**Investigating the System Behaviors of a 10 kW Organic Rankine Cycle (ORC) Prototype Using Plunger Pump and Centrifugal Pump**

#### **Xin Wang 1, Yong-qiang Feng 1,\*, Tzu-Chen Hung 2,\*, Zhi-xia He 3, Chih-Hung Lin <sup>4</sup> and Muhammad Sultan <sup>5</sup>**


Received: 31 January 2020; Accepted: 20 February 2020; Published: 3 March 2020

**Abstract:** Based on a 10-kW organic Rankine cycle (ORC) experimental prototype, the system behaviors using a plunger pump and centrifugal pump have been investigated. The heat input is in the range of 45 kW to 82 kW. The temperature utilization rate is defined to appraise heat source utilization. The detailed components' behaviors with the varying heat input are discussed, while the system generating efficiency is examined. The exergy destruction for the four components is addressed finally. Results indicated that the centrifugal pump owns a relatively higher mass flow rate and pump isentropic efficiency, but more power consumption than the plunger pump. The evaporator pressure drops are in the range of 0.45–0.65 bar, demonstrating that the pressure drop should be considered for the ORC simulation. The electrical power has a small difference using a plunger pump and a centrifugal pump, indicating that the electric power is insensitive on the pump types. The system generating efficiency for the plunger pump is approximately 3.63%, which is 12.51% higher than that of the centrifugal pump. The exergy destruction for the evaporator, expander, and condenser is almost 30%, indicating that enhancing the temperature matching between the system and the heat (cold) source is a way to improve the system performance.

**Keywords:** organic Rankine cycle (ORC); plunger pump; centrifugal pump; pressure drop; temperature utilization rate; system generating efficiency

#### **1. Introduction**

The issues of energy high-speed consumption and safe supply have aroused widespread concern in society. In order to effectively solve the energy problem, countries around the world have proposed measures that focus on both energy development and conservation. According to statistics, 50% of the energy used by humans is directly emitted by low-temperature waste heat. If this energy can be used, it will not only solve some energy problems but also reduce environmental pollution. Among much of the low-grade thermal energy conversion and utilization technologies, the organic Rankine cycle is extensively applied on account of its wide temperature range and moderate power [1–3]. In addition, the organic Rankine cycle is often used in conjunction with other systems to achieve higher efficiency. Peris et al. [4] were interested in using ORC for combined heat and power (CHP) applications, and Capata et al. [5] recovered vehicle waste heat with small-scale ORC. In addition, solar

energy, wind energy, and ocean temperature difference energy are of particular interest in small-scale ORC systems [6–8]. Therefore, extensive research studies have been conducted on the ORC.

For the industrial ORC prototype, the back work ratio is as high as 25%, indicating that improving the pump performance is a key for ORC commercial application. Numerous studies devoted main efforts on the pump improvement, including piston pumps, gear pumps, and centrifugal pumps. The vane pump delivers energy by the impeller, while the positive displacement pump is dependent on the periodic variation of the volume. Mathias et al. [9] conducted a comparison between the piston pump and gear pump, representing that the piston pump was preferred for the ORC system. Lei et al. [10] tested an ORC system using a roto-jet pump, stating that the pump efficiency of 11–23% was obtained. Bianchi et al. [11] conducted a test on an ORC system using a sliding vane pump, reporting that the shaft power has a significant influence on mass flow rate and pressure. Villani et al. [12] proposed two different ORC systems combined with the heavy diesel engines. One is that the pump and the expander are connected to achieve a fixed speed, and the other is that the pump and expander are separated, the pump optimal speed and expander optimal speed are selected by adjusting parameters. Zeleny et al. [13] applied a gear pump on the ORC system to evaluate the pump mechanical losses. Xu et al. [14] tested the operation characteristics of a piston pump on an ORC system, demonstrating that the low pump frequency was applicable to all expander torques. Carraro et al. [15] integrated a multi-diaphragm positive displacement pump into a 4-kW experimental prototype and found that the pump global efficiency was about 45–48%. Bianchi et al. [16] changed the pump speed to measure the performance of the pump and the overall system in a micro-ORC and found that the pump has a back-work ratio of 50–75% and causes a lot of power consumption. Therefore, special attention should be paid to the design of the pump in micro-ORC. Zhang et al. [17] experimentally studied the change in pump characteristics with evaporation and condensation temperatures. The pump consumption decreases with increasing condensation temperature and presents a non-linear relationship with increasing evaporation temperature. Xi et al. [18] experimentally tested the transient process for the sudden stop of the working fluid pumps in the ORC and regenerative ORC (RORC) systems and found that the expander showed good performance if the pumps were closed when the working fluid was overcharged. Abam et al. [19] analyzed the exergy performance for each component of the four different ORCs and showed that the exergy destruction of evaporators was the largest and that of the pumps was the smallest. Aleksandra et al. [20] integrated that the use of different refrigerants can produce different pump work. Wu et al. [21] utilized a booster pump instead of a common working pump to optimize system characteristics. Meng et al. [22] investigated the performance of the centrifugal pump applied to the engine exhaust recovery ORC device and found that the total efficiency of the pump was 15–65.7%. In addition, Yang et al. [23] and Sun et al. [24] compared a variety of pumps that can be applied to the ORC in order to find the most suitable pump for ORC systems, indicating that the hydraulic diaphragm metering pump was suitable for low heat capacity, whereas the multistage centrifugal pump was preferred for higher heat capacity. Feng et al. [25–27] experimentally compared the system behaviors on a 3kW ORC between pure working fluids and mixture working fluids using a scroll expander. In addition, when the working fluids are condensed in a condenser, the working fluids' temperature and pressure decrease, resulting in the working fluid pump cavitation. Cavitation affects the stability of the system, resulting in a decrease of system efficiency. D'amico et al. [28] introduced the thermodynamic model of a piston pump in the ORC and proposed the prediction of available head margin to avoid cavitation. Liu et al. [29] found that cavitation can occur when the working fluid was insufficient and proposed overcharging working fluid to avoid cavitation. Yang et al. [30] stated that a subcooling of 20 ◦C was needed to prevent the cavitation of the piston pump. Pei et al. [31] emphasized the use of a bypass tube to balance the pressure of the pump and the tank to solve the cavitation. Galindoe et al. [32] and Dumont et al. [33] used a liquid sub-cooler to prohibit the cavitation.

To lessen the influence of the pump on the ORC property, a novel concept was proposed—pumpless ORC. Gao et al. [34] raised the gravity-type pumpless ORC to ensure the stability and continuity of the system shaft power output. Bao et al. [35] believed that an ORC system without a pump can achieve a more compact and efficient arrangement, which can improve the system's net efficiency. Jiang et al. [36] raised a cascade cycle of power and refrigeration, applying the pumpless ORC to the upper cycle and the adsorption refrigeration cycle to the lower cycle. Within the range of experimental parameters, the maximum power is 232 W and the maximum cooling capacity is 4.94 kW.

As mentioned above, it is evident that several experimental investigations using different pumps have been performed. However, limited studies fulfilled the work on the experimental comparison on an ORC operation characteristic using different pumps. Simultaneously, micro- ORC is still in infancy, and more effort should be focused on the components' design and test. For the micro-ORC prototype, the considerably low efficiency of the pump may heavily affect the overall performance. Therefore, comparing the operation characteristics of small-scale ORC prototypes using different pumps is certainly of great interest. In the present study, a 10 kW R245fa-based ORC experimental prototype is used to study the operation characteristics. A plunger pump and centrifugal pump are adopted, which were widely used in previous experimental tests. The basic operation characteristics for the plunger pump and centrifugal pump are first analyzed. The components' behaviors are addressed, and the overall performance is examined.

#### **2. Experimental Setup Description**

#### *2.1. System Design and Operating Method*

A 10 kW ORC test platform is adopted. Figure 1 displays a schematic diagram of the experimental bench, and Figure 2 presents the pictures of the experimental equipment. To provide a simulated heat source, diathermic oil is adopted and heated by an electric heater. An electric heater has twelve electric heating rods, and each rod has a capacity of 10 kW. The heating rods are connected in series with an SCR power regulator to adjust the input electric. The heat source temperature is from 85–105 ◦C and each variation increases by about 5 ◦C. The heat input is in the range of 45–85 kW. The evaporator and condenser are both plate heat exchangers and the specific parameters for the heat exchangers are listed in Table 1.

**Figure 1.** Schematic diagram of the experimental bench.

**Figure 2.** The pictures of (**a**) experimental setup; (**b**) the electrical load; (**c**) the circuit and (**d**) centrifugal pump.



A centrifugal pump and a plunger pump are adopted in this experimental prototype. The mass flow rates are adjusted by the rotating speed of the pump and the pump rotating speed is controlled by a frequency converter. Meanwhile, the pump raises the refrigerant to reasonable working pressure and the refrigerant enters the evaporator to absorb heat. R245fa is chosen as the refrigerant because of its good thermodynamics and economic characteristics. The scroll expander is adopted, which is improved by a scroll air compressor that is operating in reverse. The product of the system is consumed by the electrical resistance and capacitance, which determines the expander speed. The speed of the expander is measured at 2500–2900rpm and the expander specifications are listed in Table 2. The steam refrigerant absorbed heat enters the expander which exports power. In Figure 2, the scroll expander is encapsulated with a generator, and the shaft power is hard to measure. Therefore, the expander shaft power is expressed by the mass flow rates and expander enthalpy difference. Mass flow rates are converted from volume flow rates directly measured by the flowmeter. The enthalpy difference is determined by checking the REFPROP(a software that can check physical properties) according to the temperature and pressure at both ends of the expander. An inductive generator is used as the power output device.

**Table 2.** Parameters of the scroll expander.


A 3% lubricating oil is added in the expander to avoid the leakages and reduce the friction losses in the expander. In addition, the compatibility of the lubricating oil and R245fa is tested at first. After the expansion, the gaseous refrigerant enters the condenser and transfers the residual heat to the cooling water. The mass flow rate of cooling water is 4m/s, which is regulated by the cooling pump frequency. To better ascertain the effect of the pump on the system behavior, a plunger pump and centrifugal pump are tested and compared in this study.

#### *2.2. Plunger Pump and Centrifugal Pump*

The plunger pump has a high volume ratio, small flow rate, good characteristic curve, and low cost. It sucks and discharges the working fluid through the reciprocating motion of the plunger. The maximum flow rate of the reciprocating plunger pump is 15.5 L/min with the maximum pressure of 20 bar.

The centrifugal pump has a small area, less material consumption, less manufacturing and installation costs, and can run at high speeds. The centrifugal pump is driven by centrifugal force. The liquid is pumped out from the center to the periphery along the blade flow path and is sent to the discharge pipe through the volute. The centrifugal pump has a maximum flow rate of 36.7 L/min and the delivery pressure of 25 bar. More detailed information about the pumps is displayed in Table 3.


**Table 3.** Parameters of the plunger pump and centrifugal pump.

#### **3. Measuring Device and Thermodynamic Analysis**

The detailed operation parameters are measured, including temperature, pressure, and mass flow rate. A vortex flowmeter placed at the pump outlet is used to measure volume flow rates, and then the volume flow rates are converted into mass flow rates, with the detailed location shown in Figure 1. The heat source temperature for both pump experiments was 85–110 ◦C. The system

performance can be obtained based on the measured operation parameters, while an uncertainty analysis is conducted [37].

$$
\Delta Y = \sqrt{\sum\_{i} \left(\frac{\partial Y}{\partial X\_i}\right)^2 \Delta X\_i^2} \tag{1}
$$

where *X* and Δ*Y* are the independent variable and uncertainty, respectively. Table 4 lists the measuring devices and the uncertainties for system parameters.


**Table 4.** The measuring devices and the uncertainties for system parameters.

Figure 3 shows the *T-s* diagram of the ORC system, the expander isentropic efficiency is calculated based on the ideal expansion process and actual expansion process. The expander isentropic efficiency (ηis,exp) and pressure difference (Δ*P*) can be calculated as follows:

$$
\eta\_{\text{lis,exp}} = \frac{h\_1 - h\_2}{h\_1 - h\_{2s}} \tag{2}
$$

$$
\Delta P = P\_1 - P\_2 \tag{3}
$$

where *h*<sup>1</sup> and *p*<sup>1</sup> represent the enthalpy and pressure of the expander inlet, and *h*2, *p*<sup>2</sup> and *h*2*<sup>s</sup>* represent the enthalpy, pressure and isentropic enthalpy of the expander outlet.

**(QWURS\ N-NJ.**

**Figure 3.** *T-s* plot of the organic Rankine cycle system.

The condenser heat transfer rate (*Qcond*), the logarithmic mean temperature difference (LMTD) (Δ*Tcond*), heat transfer coefficient (*Ucond*) and pressure drop(Δ*P*cond) can be calculated as follows:

$$Q\_{\rm cond} = m(h\_2 - h\mathfrak{s})\tag{4}$$

$$
\Delta T\_{\text{cond}} = \frac{\Delta T\_{\text{max}} - \Delta T\_{\text{min}}}{\ln \frac{\Delta T\_{\text{max}}}{\Delta T\_{\text{min}}}} = \frac{(T\_{13} - T\_5) - (T\_{16} - T\_2)}{\ln \frac{T\_{13} - T\_5}{T\_{16} - T\_2}}\tag{5}
$$

$$
\Delta U\_{\text{cond}} = \frac{Q\_{\text{cond}}}{\Delta T\_{\text{cond}} \cdot \mathbf{A}} \tag{6}
$$

$$
\Delta P\_{\text{cond}} = P\_2 - P\_5 \tag{7}
$$

where *h*<sup>5</sup> is the outlet enthalpy of the condenser; Δ*T*max and Δ*T*min are the maximum and minimum temperature difference at the condenser, respectively; and *A* represents the surface area of the heat exchanger.

The pump isentropic efficiency is calculated by the actual compression process and the ideal compression process. The pump shaft power (*W*sh,pump) and isentropic efficiency (ηis,pump) are expressed as:

$$\mathcal{W}\_{\text{sh},\text{pump}} = m(h\_6 - h\_5) \tag{8}$$

$$
\eta\_{\text{lis,Pump}} = \frac{h\_{56} - h\_5}{h\_6 - h\_5} \tag{9}
$$

where *h*5s and *h*<sup>6</sup> denote the pump outlet enthalpy and isentropic enthalpy.

Similarly, the evaporator heat transfer rate (*Q*eva), LMTD (Δ*T*eva), heat transfer coefficient (*U*eva) and pressure drop (Δ*P*eva) can be expressed as:

$$Q\_{\rm eva} = m(h\_1 - h\_6) \tag{10}$$

$$
\Delta T\_{\text{eva}} = \frac{\Delta T\_{\text{max}} - \Delta T\_{\text{min}}}{\ln \frac{\Delta T\_{\text{max}}}{\Delta T\_{\text{min}}}} = \frac{(T\_{12} - T\_6) - (T\_9 - T\_1)}{\ln \frac{T\_{12} - T\_6}{T\_9 - T\_1}} \tag{11}
$$

$$
\Delta L\_{\text{eva}} = \frac{Q\_{\text{eva}}}{\Delta T\_{\text{eva}} \cdot \text{A}} \tag{12}
$$

$$
\Delta P\_{\text{eva}} = P\_1 - P\_6 \tag{13}
$$

To better understand the heat source utilization, the temperature utilization rate of the heat source (θ) is proposed [38]. Assuming that the lowest heat source temperature can reach 60 ◦C (333.15 K), the denominator of temperature utilization rate θ indicates the heat that the system can use. The numerator denotes the actual heat used by the ORC system. So θ can be expressed as:

$$\theta = (T\text{H}, \text{in} - T\text{H}, \text{out}) / (T\text{H}, \text{in} - 333.15) \tag{14}$$

The generating efficiency can be expressed as:

$$
\eta\_{\rm ele} = \frac{\mathcal{W}\_{\rm ele,exp} - \mathcal{W}\_{\rm ele,pump}}{Q\_{\rm eva}} \tag{15}
$$

where *W*ele,exp and *W*ele,pump represent the electrical power and pump consumption power.

The exergy destruction of the four components including the pump (*E*d, pump), evaporator (*E*d, eva), expander (*E*d, exp) and condenser (*E*d, cond) can be calculated as follows:

$$E\_{\rm d,pump} = T\_0 m (s\_\theta - s\_5) \tag{16}$$

$$E\_{\rm d,eva} = T\_0 m \left[ (s\_1 - s\_6) - 2(h\_1 - h\_6) / (T\_9 + T\_{12}) \right] \tag{17}$$

$$E\_{\rm d,exp} = T\_0 m (s\_2 - s\_1) \tag{18}$$

$$E\_{\rm d,con} = T\_0 m \left[ (s\_5 - s\_2) - 2 (h\_5 - h\_2) / (T\_{13} + T\_{16}) \right] \tag{19}$$

#### **4. Results and Discussion**

To better compare the cycle behaviors of a 10-kW experimental prototype using two different pumps, the system operation parameters at different heat inputs are collected. The heat input for the plunger pump and centrifugal pump are in the range of 44.74–76.48 kW and 45.61–81.35 kW, respectively. The basic operating parameters using the plunger pump and centrifugal pump are displayed in Section 4.1. The detailed components' behaviors are described in Section 4.2, while the overall cycle characteristics, including system generating efficiency and exergy destruction are expressed in Section 4.3.

