Comprehensive Performance and Economic Analyses of Transcritical CO₂ Heat Pump Water Heater Suitable for Petroleum Processes and Heating Applications

Abstract

With the intensification of the global energy crisis, the application of air-source transcritical CO₂ heat pumps has attracted increasing attention, especially in cold regions. Existing research mainly focuses on the evaluation of steady-state performance while paying less attention to the dynamic characteristics of the system during the actual operation process. In order to deeply study the dynamic performance of the air-source transcritical CO₂ heat pump system under the winter climate conditions in the Yan‘an area, this study established a system simulation model with multiple parameter inputs and systematically analyzed the influences of ambient temperature, discharge pressure, and inlet and outlet water temperatures on the heating capacity and COP. The research starts from both dynamic and steady-state perspectives, revealing the variation law of system performance with environmental temperature and conducting a quantitative analysis. As the ambient temperature rose from −11 °C to 2 °C, the COP of the system increased by approximately 15% and exhibited significant dynamic response characteristics, indicating that the increase in ambient temperature significantly improved system efficiency. At different ambient temperatures, the optimal discharge pressure increased with the rise in temperature. At the highest ambient temperature (2 °C), the optimal discharge pressure was 11.7 MPa. Compared with the optimal discharge pressure of 11.0 MPa at −11 °C, the performance improved by nearly 13.3%. Through the dynamic simulation method, theoretical support is provided for the optimization of energy-saving control strategies in cold regions, and thoughts are offered regarding the application of transcritical CO₂ systems under similar climatic conditions.

1. Introduction

Currently, the world faces severe challenges of climate change and energy depletion [1]. These issues have compelled over 100 countries and regions to establish “net-zero carbon emission” plans [2]. Amid this global energy transition, oil remains a strategic resource underpinning modern industrial systems, accounting for one-third of the total global energy consumption [3]. However, high-heat-load production processes derived from the petroleum industry chain have become a critical bottleneck hindering sustainable development [4]. Notably, industrial heat supply still heavily relies on direct fossil fuel combustion—a primitive “carbon-for-heat” approach that causes over 40% energy waste [5] while exacerbating greenhouse gas emissions and thermal pollution. To achieve global carbon neutrality goals [6], the petroleum industry must urgently reform its energy structure, particularly in heating systems, through comprehensive technological upgrades and structural transformation [7].

Unlike traditional coal-fired boilers and electric heating systems, air-source heat pump technology absorbs low-temperature waste heat from the environment to deliver multiple times more thermal energy than the electricity consumed by the system [8]. This significantly enhances energy utilization efficiency [9,10]. Consequently, air-source heat pumps have gained global attention and are recognized as an effective approach to reducing operational costs and CO₂ emissions [11,12]. Clearly, replacing conventional heating equipment with heat pump systems not only improves energy efficiency but also substantially mitigates greenhouse gas emissions, positioning this technology as a critical pathway for future development [13].

However, most air-source heat pumps on the market still rely on traditional fluorinated refrigerants such as R134a, R410A, and R32 [14]. These refrigerants exhibit high global warming potential (GWP) [14], posing significant threats to the climate. For instance, R134a has a GWP value of 1430 [15], indicating that its climate impact is 1430 times greater than CO₂. To address this issue, the international community and national governments have implemented measures to phase out high-GWP refrigerants [16]. The Montreal Protocol and its Kigali Amendment under the United Nations have established strict regulations requiring countries to gradually reduce and eliminate these high-emission chemicals [17]. Meanwhile, low-GWP alternatives such as carbon dioxide (CO₂) and R290 [18] are being developed and promoted as eco-friendly substitutes. Nevertheless, R290 faces limitations in large-scale industrial applications like petroleum and construction due to flammability risks [19]. In contrast, CO₂, as a natural refrigerant, has emerged as a preferred environmentally friendly solution due to its safety, stable chemical properties, non-toxicity, GWP of 1, and zero ozone depletion potential (ODP) [20,21].

