Performance Evaluation of CO₂ + SiCl₄ Binary Mixture in Recompression Brayton Cycle for Warm Climates

Abstract

This work demonstrates the potential of CO₂ + SiCl₄ binary mixture as a working fluid for power generation cycle. Recompression Brayton cycle configuration is considered due to its proven record of high performance for medium- to high-temperature sources. The objective of this study is to assess the thermodynamic performance of a recompression Brayton cycle using a CO₂ + SiCl₄ binary mixture as a working fluid, particularly under warm climate conditions. The cycle is simulated using the Peng–Robinson equation of state in Aspen Hysys (v11) software, and the model is validated by comparing VLE data against experimental data from the literature. The analysis involves the assessment of cycle’s thermal efficiency and exergy efficiency under warm climatic conditions, with a minimum cycle temperature of 40 °C. The results demonstrate a notable improvement in the cycle’s thermodynamic performance with CO₂ + SiCl₄ binary mixture compared to pure CO₂. A small concentration (5%) of SiCl₄ in CO₂ increases the thermal efficiency of the cycle from 41.7% to 43.4%. Moreover, irreversibility losses in the cooler and the heat recovery unit are significantly lower with the CO₂ + SiCl₄ binary mixture than with pure CO₂. This improvement enhances the overall exergy efficiency of the cycle, increasing it from 62.1% to 70.2%. The primary reason for this enhancement is the substantial reduction in irreversibility losses in both the cooler and the HTR. This study reveals that when using a CO₂ + SiCl₄ mixture, the concentration must be optimized to avoid condensation in the compressor, which can cause physical damage to the compressor blades and other components, as well as increase power input. This issue arises from the higher glide temperature of the mixture at increased SiCl₄ concentrations and the limited heat recovery from the cycle.

1. Introduction

In recent decades, carbon dioxide (CO₂) has been proven to be an efficient alternative working fluid for power generation cycles with a medium to high heat source, whether subcritical, transcritical, or supercritical [1,2,3,4]. This is mainly due to the thermodynamic properties of the carbon dioxide near its critical point, which helps in reducing compression work. Over the last two decades, there has been growing interest in power generation cycle using CO₂ as an alternative to steam Rankine cycle. CO₂ offers superior energetic and exergetic performance than steam-driven power cycles that are inherently inefficient due to high irreversibility losses associated with a phase change during the heat rejection process [5]. Moreover, CO₂ is eco-friendly and requires relatively compact turbomachinery [6,7]. CO₂-driven power generation cycles have also been extensively studied for various types of heat sources, including nuclear, solar, and waste heat recovery modules [8,9,10,11,12,13].

From a design point of view, CO₂ as a working fluid must be compatible with different cycle components, especially pumps, compressors, and heat exchangers. Compressors must be designed to operate near the critical state of CO₂, as a slight change in the inlet conditions (temperature and pressure) can lead to the initiation of dew formation near compressor blades due to the local acceleration of the fluid [14]. The critical pressure of CO₂ is nearly 7.4 MPa, which is generally the minimum cycle pressure. Therefore, the cycle operating above critical pressure must have components specially designed to withstand extremely high pressures. Among heat exchangers, printed circuit heat exchanger (PCHE) technology is the most promising to use for supercritical carbon dioxide (sCO₂) cycles [15,16]. There are many studies available on PCHEs in the context of their use for supercritical carbon dioxide applications [17,18]. Wang et al. investigated the structural integrity of PCHEs [19]; they analyzed how temperature, pressure, and the variations between them impact stress levels in PCHEs. Their work suggests the structural robustness of PCHEs employed in supercritical carbon dioxide Brayton cycles. Liu et al. investigated the heat transfer characteristics of CO₂ in PCHE in transcritical and supercritical states. The suggested heat transfer correlation works well with the experimental findings [20].