#### *4.1. Basic Operating Parameters*

In particular, the present data is collected at different time periods. It is difficult to keep the ambient temperature constant because of the fluctuating ambient conditions. However, the environment temperature has a great influence on the condensation process, so it has a strong guiding significance for explaining many basic operating parameters of ORC, such as pump inlet temperature and shaft work, etc. The environment temperatures for the ORC system using the plunger pump and centrifugal pump are listed in Tables 5 and 6, respectively. The environment temperature for the plunger pump is approaching 23 ◦C, which is 4 ◦C higher than that of the centrifugal pump. Figure 4 illustrates the relationship between mass flow rate and heat input using the plunger pump and centrifugal pump. When the heat input keeps rising, more working fluids are needed to absorb the heat from the evaporator. It also can be found that the centrifugal pump has a slightly higher mass flow rate than the plunger pump for the same heat input, which may be contributed to the centrifugal pump having the higher rotating speed and greater flow per revolution. The mass flow rate for the centrifugal pump is from 0.17 to 0.31 kg/s, which is 6.7% higher than that of the plunger pump.

**Table 5.** The environment temperature for using the plunger pump.


**Table 6.** The environment temperature for using the centrifugal pump.


**Figure 4.** Mass flow rates with heat input using the plunger pump and centrifugal pump.

Figure 5 shows details of the temperature and pressure for the pump inlet and outlet with heat input using the plunger pump and centrifugal pump. In Figure 5a, the centrifugal pump inlet temperature and pressure have no obvious variation with the heat input. However, the plunger pump inlet temperature appears to suddenly decrease when the heat inputs exceed 66.53 kW, owing to the fluctuating environmental temperature. The environment temperature decreases slightly for heat inputs over 66.53 kW, resulting in a decrease of cooling water temperature and the pump inlet temperature. In Figure 5b, the pump outlet temperature has a similar trend to the state at the pump inlet, whereas the pump outlet pressure shows a sharp increase with the heat input. Because of the difficulty in repeating tests with similar environmental temperatures, the non-dimensional operating parameter (pump pressure ratio) is chosen to compare the characteristic of the two pumps, which is shown in Figure 5c. The centrifugal pump pressure ratio is much higher than the plunger pump. The pump outlet pressure for the plunger pump is in the range of 7.58–10.87 bar, which is 0.3 bar higher than that of the centrifugal pump ranging from 7.29 bar to 10.84 bar.

**Figure 5.** Pressure and temperature at the pump inlet and outlet with heat input using the plunger pump and centrifugal pump: (**a**) pressure and temperature at the pump inlet; (**b**) pressure and temperature at the pump outlet and (**c**) pump pressure ratios.

Figure 6 presents the comparison of expander inlet and outlet temperatures and pressure with heat input using the plunger pump and centrifugal pump. In Figure 6a, the expander inlet temperature and pressure increase monotonically with heat input. The expander inlet temperature of the plunger pump rises from 82.20 ◦C to 97.74 ◦C for heat inputs increasing from 45 kW to 85 kW, with the corresponding expander inlet pressure ranging from 7.13 bar to 10.23 bar. Meanwhile, the plunger pump demonstrates a higher expander inlet pressure and temperature than the centrifugal pump. The expander outlet pressure and temperature keep rising in Figure 6b, which is similar to that at the expander inlet. Similarly, in order to more clearly compare the features of the expander using the two pump systems, the pressure ratio for the expander is shown in Figure 6c. The expander pressure ratio in the system using the centrifugal pump is more favorable than that using the plunger pump because the centrifugal pump can provide higher pressure to the system.

(**c**)

**Figure 6.** Temperature and pressure at the expander inlet and outlet with heat input using the plunger pump and centrifugal pump: (**a**) pressure and temperature at the expander inlet; (**b**) pressure and temperature at the expander outlet; (**c**) expander pressure ratios.

#### *4.2. Detailed Components' Behavior*

#### 4.2.1. Pump Behavior

The pump shaft power cannot be tested and is expressed by Equation (8). Figure 7 demonstrates the details of shaft power using the plunger pump and centrifugal pump with heat input. Apparently, the pump shaft power of the centrifugal pump keeps increasing with heat input, which may be caused by the increase in mass flow rate and pump enthalpy difference. However, the shaft power of the plunger pump presents a slight decrease when heat inputs exceed 66.53 kW because of the higher sensitivity to the environmental temperature. The pump shaft power using the centrifugal pump increases from 0.51 kW to 0.85 kW, which is 37% higher than that of the plunger pump.

**Figure 7.** Pump shaft power with heat input using the plunger pump and centrifugal pump.

The pump isentropic efficiency can be considered as an important parameter to ascertain pump characteristics. Figure 8 displays the pump isentropic efficiency of the plunger pump and centrifugal pump. The isentropic efficiency keeps increasing with heat input because the pump compression process gets closer to the ideal isentropic process. The isentropic efficiency of the plunger pump and centrifugal pumps is in the range of 13.2–26.1% and 15.3–24.5%, respectively. The pump isentropic efficiency is really low because there is no specialized pump for the ORC system. Moreover, the centrifugal pump isentropic efficiency is higher than the plunger pump for low heat inputs, while a reverse trend for higher input heats. Meanwhile, the low pump isentropic efficiency reminds us that enhancing the pump's behavior is vital for the improvement in ORC performance.

**Figure 8.** Pump isentropic efficiency with heat input using the plunger pump and centrifugal pump.

#### 4.2.2. Heat Exchanger Behavior

The details of evaporator and condenser heat transfer coefficients with heat input using the plunger pump and centrifugal pump are plotted in Figure 9. In Figure 9a, the evaporator heat transfer coefficient of the centrifugal pump keeps increasing, whereas that of the plunger pump displays a parabolic trend with a maximum with heat input, which may be caused by both the evaporator heat transfer rate and LMTD. The condenser heat transfer coefficient keeps rising with heat input in Figure 9, this is because of an increasing expander outlet temperature. The increasing condenser heat transfer rate is greater than that of condenser LMTD, which causes an increasing condenser heat transfer coefficient. Meanwhile, the cycle using the centrifugal pump has a relatively higher heat transfer coefficient than that using the plunger pump (whether evaporator or condenser). The evaporator heat

transfer coefficients for the cycle using the plunger pump and centrifugal pump are in the range of 116.45–147.01 W/m2 ◦C and 126.95–149.58 W/m<sup>2</sup> ◦C, and the corresponding condenser heat transfer coefficients are 1003.18–1371.33 W/m2◦C and 1092.74–1608.27 W/m2 ◦C, respectively.

**Figure 9.** Evaporator and condenser heat transfer coefficients with heat input using the plunger pump and centrifugal pump: (**a**) evaporator heat transfer coefficients; (**b**) condenser heat transfer coefficients.

As for the ORC simulation, the pressure drop in the evaporation and condensation processes are usually ignored. However, for the actual cycle, having pressure drops can decrease the expander inlet pressure, and thus affect the overall system property. Figure 10 demonstrates the variation of condenser and evaporator pressure drop with heat input using the plunger pump and centrifugal pump. Obviously, the pressure drops for evaporator and condenser increase with the heat input, which may be caused by the increasing mass flow rate. A small difference in the evaporator pressure drop appeared between the plunger pump and the centrifugal pump. However, when the heat inputs raise from 40 kW to 82 kW, the condenser pressure drops using the centrifugal pump are 0.13–0.53 bar, which is 0.07 bar higher than that using the plunger pump. The evaporator pressure drops are in the range of 0.45–0.65 bar. It indicates that the pressure drop should be considered for the ORC simulation and decreasing the pressure drop is one way to improve the system performance.

**Figure 10.** Condenser and evaporator pressure drop with heat input using the plunger pump and centrifugal pump.

The variation of temperature utilization rate with heat input using the plunger pump and centrifugal pump is plotted in Figure 11. For a specific heat source temperature, a higher thermal efficiency does not represent a higher net power output. Therefore, the temperature utilization rate is used to appraise the heat source utilization. As illustrated in Figure 11, the temperature utilization rate for the centrifugal pump has a slight decrease whereas the plunger pump has almost no change with the heat input. The average heat source temperature utilization rate for the centrifugal pump is about 30%, which is 5% higher than that of the plunger pump, indicating that the centrifugal pump absorbs more heat than the plunger pump at the same heat source condition.

**Figure 11.** Temperature utilization rate with heat input using the plunger pump and centrifugal pump.

#### 4.2.3. Expander Behavior

Figure 12 shows the expander isentropic efficiency with heat input using the plunger pump and centrifugal pump. It should be reminded that the scroll expander is designed with a nominal expander shaft power of 10 kW, indicating a heat input of 40–200 kW is needed. However, the heat input is set from 45 kW to 85 kW because of the power limitation. Therefore, the expander isentropic efficiency presents an apparent decrease trend from 58.8% to 39.1% with heat input because of the insufficient expansion. The expander isentropic efficiency for the plunger pump is in the range of 46.5–58.8%, which is 12.6% higher than that of the centrifugal pump.

**Figure 12.** Expander isentropic efficiency with heat input using the plunger pump and centrifugal pump.

The variation of electrical power with heat input using the plunger pump and centrifugal pump is illustrated in Figure 13. The electrical power for the centrifugal pump rises from 1.83 kW to 3.01 kW, while that of the plunger pump is in the range of 1.76–2.87 kW. The reason is that the increment in

pressure difference causes an increase in the expander rotational speed, resulting in an increase in electrical power. The electrical power has a small difference using the plunger pump and centrifugal pump, indicating that the electric power is insensitive on the pump types.

**Figure 13.** Electrical power with heat input using the plunger pump and centrifugal pump.

#### *4.3. Overall System Performance*

Figure 14 displays the system generating efficiency of the plunger pump and centrifugal pump. In this study, system generating efficiency is utilized as an evaluation criterion for this system, which is obtained based on the net electrical power and heat input. The system generating efficiency has no obvious change with heat input, demonstrating that the system generating efficiency has little effect on the heat input. The increasing net electrical power and the increasing heat input enable the almost unchanged system generating efficiency. The system generating efficiency for the plunger pump is approximately 3.63%, which is 12.51% higher than that of the centrifugal pump. One reason for the low overall system performance is that the pump consumed more power (as shown in Figure 7).

**Figure 14.** System generating efficiency with heat input using the plunger pump and centrifugal pump.

Figure 15 presents the details of the exergy destruction of the four important components with the heat input using the plunger pump and centrifugal pump. It is obvious that the exergy destruction for the evaporator, expander and condenser keep rising, whereas that of the pump almost has no change with the heat input. Besides, the exergy destruction of the piston pump is almost the same as that of the centrifugal pump. However, for the other three components, the exergy destruction using the centrifugal pump is higher than that using the plunger pump, because of the relatively higher mass flow rate for the centrifugal pump. For a specific heat input of 68.6 kW using the plunger pump, the exergy destruction for the pump, evaporator, expander, and condenser is 0.5 kW, 3 kW, 2.5 kW, and 3.2 kW, respectively.

**Figure 15.** Exergy destruction of the four important components using the plunger pump and centrifugal pump: (**a**) pump exergy destruction; (**b**) evaporator exergy destruction; (**c**) expander exergy destruction; (**d**) condenser exergy destruction.

To ascertain which component contributes the maximum exergy destruction, the proportion of exergy destruction for each component using the plunger pump and centrifugal pump is shown in Figure 16. For the plunger pump and centrifugal pump, the exergy destruction for the evaporator, expander and condenser is almost 30%, indicating that improving the temperature matching between the cycle and the heat (cold) source is a way to improve the system property.

**Figure 16.** The proportion of exergy destruction for each component with heat input using the plunger pump and centrifugal pump: (**a**) the proportion of exergy destruction using the plunger pump; (**b**) the proportion of exergy destruction using the centrifugal pump.

#### **5. Conclusions**

The system behaviors using the plunger pump and centrifugal pump have been investigated experimentally. A 10 kW R245fa-based experimental prototype is adopted. The heat source temperature for both pump experiments was 85–106 ◦C. The heat inputs for the plunger pump and centrifugal pump are in the range of 44.74–76.48 kW and 45.61–81.35 kW, respectively. Simultaneously, the mass flow rates of the plunger pump are from 0.16–0.26kg/s and those of the centrifugal pump are in the range of 0.19–0.31 kg/s. The temperature utilization rate is used to appraise the heat source utilization. The detailed components' behaviors with the varying heat input are discussed, while the system generating efficiency is examined. The exergy destruction of the four main components is addressed. The conclusions are summarized below:

(1) The mass flow rates of the centrifugal pump are from 0.19–0.31 kg/s, which is 19% higher than that of the plunger pump. Compared with the plunger pump, the centrifugal pump owns a relatively higher mass flow rate and more pump shaft power.

(2) A small difference of evaporator pressure drop appeared between the plunger pump and the centrifugal pump. The condenser pressure drops using the centrifugal pump are 0.13–0.53 bar, while the evaporator pressure drops are in the range of 0.45–0.65 bar, demonstrating that the pressure drop should be considered for the ORC simulation.

(3) The average heat source temperature utilization rate for the centrifugal pump is about 30%, which is 5% higher than that of the plunger pump, indicating that the centrifugal pump absorbs more heat than the plunger pump at a same heat source condition.

(4) The electrical power for the centrifugal pump rises from 1.83 kW to 3.01 kW, while that of the plunger pump is in the range of 1.76–2.87 kW. The electrical power has a small difference using the plunger pump and centrifugal pump, indicating that the electrical power is insensitive of the pump types. The system generating efficiency for the plunger pump is approximately 3.63%, which is 12.51% higher than that of the centrifugal pump. It indicates that the plunger pump is more suitable for the ORC system in this study. The system generating efficiency is insensitive of the heat input.

(5) No matter which pump is used in the ORC, evaporator, expander, and condenser exergy destruction accounts for almost 30%.

(6) The exergy destruction for evaporators, expanders, and condensers is almost 30%, indicating that improving temperature matching between the system and the heat (cold) source is a way to improve the system property

**Author Contributions:** Y.-q.F., Q.W. and T.-C.H. conceived of the presented idea. X.W. and C.-H.L. developed the theory and performed the computations. Z.-x.H. and M.S. verified the analytical methods. All authors discussed the results and contributed to the final manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research work has been supported by the National Natural Science Foundation of China (51806081), the Key Research and Development Program of Jiangsu Province, China (BE2019009-4), the Natural Science Foundation of Jiangsu Province (BK20180882), the China Postdoctoral Science Foundation (2018M632241), the 2019 Scholarship of the Knowledge Center on Organic Rankne Cycle (KCORC, www.kcorc.org), the Key Research and Development Program of Zhenjiang City, China (SH2019008), and the Key Project of Taizhou New Energy Research Institute, Jiangsu University, China (2018-20). The authors are grateful for the Ministry of Science and Technology, Taiwan under the grants of Contract No. MOST 107-2221-E-027-091, and by "Research Center of Energy Conservation for New Generation of Residential, Commercial, and Industrial Sector" from The Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

1. Johnson, I.; Choate, W.T.; Davidson, A. *Waste Heat Recovery: Technology and Opportunities in U.S. Industry*; BCS, lnc.: Laurel, MD, USA, 2008.


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Modelling of Polymeric Shell and Tube Heat Exchangers for Low-Medium Temperature Geothermal Applications**

#### **Francesca Ceglia 1,\*, Adriano Macaluso 2, Elisa Marrasso 1, Maurizio Sasso <sup>1</sup> and Laura Vanoli <sup>2</sup>**


Received: 30 March 2020; Accepted: 26 May 2020; Published: 29 May 2020

**Abstract:** Improvements in using geothermal sources can be attained through the installation of power plants taking advantage of low and medium enthalpy available in poorly exploited geothermal sites. Geothermal fluids at medium and low temperature could be considered to feed binary cycle power plants using organic fluids for electricity "production" or in cogeneration configuration. The improvement in the use of geothermal aquifers at low-medium enthalpy in small deep sites favours the reduction of drilling well costs, and in addition, it allows the exploitation of local resources in the energy districts. The heat exchanger evaporator enables the thermal heat exchange between the working fluid (which is commonly an organic fluid for an Organic Rankine Cycle) and the geothermal fluid (supplied by the aquifer). Thus, it has to be realised taking into account the thermodynamic proprieties and chemical composition of the geothermal field. The geothermal fluid is typically very aggressive, and it leads to the corrosion of steel traditionally used in the heat exchangers. This paper analyses the possibility of using plastic material in the constructions of the evaporator installed in an Organic Rankine Cycle plant in order to overcome the problems of corrosion and the increase of heat exchanger thermal resistance due to the fouling effect. A comparison among heat exchangers made of commonly used materials, such as carbon, steel, and titanium, with alternative polymeric materials has been carried out. This analysis has been built in a mathematical approach using the correlation referred to in the literature about heat transfer in single-phase and two-phase fluids in a tube and/or in the shell side. The outcomes provide the heat transfer area for the shell and tube heat exchanger with a fixed thermal power size. The results have demonstrated that the plastic evaporator shows an increase of 47.0% of the heat transfer area but an economic installation cost saving of 48.0% over the titanium evaporator.