The most significant distinction from conventional heat pump cycles lies in the heat rejection process of air-source CO₂ heat pumps, which occurs in the supercritical region [22]. This characteristic defines them as transcritical CO₂ heat pumps. During the supercritical CO₂ cooling process, a relatively large temperature glide occurs, substantially enhancing the system’s heating performance [23]. However, the operational efficiency of air-source heat pumps exhibits significant fluctuations under varying environmental conditions [24], with pronounced performance degradation under extreme scenarios [25]. Such variability limits their energy-saving potential in specific applications. Investigating the efficiency characteristics and performance of air-source heat pumps across diverse environmental conditions—particularly under extreme operating states—is imperative [25].

However, current research on air-source transcritical CO₂ heat pumps remains predominantly focused on steady-state simulation models and testing [26]. These tests are typically conducted under assumed stable operating conditions and offer preliminary theoretical guidance for system design [27]. A key limitation of this steady-state approach is its neglect of dynamic variations during real-world operation [28]. For instance, factors such as climate variations and load fluctuations cause heat pumps to exhibit varying energy efficiency and performance across operational cycles [29,30]. It is crucial to recognize that the heat supply demands of air-source heat pumps in industrial sectors such as petroleum are not static but rather a complex and constantly evolving dynamic process [31]. In petroleum applications, many thermal load processes are subject to dynamic variations throughout production phases and in response to changing external environmental conditions. Consequently, steady-state experiments where environmental parameters and other conditions remain constant do not represent actual operating scenarios. They will fail to capture the true system behavior and overlook many critical factors [32].

To more accurately evaluate the performance of air-source transcritical CO₂ heat pumps in high-heat-load scenarios such as those in the petroleum industry, this study integrates real-world environmental conditions into a dynamic simulation model. During this process, critical parameters including system operating temperatures and pressures vary over time, directly affecting key performance indicators such as heating capacity, power consumption, and COP. By incorporating dynamic operational conditions, the model generates comprehensive metrics like the total heating output, cumulative energy consumption, and overall energy efficiency coefficients across full operational cycles. Compared to steady-state simulations, this dynamic approach better reflects real-world complexities and enables more precise energy efficiency assessments. These insights are vital for optimizing system design, enhancing stability and reliability, and informing operational control strategies. Furthermore, dynamic simulations reveal potential issues under practical conditions, such as system responsiveness to load fluctuations or environmental changes that steady-state methods often overlook. This underscores the importance of dynamic validation in real-world applications. Based on this framework, this study provides simulation results and experimental validation to guide energy efficiency optimization, operational management, and equipment selection for the petroleum industry and other energy-intensive sectors.

2. System Description

A simplified flowchart of the air-source transcritical CO₂ heat pump system for petroleum processes is shown in Figure 1. The system comprises three loops: a refrigerant cycle (high pressure in orange, low pressure in yellow), an oil heat exchange process (dark red), and a water heating process (high-temperature water in bright red, medium temperature in light orange, and low temperature in dark blue). During operation, the refrigerant releases heat through the gas cooler to heat low-temperature water to over 80 °C. This high-temperature water is stored in a storage tank to ensure immediate availability for initiating petroleum processes. The heat recovery system extracts hot water from the storage tank to preheat oil in the petroleum preheater, reducing energy consumption. As hot water is consumed, cold water is reheated by the CO₂ gas cooler to replenish the storage tank. High-temperature water undergoes counterflow heat exchange in the petroleum preheater, raising the oil temperature before it flows to desalination and dehydration units. Post-exchange water retains sufficient heat and is stored in a thermal buffer tank for reuse. During active operation, medium-temperature water from the buffer tank is diverted into two subsystems: pipeline tracing to maintain oil temperature during transport and desalination modules to remove impurities. In non-operational states, the buffer tank supplies water to pipeline cleaning devices for residue removal. This cascaded utilization of heated water maximizes thermal efficiency, making the system particularly suitable for industrial applications like petroleum processing that require multi-tiered temperature management.

