Study on the thermodynamic and economic performance of power generation cycle with small temperature difference

The low thermal efficiency and low economic benefits of power generation systems under small temperature difference conditions have always hindered their practical operation. In order to explore effective ways to achieve performance optimization of thermodynamic cycle electrical power generating systems under small temperature difference conditions, this study constructs a static analysis model of an organic Rankine cycle with small temperature difference, selects six different commonly used refrigerants, and investigates the influence of key parameters on the thermodynamic and economic performance of the system using difference working fluids. The outcomes indicate that key parameters such as evaporation temperature and condensation temperature play a critical role in the thermodynamic and economic performance of the power generation system. For the working fluids, R227ea provides the highest net power output, while ammonia (R717) is the best performer in regard to system thermal efficiency and economic performance.


Introduction
For a long time, converting temperature difference energy into electricity through thermodynamic cycles under small temperature difference conditions has been widely regarded as a power generation method with great application prospects and potential [1][2].For example, the vast amount of ocean thermal energy stored in the vast oceans is a form of small temperature difference energy.At low latitudes, the temperature of the surface ocean water remains between 25-30°C all year round, while deep ocean water at a depth of 1000~1200m maintains a temperature of 4~6°C [3][4].Ocean thermal energy is a massive amounts of heat power stored in the temperature difference between different depths of seawater.It has abundant reserves, is clean and sustainable, and is considered the most promising renewable energy source for deepsea electricity supply.
The key to utilizing small temperature difference energy to stably and sustainably supply electricity is to master the technology of converting small temperature difference energy into electricity through thermodynamic cycle systems [5].The organic Rankine cycle(ORC) is one of the broadest and most commercially viable power generation cycle systems under small temperature differentials [6].It uses low-boiling organic substances as working fluids to achieve power generation under small temperature differences.Due to the relatively small temperature differences in the system, the selection of different working fluids often leads to a significant impact on the performance of the heat exchanger, expander and thermal cycle.Therefore, the selection of a suitable working fluid is very significant in enhancing the performance of the system.
Scholars from various countries have conducted a considerable amount of research on the optimization of working fluids in ORC under small temperature difference conditions [7][8][9].For example, Rosard et al. [10] compared ammonia with 11 other working fluids including propane and the results show that the volume of carbon dioxide turbine is the smallest when the generating power is the same.In the case of the same turbine volume, the power of the turbine with ammonia as the working fluid is twice that of the carbon dioxide turbine.Stoecher et al. [11] compared R134a,ammonia and R22 as working fluids, and the results certificate that under the same heat flow conditions, systems using ammonia as the working fluid cost up to 10 times less than R134a and R22.Kim et al. [12] developed computer modeling programs for five forms of thermal cycles, including the ORC, and compared several different working fluids.The outcomes suggest that the capabilities of R410a and R32 is comparable to that of R22 and ammonia.Sun et al. [13] optimized ammonia and R134a as working fluids with the objective of power output maximization, and the outcomes indicate that ammonia and R134a showed good performance in terms of thermal and exergy efficiencies.Yang et al. [14] quantitatively studied systems based on ORC and compared five commonly used working fluids: ammonia, R600a, R245fa, R152a, and R134a, based on net output per unit area.The outcomes indicated that ammonia performed the best in the evaluation of target parameters, while R600a performed better in the evaluation of thermal efficiency.Yoon et al. [15] compared thermal efficiency and major component sizes of three working fluids, and the outcomes indicated that ammonia is the preferred fluid.However, ammonia can present environmental and safety hazards.
However, in the work of the above scholars, the index parameters to measure the system performance often fail to combine the utilization rate of heat source and the initial investment cost of system equipment.Based on it, this study aims to explore effective ways to improve the performance of thermodynamic cycle power generation systems under small temperature difference conditions.Firstly, based on the operating conditions of small temperature differences, common organic working fluids were selected, and six working fluids capable of small temperature difference ORC.Then, a static analysis model of ORC power generation system was constructed, and the rationality of the model was verified using literature data.Finally, through the constructed model, the effects of the key parameters of the system, such as evaporation temperature and condensation temperature, as well as different work fluids on the thermodynamic and economic performance of the system are investigated.

