Introduction

As the world’s population grows fast, and the pattern of life changes, the consumption of fossil fuels gradually increases. Using fossil fuels causes some problems, including environmental pollution and depletion of limited resources [1, 2]. Therefore, renewable resources such as geothermal energy are already expanding, because they are environment friendly as well as spontaneously refresh in a natural process.

The heat pumps are technologies that can use renewable sources and utilize the thermal energy of various sources at relatively high temperatures to be used in the process of air conditioning for different sectors. Because heat pumps could work with low-temperature energy sources such as solar energy, waste heat from industries, and low-temperature geothermal energy, these energies could be used in the heat pump cycle. Recently, the examination of the heat pump with a relatively low-temperature source focused on the choice of suitable operating fluid based on the typical temperature of the heat pump cycle equipment [3,4,5,6,7,8,9,10]. The energy analysis is employed to evaluate the use of low-temperature source in heat pumps. It is found that the coefficient of performance (COP) of the geothermal heat pump is higher than the air-source heat pump [11]. In another study, Lee et al. [12] determined the location of the optimum borehole of the geothermal heat pump. Their results show that smaller borehole separation and higher groundwater flow cause thermal efficiency improvement.

Refrigerants play a vital role in the heat pump performance regarding the thermodynamic properties. Some properties such as compatibility, safety, stability, availability of refrigerant, cost, and environmental influences are attention for these systems. Common refrigerants used in the heat pump cycles are usually between the two primary refrigerants of the halocarbons and hydrocarbons. Due to the environmental effects, using some refrigerants, especially chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs), is limited for their use. The Montreal Protocol to protect the environment seriously emphasizes the issue of reducing the consumption and production of CFCs and HCFCs. [13]. Some articles [14,15,16,17] carried out experimental researches on many pure and mixtures of fluorinated fluids. Wang [18] studied the usage outlook of natural working fluids in China. Also, based on these studies, the development of the compressor in the heat pump system is studied. Hydrocarbons are also considered to be fine CFCs substitutes [19]. Some investigations [20,21,22] conducted on the compression refrigeration cycle with working fluid. They explored that the essential parameters can be controlled by changing the speed of compressor rotation. Some hydrocarbons have high cycle performance, but their use is limited due to their explosiveness.

Many refrigerants in HFCs group, such as R125, R134a, R404A, R407C, R410A, R422A, R422B, R422C, R422D, and R507A, are good choices to replace CFCs, because they neither contain chlorine and bromine nor deplete the ozone layer (ODP = 0) [23]. Based on this, various studies performed energy analysis to replace hydrochlorofluorocarbons (HCFC) as R22 refrigerant [24,25,26,27,28,29,30,31]; however, exergy analysis is instrumental in improving the engineering systems [32, 33].

The heat pump cycle saves energy and is very efficient in recycling heat. However, when these systems are used to supply heat under conditions such as high-temperature supply and the high-pressure ratio between condensation pressure and evaporation pressure, the efficiency of these cycles is reduced. Therefore, many studies have been done to prevent COP depletion in heat pump systems [34,35,36,37,38,39,40,41,42]. Also, in these systems, the high-temperature difference between the supply water and the operating fluid in the condenser causes plenty of irreversible losses in the heat transfer process. Many kinds of research are performed to increase the performance of high-temperature heat pumps [43,44,45,46,47].

In the present research, a simulation of a geothermal heat pump sample is performed. In addition to the use of various HFC refrigerants’ impact on the performance cycle, the effect of different temperatures of the exhaust fluid from the geothermal source is investigated. Also, the impact of changes in the isentropic efficiency of the compressor in the COP and exergy efficiency of the geothermal heat pump cycle is carried out. A thermodynamic model based on mass, energy, and exergy balance is developed to calculate the variation in the COP, exergy efficiency, and exergy destruction for geothermal heat pump cycle equipment. The analysis is done to improve the coefficient of operation of the geothermal heat pump cycle and select the best refrigerant according to those five refrigerant operating conditions.

Configuration of a geothermal heat pump cycle

In Fig. 1, the schematic of a geothermal heat pump is observed in the heating process. This cycle includes three primary parts: the ground heat source circuit, the refrigerant circuit, and the output heat circuit. The main components of this cycle are geothermal exchangers, evaporators, compressors, condensers, expansion valves, accumulation tank, output heat panels, and three pumps. A 500-L storage tank is used in this cycle, which is insulated to prevent heat losses. This accumulation tank is consistently providing the required heating load. Heat output panels are considered as a heat exchanger that has the duty of distributing energy in the building. In the ground heat circuit, the heat is transmitted between the soil and the geothermal exchangers (\(\dot{Q}_{\text{G}}\)). The output fluid of accumulation tank is transferred to various places through the output panels (\(\dot{Q}_{\text{P}}\)). The studied case is proposed to use in a residential building with a 5.7 kW heat load.