From an ambient operating conditions point of view, warm and hot regions do not allow CO₂ to cool down to its near critical temperature (nearly 31 °C), and so the cycle loses the advantage that CO₂ offers. Studies found in the literature suggest that the use of proper additives to CO₂ potentially improves the overall thermodynamic performance of the power generation cycle operating in warm and hot environments [21,22,23]. Various additives for CO₂, primarily organic fluids, have recently been proposed to enhance the critical temperature and thereby mitigate this issue [24,25]. The selection of additives is not a straightforward process; it depends on multiple factors, including cycle maximum operating temperature and pressure, ambient conditions, compatibility with cycle components, thermal stability, and so on. Most organic fluids, commercially available ones and those used in organic Rankine cycles, are thermal unstable when operated at higher temperatures. The thermal breakdown threshold for some of these organic fluids is listed in

Table 1. Maximum operating temperature limits of various potential working fluids for ORCs.

Organic Fluids	Chemical Formula	Thermal Stability Cutoff (°C)	Reference
R-1311	CF3I	102	[27]
R-141b	C2H3Cl2F	90	[27]
HFC-245fa	C3F5H3	300–320	[28]
HFC-143a	C2H3F3	350	[28]
HFC-236fa	C3H2F6	400	[28]
HFC-23	CHF3	400	[28]
HFC-227ea	C3HF7	425	[28]
HFC-134a	C2H2F4	368	[27]
HFO-1336mzz(Z)	C4H2F6	250–270	[29]
HFO-1336mzz(E)	C4H2F6	230–250	[30]
HFO-1234ze(E)	C3H2F4	180	[31]
HFO-1234yf	C3F4H2	170–200	[32]
HFC-32	CH2F2	250–270	[30]
HFC-125	CH2F5	396	[27]
TFE	C2H3F3O	250	[33]
n-butanol	C4H10O	220	[33]
n-butane	C4H10	290	[34]
Isopentane	C5H12	290	[34]
Cyclopentane	C5H10	350	[34]
n-pentane	C5H12	280–320	[26,27]
Toluene	C7H8	400	[26]
n-hexane	C6H14	260–280	[35]
Perfluorohexane	C6F14	350–400	[36]

Part of this table is reproduced from [37].

. For this reason, organic Rankine power generation systems generally operate below 350 °C [26].

Building upon the work carried out and present in the literature, this study explores how incorporating SiCl₄ can further improve the performance of CO₂-based cycles, especially in warm climates where pure CO₂ has a limited cooling capacity. In essence, the present work is motivated by a recent proposal from Doninelli et al. [38] regarding the use of the novel fluid silicon tetrachloride (SiCl₄) as a potential additive to CO₂. Through an experimental evaluation, they found that the CO₂ + SiCl₄ mixture exhibited remarkable thermal stability, withstanding temperatures exceeding 650 °C without decomposition. The literature also suggests the usage of titanium tetrachloride (TiCl₄) as an additive for high-temperature operations due to its high thermal stability, which is nearly 500 °C [39,40]. However, the rate of the decomposition of SiCl₄ is much slower than TiCl₄. Moreover, the manufacturing process of solar-grade silicon is accompanied by a substantial byproduct in the form of silicon tetrachloride (SiCl₄) [41]. This is reflected in the high market availability of SiCl₄, which thus makes it relatively cheaper. The current study aims to assess the thermodynamic performance of the recompression Brayton cycle (RBC) using pure CO₂ and a CO₂ + SiCl₄ mixture at varying molar concentrations of SiCl₄. The performance indicators are assessed using energy and exergy analyses of the cycle. The cycle is studied for warm climate regions with a minimum cycle temperature of 40 °C.

2. System Arrangement: Modeling and Operating Parameters

The recompression Brayton cycle (RBC) is considered for studying the CO₂ + SiCl₄ binary mixture. For medium to high source temperatures, the simple Brayton cycle’s efficiency is limited due to restricted heat recovery resulting from the pinch temperature in the heat exchange process. This limitation is overcome by employing RBC configuration, which allows for more effective heat recovery, thereby enhancing the overall performance of the cycle [42,43,44].

