Parametric Analysis of a Polygeneration System with CO 2 Working Fluid

: The objective of the present work is the investigation of a novel polygeneration system for power, refrigeration and heating production at two temperature levels. The present system uses CO 2 as the working ﬂuid, which is an environmentally friendly ﬂuid. The total conﬁguration is a combination of a transcritical refrigeration cycle coupled to a Brayton cycle with recompression, which is fed by a biomass boiler. The examined system, at nominal operating conditions, produces refrigeration at 5 ◦ C, and heating at 45 ◦ C and 80 ◦ C. Additionally, the system can be converted into a trigeneration system where the two heating outputs are produced at the same temperature level. The system was studied parametrically by changing the following seven critical parameters: turbine inlet temperature, high pressure, medium pressure, heat exchanger effectiveness, refrigeration temperature, heat rejection temperature and high heating temperature. In nominal operating conditions, the system energy and exergy efﬁciencies were 78.07% and 26.29%, respectively. For a heat input of 100 kW, the net power production was 24.50 kW, the refrigeration production was 30.73 kW, while the low and high heating production was 9.24 kW and 13.60 kW, respectively. The analysis was conducted with a developed model in Engineering Equation Solver.


Introduction
Renewable energy utilization is an important weapon for tackling critical energy problems such as fossil fuel depletion, global warming, increasing energy demand and increasing electricity prices [1][2][3]. Furthermore, trigeneration and polygeneration systems are highly efficient units that can produce numerous useful outputs simultaneously [4,5]. Thus, the concept of using renewable energy sources to feed polygeneration systems is a viable and environmentally friendly solution for future sustainable systems. Another important aspect of these systems is their use of environmentally friendly working fluids, which are usually natural fluids such as CO 2 , NH 3 , propane and butane [6]. However, these fluids present some limitations, which are related to performance, toxicity and flammability. CO 2 seems to be the most promising fluid as it can operate both in transcritical and supercritical configurations and it is not toxic, not flammable and it is a cheap working fluid [7]. Moreover, there are alternative working fluids (not natural) that have zero ODP and a not so high GWP (<1000) that can be used, like R32, R245ca, R245fa, R365mfc and R1336mzz [8].
In the literature, there are many studies that examine polygeneration systems driven by renewable energy sources (solar, geothermal, biomass and wind) [9]. Al-Sulaiman [10] studied a system with an organic Rankine cycle (ORC), absorption heat pump and parabolic trough solar collectors, which presented a 20% exergy efficiency. A similar configuration was examined and optimized by Bellos and Tzivanidis [11], who found a global maximum exergy efficiency of 29.4% with an energy efficiency of about 150%. A trigeneration system driven by solar energy was studied by Eisavi et al. [12]. This system incorporated an ORC heat input (biomass in this case) and a natural refrigerant as the only working fluid. Thus, this work suggests a totally new, and source configuration. The system was examined in steady-state conditions and it was analyzed parametrically. The study was conducted by using a developed thermodynamic model in Engineering Equation Solver [27].

The Examined System
In this work, a polygeneration system was investigated as shown in Figure 1. A biomass boiler was used as the energy heat input and it gives the proper energy for the system operation. The working fluid in the examined thermodynamic cycle is CO 2, which is an environmentally friendly fluid. This fluid has a relatively low critical point with the critical pressure being 73.8 bar and the critical temperature being 31.1 • C.
Appl. Sci. 2021, 11, x FOR PEER REVIEW 4 of 21 were selected to be 100% and the heat exchange modeling from the heat exchanger to the ambient and to the heating production were done without taking the overall heat transfer coefficient into consideration. An alternative design could be with a medium pressure lower than the critical pressure of the CO2, and in this case, the heat rejection in the ambient could be conducted with a condenser and at a lower temperature. However, this configuration would only operate in relatively cold conditions with an ambient temperature up to 25 °C. Thus, this work rejected heat in a supercritical pressure in order to avoid having restrictions and the system was designed to take advantage of this section by using the proper heat exchanger devices. Moreover, another option is to couple the turbine with the compressors in the same shaft in order to improve the overall performance of the systems, to reduce the cost and to develop a compact design.