Some characteristics of HFC refrigerants used in this study are given in Table 1. As evident, different groups of HFCs, including pure refrigerants (R125 and R134A), zeotropic mixtures (R404A and R407C), and azeotropic mixtures (R507A), are selected.

Table 1 Some characteristics of HFC refrigerants
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As shown, although some HFCs have high GWPs due to the higher COP factor and lower CO2 emissions caused by energy consumption, the use of these refrigerants is common in the heat pumps. Besides, in many places around the world, recycling and reclamation of these refrigerants are counseled to decrease its direct global warming influence [23].

Thermodynamic model

Some assumptions are made for thermodynamic analysis of the heat pump system as follows:

  • The investigated system is in steady-state conditions.

  • The compressor isentropic efficiency is constant, and the compression process in compressors is considered as adiabatic.

  • The throttling processes in throttling valves are considered as isenthalpic.

  • The pressure drop and heat loss of refrigerant in the cycle are neglected, and heat transfer processes in evaporator and condenser are constant pressure process.

  • The kinetic and potential energy variations are neglected.

The thermodynamic model is obtained according to the conservation principle of mass, energy, and exergy of the main components of the heat pump cycle.

The detailed formulations about energy analysis of the case study with the mentioned assumptions are presented as Eqs. (1), (2), and (3):

$$\dot{E}_{\text{in}} - \dot{E}_{\text{out}} = \Delta \dot{E}_{\text{system}}$$
(1)
$$\dot{m}_{\text{in}} h_{\text{in}} = \dot{m}_{\text{out}} h_{\text{out}}$$
(2)
$$\dot{Q}_{\text{in}} + \dot{W}_{\text{in}} + \dot{m}_{\text{in}} h_{\text{in}} = \dot{Q}_{\text{out}} + \dot{W}_{\text{out}} + \dot{m}_{\text{out}} h_{\text{out}}$$
(3)

In Eqs. (4), (5) and (6), (\(\dot{Q}_{\text{G}}\)) and (\(\dot{Q}_{\text{P}}\)) indicate the heat transfer to the underground heat exchanger and the required heating load, respectively. Also, (\(\dot{W}_{\text{comp}}\)) and \(\left( {\dot{W}_{\text{p}} } \right)\) are consuming work of the compressor and pumps, respectively.

For all heating processes based on Fig. 1, energy conservation is written as below:

$$\dot{E}_{\text{in}} = \dot{Q}_{\text{G}} + \dot{W}_{\text{comp}} + \dot{W}_{{{\text{P}}1}} + \dot{W}_{{{\text{P}}2}} + \dot{W}_{{{\text{P}}3}}$$
(4)
$$\dot{E}_{\text{out}} = \dot{Q}_{\text{P}} + \dot{Q}_{\text{loss}}$$
(5)
$$\dot{Q}_{\text{P}} + \dot{Q}_{\text{loss}} = \dot{Q}_{\text{G}} + \dot{W}_{\text{comp}} + \dot{W}_{{{\text{P}}1}} + \dot{W}_{{{\text{P}}2}} + \dot{W}_{{{\text{P}}3}}$$
(6)

The coefficient of efficiency of the system in the heating process based on Fig. 1 is calculated by Eq. (7).

$${\text{COP}}_{\text{heating}} = \frac{{\dot{Q}_{\text{P}} }}{{\dot{W}_{\text{comp}} + \dot{W}_{{{\text{P}}1}} + \dot{W}_{{{\text{P}}2}} + \dot{W}_{{{\text{P}}3}} }}$$
(7)

Exergy is the maximum useful work that can be obtained from the energy. Exergy analysis is a method that evaluates the thermodynamic performance of different systems based on the second law of thermodynamics. The equation of exergy balance can be defined as Eq. (8).

$$\dot{E}x_{\text{in}} - \dot{E}x_{\text{out}} = \dot{E}x_{\text{dest}}$$
(8)

Therefore, using Eq. (9), the exergy balance in general mode is introduced as Eq. (10).

$$\psi = (h - h_{0} ) - T_{0} (s - s_{0} )$$
(9)
$$\dot{Q}_{\text{a}} \left( {1 - \frac{{T_{0} }}{{T_{a} }}} \right) - \dot{W} + \dot{m}_{\text{in}} \psi_{\text{in}} - \dot{m}_{\text{out}} \psi_{\text{out}} = \dot{E}x_{\text{dest}}$$
(10)

where \(\dot{W}\) is the work rate and \(\dot{Q}_{\text{a}}\) is the heat transfer rate at temperature \(T_{\text{a}}\) at the location a. The reference temperature of the environment is (\(T_{0}\)) and the exergy destruction is (\(\dot{E}x_{\text{dest}}\)).

