In recent years, the utilization of renewable energy sources has become increasingly critical for sustainable development. Among these, solar energy stands out due to its vast potential and accessibility. We focus on harnessing low-temperature solar thermal energy, typically ranging from 65°C to 90°C, which is commonly achieved through vacuum tube solar collectors. This temperature range is ideal for organic Rankine cycle (ORC) systems, which efficiently convert low-grade heat into electrical energy. The integration of ORC technology with solar power systems offers a promising solution for decentralized power generation, especially in regions with abundant sunlight. In this study, we simulate and optimize a solar organic Rankine cycle power generation system using various working fluids to maximize performance metrics such as net power output, thermal efficiency, and exergy efficiency. Our analysis leverages the Engineering Equation Solver (EES) platform to model the thermodynamic processes and compare the behavior of different organic fluids under varying heat source temperatures. The system not only generates electricity but also utilizes the condenser waste heat for soil thermal storage, addressing issues like thermal imbalance in ground-source heat pump applications and enhancing overall solar energy utilization. By optimizing key parameters, we aim to contribute to the advancement of efficient and practical solar power systems.
The core components of a solar organic Rankine cycle power system include an evaporator, a screw expander, a condenser, and a working fluid pump. Solar-heated water serves as the heat source, while groundwater or soil-based circulating water acts as the heat sink. The process begins with the organic working fluid absorbing heat from the solar-heated water in the evaporator, where it vaporizes into a high-pressure gas. This vapor then drives the screw expander, producing mechanical work that is converted into electricity via a generator. The exhaust vapor from the expander enters the condenser, where it is cooled and condensed by the circulating cold water. Finally, the liquid working fluid is pumped back to the evaporator to repeat the cycle. This closed-loop system is particularly suited for low-temperature applications due to its simplicity and reliability. The integration of thermal storage through soil heating further improves the system’s sustainability by utilizing waste heat, thereby reducing exergy losses and increasing the overall efficiency of the solar power system.
To accurately model the solar organic Rankine cycle power system, we establish a comprehensive mathematical framework based on thermodynamic principles. The system is assumed to operate under steady-state conditions, with negligible heat losses to the environment and minimal pressure drops in components. The evaporation and condensation processes are considered isobaric. The key equations governing the system are derived from energy and exergy balances. For instance, the heat absorbed by the working fluid in the evaporator is given by:
$$ Q_z = c_p m_r (T_a – T_b) = m_g (h_1 – h_5) $$
where \( Q_z \) is the evaporator heat absorption rate in kW, \( c_p \) is the specific heat capacity of water in kJ/(kg·°C), \( m_r \) is the mass flow rate of solar hot water in kg/s, \( T_a \) and \( T_b \) are the inlet and outlet temperatures of the hot water in °C, \( m_g \) is the mass flow rate of the working fluid in kg/s, and \( h_1 \) and \( h_5 \) are the specific enthalpies at the evaporator outlet and inlet, respectively, in kJ/kg. The mechanical work output from the screw expander is calculated as:
$$ W_{sc} = m_g (h_1 – h_2) $$
where \( W_{sc} \) is the expander output in kW, and \( h_2 \) is the specific enthalpy at the expander outlet in kJ/kg. The net electrical power output of the system accounts for the efficiencies of the expander and generator:
$$ W = m_g (h_1 – h_2) \eta_j \eta_c \eta_f $$
Here, \( W \) is the net power output in kW, \( \eta_j \) is the mechanical efficiency of the expander, \( \eta_c \) is the transmission efficiency, and \( \eta_f \) is the generator efficiency. The isentropic efficiency of the screw expander is defined as:
$$ \eta_s = \frac{h_1 – h_2}{h_1 – h_{2s}} \times 100\% $$
where \( h_{2s} \) is the theoretical enthalpy at the expander outlet under isentropic conditions. The heat rejected in the condenser is expressed as:
$$ Q_l = c_p m_l (T_d – T_c) = m_g (h_2 – h_4) $$
where \( Q_l \) is the condenser heat rejection rate in kW, \( m_l \) is the mass flow rate of the cooling water in kg/s, and \( T_c \) and \( T_d \) are the inlet and outlet temperatures of the cooling water in °C. The power consumed by the working fluid pump is:
$$ W_b = \frac{m_g (h_5 – h_4)}{\eta_p} $$
where \( \eta_p \) is the pump efficiency. The thermal efficiency of the system, which indicates the conversion efficiency of heat to electricity, is given by:
$$ \eta_1 = \frac{W_{sc} – W_b}{Q_z} \times 100\% $$
Additionally, the exergy efficiency, which measures the system’s effectiveness in utilizing the available energy, is calculated as:
$$ \eta_2 = \frac{(h_1 – h_2) – (h_5 – h_4)}{(h_1 – h_5)\left(1 – \frac{T_l + 273}{T_h + 273}\right)} \times 100\% $$
where \( T_l \) is the average temperature of the cooling water in °C, and \( T_h \) is the average temperature of the hot water in °C. These equations form the basis for our simulation and optimization of the solar power system.