System description and model
The ORCs refers to the Rankine power cycle that uses organic refrigerants as working fluids.It is the most widely used and structurally simple cycle system in thermodynamic cycle power generation systems under small temperature difference conditions.This study takes the ORC power generation system based on ocean thermal energy as an example to investigate capacity of the ORC system for small temperature differences.The system diagram is illustrated as Figure 1.The main equipment involved are an evaporator, an expander, a condenser and a pump in the cycle.The liquid working fluid gain the heat and evaporated by the heat source in the evaporator.The evaporated vaporized working fluid flows into the expander to expand and generate electricity.The vapor from the expander flows into the condenser, where cold source water is liquefied.Finally, the liquefied working fluid is pumped into the evaporator and a novel cycle begins.In addition, due to the long length and large flux of the seawater pipeline, the power consumption of the seawater pump is to be also taken into account for modelling the system.
Figure 1.Schematic diagram of ORC power generation system using ocean thermal energy.

Primary selection of working fluids
The working fluid usually requires to satisfy the following requirements [16][17][18][19]: (1) The working fluid should meet safety requirements (non-toxic or low toxicity, nonflammable, non-explosive, non-corrosive to pipelines and equipment).
(2) The working fluid should be environmentally friendly, that is, it should not cause damage to the ozone layer, and the Ozone Depletion Potential (ODP) should be 0.
(3) Chemical stability is necessary for the working fluid and its decomposition temperature significantly higher than the system operating temperature.(4) Critical temperature should optimally be higher than the heat source temperature.Furthermore, drop of pressure in the piping reduces the pressure of the steam entering the expander, thus influencing the thermal efficiency of the system.Consequently, the pressure difference between the high and low pressures in the system loop should not be too small.In this study, with a reference evaporation temperature of 24°C and condensation temperature of 8°C, it is required that the pressure drop between the evaporator and the condenser is greater than 150 kPa.Under the above requirements, this paper considers six commonly used refrigerants with an ODP of 0 as alternative working fluids, consisted by three types of dry fluids and three wet fluids.The thermophysical properties of the six components are illustrated in Table 1.

Model Description
Based energy conservation principle, this paper develops the static model on the key facilities, including the evaporator, the expander, the compensator, the working fluid pump and cold water pump, and solves the governing equations of the static model.To simplify the calculations, certain assumptions need to be made for the system model.This model assumes that the power output of the expander is fixed at 50 kW.The power consumption of the pumps is calculated based on the pressure drop in the pipeline.In addition, made some general assumptions: (1) System is in steady state operation.
(2) Heat exchange between the pipes, equipment, and the external environment is ignored.For a pure substance, the pinch point is in the saturated liquid phase, and its temperature difference is calculated by The evaporator outlet superheat is defined by sh 5 4 ΔT T T (3 The expander is a component that outputs power to the outside, and its power output is calculated by The isentropic efficiency of the expander is assumed to be constant and is calculated by The energy conservation equation for the condenser is The isentropic efficiency of the working fluid pump is presumed to be constant and is calculated by the rate of the isentropic enthalpy increase to the practical enthalpy increase The power consumption of the cold water pump is calculated based on the pressure drop in the cold water pipeline 2 sw(dw) sw(dw) sw(dw) sw(dw) h Δ 2 where f is the Darcy friction factor, which is a dimensionless parameter calculated by h 1 25 1 2log 3 72 The net power output of the system is defined as net,OTEC exp p sw dw The net efficiency of the system is defined as net,OTEC OTEC eva The specific net output power of the system is defined as: net,OTEC net sw In addition, a simple indicator is used to characterize the economy of the system, which is the net power output per unit area of heat transfer net,OTEC tot Where Atot is the complete area of heat transfer of the system, and is calculated by tot eva con The evaporator and condenser in the system are plate heat exchangers.According to the working fluid state, the evaporator is divided into three parts: liquid phase, two-phase and gas phase.For wet fluids, the condenser has only one part of the two-phase region, and for dry fluids, the condenser is divided into two parts: the gas phase and the liquid phase.The heat transfer area of each part can be calculated by Newton's cooling formula The total heat transfer coefficient is expressed as the sum of the thermal resistance of each heat transfer link The convective heat transfer coefficients of the seawater side and the working fluid side in the single-phase zone (supercooled zone and superheated zone) were calculated using Muley correlation.The evaporative heat transfer coefficient on the working fluid side of the evaporation zone is calculated by the Amalfi correlation equation.The condensing heat transfer coefficient of the working fluid side of the condensing zone is calculated by Shah correlation equation.