Specific exergy in an open system (\(\psi\)) of a flowing fluid is illustrated as follows:

For the analyzed system, general exergy balance based on Fig. 1 is defined by Eq. (11):

$$\dot{Q}_{\text{G}} \left( {1 - \frac{{T_{0} }}{{T_{G} }}} \right) + \dot{W}_{\text{comp}} + \dot{W}_{{{\text{P}}1}} + \dot{W}_{{{\text{P}}2}} + \dot{W}_{{{\text{P}}3}} - \dot{Q}_{\text{P}} \left( {1 - \frac{{T_{0} }}{{T_{\text{P}} }}} \right) = \dot{E}x_{\text{dest}}$$
(11)

For general examples that do not produce or consume work, the exergy efficiency is expressed as Eq. (12) [23]:

$$\eta_{\text{Exergy}} = \frac{{{\text{Exergy}}\,{\text{recovered}}}}{{{\text{Exergy}}\,{\text{supplied}}}}$$
(12)

The exergy efficiency for this system based on Fig. 1 is expressed by Eq. (13):

$$\eta_{\text{Exergy}} = \frac{{\dot{Q}_{\text{P}} \left( {1 - \frac{{T_{0} }}{{T_{\text{P}} }}} \right)}}{{\dot{W}_{\text{comp}} + \dot{W}_{{{\text{P}}1}} + \dot{W}_{{{\text{P}}2}} + \dot{W}_{{{\text{P}}3}} + \dot{Q}_{\text{G}} \left( {1 - \frac{{T_{0} }}{{T_{\text{G}} }}} \right)}}$$
(13)

For the thermodynamic analysis, the equations illustrated in Table 2 are used for the equipment of the investigated cycle in the heating process based on Fig. 1.

Table 2 Energy and exergy balance of equipment in the heating process
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Model validation

To validate the mathematical method in this study, the results of the numerical method are compared with available experimental results [48]. The specifications of the input variables for validation are presented in Table 3. Also, the COP of the heat pump is computed for R410A refrigerant in comparison with the experimental data found in Ref. [48]. The COP obtained from the experimental data is 4.23, and, with our calculation, it is 4.07. The relative errors between the experimental outcomes and our simulations are about 3.93%. Also, the experimental temperature of different points of Ref. [48] cycle and COP and energy consumption of the compressor is compared with the calculation program and presented in Tables 4 and 5. As shown in this table, there is good accordance between the numerical and experimental results.

Table 3 Specifications of the cycle in Ref. [48]
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Table 4 Some comparison of temperature points of the cycle of calculation program with Ref. [48]
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Table 5 Comparison of COP and energy consumption of the compressor with Ref. [48]
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Results and discussions

In this investigation, the heat pump is studied concerning the cooling capacity of 5.7 kW with condenser temperature of 303.15 K and evaporator temperature of 272.15 K. Based on this, the influence of different HFC refrigerants is investigated on the performance of the geothermal heat pump. The first and second laws of thermodynamic equations are solved to study the effect of varying temperature of the exhaust fluid from the geothermal source on the geothermal heat pump operation.

According to Fig. 2, the work of compressor with the temperature of the exhaust fluid from the geothermal source for R125, R134A, R404A, R407C, and R507A refrigerants is plotted. As shown in Fig. 2, R125 refrigerant has a higher function of the compressor. Also, R134A and R407C refrigerants have lower compressor work, respectively. R507A and R404A refrigerants also have moderate compressor work. It is also observed that, with the increment of the temperature of the exhaust fluid from the geothermal source, the compressor work is accordingly augmented. The rate of change in the compressor work with the temperature of the exhaust fluid from the geothermal source is higher for R407C, R134A, R404A, R507A, and R125 refrigerants, respectively.

Fig. 2
figure 2

Change of the compressor work for various refrigerants with the outlet temperature of the geothermal source

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According to Fig. 3, the heat pump cycles using R4134A and R125 refrigerants have the highest and lowest COP among the compared refrigerants based on Eq. (7). Due to the increasing temperature of exhaust fluid from the geothermal source, the heat output from the panel increases more than the work of the compressor, thus expanding the COP. Also, as illustrated, increasing the temperature of exhaust fluid from the geothermal source enhances the COP of the cycle for all the refrigerants. Increasing the temperature of the exhaust fluid from the geothermal source for R125, R507A, and R404A, respectively, is more effective than the other refrigerants, and the slope of COP of these refrigerants is higher. R407C and R134A refrigerants show the slightest variation with an enhancement in the exhaust fluid temperature from the geothermal source.