Mathematical Formulation
This section includes the basic mathematical equations for the simulation of the suggested system. These equations are developed by the energy balance in the various Refrigeration is produced from the evaporator and saturated vapor (quality equal to 100%) is produced (Figure 1, state point 1). This quantity is compressed from low pressure to medium pressure with the use of the compressor (state point 2). After this, a proper heat exchanger is used in order to produce low-temperature heating at 45 • C and state point 3 is selected as 50 • C in all the cases. Practically, a temperature difference of 5 • C [28] is used in order to ensure proper heat transfer. Moreover, a gas cooler is used in order to reject heat to the ambient and so the CO 2 reaches state point 4. A second compressor re-compresses this quantity up to state point 5. The present configuration has intercooling in order to reduce the compressing work and to recover heating. Moreover, the recompression from state point 4 to state point 5 needs a small amount of work because state point 4 is close to the critical point of the CO 2 (from the supercritical side) and so the density of the CO 2 is relatively high, which reduces the pumping work.
After the second compressor, there is a heat exchanger in order to preheat the CO 2 before the biomass boiler. So, the CO 2 is warmed up to state point 6 and goes into the boiler where its temperature is increased up to the turbine inlet temperature (TIT) at state point 7. The turbine receives fluid of high pressure at state point 7 and expands it up to state point 8 (medium pressure), and so, work is produced. The heat exchanger reduces the temperature of the supercritical CO 2 (state point 9) and the next step is the heat recovery in the high-temperature levels (state point 10). A pinch point of 5 • C was also applied in this device, and when the high heating temperature is 80 • C, for example, the temperature level in state point 10 is 85 • C in this case [28]. The gas cooler follows the heating device and heat is rejected to the ambient up to state point 11. A throttling valve is used to reduce the pressure from the medium to a low level. This device is assumed to be adiabatic, and so, the enthalpy is the same in its inlet and outlet. The state point after the valve (12) is the inlet in the evaporator and so the cycle closes.
A general overview of the present system can be performed by explaining the heat exchanges of the examined system with the ambient and the external sources. The examined system takes heat from a biomass boiler (Q b ) at a high temperature (e.g., 700 • C) and there is a heat input in the evaporator (Q ref ), which is the refrigeration load in the lowest cycle temperature (e.g., 5 • C). The system rejects heat to the ambient in the gas coolers (Q gc,1 and Q gc,2 ) as it has a relatively low temperature of 35 • C, and so these heat rates are rejected and not reused. There are also the heating heat exchangers, which perform energy recovery, and consequently, heating production. More specifically, the (Q heat,low ) is produced at 45 • C, while the (Q heat,high ) is produced at a higher temperature (e.g., 80 • C). The compressors consume a part of the work that the turbine produces, while there is a net-work production from the system to the grid.
It should be noted that this study is a thermodynamic work and some parameters have been selected to have their ideal values. In this direction, the mechanical efficiencies were selected to be 100% and the heat exchange modeling from the heat exchanger to the ambient and to the heating production were done without taking the overall heat transfer coefficient into consideration.
An alternative design could be with a medium pressure lower than the critical pressure of the CO 2 , and in this case, the heat rejection in the ambient could be conducted with a condenser and at a lower temperature. However, this configuration would only operate in relatively cold conditions with an ambient temperature up to 25 • C. Thus, this work rejected heat in a supercritical pressure in order to avoid having restrictions and the system was designed to take advantage of this section by using the proper heat exchanger devices. Moreover, another option is to couple the turbine with the compressors in the same shaft in order to improve the overall performance of the systems, to reduce the cost and to develop a compact design.

Mathematical Formulation
This section includes the basic mathematical equations for the simulation of the suggested system. These equations are developed by the energy balance in the various devices. Firstly, the equations for the determination of the energy inputs/outputs are given: The heat input (Q b ) in the system can be written as: The useful heat input in the system is written by using the energy balance in the boiler and with the use of the boiler efficiency (η b ): The refrigeration production (Q ref ) in the evaporator is written as: The low-heating production is calculated as: The high-heating production is calculated as: The turbine power production (P tur ) is given as: The low compressor consumption (P com,low ) is given as: The high compressor consumption (P com,high ) is given as: The net power production of the system (P net ) is calculated as: The system energy efficiency (η en ) is given as: The system exergy efficiency (η ex ) is given as: In the previous equation, the temperature levels are in Kelvin units and the reference temperature (T 0 ) is selected as 298.15 K.
Moreover, the energy balance in the gas coolers can be written as below. The subscript "1" corresponds to the gas cooler between the two compressors and the subscript "20" indicates the gas cooler after the turbine.
The throttling valve reduces the CO 2 pressure and this device is assumed to be adiabatic. This fact makes the process isenthalpic and more specifically: Appl. Sci. 2021, 11, 3215 6 of 21 The heat transfer in the heat exchanger can be described by the energy balance between the two streams and the heat exchanger's effectiveness.
The process in the turbine is described by the isentropic efficiency which is defined as below: For this work, the following formula was used to calculate the turbine isentropic efficiency [29]: The process in the low-pressure compressor is described by the isentropic efficiency, which is defined below for the two compressors: The following formula was used for calculating the low-pressure compressor isentropic efficiency [29]: The process in the high-pressure compressor is described by the isentropic efficiency, which is defined below for the two compressors: The following formula was used for calculating the high-pressure compressor isentropic efficiency [29]: The selected formulas for the isentropic efficiencies for the compressors and the turbine are frequently chosen in the literature on CO 2 as the working fluid [29].