**Keywords:** plastic heat exchanger; Organic Rankine Cycle; geothermal energy; shell and tube heat exchanger; fouling resistance

#### **1. Introduction**

Climate change, rising pollution, and the fossil fuel depletion encourage many countries to push towards renewable-based energy conversion systems [1]. In particular, the European Union energy policy gives a high priority to the increasing use of renewable energy sources (RESs), because of their strong contribution to the diversification of energy supply, the improvement of the security of energy systems, the minimization of greenhouse effects and social and economic cohesion. In 2014 the European Union (EU) agreed to implement strategies and targets (revised in 2018) to move toward a low carbon economy. One of the pillars of EU policy in energy and environmental matters consisted

of the RESs share increase in final energy consumption by at least 32.0% in 2030 compared to the 1990 level [2]. The attainment of the EU renewables target is ensured by the governance system based on national and local energy planning. Indeed, in recent years, it can be observed that a proliferation of ambitious commitments and policies in the RESs field adopted by national, regional, and local governments aimed to achieve EU goals [3]. Moreover, the support policies and strategies offer useful instruments to encourage renewable energy use and to ensure the full exploitation of RES's potential in territorial areas where the energy policies' actions are in force [4].

According to Eurostat [5] renewable energies covered 17.5% of final EU energy consumption in 2017. It has been estimated that the main renewable energy options which will contribute to the additional EU potential in 2030 are: wind power (239 TWh), transport biofuels (218 TWh), solar thermal in industry and buildings (117 TWh), biomass in industry and buildings (105 TWh), and solar photovoltaic (93.0 TWh) [6]. Unfortunately, the widely used and most promising RESs (such as solar and wind) are not programmable. Their availability varies throughout hours and seasons and, as a consequence, their use has to be accurately designed in conjunction with management strategies such as load shifting and energy storage. Thus, one of the possible pathways to mitigate the criticalities of this uncertainty is the exploitation of more flexible and stable RESs such as geothermal and biomass energy sources. In particular, geothermal energy is an abundant renewable source with significant potential. The geothermal reservoirs could be employed in direct use such as in district heating systems, in indirect use to produce electricity, and in cogeneration systems for the combined production of power, heating, and cooling energy [7]. The hot water reservoirs in low deep sites are used for direct scopes and/or district heating systems. Native American, Chinese, and Ancient Roman people adopted hot mineral springs for cooking and bathing; currently these could be used for thermal scope, heating, and domestic hot water. Geothermal energy provides heat requirements to buildings by means of district heating systems. Surface hot water is directed to buildings in the intermediate circuit. For example, in Reykjavik (Iceland), a district heating system supplies thermal energy to most of the buildings. On the other hand, the use of geothermal energy in industrial fields concerns gold mining, food dehydration, and milk pasteurizing. One of the most widespread industrial application of geothermal energy is represented by the dehydration of vegetables and fruit drying [8]. As concerns the electricity production from geothermal sources, traditional geothermal power plants exploit steam or water at high temperatures (150 to 370 ◦C). Geothermal power plants are usually located near reservoirs within one or two miles of the Earth's surface.

Otherwise, geothermal sources are mostly available worldwide at medium and low enthalpy. In past years, geothermal energy has primarily been used in zones with a volcanic activity where there was a near sub-surface heat availability. Whereas, in recent decades geothermal energy usage has spread in many regions of the world thanks to the possibility of drilling to depths of several kilometres. In developed countries geothermal energy supply is especially widespread due to their flourishing economic means and industrial advances, as well as their availability of know-how and expertise. Besides, geothermal energy can be useful in developing countries to solve the energy access problems [9]. In Asia, only China owns 8.00% of world's geothermal resources and it has 27.8 MW of geothermal installed power generation [10]. In Canada and Australia there is a large availability of geothermal resources at 100 ◦C near the land surface [11,12]. In South Africa (Main Karoo Basin region) a geothermal potential has been recently addressed, finding a geothermal gradient ranging from 24.5 ◦C/km to 28.2 ◦C/km at 3500 m depth [13].

On the other hand, in many countries geothermal sources have remained unused because of the acceptability problems of geothermal installations. Meller et al. [14] have identified the precondition for public acceptability of geothermal power plants, and they have analysed the social response to novel geothermal activity. The aim of their study has been to develop technological and scientific options by means of sociological studies for the responsible use of geothermal resources. Indeed, the participation of the public into geothermal projects should go further with communication and awareness-raising measures. By respecting the research rules and the development steps of technological solutions it is

necessary for an open approach aimed to include governance structures. In some European countries (such as Germany, France, and Italy) the social response to geothermal projects evidences the reticence of the public and relevant stakeholders to eventual geothermal development in all considered countries. In addition to these issues, the high cost of geothermal installations and the regulatory uncertainty have jeopardized the diffusion of energy conversion systems based on low and medium enthalpy geothermal sources.

This is an Italian case in which the massive presence of geothermal sources (at high, medium, and low temperatures) is not completely exploited even if its potential has been recognised since the 1980s [15]. Interesting geothermal areas had been found in the southern Alps region at a temperature of 80–120 ◦C and a depth of about 3000 m [16]. In the transition zone between the chain and the basin of the Po plain, a certain heat flow anomaly (80.0 mW/m2) attributable to a geothermal gradient has been discovered. This heat flow is 21.3% higher than the Italian heat flow mean value (63.0 mW/m2) [17]. Moreover, a great heat flow anomaly affects the Mediterranean and central/southern Tyrrhenian Sea (>150.0 mW/m2). Intensive volcanic activity occurs on the Aeolian and Pantelleria islands (in Sicily) and in the Phlegraean Fields area (near Naples, South of Italy), resulting in geothermal fluid temperatures of 100–150 ◦C located near the Earth's surface [18]. Despite this large availability, the only Italian geothermoelectric power plants are installed in Tuscany, characterised by high-temperature geothermal sources covering a power equal to 915 MW. These power plants are all traditional flash steam technologies that can use only geothermal high temperature fluids letting the low-medium resources go unused [19,20].

The major possibility of employing the low-medium enthalpy reservoirs for geothermoelectric applications is represented by binary cycles such as the Rankine Cycle with organic working fluids (ORC) [21]. Its layout is the same as an ordinary Rankine cycle, with the main difference being that in the ORC an organic fluid is used instead of water. The liquid-vapour phase change of an organic fluid occurs at a temperature lower than the phase change of water-steam, allowing for the use of low-medium temperature sources. In addition, the use of an organic fluid results in further advantages related to the thermo-physical proprieties of the fluid. The major used fluids in ORC systems are characterized by a positive slope of the vapour saturation curve which permits the avoidance of both superheating at the inlet of the turbine and condensation during the expansion process.

Among the different sources for an ORC, the most used and promising are biomass, sun, geothermal brines, and exhaust gases from industrial processes and engines. ORC plants can be characterized by their wide size range from a few kWel (in residential cogeneration applications) up to tens of MWel (in large power plants uses). As regards geothermoelectric plants based on ORC systems, worldwide only 16.0% of geothermal power plants are based on ORC technology such as those in Italy [21]. In particular, ORC power plants activated by geothermal sources number about 337, and these represent 19.2% of total ORC plants feeding by different sources. Geothermal ORC power plants cover 2021 MWel representing 74.9% of the total power installed for the ORC systems. These data highlight that the geothermal ORC plants have higher size than other ORC plants fed by different RESs, and their medium power is 6.00 MWel for a single plant [22].

The rising interest in ORC power plants is demonstrated by several works conducted in recent years to investigate their performances in different applications.

In [23,24] a binary ORC power plant for the use of medium-low enthalpy geothermal reservoirs is analysed firstly in a thermodynamic investigation/optimization, and secondly from an economic aspect. In [23] a Matlab code is defined to find the optimal match cycle parameters, configuration, and fluid taking into account geothermal waters in the temperature range of 120–180 ◦C. Thermodynamic optimization results show that the highest plant efficiencies are obtained for fluids that present a range of 0.88–0.92 of the ratio between critical working fluid temperature and inlet geothermal temperature and a supercritical cycle with a reduced pressure between 1.10 and 1.60 bar. Meanwhile, in the economic optimization these values are slightly lower and the advantages of supercritical cycles usage are less present.

In [24] an ORC powered by diesel engine waste heat recovery with different selected working refrigerant fluids such as R123, R134a, R245fa, and R22 is modelled and optimized. The optimization results, conducted by means of a genetic algorithm, show that the R123 is the best working fluid in both an economical and a thermodynamic sense for a defined value of output power. The optimum result of R123 determines the 0.01%, 4.39%, and 4.49% improvement for the yearly cost compared to R245fa, R22, and R134a, respectively. As regards thermodynamic optimization, the percentages of efficiency increase using R123 and other fluids (R245fa, R22, and R134a) are 1.01%, 12.79%, and 10.6%, respectively.

Regarding the geothermal applications of ORC systems, many studies have been aimed to assess the performance of the cascade geothermal plants based on ORC systems [25], and the performance of this technology through numerical [26–29] and experimental [30] works has been evaluated.

The cascade geothermal plants based on ORC systems coupled with other components, such as absorption heat pumps and heat exchangers for heat recovery, were analysed in many studies. In [25] Pastor-Martinez et al. have compared different polygeneration systems activated by low and medium geothermal sources (80–150 ◦C). The systems consist of an ORC (to produce electricity), an absorption heat pump (to provide cooling energy), and a heat exchanger (for heat recovery) arranged in different cascade configurations, with parallel or series geothermal fluid use. The study considers two possible plants in two different temperature ranges. For the first case, from 80 to 111 ◦C, the polygeneration arrangement presents the highest exergetic performance in the hybrid arrangement for parallel-series configuration, and it reaches the exergy efficiencies varying from 42.8% to 50.1%. Instead, the second one ranges from 110–150 ◦C, and awards a series cascade configuration achieving exergy efficiencies from 51.4% to 52.9%. In [26–28] other simulation studies integrate the desalinization water system to improve the polygeneration system layout using the geothermal fluid in cascade allowing a re-injection of the fluid at a lower temperature. The hybrid multi-purpose plant consists of an ORC powered by a low-medium temperature geothermal source and by solar energy from parabolic collectors. The geothermal water is first employed to activate the ORC loop, then to supply heating needs at about 85–90 ◦C (in winter), or space cooling (in summer) using a single-effect absorption chiller. At the end of the cycle, the geothermal water is used to feed a multi-effect distillation system. In this process the seawater is turned into freshwater. The results determine an energy efficiency of the ORC plant equal to 11.6% and a simple payback of 4.47 years. Another simulation study [29] is based on a zero-dimensional model of an ORC that allows for the investigation of the effects on the main output parameters (heat exchangers efficiency, ORC power output, ORC first law efficiency) by only changing the heat transfer coefficients correlations of the vapour generator available in literature. Two ORC plants both activated by a medium-temperature geothermal source supplying a constant thermal load are analysed in the study. The first case study regards an ORC module with a size of 1.20 MWel fed by a geothermal fluid with a temperature of 160 ◦C and 7.00 bar and using n-pentane. The second ORC plant uses R245fa providing 8.00 kWel and it is activated by a geothermal fluid at 95.0 ◦C and 3.00 bar. The first plant shows an electric efficiency of about 14% for all correlations investigated, while the second plant obtains an electric efficiency ranging from 7.00–10.0%. In [30], a real ORC plant in Huabei (China) shows the possibility for providing geothermoelectric energy from different thermal fluids in an aggressive environment. The plant with 500 kWel employs fuel oil from an abandoned well using an intermediate circuit with an efficiency between 4.00–5.00% and consequently the output power of the turbine varies from 160–60.0 kWel.

Even if ORC technology is very promising in low enthalpy geothermal applications, it is affected by a problem common to all technology exploiting geothermal sources. Geothermal fluids are often very aggressive (depending on geothermal sites) and they cause surface fouling, corrosion, and scaling over the heat exchanger (HEX) surface in which the heat transfer occurs through the working fluid evaporation. The scale formations threaten the heat transfer between geothermal and organic fluids, and they have also an impact on HEX performance in terms of flow velocity and pressure drop. Thus, they force the plant to turn off in order to clean or replace the HEX [31–33]. This issue causes an operating cost increase; indeed, it has been estimated that the impact of the HEX cost on the

total plant investment costs ranges from 20.0% to 30.0% [34]. The HEX used in an ORC system is traditionally a metallic shell and tube type heat exchanger that has a high cost and low resistance to corrosion [35]. In [36] a mathematical model of the shell and tube heat exchanger (STHEX) is proposed for the capture and predicting fouling trends on both the shell and tube sides. The literature review is typically focused on fouling inside the tubes, and instead fouling on the shell side is not usually considered. In this work, instead, it has been demonstrated that fouling deposition on the shell side may be significant. It determines the not-equal heat transfer, growing pressure drops, and flow path modifications. Different solutions have been investigated to solve the fouling problems.

In [37] a study has been conducted to improve the corrosion-erosion features of carbon steel by using a multilayer composite coat for carbon steel plates. This solution is adopted to obtain better tribological behaviours and a lower wear rate of coatings than the untreated steel. In this application the nickel is linked with chromium to form Cr2O3 which allows us to use the material until 1200 ◦C. In particular the material use is ensured for temperatures lower than 800 ◦C thus, it could be used in both geothermal plant components and gas combustion applications. These coatings, however, produce very dense layers with a porosity under 0.500–1.00%. In [38] the performance of the HEX ceramic prototype has been evaluated. It is able to achieve a heat transfer of up to 6.00 kW and an effectiveness of up to 97.0%. It could operate at high temperatures and in harsh environments exceeding also the performance of a comparable metal HEX.

Another alternative path that can be followed is the replacement of the metallic HEX in geothermal ORC with a plastic (polymer) heat exchanger (PHEX). Indeed, a PHEX in ORC systems activated by geothermal sources ensures a higher inhibition of the scale depositions and the corrosion resistance limiting the maintenance periods for chemical or mechanical and/or hydrodynamic washing affecting the carbon steel HEX. Moreover, PHEX investments and maintenance costs are lower than those of a HEX with the same useful life cycle. Even if it is possible to consider the advantage of a PHEX for aggressive environment applications it is necessary to underline that the market for these components is thin for high working temperatures and pressures. The low operating temperature is compatible with geothermal sources, but the low pressure of exercise is not performing for organic fluids used in ORC systems. Thus, some advances are still required for the widespread use of plastic heat exchangers, but great improvements are expected in their market to justify the investigation on PHEX performance in innovative applications such as in ORC plants. This is the main topic of this work and in the following section the available literature information regarding PHEXs operating and design conditions in comparison with HEXs have been collected and summarised; in addition, the motivation and aims of the paper have been discussed too.

#### **2. Polymeric Heat Exchanger: State of Art and Aim of the Study**

Currently, the used materials for HEXs are metallic alloys, such as 70.0% Cu, 30.0% Ni, or titanium, with high thermal conductibility but with high corrosion and fouling resistances, especially in aggressive environments [39,40]. The types of fouling occurring in a HEX could be different, such as the precipitation of solid deposits in a fluid on the heat transfer surfaces (that can be cleaned by chemical treatment) or corrosion and other chemical fouling. The growth of algae in hot fluids can be a cause of contaminations in the heat exchangers. The biological fouling that the algae may determine can be avoided by chemical techniques. Moreover, in geothermal applications, the chemical aggressive composition of geothermal brines (strictly depending on geothermal site) determines the fouling on the HEX's surface. All these problems cause the deterioration of material, the worsening of heat transfer efficiency, the increase of pressure losses due to friction, the reduction of crossing flow section, and the need for HEX replacement and cleaning. As a consequence, it may be necessary to employ a larger, and thus more expensive, HEX to achieve the required heat transfer performance when fouling takes place. All of these categories of fouling can be reduced by using plastic pipes instead of metal ones or by coating metal pipes with glass. Regarding polymer heat exchangers, their main advantages are: low cost, low weight, anti-corrosion, antifouling, manufacturing simplicity, electrical

insulation, high chemical resistance, high modelling, and excellent elasticity (depending upon the working temperatures) [41,42]. The low PHEXs' costs result in a decrease of up to 20% on power plant investment costs in which a titanium HEX evaporator is replaced by a PHEX one by considering the same life cycle [34]. Thus, the PHEX's opportunities are evident in small-size applications and when the specific unitary cost is high. Indeed, with reference to a metal HEX's cost in Figure 1, the investment cost of a common metal HEX against its heat transfer area is plotted starting from data available in literature for different heat exchangers' geometries [43]. In Figure 1, the *x*-axis is stopped at 120 m2 because it is the maximum size of the heat transfer area for the plate heat exchanger available from the market data comparable to other models. In addition, a HEX's maintenance cost for 20 years of its life cycle is equal to 10.0–11.0% of the initial investment. Therefore, PHEXs offer an interesting alternative to the high cost of metal heat exchangers concerning both the investment and the maintenance costs, especially in aggressive operating conditions.