The RBC layout is shown in Figure 1a. The system is designed with two compression processes and two heat recovery stages. Notably, at the cycle’s minimum pressure–temperature operating condition (at the cooler outlet), the CO₂ + SiCl₄ binary mixture can be cooled down to the liquid phase; therefore, a pump is utilized instead of a compressor (which is originally used in a pure sCO₂ cycle). After the turbine discharge at state 2, the working fluid undergoes a series of heat recovery processes. It first flows through the high-temperature recuperator (HTR) and then proceeds to the low-temperature recuperator (LTR). The working fluid exiting the LTR splits into two paths. One stream moves toward the cooler, where it releases heat to the ambient sink (with water utilized as the coolant), followed by a compression process to achieve the cycle’s high pressure. The second stream combines with the first stream after being compressed in the compressor and preheated in the LTR. The combined flow at state 9 undergoes heat recovery in the HTR before being heated further in the heater to reach the target turbine inlet temperature (TIT).

Figure 1b presents the temperature–entropy diagram of the cycle with a 2% molar concentration of SiCl₄ in the CO₂ + SiCl₄ binary mixture. It can be seen that the temperature of the mixture at the turbine exit is significantly higher than the ambient temperature. Therefore, the available heat energy is recuperated in the HTR, followed by the LTR, before being rejected in the cooler. In other words, an increased temperature difference between the hot and cold streams in either the HTR or LTR will result in higher heat recovery, reflected by the higher exit temperature of the cold stream from the HTR and LTR. Improvement in heat recovery will result in decreased heat input and improved overall performance of the cycle. The state of the mixture at the pump inlet is saturated liquid, while it is in a supercritical state at the compressor inlet.

The cycle is simulated in Aspen Hysys (V11), and the Peng–Robinson model is employed to calculate the thermodynamic properties of the CO₂ and CO₂ + SiCl₄ binary mixture. The model has been validated in previous studies for various configurations of the cycle, including RBC for pure CO₂ as a working fluid [1]. The current study utilizes CO₂ + SiCl₄ mixture as a working fluid; thus, it is imperative to validate the model (Peng–Robinson) used to obtain the thermo-physical properties in the analysis. Therefore, the vapor–liquid equilibrium (VLE) data obtained from the model are compared with recently published experimental data by Doninelli et al. [38]. Figure 2 shows the vapor–liquid equilibrium (VLE) diagram for the CO₂ + SiCl₄ mixture obtained using the Peng–Robinson model at mixture temperatures of 35 °C, 60 °C, and 70 °C. The experimental data for bubble pressure are also plotted. It should be noted that experimental data from the cited literature are only available for the molar concentrations of CO₂ between 80% and 90%.

Table 2. Percentage errors in bubble pressures between experiments and model data.

Molar Fraction of CO2 in CO2 + SiCl4 Mixture	Mixture Temperature
	35 °C	60 °C	70 °C
0.80	5.5%	4.2%	4.2%
0.85	2.6%	1.5%	1.8%
0.88	2.0%	1.4%	1.2%

shows the percentage errors in bubble pressures between the experimental data and the model predictions. It is observed that the model produced very good results, especially for molar concentrations above 85%, where the error is less than 2% [38]. The operating conditions of the cycle are provided in

Table 3. Working parameters of the cycle for CO₂ and CO₂-SiCl₄ binary mixture.

Cycle Components/Parameters	Operating Conditions
Source Temperature	550 °C (Air)
Coolant Temperature	35 °C (Water)
Turbine Inlet Temperature	500 °C
Cycle Maximum Pressure (State 1)	25 MPa
Cycle Minimum Temperature (State 5)	40 °C
Cycle Minimum Pressure (State 5)	Saturation Pressure at 40 °C
Minimum Pinch Temperature in HTR, LTR, and Cooler	5 °C [38]
Minimum Pinch Temperature in Heater	10 °C
Turbine Isentropic Efficiency	92% [38]
Pump/Compressor Isentropic Efficiency	88% [38]
Pressure Loss in Heat Exchangers and in Pipelines	Neglected
Dead State	101 kPa; 35 °C

.