The selection of an appropriate working fluid is crucial for the performance of a solar organic Rankine cycle power system. We evaluate six organic fluids—R134a, R152a, R600a, RC318, R600, and R245fa—based on their thermodynamic properties, environmental impact, and safety. These fluids have zero ozone depletion potential (ODP) and vary in characteristics such as critical temperature, critical pressure, and boiling point. The properties of these working fluids are summarized in Table 1.
| Working Fluid | Critical Temperature (°C) | Critical Pressure (MPa) | Boiling Point (°C) | Safety Class |
|---|---|---|---|---|
| R245fa | 154.01 | 3.65 | 15.14 | B1 |
| R600 | 151.98 | 3.80 | -0.49 | A3 |
| R600a | 134.66 | 3.63 | -11.75 | A3 |
| RC318 | 115.23 | 2.78 | -5.98 | A3 |
| R134a | 101.10 | 4.07 | -26.10 | A1 |
| R152a | 113.26 | 4.57 | -24.00 | A2 |
Our simulation assumes constant cold source inlet temperature of 16°C, while the hot source temperature varies from 65°C to 90°C. The mass flow rates for both hot and cold water are set to 12 t/h, and the screw expander has a rated volume flow of 20 m³/h. The pinch point temperature differences in the evaporator and condenser are maintained at 5°C. Other efficiencies include a pump efficiency of 0.8, expander isentropic efficiency of 0.7, mechanical efficiency of 0.9, transmission efficiency of 0.9, and generator efficiency of 0.95. These parameters ensure a realistic representation of a typical solar power system.
We analyze the evaporation temperature and pressure for each working fluid across the specified heat source temperature range. The results indicate that both evaporation temperature and pressure increase proportionally with the heat source temperature. The working fluids can be categorized into two distinct groups: wet fluids (R134a and R152a) and dry fluids (R600a, RC318, R600, and R245fa). Wet fluids exhibit lower evaporation temperatures but higher evaporation pressures compared to dry fluids. For instance, at a heat source temperature of 90°C, the evaporation temperature for dry fluids is approximately 82°C, while for wet fluids, it is around 78.6°C. The evaporation pressure for wet fluids exceeds 2.2 MPa, whereas dry fluids operate below 1.4 MPa, making dry fluids more suitable due to their lower operational pressures and enhanced safety. The trends for evaporation temperature and pressure are summarized in Table 2.
| Heat Source Temperature (°C) | Working Fluid | Evaporation Temperature (°C) | Evaporation Pressure (MPa) |
|---|---|---|---|
| 65 | R245fa | 58.2 | 0.45 |
| R600 | 57.8 | 0.48 | |
| R600a | 58.1 | 0.52 | |
| RC318 | 57.9 | 0.55 | |
| R134a | 56.5 | 1.65 | |
| R152a | 56.8 | 1.72 | |
| 90 | R245fa | 82.1 | 1.12 |
| R600 | 81.9 | 1.18 | |
| R600a | 82.0 | 1.25 | |
| RC318 | 82.2 | 1.30 | |
| R134a | 78.6 | 2.35 | |
| R152a | 78.7 | 2.40 |
The net power output of the solar organic Rankine cycle power system shows a positive correlation with the heat source temperature. As the temperature increases from 65°C to 90°C, the net power output rises for all working fluids, with the rate of increase accelerating at higher temperatures. Among the fluids, RC318 achieves the highest net power output, reaching 12.27 kW at 90°C, which is 2.51 kW higher than R134a and 6.8 kW higher than R245fa. The ranking of net power output across fluids is consistent: RC318 > R134a > R152a > R600a > R600 > R245fa. This demonstrates the superior performance of RC318 in converting solar thermal energy into electricity. The net power output values are detailed in Table 3.
| Heat Source Temperature (°C) | R245fa | R600 | R600a | RC318 | R152a | R134a |
|---|---|---|---|---|---|---|
| 65 | 2.15 | 2.89 | 3.12 | 4.56 | 3.45 | 4.01 |
| 70 | 2.98 | 3.75 | 4.03 | 5.87 | 4.52 | 5.23 |
| 75 | 3.92 | 4.81 | 5.14 | 7.45 | 5.78 | 6.67 |
| 80 | 5.01 | 6.08 | 6.48 | 9.32 | 7.25 | 8.35 |
| 85 | 6.27 | 7.59 | 8.06 | 11.52 | 8.94 | 10.29 |
| 90 | 7.73 | 9.36 | 9.91 | 12.27 | 10.89 | 12.51 |
Thermal efficiency, which reflects the effectiveness of heat-to-electricity conversion, also increases with the heat source temperature, though the rate of increase slows at higher temperatures. Dry fluids generally exhibit higher thermal efficiencies than wet fluids. At 90°C, RC318 achieves the highest thermal efficiency of 15.42%, followed by R600 (12.01%), R245fa (11.78%), R600a (11.52%), R152a (9.23%), and R134a (8.89%). This highlights RC318’s advantage in maximizing energy conversion in solar power systems. The thermal efficiency trends are presented in Table 4.