Model Validation
In an attempt to test the correctness of the static analysis of the model of the system constructed in this paper, a comparison analysis was conducted with the calculated results in reference [20].The parameter settings are shown in Table 2 From the verification results in Table 3, the maximum error of the model parameters is 3.6%, which comes from the system net efficiency and is within an acceptable range, indicating that the model is reasonable.

Impact of Key Parameters on System Performance
Based on the established static analysis model, the system net efficiency, specific net output power, and economy are considered as indicators, and the influence of evaporation temperature, condensation temperature on system performance indicators is analyzed.

Evaporation Temperature
The Carnot cycle thermal efficiency is the highest theoretical thermal efficiency achievable for all thermodynamic cycles, where the evaporation temperature is equal to the temperature of the heat supply and the condensation temperature is equal to the temperature of the cold supply.Thus, all other things being equal, a higher evaporation temperature means a higher system thermal efficiency, closer to a theoretical maximum thermal efficiency.In addition, the increased evaporation temperature leads to an increase in the flow rate of the heat source water and an increase in the power consumption of the heat source pump due to the limitation of the temperature difference between the pinch points, leading to a decrease in the net efficiency of the system.Considering these two factors, the impact of evaporation temperature on the net efficiency of the system is shown in Fig. 3.It can be seen from the figure that the net efficiency of the proposed system improves with increasing evaporation temperature.In the example of ammonia (R717), the net efficiency of the system increased from 2.07% to 4.06% as the evaporation temperature increased from 18°C to 27°C.This suggests that the system thermal efficiency is more sensitive to changes in evaporation temperature than the power dissipation of the seawater pumps.Therefore, if a high net system efficiency is required, the evaporation temperature should be as high as possible.In terms of the choice of working fluids, as can be seen in the figure that R1234ze performs better in terms of net efficiency in the dry fluid, while ammonia (R717) has the highest net efficiency in the wet fluid, followed by R152a, and R32 performs the worst, and this difference also grows as the evaporation temperature increases.The specific net output power of the system is defined as the net output power of the system under the unit heat source water flow.This index can not only compare the output power capacity of each working fluid at the same level, but also take into account the utilization rate of heat source water.Figure 3-2 shows the effect of evaporation temperature on the specific net output power of the system.As can be seen from the figure, with the increase of evaporation temperature, the net efficiency of the system increases, but due to the limitation of the temperature difference of the evaporator pinch point, the seawater temperature at the evaporator outlet increases, and the water utilization rate of the heat source decreases.Therefore, the net specific output power of the system first increases and then decreases with the evaporation temperature, and reaches the maximum value around 19 .Taking ammonia (R717) as an example, the net specific output power of the system reaches the maximum value of 870.53W/kg when the evaporation temperature is 19 .In addition, no matter the dry fluid or the wet fluid, the specific net output power of each fluid is not much different, but the dry working fluid R227ea shows a slightly higher specific net output power than the other 5 working fluids.
The upfront capital expense depends on evaporator and condenser heat transfer area, especially if the heat transfer area is large.Thus, a simple metric was used to measure the economic feasibility, which is net power generation capacity of a unit area.Figure 5 illustrates the impact that evaporation temperature has upon system unit area in terms of clear power output.With increasing evaporation temperature, there is an increase in net efficiency as well as net system power output.However, higher evaporation temperatures result in a decrease of thermal heat exchange temperature difference (TTD), which requires a larger evaporator heat transfer area.Taking these two factors into account, net power output per unit area of the system initially rises with the evaporation temperature and then declines, peaking at 25°C.In addition, R227ea has the highest net power output per unit area in dry operating fluids, while in wet operating fluids, ammonia offers significant strengths compared to each of 2 other working fluids.At an evaporation temperature of 25°C, ammonia (R717) has a net per-area power output of 132 W/m 2 , while R32 has the greatest net per area power output among the other 5 working fluids, at 94.87 W/m 2 .