3. Methodology

3.1. Mathematical Modeling of Air Source Transcritical CO₂ Heat Pump System

The refrigerant system is the most critical component in the petroleum preheating process. In this simulation, CO₂ is employed as the refrigerant with a charge of 7.9 kg. Key components include the compressor, plate heat exchangers (gas cooler and evaporator), electronic expansion valve, and liquid separator. The compressor operates at a fixed displacement of 25 m³/h, while discharge pressure is regulated by adjusting the electronic expansion valve opening. Water outlet temperature is controlled via pump speed modulation. Parameters such as refrigerant mass flow rate, compressor outlet state, power consumption, heat transfer in the gas cooler, inner heat exchanger, and evaporator are calculated using the equations listed in

Table 1. Main formulas of mathematical model.

Equipment Name	Formula
Compressor [33,34]	$m=N{\rho }_s{V}_c{\eta }_v$ $h_d=h_s+{\displaystyle \frac{h_{d,is}-h_s}{{\eta }_{is}}}$ $W_c={\displaystyle \frac{\dot{m}\left(h_{d,is}-h_s\right)}{{\eta }_{is}{\eta }_m}}$ ${\eta }_V=1.19379-0.13635\cdot \left({\displaystyle \frac{p_d}{p_s}}\right)$ ${\eta }_{is}=0.8014-0.04842\cdot \left({\displaystyle \frac{p_d}{p_s}}\right)$ ${\eta }_V=0.64107+0.07487\cdot \left({\displaystyle \frac{p_d}{p_s}}\right)$
Gas coolers [35,36]	$Q_{HX}={\displaystyle \sum _{j=1}^N}{\mathrm{k}}_j{A}_j\left(T_{ref,j}-T_{coolant,j}\right)$
Evaporator [37,38]	$Q_{HX}={\displaystyle \sum _{j=1}^N}{\mathrm{k}}_j{A}_j\left(T_{ref,j}-T_{air,j}\right)$
Electronic expansion valve [34]	$m_r=C_D{A}_D{(2{\rho }_{\exp ,in}(p_{\exp ,in}-p_{\exp ,out}))}^{0.5}$
Gas–liquid separator [39]	$h_{in}{m}_{in}=h_{gas}{m}_{gas}+h_{liquid}{m}_{liquid}$ $\beta ={\displaystyle \frac{m_{liquid}}{m_{in}}}$

.

3.2. Solution Method

Based on the mathematical model described above, a transcritical CO₂ air-source heat pump simulation was developed using the AMESim v2021 (Advanced Modeling Environment for Simulation) platform. This platform was developed by Siemens and is an engineering software that focuses on the dynamic performance analysis of multi-disciplinary physical systems, such as mechanical, hydraulic, pneumatic, thermal fluid, and control systems. Its core advantage lies in providing a rich library of predefined physical components, supporting coupled modeling and efficient simulation of complex systems, and it is suitable for analyzing dynamic processes involving multi-physical field interactions such as fuel cell air supply systems.

The detailed model structure is illustrated in Figure 2.

The AMESim model enables dynamic environmental condition inputs and calculates system performance parameters such as heating capacity, power consumption, and COP.

The simulation model needs to align with practical conditions. Given that the air-source transcritical CO₂ heat pump in this study is installed in Yan’an, a city in northern China, dynamic input signals reflecting Yan’an’s winter daily climate variations are integrated into the model. Climate data selection and input represent critical factors for ensuring model accuracy in this dynamic simulation study. Historical meteorological data from Yan’an Meteorological Observatory of the National Basic Meteorological Station (http://data.cma.cn) [40] were selected to ensure simulation reliability and practicality. These data include temperature, humidity, and other indicators from a typical winter day in Yan’an. The dataset features minute-by-minute temporal resolution to enhance accuracy and timeliness. As shown in Figure 3, this high-resolution data captures detailed 24-h climate fluctuations.

During model operation, climate data must be dynamically input as signal sources into the AMESim simulation. To achieve second-level and minute-level dynamic operations, we configured a 1-s time step in AMESim to capture climate change impacts instantaneously.