Methodology
In this study, the polygeneration system was investigated in steady-state conditions with a developed model in Engineering Equation Solver (EES) [27]. The presented equations of Section 2.2 were used in the simulation of the present study. Treated wood was used, with a lower heating value (H u ) equal to 15,290 kJ kg −1 [30]. More specifically, the as-received fuel had 14.6% moisture, 4.44% ash, 41.68% C, 4.88% H, 33.39% O, 0.99% N and 0.07% S. Table 1 shows the main data for the configuration that was examined. The system was firstly examined in nominal operating conditions (Section 3.1) and also it was studied parametrically (Section 3.2). The nominal values of the reference scenario are given in the table, and in all the cases, the heat input was constant at 100 kW. The parameters examined in the parametric study are the following: turbine inlet temperature, high pressure, medium pressure, heat exchanger effectiveness, refrigeration temperature, heat rejection temperature and high heating temperature. Moreover, the temperature level in the turbine inlet can be 700 • C or higher according to the literature [31].

Preliminary Analysis
The first part of the present work was the preliminary study of the examined system for the nominal operating conditions. Figure 2 shows the thermodynamic state at various points in a pressure-specific enthalpy (p-h) diagram, while Figure 3 shows the temperaturespecific entropy (T-s). The vertical axis of Figure 3 is a logarithmic axis with a ten-based logarithm. These figures show that the examined cycle is a combination of a Brayton power cycle (supercritical region) and a transcritical mechanical compression cycle. So, the total configuration is characterized as a transcritical thermodynamic cycle. Table 2 includes all the state points of the examined cycle and more specifically, the given properties are pressure, specific enthalpy, temperature and specific entropy.       Table 3 includes the main results for the operation in nominal operating conditions. These conditions were selected as typical conditions for producing adequate amounts of all the useful outputs. These conditions correspond to a system that is able to produce cooling and heating at two temperature levels for building applications (e.g., domestic hot water and heating purposes). In this scenario, the net power production was 24.50 kW, the cooling production was 30.73 kW, the heating production at 45 • C was 9.24 kW and the heating production at 80 • C was 13.60 kW. The system energy efficiency was 78.07% and the system exergy efficiency was 26.29%. Moreover, biomass consumption was calculated as 0.00654 kg s −1 . heating temperature while the exergy efficiency is maximized at 65.4 °C with a value of 26.5%, and in this case, the energy efficiency is 85.57%. Table 4 summarizes the examined parameters, the range of the examined parameters and the range of the obtained results for the energy and exergy efficiency. It is important to note that the parameters that created the greatest variation in the energy efficiency were the medium pressure (67.51% to 117.10%) and the high heating temperature variation (65.63% to 95.83%). High energy efficiency values, which can be higher than 100%, are obtained by the proper management of the refrigeration input in the system. More specifically, the examined system acts simultaneously as a power cycle and a heat pump to produce four different useful outputs. With regard to the exergy efficiency, the high-pressure variation leads to great exergy efficiency deviation (8.69% to 28.38%) and the refrigeration temperature variation results in great variation in the exergy efficiency (12.67% to 27.16%).
Moreover, Table 5 includes the "derivative" of the efficiencies to the examined parameters. Practically, the global maximum minus the global minimum efficiency values are normalized to the nominal efficiency and are divided with the parameter range normalized to the nominal value. In the majority of the cases, the curves do not change trends (from positive to negative), and thus, this table includes useful results. In the cases where there is a maximization in an internal point, it is given in the comment column and in these cases, the calculated values are not so important but they are provided for reasons of completeness. These cases are the exergy efficiency with high heating production and the energy efficiency with the refrigeration temperature. Moreover, the majority of the cases indicate that there is a positive efficiency trend with increases of the parameters, although there are some cases with negative trends. All the trends are given in the "comments" columns, and also, they are obvious in the figures given in this section. The results indicate that the pressure levels have a very important impact on the efficiency indexes, and also, the (TIT) is a very important parameter.                 . This parameter is a critical one for Brayton cycles and so it is also important for the present system. Figure 4 indicates that higher TIT increases power production and high heating, while it reduces the low heating and refrigeration production. Figure 5 proves that higher values of TIT increase both the energy and the exergy efficiency of the system. So, it is proved that higher TIT values are beneficial for the system performance, such as in the Brayton cycle where higher TIT increases the power production. Figures 6 and 7 illustrate the impact of the high-pressure level (or turbine inlet pressure) on the system performance. This is also a critical parameter for the system analysis and it is also used in Brayton cycle studies. Figure 6 shows that an increase in the highpressure level only increases electricity production and the other useful outputs show a slight decrease. However, the increase in power production is relatively strong enough and both the energy and exergy efficiency show an increasing trend with the high-pressure increase according to Figure 7. The obtained results are reasonable because according to the general thermodynamic theory of the Brayton cycle, higher turbine inlet pressure leads to higher work production. Figures 8 and 9 exhibit the impact of the medium pressure on the results. This pressure level has to be over the CO 2 critical pressure, which is 73.8 bar, and so the minimum examined value