**Figure 1.** Metal heat exchangers' (HEXs) unit price as a function of the heat transfer area.

Another advantage of PHEXs is that they are already available on the market in multiple polymeric plastic materials (such as Ethilene Chloro TriFluoroEthylene (ECTFE); polyEthylenete TetraFluoroEthylene (ETFE); polyEthylene of high and low density (PEHD/PELD); PolyVinilChloride (PVC), etc.) and different manufacturing companies already produce PHEX worldwide: TMW (La Serre, France) [44], Polytetra (Bietigheim-Bissingen, Germany) [45], Aetna plastic (Valley View, United States of America) [46], HeatMatrix Group B.V. (Geldermalsen, Netherlands) [47], Fluorotherm (Parsippany, United States of America) [48], Ametek (Berwyn, United States of America) [49], Kansetu (Osaka, Japan) [50], and Calorplast (Krefeld, Germany) [51]. The most widespread geometries of PHEXs produced by the aforementioned companies are plate and shell and tube heat exchangers; only in particular cases is it possible to find immersion, hollow plates, or tube plate PHEXs. In addition to these benefits, PHEXs show also some critical issues that can be summarised as follows [52]:

• the most relevant parameter for HEXs' design is the global heat transfer coefficient (UA) that takes into account the convective, conductive, and fouling resistances. The plastic thermal conductivity is usually equal to 1.00% of the thermal conductivity of metallic materials [53,54]. This fact determines a penalization of the heat transfer performance; thus, a higher heat transfer surface area is requested.

• the PHEX has low structural strength and poor stability in terms of mechanical resistance at high temperatures or pressures. Indeed, the limits of PHEXs are the working couple of pressure and temperature that the material can support. At high temperatures, the maximum operating pressures of the commercial devices are often incompatible with the operating pressures of organic fluids defined for ORC market applications [34]. Table 1 shows a summary of the optimal working temperature and pressure values for each plastic material available for shell and tube exchangers. It is important to underline that the maximum operating temperatures could be higher when the pressure is reduced and vice versa. In general, it should be noted that the materials most resistant to high temperatures (>100 ◦C) are Perfluoroalkoxy alkanes (PFA) and polyvinylidene difluoride (PVDF) which, however, have lower thermal conductivity (about half) than PE and PP. The limit for the PE polymers is under 100 ◦C for the hot fluid considered. Over this value of temperature, it is necessary for the use of a polymer with a higher mechanical resistance. In particular, from market analysis, it has been found that it is easy to reach operating temperatures close to 100 ◦C by improving the composition of polymers; for example, by adopting high density PE (PEHD) as suggested by the manufacturer [51].

PHEX's problems have been investigated by researchers in recent years by means of simulative and experimental applications. For instance, in [55] the authors have demonstrated through an experimental analysis that PHEXs conductive resistance (that is proportional to the inverse of thermal conductivity) amounts only to 3.00% of the total thermal resistance (including fouling, convective, and conductive resistance). Moreover, the percentage weight of conductive resistance on total thermal resistance is strictly linked to the value assumed by convective and fouling resistances which depend on many factors such as the thermodynamic condition of the fluid and the Reynolds numbers (by velocity definition) of the fluid that crosses the PHEX [56]. Other authors have found that an enhancement of the polymer heat transfer coefficient can be obtained by filling the polymeric matrix with high conductivity additives or by controlling its crystallinity [57]. In support of these theories in [58] it is experimentally shown that the specific volumetric heat transfer coefficient of a PHEX in polyamide filled with carbon fibres is 1.65 times higher than that produced with a polyamide only. On the other hand, even if polymers constituting PHEXs have a low mechanical resistance, they can deform elastically meaning that they return to their original form after thermal or mechanical stress. Moreover, PHEXs' low structural strength results in a light weight. Indeed, in [59] it has been estimated that the metal HEXs have many drawbacks related to their weight, and PHEXs ensure up to 62.2% of weight reduction.

PHEXs' applications have been recognised as particularly suitable in different fields as seawater heat exchangers, solar water systems, heat recovery applications, and for the desalination industry in a corrosive environment [60]. PHEXs can also represent a good solution for ORC applications, since ORC systems are characterized by aggressive/low temperature heat sources and a high specific cost, so the heat exchanger's cost has a great weight in the overall cost of such technology. Despite this opportunity, there is a gap in the literature review concerning the PHEX use in ORC exploiting geothermal brine. To the best of authors' knowledge, only Gomez et al. [34] have conducted a simulative analysis to investigate the possible replacement of a titanium HEX with a PHEX in low size Organic Rankine Cycles for geothermal applications to reduce plant investment costs. They have conducted a thermodynamic analysis of a 20 kWel RORC plant according to the currently available data on market for shell and tube PHEXs. Then, the authors compared a PHEX and a metallic HEX from an economic point of view finding that for a plant availability for 5000 h of functioning in a year and a discount rate of 10%, a cost of the generated electricity equal to 94.8 \$/MWh for a plastic solution and 118.9 \$/MWh for a titanium HEX can be obtained.

In this context, the main aim of this work is to determine whether it is possible to employ PHEXs as an alternative to conventional metallic HEXs in an ORC-based plant using a geothermal source. The work wants to define the advantages and disadvantages of HEX replacement considering the main design proprieties, such as the heat exchanger's surface area, the overall heat exchange coefficient, and also economic aspects. The novelty of this work concerns the development of a one-dimensional mathematical numerical model of a polymeric STHEX based on discrete elements for geothermal ORC applications. Thus, unlike other works in the literature review, PHEX is not modelled as a "black-box" accounting only for the inlet and outlet fluids' operating conditions, but the heat transfer inside tubes is modelled considering PHEXs' conductive, convective, and fouling resistances too. The study is based on a MATLAB algorithm with a REFPROP interface able to provide the value of design characteristics such as the heat transfer area, the length of tubes, and the heat transfer coefficient in a shell and tube heat exchanger configuration. A sensitive analysis is carried out varying the inlet temperature of geothermal brine using literature correlations in the worst fouling condition.


**Table 1.** Operating temperatures and pressures for different polymer materials.

#### **3. ORC Configuration with PHEX in a Geothermal Plant and Working Fluid Selection**

The most common applications provide the use of a STHEX in geothermal ORC systems because it can be cleaned easily. Among all heat exchangers, STHEXs are the most widespread heat exchangers covering 65.0% of the market in different applications [61]. The common practice considers the allocation of fluids with the maximum predisposition to scale in the side of tubes to facilitate the cleaning of the component. However, the fluid on the side of the shell can also be subjected to fouling. In such cases, the neglect of fouling effects in the shell-side may lead to great errors in the analysis of the data [36]. In this paper a shell and tube PHEX is considered as an evaporator in a geothermal ORC plant. The possibility of component cleaning is neglected due to its higher fouling resistance, whereas it is considered with the opportunity of PHEX replacement according to its low cost. Thus, this work considers the organic fluid flowing inside the tubes and the geothermal hot brine is confined in the shell, resulting in a counter-cross flow heat exchanger. This choice leads to two advantages:


The considered plant, in a regenerative ORC configuration (RORC), is represented in Figure 2. It is composed of a pump, turbine, regenerator, condenser, and evaporator that provides the interaction between the two fluids: the hot vector fluid (geothermal brine) and the organic working fluid. Geothermal fluid is taken from the aquifer and then it is pre-treated. The geothermal fluid considered in this work refers to the Phlegrean Fields area (south of Italy). The choice of the hot fluid temperature derives from a previous analysis conducted by Carlino et al. in [63] from which it has been possible to evaluate the geothermal gradient. By analysing the census relating to the area of interest an average value of the well surface temperatures has been considered excluding temperatures below 70 ◦C (temperature typically used for reinjection). The temperature of the pre-treated hot resource used in this analysis is about 95 ◦C, compatible with the ORC manufacturer data request [64]. In particular, the Phlegrean Fields area is heavily affected by medium-low enthalpy geothermal sources [65]. It has

been demonstrated that near Pozzuoli there are many zones interested by geothermal source availability with a temperature near 90 ◦C. Different studies have typically analysed the chemical composition of geothermal fluid at high deep sites and temperatures (~200–300 ◦C) [63,66], and have also presented data on flow rates and tempering available in the Campania region such as the geothermal brine chemistry characteristic. Furthermore, few literature data show the chemical composition at lower temperature conditions despite the studies evidencing the high variability of the geothermal source in Campania. However, in the Phlegrean Fields area the geothermal sites show various temperature gradients (20–180 ◦C/km) and temperature profiles, different flow rates, and heat flow density (from 20 to 140 mW/m2) [67]. Some data about the chemical-physical composition of geothermal water at low temperatures in Phlegrean Fields are reported in Table 2. The data derive from studies conducted in Phlegraean Fields before 1980 [68], during the period 1990–1999 [69,70]. In some of these studies information about the possible change in geothermal fluid composition and temperature after the bradyseism both in the fumaroles and thermal waters are reported. In addition, it has been evidenced that the shallow water system is locally activated by a deep hydrothermal element, generating in the form of boiling pools and wells the hot waters at the surface with temperatures around 90 ◦C. In Table 2 the chemical composition of geothermal fluids suitable for our simulation data set according to their temperature and chemical composition compatible with a heat exchanger and ORC considered system is reported. Both the columns (H. Tennis #1 and H. Tennis #2) are referred to *H.* Tennis well for two different periods [64,69]. Nevertheless other geothermal sites at low-medium temperatures are available in Phlegrean Fields, but because of their extreme sulfate and ammonium composition prevalence, higher presence of Fe and SiO2, and extremely low pH, they are not considered [66–68]. In fact, they could require further analyses for numerical simulation because of their large quantities of silica, iron, aluminum, and sulfate could induce massive precipitations of minerals in the PHEXs. According to the literature the prevalent elements are Na, Cl, and total dissolved solids (TDS). In this work the geothermal fluid in the water dominated condition is simulated by using the REFPROP library which allows us to evaluate the thermodynamic properties of pure water. This approximation is endorsed by a previous analysis which allowed for the estimation of the variation of the thermodynamic properties of geothermal fluid with respect to pure water for the Phlegrean Fields site in the case of the temperature of the source at 94 ◦C. The results showed that the thermodynamic parameters variation (estimated by means of a software capable of integrating the salinity of the water) is not appreciable and, therefore, does not affect the hot fluid heat transfer coefficient. The geothermal brine aggressive chemical composition determines corrosion and depositions of suspension solid particles on the heat exchanger surface. In order to consider these disadvantages in heat transfer efficiency, the fouling resistances are included in the design methodology of the heat exchanger. In addition, fouling conditions are closely related to the depth of the extraction site, the withdrawal temperature, the dominant water or steam condition, and the thermo-physical characteristics of the fluid in the geographical area of interest. Therefore, the treatment that the geothermal fluid undergoes before entering the evaporator has not been simulated.

**Figure 2.** Organic Rankine Cycle (ORC) configuration.

**Table 2.** Chemistry composition of geothermal fluid for low-medium temperature sources.


Regarding the organic fluid, a lot of works have been conducted to choose the best fluid with optimum thermo-physical, economic, and environmental properties in coupling with a low-medium temperature source [71,72]. In particular, the working fluid selection depends on the heat source temperature and the condenser cooling fluid temperature as well as on the ORC size. Some analyses show that the organic fluids characterized by high critical temperature allow for the obtainment of a higher ORC cycle efficiency, but this condition is verified only for the fluids with high reduced pressure. Indeed, the high critical temperature determines substantial expansion ratios and low condensing pressures making these fluids suitable for low-temperature applications [73]. Besides, they allow for the avoidance of the technical problems related to low evaporation pressure [74], the obtainment of an acceptable pinch point temperature difference [75], and low costs associated with the exergy destruction even if they are strongly influenced by the amount of working fluid used [76,77]. Moreover, the use of

fluids with a molecular weight greater than that of water can improve the isentropic efficiency of the turbine and it may allow for the use of single-stage expander reducing the plant costs [78].

Thus, the pentafluoropropane (R245fa) is the organic fluid chosen in this application. It is suitable for different heat transfer applications such as low-temperature refrigeration, passive cooling devices, ORC for heat recovery, and in sensible heat transfer. The R245fa is useful for its special compatibility with widespread materials of construction as metals, elastomers, and plastics. It is also assessed for its good properties concerning human safety, health, and environmental aspects as toxicity, flammability characteristics, exposure limits, global warming potential, and safe product handling [79]. Calise et al. [80] have demonstrated that R245fa is the fluid with the best performance (in terms of heat exchange efficiency and environmental pollution) among other organic fluids in geothermal applications when geothermal brine temperature is lower than 170 ◦C.

The design of the PHEX is based on the manufacturer data of an ORC system available on the market [51].

#### **4. Methodology**

This section aims to elaborate a numerical algorithm for the shell and tube ORC evaporator design carrying out a comparison among different materials for HEX construction such as PEHD, carbon steel, and titanium. The model has been developed considering the nominal thermal power ( . *Qobj*) of the STHEX provided by an ORC manufacturer [63]. The numerical model is based on physical equations developed in a MATLAB/REFPROP environment [81,82]. The physical equations presented here are equal for all the analysed materials while the parameters used in the equations vary from one STHEX material to another. Moreover, the correlations for evaluating the heat transfer coefficient used to determine the heat transfer rates are linked to the working fluid phase (single-phase or two phases) and to its position (shell or tube). The flow chart of the numerical algorithm developed and implemented in a Matlab code is reported in Figure 3. At the initial step the fixed parameters are allocated, and thermodynamic (Table 3) and geometric (Table 4) parameters are assigned as well as the thermal conductivity variable for each investigated material. At the first step of integration (j = 1), R245fa temperature (Tt,o, tube side) is set equal to its outlet temperature indicated by constructor, while the temperature of hot geothermal brine (Ts,i) is set equal to the hot source temperature required from the evaporator (since the evaporator is a HEX in counter-flow configuration). The mass flow rates in the tube side ( . mt) and shell side ( . ms) are allocated too, according to values reported in Table 3. Then, in each iteration step the heat transfer coefficients (Equations (3)–(15)), the overall heat transfer coefficient (Equation (2)), and the elementary thermal power (Equation (1)) are evaluated. At step j+1, the geothermal brine temperature in the shell side (Ts (j+1)) and the specific working fluid enthalpy in the tube side (ht (j + 1)) are evaluated. Enthalpy at the tube side is obtained from REFPROP software.

This procedure must be repeated until the heat power target is achieved ( . *Qobj*). Finally, the total evaporator length L and the total heat exchanger surface (A) can be evaluated for each investigated material.

**Figure 3.** Flow chart of numerical algorithm.

**Table 3.** ORC nominal data [63].


**Table 4.** Shell and tube heat exchanger data.


#### *4.1. Model Equations*

The proposed configuration for counter-flow STHEX is shown in Figure 4. The working fluid (R245fa) flows in the tubes (with a total length named Lt and a diameter called di) while geothermal hot water crosses the shell with a diameter indicated as Ds and a length called LS.

**Figure 4.** Shell and tube heat exchanger model.

The Matlab model is developed to define the STHEX area needed to obtain the fixed evaporator thermal power for each selected material.

The STHEX modelling depends on the following assumptions:


MATLAB model calculates the infinitesimal thermal power for each dL in every iteration using Equation (1). The calculation process stops when the sum of the infinitesimal thermal power (δ . *Q*) is equal to the nominal thermal power of the evaporator ( . *Qobj*). The infinitesimal temperature difference (dT) between geothermal and R245fa fluids in each dL is evaluated using REFPROP library starting from two thermodynamic properties of fluids. The overall heat transfer coefficient (U) is evaluated as the reciprocal of the thermal resistance (R) in each dL defined as expressed in Equation (2).

$$
\delta \dot{Q} = \int\_0^\mathcal{L} \frac{\mathcal{dT} \cdot \mathbf{d} \mathcal{A}}{\mathcal{R}} \mathcal{dL} \tag{1}
$$

$$\mathbf{U} = \frac{1}{\mathbf{R}} = \frac{1}{\mathbf{R\_s} + \mathbf{R\_{5,f}} + \mathbf{R\_w} + \mathbf{R\_t} + \mathbf{R\_{t,f}}} = \frac{1}{\frac{1}{\mathbf{a\_s}} + \frac{1}{\mathbf{a\_t}f} + \mathbf{R\_w} + \frac{1}{\mathbf{a\_t}} + \frac{1}{\mathbf{a\_t}f}} \tag{2}$$

Thermal resistance considers the convective heat transfer process in the tube (Rt) and shell (Rs) side, fouling in the tube (Rt,f) and shell (Rs,f), and conductive heat transfer through wall material (Rw).