COP is a key performance indicator for heat pump systems and is defined as follows:

$$\begin{array}{c}COP={\displaystyle \frac{Q}{W_C}}\end{array}$$

(1)

And the total COP is calculated as shown below [41]:

$$\begin{array}{c}{Q}_{ALL}={\displaystyle \sum _{i=0}^{\mathrm{86,400}}}{Q}_i\end{array}$$

(2)

$$\begin{array}{c}{W}_{c,ALL}={\displaystyle \sum _{i=0}^{\mathrm{86,400}}}{W}_c\end{array}$$

(3)

$$\begin{array}{c}CO{P}_{ALL}={\displaystyle \frac{Q_{ALL}}{W_{c,ALL}}}={\displaystyle \frac{\sum _{i=0}^{\mathrm{86,400}}{Q}_{0_i}}{\sum _{i=0}^{\mathrm{86,400}}{W}_c}}\end{array}$$

(4)

COP represents the Coefficient of Performance calculated every second. COP_ALL refers to the ratio of total heat generated to total power consumed over 86,400 s.

4. Results and Discussion

4.1. Verification of Simulation Results

Table 2. The parameters of the sensors.

Measured Variable	Device	Measure Variable	Accuracy
Temperature	RTD sensors	−200~350 °C	±0.3 °C
Pressure	Pressure sensors	0~16 MPa	±0.25%
Water flow rate	Flowmeter	0~6 m3·h−1	±0.5%
CO2 volume flow	Flowmeter	0~2.3 m3·h−1	±0.5%
Power consumption	Three-phase electrical parameter comprehensive measuring instrument (AN7931A, Qingdao Aino Electronic Instrument Co., Qingdao, China)	0~55 kW	±0.1%

specifies the measurement accuracies of instruments, including temperature and pressure sensors.

Using error propagation formulas, the experimental uncertainties for heating capacity and power consumption are calculated to remain below 5%, as illustrated in Figure 4. This demonstrates strong agreement between the experimental and simulation models, thereby validating the simulation’s accuracy.

4.2. Parametric Analysis of Air Source Transcritical CO₂ Heat Pumps

In air-source transcritical CO₂ heat pump systems, performance parameters such as the heating capacity and COP are influenced by a combination of system operating parameters and external environmental conditions.

(1)

Static analysis

Discharge pressure is a critical variable influencing heat pump performance as it directly impacts compressor power consumption and gas cooler heat exchange efficiency. In CO₂ transcritical cycles, discharge pressure selection affects not only compressor workload and gas cooler heat transfer intensity but also alters the distribution of sensible and latent heat at the high-pressure side through significant changes in refrigerant properties. Dynamically optimizing the discharge pressure range via simulation combined with the temperature glide characteristic unique to transcritical cycles serves as a core strategy for balancing the heating capacity and COP in heat pump systems.

Figure 5 illustrates the steady-state analysis of discharge pressure effects on system heating capacity and the COP under varying environmental conditions. Environmental temperature and discharge pressure show significant correlations with the COP and heating performance. As shown in Figure 5a, higher ambient temperatures and discharge pressures increase heating capacity. Elevated ambient temperatures enhance the evaporator inlet air temperature, allowing CO₂ to absorb heat more efficiently during evaporation. This raises the refrigerant’s enthalpy entering the compressor, providing greater initial energy for subsequent compression and heat release. Increased discharge pressure shifts the CO₂ temperature profile upward in the gas cooler, amplifying the temperature difference with the water side. This strengthens the driving force, enabling each unit mass of CO₂ to release more heat.

The steady-state analysis of discharge pressure effects on system heating capacity and the COP under varying inlet and outlet water temperatures is shown in Figure 6 and Figure 7. As illustrated in Figure 6a, the heating capacity decreases with a rising outlet water temperature. This occurs because higher outlet temperatures elevate the overall water-side thermal level, reducing the mean temperature difference between CO₂ and water in the gas cooler. Consequently, the heat released by CO₂ per unit time diminishes, lowering heat exchange efficiency. Similarly, as illustrated in Figure 7a, increased inlet water temperature reduces heating capacity due to weakened thermal driving forces within the gas cooler. Higher inlet temperatures raise the water-side thermal level, further degrading heat transfer efficiency. To heat CO₂ sufficiently to match elevated water outlet temperatures under these conditions, the compressor must operate at higher compression ratios and deliver greater work input. This significantly increases energy consumption. The combined effects of reduced heating capacity and elevated input power result in COP decline, as demonstrated in Figure 6b and Figure 7b.

