pressure ratio for optimal operation were the lowest for SiCl₄ among the evaluated additives. This lower operating pressure requirement could potentially lead to reduced material and overall plant costs.