was 75 bar. Generally, values very close to the critical point were avoided because of stability problems in this area. The increase of medium pressure leads to a higher low-heating temperature level and to lower net electricity production. The refrigeration production increases at a great pace up to 85 bar and after this limit, at a slower pace. The high heating production reduces up to 81 bar at a great pace, and then at a slower pace, it was minimized approximately at 95 bar and after this limit, it presents a rough increase. The above-described behavior of the Figure 8 curves can be explained by the great deviation of the CO 2 thermal properties with its pressure, in the cases with pressure levels close to the critical point (75-85 bar). Figure 9 indicates that the increase of the medium pressure leads to higher energy efficiency but to lower exergy efficiency. So, there is no global optimum value for this parameter and an intermediate value is maybe the optimum one. Moreover, different values of this parameter can be selected in order to adjust the useful output values (or fraction) according to the energy rate demands in every application. Figures 10 and 11 illustrate the system behavior with the increase of the heat exchanger effectiveness. According to Figure 10, this parameter leads to higher electricity, refrigeration and low heating production but to lower high heating production. Practically, the higher effectiveness of the heat exchanger gives a lower margin for high heating production after the heat exchanger, and thus, this parameter has different behavior than the other parameters. Figure 11 shows that the exergy efficiency is enhanced by the improvement of the heat exchanger effectiveness but the energy efficiency is reduced with the increase of the effectiveness value. Figures 12 and 13 give the system performance for different refrigeration temperature levels. Figure 12 shows that refrigeration production is not so affected by the refrigeration temperature, as well as the high heating production. On the other hand, it is obvious that a higher refrigeration temperature leads to a significant increase in electricity production and an important decrease in low heating production. Figure 13 indicates that a higher refrigeration temperature increases the system exergy efficiency, while the energy efficiency is maximized for refrigeration production at around −25 • C. Generally, the energy efficiency is not so variable in the range between −35 • C and −15 • C, while for higher refrigeration temperatures it shows a significant decrease. At this point, it is important to note that CO 2 operation in temperatures as low as −35 • C is not a difficult task because CO 2 is used in supermarket refrigeration applications where temperature levels of around −35 • C are usually applied. Figures 14 and 15 show the system behavior with different heat rejection temperature levels. Practically, this parameter is the temperature level in the outlet of the gas cooler and it has to be 3 to 5 • C more than the ambient temperature. In this work, it was studied from 20 • C to 45 • C and in all cases, the medium pressure was more than the critical pressure. Figure 14 shows that the electricity and the low heating production increase sightly with the heat rejection increase. On the other hand, the high heating and the refrigeration show more intense behavior with the first increasing and the other reducing with the heat rejection temperature augmentation. The behavior of these curves is a bit strange after 35 • C because of the variation in the CO 2 properties in this region (close to the critical point). Figure 15 shows that higher heat rejection temperatures lead to higher exergy efficiency and to lower energy efficiency.
Figures 16 and 17 present the system behavior for different values of the high heating temperature. Practically, all of the useful outputs are not affected and only the high heating temperature is decreased with the increase of its temperature level, as Figure 16 shows. Figure 17 indicates that the energy efficiency reduces with the increase in the high heating temperature while the exergy efficiency is maximized at 65.4 • C with a value of 26.5%, and in this case, the energy efficiency is 85.57%. Table 4 summarizes the examined parameters, the range of the examined parameters and the range of the obtained results for the energy and exergy efficiency. It is important to note that the parameters that created the greatest variation in the energy efficiency were the medium pressure (67.51% to 117.10%) and the high heating temperature variation (65.63% to 95.83%). High energy efficiency values, which can be higher than 100%, are obtained by the proper management of the refrigeration input in the system. More specifically, the examined system acts simultaneously as a power cycle and a heat pump to produce four different useful outputs. With regard to the exergy efficiency, the high-pressure variation leads to great exergy efficiency deviation (8.69% to 28.38%) and the refrigeration temperature variation results in great variation in the exergy efficiency (12.67% to 27.16%). Moreover, Table 5 includes the "derivative" of the efficiencies to the examined parameters. Practically, the global maximum minus the global minimum efficiency values are normalized to the nominal efficiency and are divided with the parameter range normalized to the nominal value. In the majority of the cases, the curves do not change trends (from positive to negative), and thus, this table includes useful results. In the cases where there is a maximization in an internal point, it is given in the comment column and in these cases, the calculated values are not so important but they are provided for reasons of completeness. These cases are the exergy efficiency with high heating production and the energy efficiency with the refrigeration temperature. Moreover, the majority of the cases indicate that there is a positive efficiency trend with increases of the parameters, although there are some cases with negative trends. All the trends are given in the "comments" columns, and also, they are obvious in the figures given in this section. The results indicate that the pressure levels have a very important impact on the efficiency indexes, and also, the (TIT) is a very important parameter.