(2)

Impact of discharge pressure under dynamic environmental conditions

Figure 8 presents the dynamic analysis of discharge pressure’s impact on system heating capacity and the COP under dynamic environmental input conditions. The temporal variation reflects ambient temperature changes during heat pump operation, with specific temperature–time correlations shown in Figure 3. Ambient temperature transitions from −11.4 °C to 2.5 °C before gradually returning to −11 °C, simulating winter temperature variations during continuous operation in Yan’an. A comparison between Figure 3 and Figure 8 demonstrates that ambient temperature significantly influences the heating capacity and COP. These parameters are jointly determined by both ambient temperature and discharge pressure in governing system performance.

The heating capacity and COP demonstrate significant upward trends with rising ambient temperatures. In low-temperature zones (below −10 °C), the system exhibits a universally low heating output with the COP stabilized at 2.60–2.70 regardless of discharge pressure adjustments. When ambient temperatures exceed −5 °C, particularly within the 0–2.5 °C range, both the heating capacity and COP rapidly surge, indicating system transition to high-efficiency operation. This improvement stems from increased evaporator heat transfer differentials caused by warmer environments, which elevate the CO₂ evaporation pressure and enhance the heat absorption capacity. Simultaneously the refrigerant’s enthalpy entering the compressor rises while the compression ratio decreases, creating greater heat release per unit mass with compressor power consumption growing slower than heating output, thereby driving COP enhancement.

System performance exhibits distinct variations under different discharge pressures. As shown in Figure 8a, the heating capacity generally increases with rising discharge pressure, particularly demonstrating optimal performance within the 11.3–11.6 MPa range. A higher discharge pressure elevates the CO₂ heat rejection temperature in the gas cooler, enhancing the average heat transfer temperature difference with the water side to facilitate greater heat release. However, further pressure increases beyond 11.7 MPa gradually flatten the heating capacity growth with occasional declines attributed to reduced CO₂-specific heat or restricted heat transfer efficiency caused by excessive gas cooler outlet temperatures. Figure 8b reveals power consumption trends resembling heating capacity patterns. Power usage gradually increases with rising ambient temperature, peaking at maximum temperature conditions. Lower ambient temperatures require increased compressor work to maintain adequate heating output. As ambient temperature rises, the evaporator’s heat absorption capacity strengthens while the evaporation temperature elevates. This causes higher system superheat and an intensified compressor load, driving power consumption upward. Similarly, an elevated discharge pressure raises the compression ratio, further increasing system power demand. Figure 8c demonstrates the dynamic response of system COP under varying ambient temperatures. When the discharge pressure exceeds 10.8 MPa, the COP progressively increases with a rising ambient temperature and reaches its peak at approximately 2.5 °C. For discharge pressures between 10.5 and 10.8 MPa, the COP initially rises as the ambient temperature increases to −1 °C but slightly declines upon further temperature elevation. This occurs because lower discharge pressures insufficiently release heat from the CO₂ high-pressure side, particularly under higher temperatures, which compromises heat transfer efficiency. Additionally, reduced discharge pressures demand greater compressor power to achieve equivalent heating capacity, ultimately degrading overall energy efficiency and COP.

Ambient temperature serves as the primary external factor influencing heat pump performance, while discharge pressure acts as the key control parameter regulating thermodynamic states and the COP. As shown in the Figure 8, lower ambient temperatures correspond to reduced optimal discharge pressure, with this parameter gradually increasing alongside ambient temperature elevation, aligning with the steady-state analysis results. The discharge pressure and ambient temperature constitute tightly coupled variables requiring coordinated optimization rather than isolated parameter adjustments to achieve peak performance. Based on combined dynamic and steady-state analyses, a coupled correlation equation for discharge pressure was derived and applied in subsequent research. The specific correlation is as follows:

$$\begin{array}{c}{P}_{d,opt}=0.049T_{amb}+11.67\end{array}$$

(5)

(3)

Impact of inlet and outlet water temperatures under dynamic environmental conditions

Figure 9a,b illustrate the dynamic variations in the COP and heating capacity during operation for the air-source transcritical CO₂ heat pump system under different water inlet temperature settings (5–35 °C). System performance exhibits marked differences in ambient temperature responsiveness across these settings.