The correlations used to calculate the resistances in the shell and tubes are described in the following subsections. Additionally, the fouling resistances both in the shell and tube's side are constant and they depend upon the fluid.

#### *4.2. Shell-Side Model Equations*

The heat transfer convective coefficient into the shell side can be obtained considering the fluid in static condition assimilated to liquid water at a temperature range defined by the manufacturer. The convective coefficient for the shell side α<sup>s</sup> depends on the Nusselt number (*Nu*), the diameter of shell (DS) and thermal conductivity (ks) as reported in following Equation (3):

$$\alpha\_{\sf s} = \frac{N\iota \cdot \mathbf{k}\_{\sf s}}{D\_{\sf s}} \tag{3}$$

where the Nusselt number is calculated according to Equation (4) in laminar condition [83] and to Equation (5) for turbulent regime [84].

$$Nu = 1.04 \cdot \text{Re}^{0.4} \cdot \left(\frac{\text{Pr}}{\text{Pr}\_w}\right)^{0.36} \tag{4}$$

$$Nu = 0.023 \cdot \text{Re}^{0.8} \cdot \text{Pr}^{\text{u}} \tag{5}$$

In Equation (4) t Prw is the Prandtl number value on the wall. In Equation (5) *n* parameter assumes the value 0.300 if the shell side fluid is the cold one or 0.400 if it is the hot fluid. The Reynolds (Re) and Prandtl (Pr) numbers are defined as in Equations (6) and (7), respectively:

$$\text{Re} = \frac{\dot{\mathbf{m}} \cdot \mathbf{D}}{\mu \cdot \mathbf{A}} \tag{6}$$

$$\text{Pr} = \frac{\mu \cdot c\_p}{\text{k}} \tag{7}$$

where . m represents the mass flow rate, D is the diameter, A is the area, μ is the dynamic viscosity, *cp* is the specific heat at constant pressure, and k the thermal conductivity. Generally, α<sup>s</sup> is multiplied by a corrective factor *J* that considers different parameters such as the number of baffles and their configuration, dispersion, and losses in shells and deflectors, and losses in the nozzles and temperature gradients that could cause accumulations. The presence of the baffles which cut the diameter by 20.0%–45.0% allows for support and prevents vibrations and vortices in the pipes. In this work as suggested by the literature, *J* is equal to 0.60 [56].

#### *4.3. Tube Side Model Equations*

For the tube side of STHEX the organic working fluid (R245fa) chosen for the simulation is in phase-transition; therefore, it is not advisable to consider it as a liquid for all tubes length. It is necessary to distinguish if the fluid is in two-phase or single-phase condition for convective heat transfer coefficient (αt) evaluation. In a single phase condition, the equation used is Equation (5). In a two-phase condition α<sup>t</sup> corresponds to αtp expressed by the correlation of Gungor-Winterton [85] reported in Equation (8). It takes into account two contributions: a convective boiling term (αcb) and a nucleate boiling term (αNB).

$$
\alpha\_{\rm tp} = \mathbb{S} \cdot \alpha\_{\rm NB} + \mathbb{E} \cdot \alpha\_{\rm cb} \tag{8}
$$

where α*NB* term is calculated from Cooper correlation [86] (Equation (9)):

$$\mathbf{a}\_{\rm NB} = \mathbf{55} \cdot \mathbf{pr}^{0.12 - 0.2 \cdot \log\_{10} \mathbf{R} \cdot} \left( -\log\_{10} \mathbf{pr} \right)^{-0.55} \cdot \mathbf{M}^{-0.5} \cdot \mathbf{q}^{0.67} \tag{9}$$

M is molecular weight of the substance, pr represents the ratio between the operating pressure and critical pressure and q is the heat flow.

αcb term in Equation (8) is calculated from the Dittus–Boelter correlation that is employed to calculate the heat transfer of liquid only in the tubes (Equation (10)) [87]:

$$\alpha\_{\rm cb} = 0.023 \cdot \frac{\mathbf{k\_t}}{\mathbf{d\_i}} \cdot \text{Pr}\_{\mathbf{t}}^{1/3} \cdot \text{Re}\_{\mathbf{t}}^{0.8} \cdot \left(\frac{\mu\_{\rm t}}{\mu\_{\rm t,w}}\right)^{0.14} \tag{10}$$

where kt is thermal conductivity, and μ<sup>t</sup> and μt,w are the viscosity in the tube and wall, while Prt and Ret are Prandt and Reynolds numbers, respectively, referred to the tube side as well, as kt is the thermal conductivity of tube.

S (Equation (8)) shows the suppression factor of a nucleate boiling term that takes into account the decrease of fluid layer thickness as the vapour quality grows. E (Equation (8)) is the enhancement factor of the convective boiling process due to the increase of flow velocity when the vapour quality increases. The heat transfer coefficient is strongly and positively influenced by the vapour quality [88] and also by the frictional pressure gradient [89].

E and S factor are defined as in Equations (11) and (12), respectively:

$$\mathbf{E} = 1 + 24000 \cdot \left( \text{Bo}^{1.16} \right) + 1.37 \cdot \frac{1}{\chi\_{\text{tt}}}^{0.86} \tag{11}$$

$$\text{S} = \frac{1}{1 + 1.15 \cdot 10^{-6} \cdot \text{E}^2 \cdot \text{Re}\_{\text{l}}^{1.17}} \tag{12}$$

In Equation (12) Reynolds number is referred to liquid condition (*l*).

In Equation (11) two dimensionless numbers are considered: the Martinelli parameter (Xtt*)* and the Boling number (Bo) defined in Equations (13) and (14), respectively:

$$\mathbf{X\_{tt}} = (\frac{1-\mathbf{x}}{\mathbf{x}})^{0.9} \cdot (\frac{\rho\_{\rm v}}{\rho\_{\rm l}})^{0.5} \cdot (\frac{\mu\_{\rm v}}{\mu\_{\rm l}})^{0.1} \tag{13}$$

$$\text{Bo} = \frac{\text{q}}{\text{G}\_{\text{t}} \lambda\_{\text{l}, \text{v}}} \tag{14}$$

where x is the title, ρl, ρ<sup>v</sup> are density in liquid and vapour condition, λ represents the latent heat and Gt is the flow rate in the tube.

#### *4.4. Case Study*

As before mentioned, the PHEX design is based on the manufacturer's data of an ORC system available on the market that delivers 30.0 kWel with a primary power input equal to 450 kWth.

In Table 3 the ORC module parameters that were considered for the modelling and simulation analysis are reported.

The geometrical construction data of the STHEX are referred to the schedule of PHEX company and they are listed in Table 4, while in Table 5 the thermal conductivity of simulated materials (kw) are showed.

**Table 5.** Thermal Conductivity of simulated Materials.


#### **5. Results**

The numerical algorithm has been employed with the aim of returning the heat transfer area (A) at the manufacturer's conditions for each considered material. The evaporator area needed to provide the required electric output, for the simulated ORC system is higher in the case of plastic material with respect to the other ones. In particular, the increase percentage between *A* of PHEX and HEX in carbon steel amounts to 48.5%. The percentage decreases to 47.5% and 47.0% if the PHEX's area is compared to area of a HEX made of inox steel and titanium, respectively. The difference among the area values is mainly due to the conductive and fouling resistance since the convective coefficients are similar for each material. In Figure 5 the values of the overall heat transfer coefficients and the heat transfer area of STHEX in plastic and metal materials are shown. As expected, PHEX provides the lowest value of U (88.5 W/m2K) and its contemporary needs the highest A (524 m2).

STHEX length and the heat transfer coefficient are summarized in Table 6 for all considered materials. The length as well as the heat transfer area (Figure 5) are evaluated by summing the values in each iteration step, while UA and U values are calculated in each iteration. Table 6 and Figure 5 average values of UA and U weighted on the infinitesimal area are listed, respectively.


**Table 6.** Simulation results data.

The purchase cost (*PC*) evaluation for STHEX made of common steel materials (inox steel and carbon steel) is carried out by means of a literature correlation (Equation (15)) suitable for evaporators at high-pressure conditions [90]:

$$PC = 190 + 310 \text{ A} \tag{15}$$

On the other hand, the evaluation of plastic and titanium STHEX costs have been conducted through a market analysis. The comparison is based on PC neglecting the maintenance and cleaning cost. In Figure 6 PCs for a PHEX (green bar) and metal materials (orange bars) are showed. The purchase cost of a STHEX in plastic material (27,597€) is significantly lower than a titanium STHEX (56,155€) while it is higher than a STHEX in inox steel (14,595€) and carbon steel (14,265€). Nevertheless, the economic comparison aimed to evaluate PC saving is relevant only between PHEX and HEX in titanium since in these two cases,the life cycle of two components are equal [91] and it is possible to neglect the cleaning cost for both STHEXs. Thereby, the percentage reduction of PC between PHEX and titanium STHEX is

48.0%. This reduction can have a significant weight for ORC plant investment costs since the unitary specific cost of the overall system is high.

**Figure 6.** Length of tubes and purchase cost for different materials STHEXs.

In Figure 7 the convective heat transfer coefficient for the tube αt, Figure 7a), for the shell αs, Figure 7b) and overall heat transfer coefficient (U, Figure 7c) are shown as a function of heat exchanger length. These trends result from simulations in a MATLAB/REFPROP environment.

Since STHEX is in counter flow configuration, at L equal to 0 m (that represents the end of length integration) the geothermal brine is in inlet condition in the shell and the organic fluid is in the outlet condition of tubes side.

As reference to α<sup>t</sup> (Figure 7a) at the integration start point of the evaporator (L = 0 m) the organic fluid in tubes is in satured vapour condition. Subsquently, α<sup>t</sup> increases assuming a bell curve shape, and in this condition the organic fluid is in a two-phase state. As a matter of fact, in the two-phase condition the convective heat exchanger coefficient (αcb) is characterized by two contributes (a convective boiling term αNB and a nucleate boiling term αNB) as reported in Equation (8). After that, α<sup>t</sup> decreases and the curves becomes flat near the exit of the evaporator when the R245fais in the liquid condition (the condition of inlet state in STHEX) and the convective heat transfer coefficient is calculated through (Equation (10)). α<sup>t</sup> curves for all metal materials have the same trend and are very similar; indeed, they are almost overlapping. α<sup>t</sup> curve for plastic material has a larger bell, even if it shows the same trend of the metal materials' α<sup>t</sup> curves. For this reason, if an L value is assigned, α<sup>t</sup> value in metal STHEXs is very different from the α<sup>t</sup> value of PHEX (for example for L = 5 m α<sup>t</sup> is equal to 4024 W/m2K and 3601 W/m2K for PHEX and titanium, respectively). α<sup>s</sup> (Figure 7b) shows a decreasing trend and it is proportional to the geothermal brine temperature; therefore, during the fluid cooling the efficiency of heat exchange is down. At the evaporator integration starting point (L = 0) geothermal fluid has a high temperature, and so also α<sup>s</sup> is high. Then it decreases with the increase of length for all materials. α<sup>s</sup> stops at L = 12.2 m for PHEX because it is the needed length to ensure the required ORC electric output. In Figure 7 Rw, αs,f, and αt,f are not shown even if they are accounted for in the overall heat exchanger coefficient evaluation according to Equation (2). They are constant along whole STHEXs and they are calculated as following: Rw depends upon kw of each material reported in Table 5, while αs,f and αt,f are the reciprocal of Rs,f and Rt,f evaluated for the geothermal brine and R245fa, respectively, according to values listed in Table 4. The overall heat transfer coefficient Figure 7) follows α<sup>t</sup> trend for all materials since this term has the higher weight in Equation (2). Among metal materials the carbon steel STHEX has the highest U for a fixed L value since it shows the greatest kw. PHEX has the lowest U for along whole evaporator.

**Figure 7.** Convective heat transfer coefficient on tube side (**a**) and shell side (**b**) and overall heat transfer coefficient (**c**) as a function of evaporator length.

#### *Sensitivity Analysis*

The Figure 8 reports the purchase cost and the needed heat transfer area value for a STHEX made of PEHD and titanium by varying the inlet temperature of geothermal brine in the range 94–99 ◦C. The temperature range for this sensitivity analysis is chosen considering the temperature availability of geothermal brine in selected sites and the possible operating couple temperature-pressure in polymeric heat exchanger applications. These values of inlet temperature allow the use of the same correlation (Equations (3)–(7)) for the shell side of the main case analysed. In Figure 8 the values in red points and red bars correspond to the inlet geothermal fluid temperature provided by the manufacturer (94 ◦C). The PC and the heat transfer area diminishes with the increment of inlet temperature of geothermal sources in both PEHD and titanium evaporators.

**Figure 8.** Purchase cost and area of evaporator in PEHD and titanium as a function of inlet temperature of geothermal brine.

In particular, the reduction of the heat transfer area for each degree of geothermal brine inlet temperature increase is higher for the PEHD evaporator than the titanium one. Vice versa, referring to PC the cost reduction is more rapid for the titanium than the PEHD evaporator. For example, by going from T = 95 ◦C to T = 96 ◦C the reduction of PC amounts to 2633€ for PHED and to 5612€ for titanium. Considering the same temperature range, the heat transfer area reduction is equal to 8.4 m2 for the PHED evaporator and 4.7 m<sup>2</sup> for the titanium STHEX. In particular, the installation of the titanium STHEX evaporator in an ORC plant is responsible of an extra-cost equal to 28,558€ with respect to the PHED one when the inlet temperature of geothermal brine is 94.0 ◦C. This extra-cost ranges from 25,578€ to 17,799€ when the inlet temperature changes in the range of 95.0–99.0 ◦C. On the other hand, the heat transfer area growth by using a PHED evaporator instead of a titanium one varies from 41.6 m2 to 29.8 m2, when the inlet temperature of geothermal fluid goes from 94 ◦C to 99 ◦C.

#### **6. Conclusions**

Organic Rankine Cycle technologies are employed worldwide in different fields. Among other applications, this work is focused on ORC plants using a geothermal source. Such systems are affected by different issues: a corrosive heat source, low exercise temperatures, and high specific costs, thus evaporator cost has a great weight on the overall plant costs. These problems can be making possible the using of plastic evaporators instead of traditional ones made of metal materials with a high cost and a low corrosion resistance.

For these reasons in this work a one-dimensional model of a heat exchanger used as an evaporator in an ORC available on market, has been realized. The design modelling is grounded on physical equations describing the organic and geothermal fluid behaviours. The choice of installation site for the ORC plant (Phlegrean Fields, South of Italy) and the definition of working fluid have been conducted according to an analysis of the chemical composition of geothermal brine available in the chosen installation area.

The numerical model implemented in the MATLAB/REFPROP environments has been used to define the design properties of the plastic evaporator used to replace a metal one in the selected ORC plant. Furthermore, a comparison between plastic evaporator geometrical parameters and costs with those of evaporators made of titanium, inox steel, and carbon steel, has been carried out. The main outcomes of the simulation analysis can be summarised as following:


As a general consideration, this work assesses that the plastic evaporators used in geothermal ORC plant can, therefore, be chosen nowadays as an encouraging technological option in order to reduce costs in small size plants. The analysis results can also be used to design the plastic evaporator for other ORC plants available on the market. Furthermore, the use of an ORC plant activated by a geothermal source allows us to address three goals:


In future works, a sensitivity analysis varying the evaporator thermal power or its geometry and fluid distribution could be conducted in order to analyse the effect of the replacement of a metal evaporator with a plastic one in these new cases. In addition, the numerical model of a plastic heat exchanger can be used to design other ones exploited in direct geothermal ways too, such as the thermal heating networks.

**Author Contributions:** F.C., A.M., E.M., M.S. and L.V. contributed to the design and implementation of the research, to the analysis of the results and to the writing of the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding

**Acknowledgments:** The authors gratefully acknowledge the financial support of GeoGrid project POR Campania FESR 2014/2020 CUP B43D18000230007.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Nomenclature**



#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Thermo-Economic Analysis of Hybrid Solar-Geothermal Polygeneration Plants in Di**ff**erent Configurations**

#### **Francesco Calise, Francesco Liberato Cappiello \*, Massimo Dentice d'Accadia and Maria Vicidomini**

Department of Industrial Engineering, University of Naples Federico II, 80125 Naples, Italy; frcalise@unina.it (F.C.); dentice@unina.it (M.D.d.); maria.vicidomini@unina.it (M.V.)