Fig. 3
figure 3

Change of COP for various refrigerants with the outlet temperature of the geothermal source

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As shown in Fig. 4, the impact of changes on the isentropic efficiency of the compressor on the COP is investigated. It is observed that the isentropic efficiency of the compressor has a direct effect on all the refrigerants. Increasing isentropic efficiency reduces the work of the compressor and enhances the COP based on Eq. 7. The enhancement of the COP is not the same as different refrigerants with an isentropic efficiency of the compressor, and R125 and R507A refrigerants have the lowest variations, respectively; R134A and R407C refrigerants, respectively, have the most significant changes in terms of this parameter.

Fig. 4
figure 4

Change of COP for different refrigerants with isentropic efficiency of the compressor

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In Fig. 5, the exergy destruction of the heat pump equipment is plotted for different HFC refrigerants. Based on Eq. (10), R125 and R134A have the highest and lowest exergy destruction in the heat pump cycle. On the other hand, among the heat pump equipment, the compressor has the most top exergy destruction. Also, R125 refrigerant has the highest exergy destruction due to the compressor, and its value is 0.2921 kW.

Fig. 5
figure 5figure 5

Comparison of exergy destruction due to the equipment in the studied cycle for different refrigerants

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In Fig. 6, the exergy destruction due to the compressor with the temperature of the exhaust fluid from the geothermal source is observed for various refrigerants. R125 refrigerant has the most exergy destruction due to the compressor, and, in contrast to R134A, the exergy destruction due to the compressor is approximately equal to the smallest amount of this parameter among the comparative refrigerants in the heat pump cycle. R134A refrigerants have the least exergy destruction due to the compressor changes with the temperature of the exhaust fluid from the geothermal source.

Fig. 6
figure 6

Comparison of exergy destruction due to the compressor for different refrigerants with the outlet temperature of the geothermal source

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The exergy destruction due to the evaporator with the temperature of the exhaust fluid from the geothermal source for various refrigerants is presented in Fig. 7. R407C refrigerant has the most exergy destruction due to the evaporator among the comparable refrigerants in the heat pump cycle. R507A refrigerant has the highest variations of exergy destruction of the evaporator with the temperature of the exhaust fluid from the geothermal source, among other refrigerants. The changes of exergy destruction due to the evaporator decrease for R404A, R125, R134A, and R407C, respectively. The variation in the temperature of the exhaust fluid from the geothermal source has a direct impact on the evaporator equipment, so according to Eq. 10, exergy destruction has a very steep slope for all refrigerants due to the increased heat exchange rate in this equipment.

Fig. 7
figure 7

Comparison of exergy destruction due to the evaporator for different refrigerants with the outlet temperature of the geothermal source

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According to Fig. 8, the exergy destruction due to the condenser with the temperature of the exhaust fluid from the geothermal source for various refrigerants is compared. R507A refrigerant has the highest amount of exergy destruction due to the condenser. The exergy destruction reduces due to the condenser for R134A, R404A, R125, and R407C refrigerants, respectively. Also, R407C refrigerant has the highest variations of exergy destruction due to the condenser with the temperature of the exhaust fluid from the geothermal source, among other refrigerants. The change of exergy destruction of the condenser decreases for R134A, R404A, R507A, and R125, respectively.

Fig. 8
figure 8

Comparison of exergy destruction due to the condenser for different refrigerants with the outlet temperature of geothermal source

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According to Fig. 9, the exergy destruction due to the accumulator tank with the temperature of the exhaust fluid from the geothermal source for the various refrigerants shows that R125 refrigerant has the highest exergy destruction due to the accumulation tank, and, then, the exergy destruction reduces due to the accumulator tank for R507A, R404A, R407C, and R134A, respectively. The change of the exergy destruction due to the accumulator tank with the temperature of the exhaust fluid from the geothermal source is approximately equal for the various refrigerants.