Discussion
In this work, a novel polygeneration system with CO 2 as the only working fluid was studied. This system is able to produce significant amounts of electricity, heating and refrigeration. Moreover, it has a relatively high performance. In nominal operating conditions (Section 3.1), the energy efficiency was 78.07% and the exergy efficiency was 26.29%. The values of the exergy efficiency are similar to those found in the literature, for example, 28.8% exergy efficiency was found in [18], and 22.5% was found in [19]. The exergy efficiency in [18] is a bit higher than in the present work but the energy efficiency was only 53%, which is much lower than the 78% found in the present study. Moreover, the parametric study (Section 3.2) and Table 4 indicate that the maximum possible exergy efficiency of the present system is 30.19%, so the suggested configuration is a highly efficient system. Moreover, previous studies [21,22] found energy efficiencies close to 45%, which is lower than those found in the present study. With regard to the exergy efficiency, some studies indicate relatively high values but it depends on the definition of exergy efficiency used in each case.
The examined system is a configuration that can operate with various heat inputs such as fuel, biomass, or solar energy. In particular, concentrating solar power is needed in order to achieve high values of the turbine inlet temperature and maybe solar tower or solar dishes. Moreover, the temperature levels of the heating and the refrigeration production can be varied in great ranges something that makes possible the use of the present system in various applications such as industries, buildings, hotels, hospitals, etc.
In the future, the present system could be optimized and examined in a specific application in steady-state or dynamic mode. Moreover, different heat sources can be studied and more specifically, the combination of solar energy and biomass can be investigated. A financial analysis should also be performed in order to determine the viability of the system.

Conclusions
The objective of this work was the investigation of a polygeneration system driven by a biomass boiler that uses only CO 2 as the working fluid. This system produces electricity, refrigeration and heating at two temperature levels. The analysis was conducted with a developed model in Engineering Equation Solver. The most important conclusions of this work are summarized below: − In the nominal operating conditions, the system energy efficiency was 78.07% and the exergy efficiency 26.29%. − In the nominal operating conditions, the net power production was 24.50 kW, the cooling production was 30.73 kW, the heating production at 45 • C was 9.24 kW and the heating production at 80 • C was 13.60 kW. − The parameters that most affect the system energy efficiency are the medium pressure and the high heating temperature. − The parameters that most affect the system exergy efficiency are the high pressure and the refrigeration temperature. − The examined system can operate in a great range of heating and refrigeration temperatures, and so, it can be applied in numerous applications in the industrial and the building sector. − The variation of the pressure levels and of the (TIT) can lead to significant deviations in the system energy and exergy efficiencies.
In the future, the system can be examined with the combination of solar energy collectors and a biomass boiler. Moreover, financial analysis can be performed, as well as a life cycle investigation. Furthermore, another idea is to perform simulations of the present system with solar energy as the heat source with or without the biomass boiler. Also, a more applied study could be performed in the future by considering the mechanical efficiency in the turbo-machinery, as well as the reduction in the performance of the turbine in extremely high temperatures (close to 1000 • C) due to the use of cooling blades.