3. Mathematical Model for the Quantitative Assessment of the Cycle

To assess the energetic performance of the cycle shown in Figure 1a, the first law efficiency (${\eta }_{th}$) of the cycle is calculated as follows:

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

(1)

where ${\dot{W}}_T$ is the power output of the turbine; ${\dot{W}}_P$ and ${\dot{W}}_C$ represent the power consumption of the pump and the compressor, respectively. ${\dot{Q}}_{in}$ denotes the heat input needed to operate the cycle at the desired temperature and pressure.

To evaluate the exergetic performance of the cycle, component wise losses are calculated. The rate of exergy at any given state point (${\dot{\psi }}_i$) in the cycle is obtained as follows:

$${\dot{\psi }}_i={\dot{m}}_i\left(h_i-T_o{s}_i\right)$$

(2)

where ${\dot{m}}_i$, $h_i$, and $s_i$, respectively, denote the mass flow rate, specific enthalpy, and specific entropy at any given state point in the cycle. $T_o$ denotes the temperature of the dead state, as specified in Table 3.

The rate of exergy loss incurred by different components in the cycle is calculated as follows:

$${\dot{\psi }}_{loss, T}=\left({\dot{\psi }}_1-{\dot{\psi }}_2\right)-{\dot{W}}_T$$

(3)

$${\dot{\psi }}_{loss,P}={\dot{W}}_P-\left({\dot{\psi }}_6-{\dot{\psi }}_5\right)$$

(4)

$${\dot{\psi }}_{loss, C}=W_{C2}-\left({\dot{\psi }}_8-{\dot{\psi }}_{4b}\right)$$

(5)

$${\dot{\psi }}_{loss, HTR}=\left({\dot{\psi }}_2-{\dot{\psi }}_3\right)-\left({\dot{\psi }}_{10}-{\dot{\psi }}_9\right)$$

(6)

$${\dot{\psi }}_{loss, LTR}=\left({\dot{\psi }}_3-{\dot{\psi }}_4\right)-\left({\dot{\psi }}_7-{\dot{\psi }}_6\right)$$

(7)

$${\dot{\psi }}_{loss, Cooler}=\left({\dot{\psi }}_{4a}-{\dot{\psi }}_5\right)+\left({\dot{\psi }}_{12}-{\dot{\psi }}_{11}\right)$$

(8)

$${\dot{\psi }}_{loss, Heater}=\left({\dot{\psi }}_{14}-{\dot{\psi }}_{13}\right)-\left({\dot{\psi }}_1-{\dot{\psi }}_{10}\right)$$

(9)

The exergy efficiency (${\eta }_{ex}$) of the cycle is calculated as follows:

$${\eta }_{ex}=\left(1-{\displaystyle \frac{{\dot{\psi }}_{loss, net}}{{\dot{\psi }}_{input}}} \right)\times 100$$

(10)

where ${\dot{\psi }}_{loss, net}$ represents the net rate of exergy loss in the cycle which can be obtained by adding the rate of exergy losses occurring in various components of the cycle from Equations (3)–(9). The rate of exergy input (${\dot{\psi }}_{input}$) to the cycle is considered the rate of exergy loss by the hot air (heat source) in the heater, and it is calculated as follows:

$${\dot{\psi }}_{input}=\left({\dot{\psi }}_{14}-{\dot{\psi }}_{13}\right)$$

(11)

It is important to note that the presented mathematical model assumes that the cycle operates under steady-state conditions, where compression and expansion processes are considered adiabatic. Furthermore, the model disregards pressure losses across the various components and within the interconnecting pipelines of the cycle.