**\*** Correspondence: francescoliberato.cappiello@unina.it

Received: 8 April 2020; Accepted: 5 May 2020; Published: 11 May 2020

**Abstract:** This work presents a thermoeconomic comparison between two different solar energy technologies, namely the evacuated flat-plate solar collectors and the photovoltaic panels, integrated as auxiliary systems into two renewable polygeneration plants. Both plants produce electricity, heat and cool, and are based on a 6 kWe organic Rankine cycle (ORC), a 17-kW single-stage H2O/LiBr absorption chiller, a geothermal well at 96 ◦C, a 200 kWt biomass auxiliary heater, a 45.55 kWh lithium-ion battery and a 25 m2 solar field. In both configurations, electric and thermal storage systems are included to mitigate the fluctuations due to the variability of solar radiation. ORC is mainly supplied by the thermal energy produced by the geothermal well. Additional heat is also provided by solar thermal collectors and by a biomass boiler. In an alternative layout, solar thermal collectors are replaced by photovoltaic panels, producing additional electricity with respect to the one produced by the ORC. To reduce ORC condensation temperature and increase the electric efficiency, a ground-cooled condenser is also adopted. All the components included in both plants were accurately simulated in a TRNSYS environment using dynamic models validated versus literature and experimental data. The ORC is modeled by zero-dimensional energy and mass balances written in Engineering Equation Solver and implemented in TRNSYS. The models of both renewable polygeneration plants are applied to a suitable case study, a commercial area near Campi Flegrei (Naples, South Italy), a location well-known for its geothermal sources and good solar availability. The economic results suggest that for this kind of plant, photovoltaic panels show lower pay back periods than evacuated flat-plate solar collectors, 13 years vs 15 years. The adoption of the electric energy storage system leads to an increase of energy-self-sufficiency equal to 42% and 47% for evacuated flat-plate solar collectors and the photovoltaic panels, respectively.

**Keywords:** hybrid renewable polygeneration plant; micro organic Rankine cycle; evacuated solar thermal collectors; photovoltaic panels

#### **1. Introduction**

Polygeneration plants based on renewable energy sources (RES) (geothermal, solar, biomass, wind and hydro), represent a suitable solution to reach the long-term goals expected by 2050, i.e., a reduction of greenhouse gas emissions by 80%–95% with respect to 1990 levels and a 100% renewable electrical system. These targets are potentially achievable by considering that policies will continue to support renewable electricity worldwide, increasingly through competitive actions rather than feed-in tariffs, and by the transformation of the power sector amplified by rapid deployment of solar photovoltaic (PV) panels and wind turbine. An RES polygeneration plant can replace the existing conventional technologies based on fossil fuels and simultaneously produce several energy vectors

(thermal, cooling and electric energy) and other outputs, by reducing significantly the primary energy consumption and CO2 emissions [1].

Several studies presented in literature about renewable polygeneration plants investigate the integration of renewable systems with different conventional systems: electric heat pump, trigeneration, gas-fired boiler, district heating and cooling and combined heating, cooling and power CHCP plants [2] for different purposes and application. In the context of power plants, the organic Rankine cycles (ORCs) [3] represent an interesting opportunity when coupled with low-medium enthalpy energy sources (biomass products [4], geothermal [5], solar [6,7], waste heat [8], ocean thermal energy [9], etc.). ORC plants adopt specific organic fluids showing an energy performance considerably better than water used in the conventional Rankine cycles, due to a higher molecular weight, lower evaporation heat, positive slope of the saturated vapor curve in the T–s diagram and lower critical and boiling temperatures [6]. In addition, for small scale units, ORC turbines are today an interesting technology, demonstrating several advantages in terms of operation life, maintenance and part-load efficiency.

Although the rapid increase in PV application, it is well-known that solar electric production is extremely variable due to the fluctuations of the solar radiation. This leads to an important increase in the electricity bought from the grid during the night, when the PV production is null, and during low solar availability hours, with the consequent reduction of the plant profitability. Therefore, the hybridization of different power systems (PV panels, PV and thermal (PVT) panels, wind turbines, ORC power plants) and the adoption of suitable electricity storage systems (ESSs) [10] with the proper ESS size determination in renewable energy systems [11] to obtain a more stable availability of the electric energy production, is an attractive solution to be investigated.

The simulation of polygeneration plants based on ORC power plants supplied by low and medium-temperature energy sources is diffusely investigated in the literature. Particularly, the integration of solar and geothermal sources is one of the most attractive configurations, mainly in volcanic areas featured by high solar radiation availability [6]. Thermal energy sources at low and medium temperature, typically within 90–130 ◦C, obtainable by solar and/or geothermal ones, are often used as input for supplying absorption chillers (ACH), multi-effect distillation (MED) systems and ORC in a unique renewable polygeneration plant. In the following section, an overview of the renewable power plants based on ORC technology coupled with PV/PVT panels and/or low-temperature geothermal energy is provided. In addition, studies investigating the combination of several thermal activated technologies (ACH, MED, ORC, etc.) in different plant configurations are also reported.

A hybrid solar and geothermal polygeneration plant, producing thermal energy for solar space heating/cooling (SHC), domestic hot water (DHW), fresh water and electric energy was studied by Calise et al. [6]. The plant includes different technologies: geothermal wells at about 80 ◦C, concentrating photovoltaic and thermal (CPVT) collectors, producing heat at about 100 ◦C, a single-stage LiBr/H2O ACH and a MED unit. The low-enthalpy geothermal energy, combined with the solar thermal energy, supplies the MED unit for fresh water production. Geothermal energy is also used to produce DHW at 45 ◦C. A dynamic simulation model is developed to simulate the whole plant performance and is applied to a suitable case study, the Pantelleria island and further volcanic Mediterranean islands. The pay back periods achieved for all the examined weather zones were extremely low, equal to about two years. Cheng Zhou [12] investigated a solar–geothermal hybrid plant, consisting of parabolic trough collectors, an ORC machine and a geothermal well at about 150 ◦C. Isopentane working fluid is adopted as working fluid and the ORC machine performance is evaluated by considering the subcritical and supercritical cycle. The studied ORC uses an air-cooled condenser for the condensation process and the exhaust fluid from the turbine by means of a recuperator. To perform the plant simulations, the Aspen HYSYS simulation tool is adopted. The supercritical ORC plant exhibits the better performance, producing from 4% to 17% more power and presenting from 4% to 19% lower solar-to-electricity cost with respect to the subcritical ORC plant.

The performance evaluation of several types of PV materials (silicon, gallium arsenide, indium phosphide, cadmium sulfide and triple-junction indium gallium phosphide/indium gallium arsenide /germanium) in a system producing electricity using PV panels and utilizing the waste heat from the cells to drive an ORC is investigated by Tourkov and Schaefer [13]. Here, the performance of a variety of fluids as working fluids for the ORC is analyzed. It was found that n-butane is the optimal selection for the proposed application and that triple-junction cells at high concentration combined with an ORC were able to achieve over 45% solar efficiency. Kosmadakis et al. [14] carried out an experimental investigation of a small-scale low-temperature ORC machine coupled with CPVT collectors. R404A is selected as working fluid. The CPVT collectors produce electricity and heat and supply it to the ORC. The tests showed that such low-temperature ORC unit exhibits a fair efficiency and that its coupling with a solar field was feasible, increasing the power production of the whole system. The most important result from the laboratory tests is that the ORC machine with a capacity of 3 kW reached an adequate thermal efficiency, about 5%, when operated at a very low temperature. An energy and exergy analysis of a hybrid polygeneration plant based on solar collectors and medium-high enthalpy geothermal sources is presented by Bicer and Dincer [15]. The plant is designed for simultaneously producing electricity, drying air, hot water and space heating and cooling. The heat provided by the geothermal energy and an air PVT drives an ORC for producing power. The ORC waste heat is employed for the activation of a LiBr/H2O ACH, which provides the energy for space cooling of a dairy farm. Whereas the energy for space heating is provided by an electric heat pump. Moreover, the outlet hot air provided by the PVT collectors was employed for the food drying process of the farm. The polygeneration plant here proposed achieved global exergy and energy efficiencies of 28% and 11%, respectively. The energy and exergy efficiencies of the ORC were 9% and 42%, respectively. The air PVT collectors reached an exergy efficiency of 12%. The COP and exergy of the ACH and electric heat pumps were 0.73 and 0.21, and 4.1 and 0.03, respectively. The optimal design of a hybrid solar power generation system for isolated zones, consisting of PV panels, diesel generators, batteries and an ORC machine is addressed in the work of Noguera et al. [16]. The novelty of this study is the adoption of the heat recovery of the exhaust gases from the diesel generator to supply the ORC machine. The selected objective function is the cost of power generation by considering as variables the nominal power of the diesel generator and the number of PV panels and batteries. Simulation results for the selected case study, the Cujubim city in Rondônia State, suggest that the optimized diesel-ORC-PV-battery hybrid system, including 6288 kW diesel generators, is able to obtain a generation cost of \$0.301/kWh, reduced approximately of 38.15% in comparison with the generation cost of a diesel system.

The above-presented literature review shows that numerous studies have examined the use of the waste heat from PVT panels for various applications, whereas there is limited research about the optimization of a combined PV panels/ORC machine system [13]. This combination could present a potential benefit in terms of efficiency and electricity cost if compared with the one of concentrating PV panels. Also, the reported literature review shows hybrid renewable energy polygeneration plants supplied by geothermal and solar energy, based on thermally-activated technologies and ORC, are investigated in different and several plant configurations. These works often examined medium-high scale ORC, with the exception of the ORC machines presented in references [5,14]. Specifically, the work presented in reference [5] is developed by some of the authors of this paper. Here a 6 kW micro-scale ORC machine supplied by solar and geothermal energy is investigated. In particular, a 25 m<sup>2</sup> solar field consisting of flat-plate evacuated thermal collectors (ETCs) is coupled with a geothermal well at 96 ◦C to produce DHW, thermal energy, cooling energy by a single-stage LiBr/H2O ACH and electricity by an ORC, for a hotel located in Ischia (South Italy). With respect to the paper presented in reference [5], where all the outputs produced by the plant are assumed to be fully consumed by the user, in this study the power production and the heat produced for space heating and cooling must match the real time-dependent loads of the investigated user, a commercial building located in Campi Flegrei, a famous volcanic area of Naples (South Italy). In addition, this paper also includes a further significant improvement, with respect to work reported in reference [5], since it presents a thermoeconomic comparison between two different solar layouts: in the first one, solar energy produced by ETC collectors is converted into electricity by an ORC; the second

layout refers to a more mature and simple configuration where ETCs are replaced by PV panels, operating independently from the ORC, supplying additional electricity to the system. In other words, this work aims to compare an innovative complex solar geothermal plant with a simpler configuration including PV collectors, considering both energy and economic aspects. Finally, this paper also includes additional novelties: (i) in order to increase the renewable energy source utilization, both renewable polygeneration plants include a biomass auxiliary heater; (ii) an electric energy storage system based on lithium-ion technology is used to mitigate power production fluctuations; (iii) a ground-cooled condenser in order to provide the required cooling energy to the ORC and to the ACH.

#### *Aim of the Study*

In this paper, dynamic simulation models of two hybrid renewable polygeneration plants based on a micro-scale ORC machine coupled with a single-stage LiBr/H2O ACH for producing power, heating and cooling are developed. The dynamic modeling involves the hybridization of geothermal, solar and biomass energy, thermal and electric energy storage systems. The thermoeconomic performance of two hybrid renewable polygeneration plants (the first based on ETCs and the second one on PV panels) are also compared. The dynamic energy models, developed by the means of the well-known TRNSYS software, include the modeling of complex operation control strategies and all the included technologies: ETCs, PV panels, micro-scale ORC, ACH, biomass auxiliary heater, lithium-ion energy storage, commercial building and all the other system components as storage tanks, heat exchangers, diverters, pumps, mixers, controllers and fan coils. From the achieved results interesting design and operating guidelines can be usefully provided for similar renewable polygeneration plants located in zones where both solar and geothermal energy are available.

#### **2. System Layouts**

The layouts of both the renewable polygeneration plants (Cases ETC and PV) are shown in Figure 1. They mainly consist of a low-temperature geothermal well (at 96 ◦C, depth 94 m), equipped with a submerged geothermal brine pump and a downhole heat exchanger, 25 m2 of solar field (ETCs or PV panels), 6 kW ORC machine, 200 kW auxiliary biomass-fired heater (AH), 17 kWf H20/LiBr single-stage absorption chiller (ACH), stratified vertical storage tanks, ground-coupled heat exchangers, 45.55 kWh lithium-ion energy storage system (ESS), equipped with an inverter and a 308.5 m<sup>2</sup> commercial building. Note that the size of the PV and ETC field are assumed equal, in fact, the aim of the proposed analysis consists of studying the performance of these two layouts occupying the same surface. This is due to the fact that the considered zone is not too vast and, therefore, occupying less space is a remarkable positive aspect. The adoption of the ground-coupled heat exchangers allows one to enhance system efficiency since both ACH and ORC efficiency significantly increases when the temperature of the cold sink decreases. During the summer season, ground temperature is significantly lower than the air temperature. Conversely, in winter, ground temperature may be higher than that of the air. In this case, using outdoor air as a cold sink would be more efficient than the use of ground. However, for this specific case, the additional cost of an air cooler would not be balanced by the income determined by the higher ORC electrical production. Therefore, it is assumed to use the ground-coupled heat exchanger all year long. Note that in the ETC case, ORC is driven by the combination of geothermal energy and solar energy supplied by ETCs. Finally, additional auxiliary heat is supplied by the biomass auxiliary heater, AH, which is used in order to achieve the minimum ORC activation temperature. Conversely, in the PV Case, the ORC is only supplied by geothermal energy and by the biomass AH. The overall electrical production is due both to the ORC and to the PV panels. The geothermal source supplies energy for both building space heating and cooling. In particular, the geothermal heat is directly exploited for building space heating, whereas the cooling energy is provided by an absorption chiller driven by the geothermal heat. The power demand of the user is met by the power production of the ORC (Case ETC) or by the power production of the ORC and PV panels (PV Case), by the electric energy stored in the lithium-ion battery and by the electricity withdrawn from the grid.

**Figure 1.** Systems layout: Case evacuated thermal collector (ETC, above) and Case photovoltaic (PV, below).

The layout of the examined plant consists of eleven main circuits:

• The solar fluid (only in Case ETC), which describes the diathermic oil flowing between the stratified vertical storage solar tank (TKs) and the evacuated flat-plate solar collectors (SC) and TKs and the ORC evaporator (EV);


**Figure 2.** Building geometrical model.

Table 1 in detail reports the fluids adopted in each heat exchanger installed in the plant, the pumps and their seasonal scheduling.

According to the activation season of the several pumps and heat exchangers, during the winter season, D2 and D1 divert the geothermal brine and the geothermal hot water to HE2 and HE1, with the aim of heating the diathermic oil and obtain the minimum activation temperature of the ORC, i.e., *Tmin,act,ORC*, equal to 90 ◦C. The outlet temperature of the geothermal hot water from HE1 is exploited for providing thermal energy for the building space heating. The geothermal hot water is delivered to the tank of the user circuit (TKu) by M3. Then, the water is supplied by the P8 constant speed pump

from TKu to the fan coil unit with the aim of reaching the selected set point indoor temperature, *Tset,heat*, equal to 20 ◦C.


**Table 1.** Heat exchangers and pumps.

\* The selected diathermic oil is a mixture consisted of biphenyl and diphenyl oxide. The analytical functions of the fluid properties are obtained by producer datasheets [17].

After the first preheating, performed by the geothermal thermal energy (HE1 and HE2), the diathermic oil is stored in the tank of the solar circuit. Then, the evacuated solar collector further heats the diathermic oil, to the selected set point temperature, *Tset,SC*, equal to 130 ◦C. The operation of the solar fluid loop is managed by a feedback controller, which varies the flow rate of the variable speed pump P2. Therefore, the controller tries to reach the outlet set point temperature *Tset,SC*, reducing the P2 flow rate. In addition, the controller stops pump P2 if the TKs bottom temperature is higher the outlet temperature of the solar collector, for preventing the dissipation of the thermal energy stored in the TKs. The P3 constant speed pump supplies the diathermic oil at a variable temperature to the ORC evaporator. In particular, the ORC feeding temperature ranges from 90 to 130 ◦C. When the top temperature of the tank TKs is lower than *Tmin,act,ORC*, a biomass condensing boiler is activated, increasing the temperature of the diathermic oil to *Tmin,act,ORC*.

During the summer season, the geothermal hot water is diverted to HE3 by D1, where the geothermal brine, diverted by the D2, further heats the geothermal hot water. This strategy allows the plant to reach a stable feeding temperature of the absorption chiller.

ACH is not in operation until the *Tbottom,TKu* ranges between 6.5 ◦C and 15 ◦C (Table 2), then, in this case, also during the summer season, D2 and D1 respectively divert the geothermal brine and the geothermal hot water to HE2 and HE1, with the aim of increasing the thermal energy availability for the ORC machine. The constant speed pump P8 is activated for supplying the chilled water to the fan coil units, in order to achieve the selected set point indoor temperature, *Tset,cool*, equal to 26 ◦C.