Condensation Temperature
In the Carnot cycle, a lower temperature of the cold source means a higher cycle thermal efficiency.Therefore, in the organic Rankine cycle, lowering the condensation temperature enhances the thermal effectiveness of the cycle.On the other hand, lowering the condensation temperature results in lower condenser outlet seawater temperatures, increasing the cold source water flow rate consumption and increasing the seawater pump consumption because of the limitation of the temperature difference between the pinch points.Effects of condensation temperature on this system are reflected in these two areas, as shown in Figure 6.As the figure indicates, the net efficiency of the system degrades monotonically as the condensation temperature is enhanced.In the case of ammonia (R717), for example, the net efficiency was reduced from 3.60% to 2.40% as the condensation temperature was increased from 8°C to 14°C.This indicates that the variation in seawater pump power consumption caused by the change in condensation temperature is not as significant as the impact on the system thermal efficiency.As indicated in Figure 7, the specific net output monotonically reduced with the increase in condensation temperature of the system.In the case of ammonia (R717), for example, with a rise in condensation temperature from 8°C to 14°C, the net output reduces from 616.52W/kg to 401.81W/kg.Since the specific net output index only takes into account the utilization efficiency of the heat source, the influences from the condensation temperature are implemented by affecting the thermal efficiency and the power consumption of the seawater pumps.Accordingly, the variation of net output power with condensation temperature is in accordance with the variation in net system efficiency with condensation temperature.The effect of condensation temperature on the system output power per unit area is shown in Figure 8.The net efficiency of the system decreases with increasing condensation temperature and the net power output decreases per unit area.However, the heat transfer temperature difference within the condenser will also increase, resulting in a smaller heat transfer area.Taking both of these factors into account, the net power output per unit area increases and then decreases, with a maximum at a condensation temperature of around 13℃.In the case of the R227ea, the net power output per unit area at a condensation temperature of 13℃ is a maximum of 119.39 W/m 2 .Ammonia (R717) exhibits the highest thermal efficiency and power output per unit area of any working medium, while R227ea has the highest specific net power output.

Conclusion
In this paper, by constructing a static analytical model of organic Rankine cycle power generation system under small temperature difference operating conditions and screening common organic workmasses, the key parameters of the system and the influence of different workmass fluids on the thermodynamic and economic efficiency of the system are studied, and the following findings are reached: (1) The net efficiencies of the system increases monotonically with the rise in the evaporation temperature.The specific net output and net output per unit area initially increase and then decrease with increasing evaporation temperature.The maximal specific net output is achieved at an evaporation temperature of 19℃, and the maximal net output per unit area is achieved at a steam temperature of 25℃ (2) Both net efficiency and specific net output decrease as the condensation temperature increases.As the condensation temperature increases, the net output per unit area shows a tendency to increase and then decrease slightly, reaching a peak value at a condensation temperature of 13℃.
(3) Among dry working fluids, R227ea typically has the highest specific net output and net output per unit area, while the R1234ze has a higher net efficiency.And ammonia (R717) has significantly higher thermal and economic performance than other wet working fluids.Overall, dry and wet working fluids perform similarly in terms of thermal performance, but in terms of economic performance, ammonia (R717) outperforms all other working fluids.
Dry fluids and wet fluids are divided on the basis of the dew point curve slope in the T-s diagram.A fluid whose dew point curve has a positive slope is a dry fluid, and a fluid whose slope is negative is a wet fluid, as shown in Figure 2. Generally, Dry fluids tend to superheat after the expander, and wet fluids are in a wet state.

( 3 )
Pressure losses of the pipelines and heat exchangers are neglected.(4) The flow velocity in the pipes remains constant.(5) The physical properties of the hot and cold water are constant and incompressible.The governing equations are listed as follows:For the working fluid condenser, the pinch point appears at the saturated vapor phase, and its temperature difference is defined as power consumption of the working fluid pump is defined as

Figure 3 .Figure 4 .
Figure 3. Impact of Evaporation Temperature on Net Efficiency of the System (a.Dry fluid; b.Wet fluid).

Figure 5 .
Figure 5.The impact of evaporation temperature on the net output per unit area of the system (a.dry fluid; b. wet fluid).

Figure 6 .
Figure 6.Influence of Condensation Temperature on System Net Efficiency (a.Dry Fluid; b.Wet Fluid).

Figure 7 .
Figure 7. Influence of Condensation Temperature on System Specific Net Output Power (a.Dry Fluid; b.Wet Fluid).

Figure 8 .
Figure 8.The Influence of Condensation Temperature on the Net Output Power per Unit Area of the System (a.Dry Fluid; b.Wet Fluid).

Table 1 .
Thermophysical and environmental properties of alternative fluids.