4. Findings and Analyses

4.1. Factors Influencing Cycle Performance

The thermodynamic performance of the cycle shown in Figure 1a depends on multiple factors, including the turbine inlet temperature and pressure, the mass flow ratio (${\dot{m}}_{4b}/{\dot{m}}_4$) at the “Flow Divider”, the cycle minimum pressure and temperature (at the pump inlet), and the pressure losses in the heat exchangers and in the pipelines connecting various components of the cycle. In the current investigation, the turbine inlet pressure and the flow ratio are the optimization variables, whereas the fixed operating parameters are mentioned in Table 3. Figure 3 shows how the efficiency of the system is affected by two factors: the ratio of the flow rates and the pressure at the turbine inlet. As evident from these plots, fixing either the turbine inlet pressure (TIP) or the flow ratio results in the cycle’s thermal efficiency reaching the same maximum value. Therefore, for the remaining study, the flow ratio is fixed at 30%, and only the turbine inlet pressure is considered an optimization variable. Readers are referred to the authors’ previous work for a detailed analysis of parameters such as flow ratio, turbine inlet pressure, and minimum allowable pinch temperature, etc., on the cycle performance [42,45].

Figure 4 presents the plots of thermal efficiency and vapor fraction at the compressor inlet (state 4b in Figure 1) versus turbine inlet pressure. As observed from the plots, the thermal efficiency of the cycle increases with increasing turbine inlet pressure, regardless of the mixture concentration. However, it is noteworthy that the system operates more efficiently when the mixture contains 6% silicon tetrachloride (SiCl₄) compared to when the SiCl₄ percentage is 4%. For example, at a 25 MPa turbine inlet pressure, the thermal efficiency of the cycle is 43.5% when operating with a 6% mole fraction of SiCl₄ in the mixture, and 43.1% with a 4% mole fraction. On the other hand, increasing the mole fraction of SiCl₄ in the mixture leads to the decreased vapor fraction of the working fluid at the compressor inlet (as evident from Figure 4). This means that the compressor will experience a wet inlet condition if the cycle is operated with a mole fraction of SiCl₄ in the mixture at or above 6%. This is mainly due to the increasing temperature glide with increasing the molar concentration of SiCl₄ in the mixture. Figure 5 presents bubble and dew lines obtained for 5% and 10% molar concentrations of SiCl₄. Recalling that the pump inlet temperature is fixed at 40 °C, this corresponds to glide temperatures of nearly 33 °C and 61 °C for 5% and 10% molar concentrations of SiCl₄ in the mixture, respectively. This implies that the LTR must recover sufficient heat energy to achieve the required glide temperature for an isobaric heat transfer process, ensuring a dry inlet condition at the compressor inlet. It is important to remember that this study does not consider pressure drops in the components, which is something that cannot be avoided in real-world situations. As a result, the temperature glide phenomenon presents significant challenges for the design and operation of the LTR. In simpler terms, to accommodate these varying temperature profiles during the phase change process, the LTR’s design may need to incorporate multiple zones with different temperatures to maintain an effective temperature difference and heat transfer throughout the phase change region.

4.2. Energy and Exergy Performance

This section discusses the energy and exergy performance of the cycle. As evident from the study in the section above, the cycle attains the maximum thermal efficiency when operated at optimal turbine inlet pressure, regardless of the molar fraction of the additive (SiCl₄) in the CO₂-based binary mixture. Therefore, a case study was conducted to find the maximum attainable performance of the cycle at various molar concentrations of SiCl₄ in the mixture. Figure 6 presents the thermal efficiency and the exergy efficiency of the cycle obtained at optimized turbine inlet pressure. It is observed that adding a small amount of SiCl₄ to CO₂ significantly improved the energetic and exergetic performance of the cycle. Considering energy performance, the thermal efficiency of the cycle increases with the increasing molar fraction reaching a maximum of nearly 43.5% at a 7% molar fraction of SiCl₄ in the mixture; this represents an increase of nearly 1.75 percentage points in thermal efficiency compared to pure CO₂ (which is nearly 41.75%). As mentioned earlier, when the mole fraction of SiCl₄ increases, the temperature glide also increases. However, if not enough heat is recovered in the LTR, this can result in a wet inlet condition at the compressor. It is important to note that the compressor will experience this wet inlet condition if the mole fraction of SiCl₄ is above 5% (see Figure 6). To ensure dry inlet conditions at the compressor inlet, the optimal molar fraction of SiCl₄ in the mixture is 5%, which achieves a nearly 43.36% thermal efficiency of the cycle, considered the highest possible in the current study. The thermal efficiency curve exhibits a steady decline, indicating poor heat recovery in the LTR and increased energy input during the compression process. A similar trend is observed for the exergy efficiency; the cycle achieves a maximum of nearly 70% exergy efficiency at a 5% molar concentration of SiCl₄. This represents a significant improvement of 8 percentage points in the exergy performance compared to pure CO₂.