**Table 2.** Design and operating parameters (1).

Finally, M2 collects the geothermal brine exiting from HE3 and HE2, in order to exploit the waste heat of the geothermal brine for producing domestic hot water in HE4.

Note that due to the lack of a cold-water source the condenser of the ORC and ACH are cooled by ground-coupled heat exchangers HE6 and HE5.

The power produced by the ORC expander (Case ETC) and by the ORC expander and PV panels (Case PV) is delivered to the user through the regulator/inverter. When the power produced is greater than the power demand, including the power supplied to the auxiliary hydronic systems, the surplus power is employed for charging the lithium-ion battery. Note that the charge of the battery is allowed only if the battery state of charge (*SoC*) ranges between the low and the high safe limit, assumed to be equal to 0.05 (*SoCinf*) and 0.95 (*SoCsup*), respectively (Table 2). Note that if the lithium-ion battery is completely charged, and the building electric load is absent, the surplus power is delivered to the electric national grid. Finally, when the power produced and the stored energy in battery are not sufficient to match the power demand, the power is withdrawn from the electric national grid.

The adoption of a lithium-ion battery is affected by some criticism regarding the battery overheating as explained by many literature works [18–20]. The battery overheating is a dangerous aspect for the lithium-ion battery use, in fact, it may cause the battery to explode in the worst case but causes the degradation of the battery integrity and consequently the deterioration of its energy performances and the reduction of battery life-cycle [18–20]. This problem is caused by the high current intensity during the phase of charge and discharge of the battery, in fact, high current intensity leads to an increase of the temperature inside the battery. In conclusion, in order to prevent this problem, many literature works ([19,21,22]) suggest limiting the discharge/charge power with respect to the maximum value (assumed equal to the power required to fully charge/discharge the battery in one hour). Therefore, the maximum allowed discharging/charging power is assumed to be equal to the power that would discharge/charge the battery in 4.5 h, in order to achieve a battery life of 10 years [23].

#### **3. System Model**

The dynamic simulation models simulating the two renewable polygeneration plants shown in Section 2 are developed in the TRNSYS environment (version 17). This is a tool widely adopted both in academic and commercial areas. Some plant components (heat exchangers, ACH, building, energy storage system, controllers, mixers, diverters, pumps, tanks, fan coil units, inverter, etc.) are simulated by the "types"(i.e., libraries) included into the TRNSYS library, whereas the models of the ORC machine and the geothermal well are developed by the authors of this work and presented in reference [5]. In this section, the models of the main components of both compared cases (Cases ETC and PV), i.e., the flat-plate ETCs and the PV panels and thermoeconomic model developed for evaluating the economic and energy performance of both plants are reported in detail. Note that the reliability of the results achieved by the developed models is based on the fact that all the components adopted are validated vs experimental data [24], vs data available in literature and/or based on manufacturers' data.

The data concerning the design and operating parameters of the main components of both the plants and the building simulation data are summarized in Tables 2–4. Conversely, the data concerning the ORC machine and geothermal well are reported in reference [5].

**Figure 3.** Daily electric load for a typical summer day (**left**) and for a typical winter day (**right**).


#### **Table 3.** Design and operating parameters (2).

**Table 4.** Building simulation data.


#### *3.1. Evacuated Thermal Collector Model*

The flat-plate evacuated solar collectors are modeled by considering the high-vacuum HT-Power collectors (version 4.0), designed and manufactured by the TVP Solar company [25]. In particular, the model, validated by several outdoors and indoors experimental campaigns, is based on a modified version of TRNSYS Type 132 [26], which considers the Hottel–Whillier equation integrated with the incidence angle modifier (IAM) coefficients (determined by the tests according to EN 12975 and EN 12976 [27]) and takes into account the wind effect on the zero loss efficiency, the wind influence on the heat losses and the long-wave irradiance dependence of the collector. Therefore, the heat transferred from the ETC per unit aperture at each time-step is:

$$\begin{cases} Q\_{th} = F' \cdot \left( \tau \alpha \right)\_{\text{eff}} \cdot \left[ \left[ 1 - b \mathbf{\cdot} \left( \frac{1}{\cos \theta\_b} - 1 \right) \right] \cdot G\_b + K\_{\ell \ell d'} \cdot G\_d \right] - a\_1 \cdot \left( t\_m - t\_d \right) \\\ -a\_2 \cdot \left( t\_m - t\_a \right)^2 - a\_3 \cdot \mathbf{u} \cdot \left( t\_m - t\_a \right) - a\_4 \cdot \left( E\_L - \sigma T\_a^4 \right) - a\_5 \cdot \frac{dt\_m}{dt} - a\_6 \cdot \mathbf{u} \cdot \mathbf{G} \end{cases} \tag{1}$$

where *F* ·(τα)*en* is the zero loss efficiency of the collector at normal incidence angle for the solar radiation onto the collector, *K*θ*<sup>d</sup>* is the IAM for diffuse radiation, *Gb* is the beam of solar radiation, *Gd* is the diffuse radiation, the factor reported in square brackets is the incidence angle modifier (IAM) for beam radiation (*b0* is the IAM determined by the collector test, θ*<sup>b</sup>* is the incidence angle for beam radiation onto the solar collector plane). The description of the coefficients of Equation (1) and their numerical values are reported in Figure 3.

#### *3.2. PV Panel Model*

The PV panel model is based on the so-called "four parameters" model, which is implemented by the Type 94 using the manufacturers' data and generating the IV curve every time step. The four parameters used are: (i) *IL,ref*, the photocurrent of module at reference condition; (ii) *I0,ref*, the diode reverse saturation current at reference condition; (iii) γ, the empirical PV curve-fitting parameter; (iv) *Rs*, the module series resistance. The main assumption of the model is that the slope of the IV curve at the short-circuit condition is zero. By considering *Rs* and γ to be constant, the current–voltage equation of the circuit is:

$$I = I\_{l,ref} \frac{G\_T}{G\_{T,ref}} - I\_{o,ref} \left(\frac{T\_c}{T\_{c,ref}}\right)^3 \left[\exp\left(\frac{q}{\gamma kT\_c} \left(V + IR\_s\right)\right) - 1\right] \tag{2}$$

where the current *I* is a linear function of *GT*, the total incident solar irradiance on the PV panel and *GT,ref*, the reference solar irradiance and depends on the temperature at the reference open-circuit condition *Tc*.

The current (*Impp*) and the voltage (*Vmpp*) at the maximum power point are evaluated by means of an iterative routine. Thus, the system of equations, that describes the four equivalent circuit characteristics, is solved. The first step is to substitute the voltage and current into Equation (2) at the short circuit, open-circuit and maximum power conditions. After some handling, one obtains the following three equations, that depend on *IL,ref* (Equation (3)), γ (Equation (4)) and *I0,ref* (Equation (5)).

$$I\_{L,ref} \approx I\_{sc,ref} \tag{3}$$

$$\gamma = \frac{q\left(V\_{mp,ref} - V\_{ac,ref} + I\_{mp,ref}R\_s\right)}{kT\_{c,ref}\ln\left(1 - \frac{I\_{mp,ref}}{I\_{sc,ref}}\right)}\tag{4}$$

$$I\_{o,ref} = I\_{sc,ref} \exp^{-(\frac{qV\_{oc,ref}}{\gamma kT\_{c,ref}})} \tag{5}$$

Another equation is needed to determine the last unknown parameter, i.e., the temperature coefficient of open-circuit voltage. This parameter is obtained by the analytical derivate of voltage *Voc* with respect to *Tc*:

$$\frac{\partial V\_{\rm oc}}{\partial T\_{\rm c}} = \mu\_{\rm rec} = \frac{\gamma k}{q} \left[ \ln \left( \frac{I\_{\rm sc,ref}}{I\_{\rm o,ref}} \right) + \frac{T\_{\rm c} \mu\_{\rm isc}}{I\_{\rm sc,ref}} - \left( 3 + q \varepsilon \left( \frac{\mathcal{Y}}{N\_{\rm s}} kT\_{\rm c,ref} \right)^{-1} \right) \right] \tag{6}$$

where μ*isc* is the temperature coefficient of short-circuit current, *Ns* is the number of individual cells in a module, *q* is the electron charge constant, *k* is the Boltzmann constant, ε is the semiconductor bandgap. The manufactures' specification about the open circuit temperature is equal to this analytical value. Therefore, a search routine is used iteratively to evaluate the equivalent open circuit characteristics.

#### *3.3. Thermoeconomic Model*

The energy and economic performance of both the renewable power plants are evaluated by the calculation of the primary energy saving (*PES*) and the simple pay back period (SPB) index. With this aim in mind, a suitable conventional reference system (RS) is selected to compare each plant with the same RS. The RS consists of a conventional vapor-compression chiller and a gas-fired heater for cooling and thermal energy production, respectively, whereas the national grid is the conventional system providing the electric energy to the user. The achievable *PES* by both renewable plants, in terms of electric, heating and cooling energy savings vs the conventional RS is calculated as in Equation (7).

$$PES = \sum\_{t} \left[ \frac{\left(\frac{E\_{d,d\text{win},t} + E\_{d,d\text{win},t}}{\eta\_{d,t}} + \frac{Q\_{th,H\text{NG},\text{ymbar},t,t} + Q\_{th,H\text{NG},\text{DH}\text{N},t}}{\eta\_{H\text{N}\text{CN},t}}\right)\_{RS} - \left(\frac{E\_{d,d\text{win},G\text{iD}\text{D},t} - E\_{d,d\text{co}\text{GDM},t}}{\eta\_{d,t}}\right)\_{PS}}{\left(\frac{E\_{d,d\text{win},t} + E\_{d,d\text{win},t}}{\eta\_{d,t}} + \frac{Q\_{th,H\text{NG},\text{ymbar},t,t} + Q\_{th,H\text{NG},\text{GDH},t}}{\eta\_{H\text{N}\text{CN},t}}\right)\_{RS}}\right) \tag{7}$$

where *Eel,fromGRID,t*/*Eel,toGRID,t* are the electric energy withdrawn/sent from/to the national grid in the proposed system (PS), respectively, *Qth*,*AH*,*biomass*,*<sup>t</sup>* is the thermal energy supplied by the auxiliary biomass-fired heater in PS, η*H,NG,t* and η*el,t* are the natural gas-fired heater efficiency and conventional thermo-electric power plant efficiency, *Eel*,*chiller*,*<sup>t</sup>* and *Eel*,*devices*,*<sup>t</sup>* are the electric energy required by the compression chiller and by the electric devices of the building, respectively, in RS, *Qth*,*H*,*NG*,*spaceheating*,*<sup>t</sup>* and *Qth*,*H*,*NG*,*DHW*,*<sup>t</sup>* are the thermal energy supplied by the natural gas-fired heater for space heating and DHW, respectively, in RS.

The corresponding potential yearly economic savings Δ*C* achievable by both renewable plants are calculated by Equation (8). Here, the yearly operating costs of both PSs (Case ETC and Case PV) due to the yearly maintenance of an ORC machine *mORC* and yearly maintenance of both solar fields *mSF* (ETCs and PV panels), are considered.

$$
\Delta \mathbf{C} = \sum\_{t} \left[ \begin{pmatrix} \left( \mathbf{E}\_{t \text{d}, \text{d} \text{wiles}, t} + \mathbf{E}\_{t \text{d}, \text{d} \text{H} \text{H}, t} \right) \mathbf{c}\_{\text{Ed}, \text{f} \text{wGs} \text{GED}} + \frac{\left( \mathbf{Q}\_{\text{fd}, \text{f} \text{M}, \text{G}, \text{puchtag}, t} + \mathbf{Q}\_{\text{fd}, \text{f} \text{M}, \text{G}, \text{H} \text{H}, t} \right) \mathbf{c}\_{\text{M}, \text{f} \text{g}} \\ + \left( \frac{\mathbf{Q}\_{\text{f}, \text{d} \text{H}, \text{f} \text{M}, \text{wGs} \text{F}} + \mathbf{E}\_{t \text{f}, \text{f} \text{GED}, \text{f} \text{M}, \text{f} \text{G}, \text{f} \text{M}, \text{G}, \text{H} \text{H}, t} \mathbf{c}\_{\text{Ed}, \text{f} \text{GED}, \text{f}} - \mathbf{E}\_{t \text{f}, \text{G}, \text{H} \text{H}, t} \mathbf{c}\_{\text{E}, \text{f} \text{G}, \text{H} \text{H}, \text{G}, \text{H}} \right) \mathbf{c}\_{\text{S}, \text{f} \text{G}} \end{pmatrix}\_{\text{FS}} \tag{8}
$$

where *cbiomass* is the biomass cost for the auxiliary biomass-fired heater, *Cex* is the fixed yearly cost due to the electric energy exchanged with the national grid, *cEel,fromGRID* is the purchasing cost of the electric energy withdrawn from the national grid, *cEel,toGRID* is the selling cost of the electric energy sent to the national grid. Note that if *fHE*<sup>4</sup> = 1, the economic saving of the PS also takes into account the thermal energy recovered by heat exchanger HE4 for DHW production. Note that the same amount of DHW is produced in RS by a conventional gas-fired boiler.

The SPB is assessed as reported in Equation (9)

$$SPB = \frac{\sum\_{i} I\_i}{\Delta \mathcal{C}} \tag{9}$$

Here, the capital costs of all the components *Ji* are considered. In particular, the capital costs for storage tanks, pumps and heat exchangers (HE1, HE2, HE3 HE4) are calculated by suitable polynomial equations [28] as a function of the rated volume, flow rate and heat exchange area, respectively. The unit capital costs assumed for the other components are summarized in Table 5. Concerning the heat exchangers HE5 and HE6, i.e., the ground-coupled heat exchangers, their capital cost *JGHE* is obtained by the calculation reported in Equation (10).

$$J\_{\rm GHE} = \mathfrak{c}\_{\rm examination'} A\_{\rm GHE} + \mathfrak{c}\_{\rm lenglat'} l\_{\rm GHE} + \mathfrak{c}\_{\rm back} j \Gamma\_{\rm back} l \Gamma\_{\rm back}' l \mathfrak{p}\_{\rm back} f \Pi \tag{10}$$

where *cexcavation* is the excavation cost assumed equal to 80 €/m2, *clenth* is the specific cost of the horizontal pipe, assumed equal to 2.72 €/m and 14.47 €/m for HE6 and HE5, respectively, note that *clength* depends on the diameter dimension, *AGHE* is the area of the ground heat exchanger, *lGHE* is the length of the ground heat exchanger (the length of the buried horizontal pipes),ρ*backfill* and *Vbackfill* are the backfill material density and volume respectively, and *cbackfill* is the cost of the backfill material (sand), assumed equal to 14.45 €/t (Table 2).


**Table 5.** Thermoeconomic assumptions.

Table 5 summarizes the thermoeconomic assumptions for the yearly economic saving.

#### **4. Case Study**

The analyzed case study refers to a real commercial user, located in Campi Flegrei (near Naples) worldwide famous for its volcanic activity. The geothermal well is located close to a small bar serving five small soccer fields. The proposed polygeneration system will provide electricity, thermal and

cooling energy to this user which is also selected to perform the dynamic simulations and the related thermoeconomic analysis.

Two innovative micro renewable power plants are presented, based on the exploiting of the solar and the geothermal energy source. Note that concerning the geothermal source of energy an existing low-temperature geothermal well at the selected user is considered.

The first one (Case ETC) uses this geothermal well and a small solar field for feeding a 6 kWe ORC machine and produce electricity and to supply a 17.1 kWf absorption chiller (supplied by the geothermal energy only), the data about the solar field are reported in Table 3. The second one (Case PV) only differs from Case ETC, a photovoltaic field of 48.27 m<sup>2</sup> is installed (design data displayed in Table 3) and no solar thermal plant is considered.

Note that ETC and PV areas are selected with the aim to obtain in both cases a similar cost. The scope of the analysis is to compare, at the same capital costs, PV and ETC configurations.

The geothermal well included in this case study was drilled several years ago for DHW production. However, due to its significantly high temperature compared to the other geothermal wells available in the selected zone, it is presently unused. Indeed, the selected zone is also rich in low temperature geothermal wells, which better suits the domestic hot water production. Whereas, the geothermal brine temperature is equal to about 96 ◦C. Therefore, this well is presently available for the research described in this work. The ORC machine is designed to be driven by the diathermic oil at an inlet temperature ranging between 90 ◦C and 130 ◦C, since the additional temperature increase can be provided by the solar field. Reference [5] in detail describes the ORC machine design parameters and operation. Note that the biomass condensing boiler is activated only if the temperature of the oil feeding ORC evaporator is below 90 ◦C (Figure 1).