| Heat Source Temperature (°C) | R245fa | R600 | R600a | RC318 | R152a | R134a |
|---|---|---|---|---|---|---|
| 65 | 7.12 | 8.45 | 8.89 | 11.23 | 7.56 | 7.34 |
| 70 | 8.01 | 9.31 | 9.78 | 12.45 | 8.45 | 8.21 |
| 75 | 8.95 | 10.22 | 10.72 | 13.72 | 9.38 | 9.12 |
| 80 | 9.94 | 11.18 | 11.71 | 14.12 | 10.35 | 10.08 |
| 85 | 10.98 | 12.19 | 12.75 | 14.89 | 11.37 | 11.09 |
| 90 | 11.78 | 12.01 | 11.52 | 15.42 | 9.23 | 8.89 |
The heat absorption rate in the evaporator, which represents the amount of solar energy utilized by the system, increases with the heat source temperature. Wet fluids generally exhibit higher heat absorption rates than dry fluids due to their higher specific heat capacities and latent heats. At 90°C, R134a has the highest heat absorption rate of 154.09 kW, while R245fa has the lowest at 60.47 kW. This indicates that while wet fluids absorb more heat, they may not convert it as efficiently into electricity, emphasizing the importance of fluid selection in solar power system design. The heat absorption data are shown in Table 5.
| Heat Source Temperature (°C) | R245fa | R600 | R600a | RC318 | R152a | R134a |
|---|---|---|---|---|---|---|
| 65 | 45.23 | 48.56 | 52.89 | 58.12 | 68.45 | 72.34 |
| 70 | 52.67 | 56.78 | 61.23 | 67.45 | 79.12 | 83.56 |
| 75 | 60.89 | 65.91 | 70.78 | 77.89 | 91.23 | 96.45 |
| 80 | 70.12 | 76.23 | 81.56 | 89.67 | 105.12 | 111.23 |
| 85 | 80.45 | 87.78 | 93.67 | 103.12 | 121.45 | 128.78 |
| 90 | 92.12 | 100.89 | 107.23 | 118.45 | 140.12 | 154.09 |
Exergy efficiency, which measures the system’s ability to utilize the available energy while accounting for irreversibilities, varies with the heat source temperature. For RC318 and R134a, exergy efficiency peaks at specific temperatures, while for other fluids, it increases monotonically but at a decreasing rate. Dry fluids consistently achieve higher exergy efficiencies than wet fluids. At 85°C, RC318 reaches its maximum exergy efficiency of 82.52%, significantly outperforming other fluids. At 90°C, the exergy efficiencies are grouped: RC318 at 82.46%, R600 and R245fa around 62%, and R152a and R134a below 48%. This underscores RC318’s superiority in minimizing exergy losses and maximizing the utilization of solar energy in the power system. The exergy efficiency values are listed in Table 6.
| Heat Source Temperature (°C) | R245fa | R600 | R600a | RC318 | R152a | R134a |
|---|---|---|---|---|---|---|
| 65 | 48.12 | 50.23 | 51.45 | 65.78 | 42.34 | 40.12 |
| 70 | 52.34 | 54.56 | 55.78 | 70.12 | 45.67 | 43.45 |
| 75 | 56.78 | 59.12 | 60.34 | 74.56 | 49.23 | 47.01 |
| 80 | 61.45 | 63.89 | 65.12 | 79.23 | 53.12 | 50.89 |
| 85 | 62.34 | 64.78 | 66.01 | 82.52 | 54.01 | 51.78 |
| 90 | 62.01 | 64.45 | 65.67 | 82.46 | 53.78 | 51.56 |
In conclusion, our simulation and optimization of the solar organic Rankine cycle power system demonstrate that RC318 is the most suitable working fluid for low-temperature applications between 65°C and 90°C. It achieves the highest net power output and thermal efficiency at 90°C, and the highest exergy efficiency at 85°C. The integration of condenser waste heat for soil thermal storage further enhances the system’s sustainability by addressing thermal imbalance issues in ground-source heat pumps. This approach not only improves the overall efficiency of the solar power system but also contributes to the effective utilization of solar energy. Future work could explore the impact of variable operating conditions and the use of zeotropic mixtures to further optimize performance. Our findings provide valuable insights for the design and implementation of efficient solar power systems in real-world applications.