Under identical ambient temperatures, higher inlet water temperatures correlate with a reduced system heating capacity. At a 5 °C inlet water temperature, the peak heating capacity exceeds 140 kW compared to approximately 100 kW at 35 °C. This occurs because elevated water temperatures raise the thermal baseline on the water side, diminishing the mean temperature difference between CO₂ and water in the gas cooler and weakening heat transfer driving forces. As shown in Figure 9b, the COP follows similar trends as the heating capacity, initially rising then declining with increasing ambient temperatures. High inlet water temperatures notably depress COP levels, achieving up to approximately 3.3 at 5 °C but dropping below 2.3 when the water temperature reaches 35 °C.

Moreover, the system exhibits distinct sensitivity to ambient temperature variations under different inlet water temperature conditions. At lower inlet water temperatures, the heating capacity and COP show more significant growth with rising ambient temperatures, indicating stronger adaptability and heat exchange resilience. Conversely, under high inlet water temperatures, performance improvements remain constrained even with ambient condition enhancements, primarily limited by the adverse effects of elevated return water temperatures on the water side.

Figure 10a,b display COP and heating capacity variations under different outlet water temperature settings. Figure 10a shows that the heating capacity increases with reduced outlet water temperatures during ambient temperature rise phases. Figure 10b reveals a similar COP improvement trend at lower outlet water temperatures. This occurs because higher outlet water temperatures demand more heat release from CO₂ in the gas cooler to reach target water temperatures. Such conditions reduce heat exchange temperature differences and cause incomplete heat dissipation. Simultaneously, elevated outlet temperatures require higher CO₂ discharge temperatures and pressures, increasing the compressor workload. Lower outlet water temperatures enhance the temperature gradient between the gas cooler and water side. This strengthens heat dissipation completeness and improves heat exchange efficiency. Consequently, heat release per unit time rises, boosting the overall heating capacity and demonstrating superior thermal economy.

However, further decreases in the outlet water temperature gradually diminish the COP and heating capacity improvements. This occurs because lower temperatures increase the compressor load. Expanding temperature differences require higher energy consumption to maintain system operation, progressively limiting efficiency. Consequently, heating capacity and COP enhancement become constrained. Additionally, the heat source temperature critically affects system performance. While a reduced outlet water temperature enlarges temperature differences, an insufficient heat source temperature restricts effective heat extraction. Even with large temperature gradients, inadequate heat source quality prevents further performance gains. Therefore, although lowering the outlet water temperature initially boosts heat pump performance, multiple factors systematically constrain efficiency improvements at lower temperatures.

5. Conclusions

This study establishes a dynamic simulation model of an air-source transcritical CO₂ heat pump system under winter conditions in Yan’an, focusing on dynamic operational behaviors under varying discharge pressures, ambient temperatures, inlet water temperatures, and outlet water settings. Through a systematic analysis of the heating capacity and COP responses to temporal and multi-parameter variations, it elucidates the influence mechanisms of critical operating parameters on system performance, providing theoretical foundations for advanced regulation and stable operation. The key findings are summarized below:

• The heat pump system exhibits distinct dynamic response characteristics under varying ambient temperatures. Both the heating capacity and COP rise synchronously during temperature escalation phases before peaking and subsequently declining as temperatures drop.
• At the highest ambient temperature (2 °C), the optimal discharge pressure is 11.7 MPa. Compared with the optimal discharge pressure of 11.0 MPa at −11 °C, the performance has improved by nearly 13.3%.
• An elevated inlet water temperature reduces the gas cooler’s heat exchange temperature difference and weakens heat release efficiency. The inlet water temperature should be maintained within a reasonable range (below 25 °C) to ensure optimal system performance.
• The environmental temperature, discharge pressure, and water temperature exhibit temporal interactions that profoundly shape the system’s dynamic thermodynamic behavior and energy efficiency levels. Dynamic analysis surpasses static evaluations in identifying operational performance boundaries and regulation strategies during real-world operation.