Fig. 9
figure 9

Comparison of exergy destruction due to the accumulator tank for different refrigerants with the outlet temperature of the geothermal source

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In Fig. 10, the exergy destruction due to the whole system is compared with the temperature of the exhaust fluid from the geothermal source for various refrigerants, according to (11). Due to the parameters in this equation and the higher exergy of the heat input to the cycle and the cycle work consumed than the exergy of the heat output from the cycle, the total system exergy destruction is increased. R125 refrigerant has the highest exergy destruction, and, after that, the exergy destruction of the system has decreased for R507A, R404A, R407C, and R134A refrigerants, respectively. Also, the most significant changes are observed in the exergy destruction due to the whole system with the temperature of the exhaust fluid from the geothermal source for R407C refrigerant and the least variation for R125 coolant.

Fig. 10
figure 10

Comparison of exergy destruction due to the whole system for different refrigerants with the outlet temperature of the geothermal source

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According to Fig. 11, the exergy efficiency calculated by Eq. (13) is shown with the temperature of the exhaust fluid from the geothermal source for various refrigerants. R134A refrigerant has the highest exergy efficiency, and, then, the exergy efficiency decreases for R407C, R404A, R507A, and R125 refrigerants, respectively. Augmenting the temperature of the exhaust fluid from the geothermal source increases the exergy efficiency of the cycle for all the refrigerants but has the most significant effect on R125 coolant, after which, R134A, R404A, and R507A refrigerants have a greater effect with the temperature of the exhaust fluid from the geothermal source, while R407C has the slightest changes.

Fig. 11
figure 11

Comparison of exergy efficiency for different refrigerants with the outlet temperature of the geothermal source

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According to Fig. 12, the exergy efficiency augments with isentropic efficiency of compressor for various refrigerants. R134A refrigerant has the highest exergy efficiency, and, then, the exergy efficiency decreases for R407C, R404A, R507A, and R125 refrigerants, respectively. Exergy efficiency changes with the isentropic efficiency of compressor for different refrigerants such as COP with the isentropic efficiency of the compressor.

Fig. 12
figure 12

Comparison of exergy efficiency for different refrigerants with isentropic efficiency of the compressor

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For the heating process, the significant thermodynamics properties data and exergy rates for geothermal heat pump with R125, R134A, R404A, R407C, and R507A refrigerants are presented in Table 6.

Table 6 Major thermodynamics properties data and exergy rates for geothermal heat pump with different refrigerants in the heating process. State numbers refer to Fig. 1
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For the heating process, exergy destruction for geothermal heat pump equipment with R125, R134A, R404A, R407C, and R507A refrigerants, presented in Table 7(a–e), is used for the exergy analysis.

Table 7 Exergy destruction for geothermal heat pump equipment with (a) R125 refrigerant in heating process, (b) R134A refrigerant in heating process, (c) R404A refrigerant in heating process, (d) R407C refrigerant in heating process, (e) R507A refrigerant in heating process
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The percentage of exergy destruction due to the compressor relative to the exergy destruction due to the overall system for each refrigerant is given in Table 8.

Table 8 Percent of exergy destruction due to the compressor of the geothermal heat pump for various refrigerants
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Conclusions

In this investigation, the energy and exergy analysis of a geothermal heat pump cycle and determination of the desired mass flow rate for the cycle are investigated. Also, the optimization of the heat pump cycle is calculated through two methods of maximizing COP and exergy efficiency. The primary outcomes are as follows:

  • In the whole system, the maximum exergy loss ratio and the minimum exergy efficiency are observed, respectively, for the compressor and the underground heat exchanger. The exergy loss ratio variations for the compressor with different refrigerants are between 0.26 and 0.29. The exergy efficiency for the underground heat exchanger is also equal to 68.1%. Thus, the compressor and the underground heat exchanger should be improved in the first place.

  • The results revealed that, by comparing the mentioned refrigerants for the heat pump cycle, it is observed that R134A and R125 refrigerants have the highest and lowest COP and exergy efficiency, respectively. The COP of the heat pump cycle investigated at the outlet temperature of the geothermal source of 278 (K) with R134A and R125 refrigerants are equal to 4.515 and 4.181, respectively. Under the mentioned condition, the exergy efficiency for R134A and R125 are equal to 0.359 and 0.337, respectively.

  • In this cycle, enhancing the temperature of the exhaust fluid from the geothermal source increases the coefficient of operation and exergy efficiency of the cycle. For example, using the R134A refrigerant and variations of outlet temperature of the geothermal source from 278 (K) to 285 (K), the COP of the heat pump cycle increased from 4.515 to 4.525, and the exergy efficiency has risen from 0.359 to 0.36. This means that at a total heating capacity of about 5.6 kW, the increase in heat generation is about 0.11 kW.

The outcomes obtained in present research may provide guidelines for the design and optimization of efficient geothermal heat pump systems, along with some related works like Refs. [49, 50].