The analysis of exergy loss rates across various components highlights critical insights into the performance of the cycle. The rate of exergy loss in various components, calculated using equations Equations (2)–(9) normalized by the net rate of the exergy input, is plotted in Figure 7 along with the exergy efficiency curve as a reference. It is found that the rate of exergy loss in various components of the cycle is less than 5% of the net rate of the exergy input, except for the cooler and heater. Focusing on the dry compressor inlet with SiCl₄ concentrations between 0% and 5%, a significant drop in irreversibility losses in the cooler and HTR is observed, compared to pure CO₂, which is ultimately reflected in an improved exergy performance of the cycle (refer to Figure 6). However, for molar concentrations above 5%, the increase in irreversibility losses in the low-temperature recuperator (LTR) and cooler becomes significant. This trend is associated with the increased temperature glide observed at higher SiCl₄ concentrations, leading to greater losses during the phase change in the mixture in the heat exchange process.

5. Conclusions

The thermodynamic performance of the CO₂ + SiCl₄ binary mixture as a working fluid for the recompression Brayton cycle was evaluated through analyses of its thermal efficiency and exergy efficiency. The cycle was modeled in the commercial software Aspen Hysys (V11) using the Peng–Robinson equation as the thermodynamic model to obtain the thermo-physical properties for CO₂ and the CO₂ + SiCl₄ binary mixture. The model worked well with the experimental findings reported in the literature. The cycle’s performance was assessed for warm climatic conditions with a cycle minimum temperature of 40 °C and turbine inlet temperature of 500 °C. The key outcomes of the present work are highlighted pointwise below.

• The cycle thermodynamic performance improved significantly when using CO₂ + SiCl₄ binary mixture as a working fluid compared to pure CO₂.
• At optimal mixture concentration, the thermal efficiency of the cycle improved by 1.6 percentage points, which corresponds to a nearly 4% improvement compared to pure CO₂.
• A great improvement in the exergy performance of the cycle was observed for CO₂ + SiCl₄ binary mixture. At optimal operating conditions, the exergy efficiency increased by 8 percentage points, reflecting a nearly 13% improvement compared to pure CO₂. This was mainly due to a significant decrease in irreversibility losses in the cooler and the HTR.
• With CO₂ + SiCl₄ as a working fluid, the energy and exergy performance parameters of the cycle improved with an increased molar concentration of SiCl₄ in the mixture to a limit, and then a decline in the performance was observed.
• The increasing molar concentration of SiCl₄ also resulted in a wet inlet condition to the compressor inlet, which resulted from the increasing trend of temperature glide with the increasing molar concentration of SiCl₄ in the mixture. This was due to limited heat recovery from the LTR between hot and cold streams.

The current study demonstrates the potential of CO₂ + SiCl₄ as a working fluid for power generation cycles. However, the scope of this research was limited to the recompression Brayton cycle. Therefore, the authors recommend exploring other configurations, such as the recompression Brayton cycle with partial cooling, to further evaluate performance.

Additionally, the observed temperature glide has a significant impact on the overall efficiency of the cycle due to its effects on heat recovery. Future work should focus on designing heat exchangers optimized for specific temperature–pressure ranges to mitigate these limitations. This targeted approach could enhance the overall performance of the cycle and broaden the applicability of CO₂ + SiCl₄ in various power generation systems.