Note that the ground heat exchangers (HE5 and HE6) are selected to cool the condenser and absorber of ACH and the condenser of the ORC machine because in the selected location no suitable cold-water source is available. In addition, the installation of cooling towers and/or dry coolers is not feasible due to space availability and noise constraints.

The ground heat exchanger for the ACH (HE5) consists of a pump (P6, Figure 1 and Table 1) which feeds a 60 m long tube of high-density polyethylene (HDPE). The heat exchange occurs in this tube, which is buried at 5 m depth. The tube diameter is chosen equal to 0.110 m (Table 2). Moreover, a layer of sand surrounds the tube, as backfill material, with the aim of enhancing the heat exchange between clay ground and the pipe. The ground heat exchanger for the ORC (HE6) is developed with the same approach, Table 2 in detail describes the characteristics and the thermodynamic features of both the ground heat exchangers.

The commercial area consists of a 308.5 m<sup>2</sup> small bar. Table 4 summarizes the opening hours, schedule of the people and machines inside the bar. The assumed machines installed inside the bar are an induction cooking professional plate, a coffee machine, a professional cooling table, an ice machine and a fryer. The five soccer fields are equipped with 48 lights of 200 W (Table 4), switched on during the same bar opening hours. Note that lights are turned on as a function of the solar radiation availability after 18:00 during summer and after 16:00 during winter. The soccer fields also include locker rooms, where the people may change and have a shower. In particular, the amount of DHW for the locker rooms showers is assumed to be equal to 30,204 l/day (Table 4).

Figure 3 displays the power demand of the selected user. The spiky shape of the power demand curve (Figure 3) is mainly due to the fact that the selected user is a small bar. Thus, the user is not able to serve many consumers at the same time. Then, the electric appliances installed into the bar are intermittently used.

The heating season is assumed to be from November 15th to March 31st with an indoor setpoint temperature equal to 20 ◦C, while the cooling season is assumed to be from May 1st to September 30th with an indoor setpoint temperature equal to 26 ◦C, according to Italian regulation (Table 4).

Finally, the proposed system is equipped with an ESS based on the lithium-ion technology. The ESS assumed for this model is the Renault Zoe ZE nickel manganese cobalt oxide (NMC) lithium-ion battery (LIB) [23], consisting of 63.35 Ah rated capacity cells [23]. In particular, the rated capacity of the battery is 45.56 kWh, while the rated voltage is 360 V (Table 3). Table 5 reports the assumptions made for the thermoeconomic analysis.

#### **5. Results and Discussion**

In this section, the results achieved by means of the dynamic simulation models of both renewable plant (Case ETC and Case PV) are presented. In particular, the dynamic, monthly and yearly results are displayed. Moreover, a parametric analysis is shown by varying the lithium-ion storage system capacity, and the PV and ETC solar field area.

#### *5.1. Daily Results*

Figure 4 displays the transient results for Case ETC and Case PV, above and below, respectively. In particular, Figure 4 plots the power produced by ORC (*Pel,ORC*), the electric load of the proposed layout (*Pel,LOAD*), the power sent and withdrawn to/from the grid (*Pel,fromGRID Pel,toGRID*), the power sent/withdrawn to/from LIB (*Pel,fromLIB Pel,toLIB*), the state of charge of the LIB battery (*SoCLIB*) and the power produced by the PV panels (*Pel,PV*).

For Case ETC, *SoCLIB* achieves its maximum value equal to 0.76 at 11:47, in fact, at this hour the load of the bar hugely increases, by reaching the value of 25.18 kW, due to the activation of the induction cooking plate (Figure 4, above). Consequently, LIB is discharged, from 11.45 to 14:31 by matching the electric load of the bar, along with the power produced by the ORC machine. Note that the residual electric load, defined as *Pel*,*residual* = *Pel*,*LOAD* − *Pel*,*ORC*, is greater than the maximum allowed discharging power (*PLIB,dicharge,max*), which is equal to 10 kW (Table 2). Therefore, the power discharged from LIB is equal to *PLIB,discharge,max*, and a rate of power equal to *Pel*,*residual* − *Pel*, *f romLIB* is withdrawn from the grid (Figure 4, above). From 14:40 to 18:05 *Pel,LOAD* decreases, while *Pel,ORC* remains almost constant, consequently, *SoCLIB* grows up from 0.40 to 0.53. Anyway, at 18:05 the increase of the bar activity and the turning on of the soccer field lights causes a dramatical growth in *Pel,LOAD*, reaching 38.47 kW. Consequently, LIB is totally discharged in 2h, and from 20:05 the load of the system is completely satisfied by the grid and ORC machine. The power produced by the ORC is averagely equal to 5.5 kW over the day (Figure 4, above).

For Case PV, *SoCLIB* achieves the high limit, equal to 0.95 (Table 2), at 10:00, when the PV field power production increases (Figure 4, below). In fact, during the daylight hours, the photovoltaic power production contributes significantly to charge the battery by matching a larger amount of the system electric load. The surplus power is supplied to the grid, with a power value equal to 5.72 kW. When the bar activity increases, from 11.45 to 14:31, the ORC and PV production and LIB discharging supply the electric load of the bar. However, at 14:31 *SoCLIB* rises again, because the overall electric production is higher than *Pel,LOAD*. Finally, at 18:05 when *Pel,LOAD* hugely increases, as explained before, LIB is discharged and it is able to supply the system for 3h. Anyway, during this period *Pel,fromGRID* is not null, indeed, *Pel*,*residual* = *Pel*,*LOAD* − *Pel*,*ORC* − *Pel*,*PV* is greater than *PLIB,dicharge,max* (Table 2). Therefore, as explained before, *Pel,fromLIB* is fixed to 10 kW and the remaining amount of power, i.e., *Pel*,*residual* − *Pel*, *f romLIB*, is withdrawn from the grid. Finally, from 21:45 the system is completely supplied by the grid and ORC machine. Obviously, the total electric production, sum of the ORC and PV production significantly increases in the middle of the day, by achieving the maximum value of 11.17 kW, due to the growth of the solar power production in these hours.

In conclusion, from Figure 4 it is clear that Case PV with respect to Case ETC produces a larger amount of power, consequently, the electric energy stored in the battery is greater. Thus, in the PV Case, LIB is able to cover a larger amount of the electric load of the system.

In Figure 5, the inlet oil temperature to the ORC evaporator (*TtoEV*) for typical summer and winter days are displayed. It is obvious that higher values of *TtoEV* are obtained in Case ETC. Obviously, the higher temperatures are reached in the middle of the day when the solar radiation is higher (the maximum value is 101.1 ◦C at 11:45). Conversely, for Case PV, *TtoEV* is averagely equal to 90–91 ◦C

during winter and summer (Figure 5) days. Anyway, during the remaining part of the day, when the solar radiation is very low or absent there are no difference between the inlet oil temperatures in ETC and PV layouts.

**Figure 4.** Dynamic results, typical summer working day: Case ETC (**above**) and Case PV (**below**).

#### *5.2. Monthly Results*

In this section, the monthly results for Case ETC and Case PV are reported. Figure 6 displays the ratios of the electric energy (i) produced by ORC *Eel,ORC*, (ii) self-consumed *Eel,self*; (iii) withdrawn from the grid *Eel,fromGRID*, (iv) sent to the grid *Eel,toGRID*, (v) discharged from LIB *Eel,fromLIB*, (vi) sent to LIB *Eel,toLIB* and (vii) produced by PV *Eel,PV* on the monthly electric load of the studied layout (*Eel,LOAD*). The total produced amount of renewable electric energy (for Case PV) *Eel,renw* is also displayed.

**Figure 5.** Feeding temperature of the evaporator of ORC: a typical summer day (**left**) and a typical winter day (**right**).

**Figure 6.** Monthly results, electric performance: Case ETC (**above**) and Case PV (**below**).

Case ETC does not achieve the energy self-sufficiency, indeed the ratio *Eel,self*/*Eel,LOAD* constantly is lower than about 45% for all months of the year. LIB is able to cover about 14%–16% of the electric energy demand of the system. Note that LIB adoption causes the absence of surplus electric energy sent to the grid during the summer season (May–October), while during the remaining part of the year the *Eel,toGRID* ratio is lower than 6.7% (Figure 6, above).

Although Case PV achieves self-consumed energy ratios *Eel,self*/*Eel,LOAD* higher than Case ETC, ranging from 40% to 52%, the energy self-sufficiency is not reached (Figure 6, below).

Note that the electric energy produced by the renewable sources (by PV and ORC) achieves higher values during the summer season due to the higher energy production by the PV field during the months of higher solar radiation. In fact, during the months of July and August *Eel,renw*/*Eel,LOAD* is equal to about 73%. Moreover, during these months (July and August) the proposed plant (Case PV) reaches the higher value of self-consumed energy, i.e., *Eel,self*/*Eel,LOAD* equal to 52% and a lower value of electric energy withdrawn from the grid, i.e., *Eel,fromGRID*/*Eel,LOAD* equal to 48% (Figure 6, below).

The adoption of PV panels instead of ETCs leads to a significant increase in the electric energy produced by the proposed renewable plant. However, this higher electric energy production is not fully self-consumed by the user, in fact, Case PV exhibits a limited increase in *Eel,self*, because the electric energy demand is not simultaneous with the electric energy production, mainly because the electric load is concentered mainly in a few hours of the day (evening hours). In addition, the battery (LIB) is not able to store all the surplus electric energy, that is delivered to the grid, see *Eel,toGRID*/*Eel,LOAD* ratio in Figure 6. Therefore, it is possible to conclude that the energy self-sufficiency is not reached in both plants.

Figure 7 shows, for both ETC and PV Cases, the thermal energy supplied to the ORC evaporator (*QtoEV,CaseETC* and *QtoEV,CasePV*), the electric energy produced by the ORC machine (*Eel,ORC,CaseETC* and *Eel,ORC,CasePV*) and the efficiency of the ORC machine (η*ORC,CaseETC* and η*ORC,CasePV*).

**Figure 7.** ORC performance: energy performance (**left**) and efficiency (**right**).

The thermal energy supplied to the ORC evaporator is about the same for both cases. The efficiencies are also similar but η*ORC,CaseETC* is slightly higher than η*ORC,CasePV*, 6.7% vs 6.4%. This is due to the fact that the ORC inlet oil temperature is averagely higher in Case ETC than in Case PV (see Section 5.1 (Figure 5).

Figure 8 plots the ratios calculated by the following equations:

$$R\_i = \frac{Q\_i}{Q\_{\text{toEV}}} = \frac{Q\_i}{Q\_{\text{solar}} + Q\_{\text{gcoth}} + Q\_{\text{biomass}}} \tag{11}$$

where *Qgeoth* is the geothermal energy provided to the ORC evaporator by means of HE1 and HE2, *Qsolar* is the solar thermal energy provided by ETCs to the ORC evaporator and *Qbiomass* is the thermal energy provided by AH to the ORC evaporator when the solar tank top temperature is lower than 90 ◦C (Table 2). In Case PV, the geothermal source provides almost the total amount of thermal energy for driving the ORC machine and reduces slightly in Case ETC due to the solar thermal energy production. Indeed, in Case ETC *Rsolar* achieves the maximum value of 5.11%, while *Rbiomass* is lower than 1.1%. Without ETCs, *Rbiomass* does not significantly increase and achieves the maximum value of 1.73%. Thus, in Case PV, the geothermal source supplies more than 98% of the thermal energy needed for the ORC (Figure 8).

In both investigated cases, the slight reduction of *Rgeoth* during the summer months (Figure 8), is due to the control strategy of the proposed system. In particular, during the summer season, the geothermal energy is used to supply the ACH producing the building space cooling, by reducing the geothermal energy sent to the ORC evaporator. In both plants, the biomass auxiliary heater could be removed without affecting significantly the overall plant performance.

**Figure 8.** ORC evaporator energy ratios: Case ETC (**left**) and Case PV (**right**).

Figure 9 displays the thermal performance of the ground heat exchangers used to cool the condenser of ORC and ACH. In particular, in this figure, the thermal energy transferred from HE5 (*QHE5*) and HE6 (*QHE6*) to the ground for both the cases studied are represented. As mentioned before, the use of PV panels vs ETCs shows minor effects on ORC operation, and consequently, the thermal energy transferred from the ORC condenser to the ground is about the same for both the cases (Figure 9). ACH operates in the same way both in Case ETC and in Case PV, consequently, the values of *QHE5* are about similar (Figure 9). Anyway, the maximum values of energy transferred to the ground occur during the summer months, when the thermal energy required for the building space cooling increases. In fact, during the months of July and August *QHE5* achieves the values of 10.7 MWh and 10.3 MWh, for both cases (Cases ETC and PV, Figure 9).

**Figure 9.** Ground heat exchanger energy performance.

#### *5.3. Yearly Results*

Considering the previously discussed results, the yearly thermo-economic and environmental results of the studied cases are discussed in Tables 6 and 7. The adoption of PV panels leads to a greater production of electric energy, in fact *Eel,prod,CasePV* is equal to 55.77 MWh/year, whereas *Eel,prod,CaseETC* is equal to 44.40 MWh/year (Table 6). Consequently, Case PV reaches a higher amount of self-consumed energy. Therefore, Case PV achieves a higher *PES* than Case ETC, 51.21% vs 37.81% (Table 7). The avoided equivalent CO2 emissions obviously follow the same trend of *PES* (Table 7).


**Table 6.** Energy yearly results.

**Table 7.** Yearly energy, economic and enviromental results.


In conclusion from and energy and environmental point of view, Case PV exhibits better performance. From an economic point of view, Case PV achieves a better SPB with respect to Case ETC. This result is mainly due to the higher electric energy produced, self-consumed and sold to the grid in Case PV. Note as *Eel,toGRID* is equal to 1.83 MWh/year and 7.63 MWh/year for Cases ETC and PV, respectively (Table 6). Therefore, the yearly economic saving for Case ETC (7.59 k€/year) is lower than the one obtained for Case PV (8.73 k€/year), while the total capital costs of both cases are about similar (Table 7). In conclusion, SPBCaseETC was equal to 7.36 years, whereas SPBCasePV was equal to 6.28 years (Table 7).

Table 8 shows the performance indexes of the studied cases. For Case ETC, the solar thermal energy meets about 3% of the thermal energy delivered to the ORC, i.e., *Rsolar* equal to 3.24%. *Rbiomass* passes from 0.31% for Case ETC to 0.42% for Case PV (Table 8). Thus, the absence of ETCs determines minor variations in the ORC electricity production. Anyway, the absence of ETC causes a lower inlet oil temperature to the ORC evaporator and consequently, ORC efficiency is slightly lower in Case PV, 6.45% vs 6.70% in Case ETC. Note that the value of the efficiency achieved by both the analyzed layouts (Case ETC and Case PV) is consistent with the values available in the literature [32]. For the reason above explained, the electric energy produced by ORC is slightly lower in Case PV, 42.86 MWh/year vs 44.40 MWh/year in Case ETC (Table 6). This difference does not affect the overall performance of Case PV, exhibiting better results from energy, environmental and economic points of view.


**Table 8.** Yearly performance index.

Finally, the yearly COP of the ACH is also evaluated (Table 8). This value, equal to 0.74, is similar to the results available in literature about the performance of single-stage LiBr/H2O ACH [33]. Note that the achieved COP of 0.74 is slightly higher than the rated value, due to the high activation temperature of the geothermal brine.

#### 5.3.1. Parametric Analysis

A parametric analysis is carried out with the aim of analyzing the effects of the variability of LIB capacity and of ETC and PV area on the energy, economic and environmental performance.

#### 5.3.2. Battery Capacity

By taking into account the proposed renewable plants, LIB capacity varied from 22.11 kWh to 227.77 kWh. Figure 10 displays the energy and environmental result of the parametric analysis for each case (Case ETC and Case PV). In particular Figure 10 (left) displays *PES* and Δ*CO2*, while Figure 10 (right) points out the ratios: (i) *Eel,fromGRID* on *Eel,LOAD*, (ii) *Eel,toGRID* on *Eel,LOAD* and (iii) *Eel,self* on *Eel,LOAD*.

**Figure 10.** Parametric analysis: *PES* and Δ*CO2* (**left**) and energy ratios (**right**).

The increase in battery capacity from 22.11 to 227.77 kWh causes a reduction in the energy performance: *PESCaseETC* passes from 40.48% to 38.59% and *PESCasePV* varies from 54.97% to 49.33% for Case PV. These trends are due to the battery discharge and charge efficiency. In fact, supplying the surplus electric energy to LIB and discharging the battery when needed, leads to a loss of electric energy, and therefore, a reduction of *PESs* (Figure 10). However, both the studied cases exhibit the same trend. In fact, after an initial decrease, the values of *PES* become almost constant by further increasing the battery capacity.

This behavior is well explained by Figure 10 (left), in fact, the *Eel,self*/*Eel,LOAD* ratio initially increases but for capacity values higher than 113.9 kWh, the ratio is almost constant, to almost 53% and 44.2% for Case PV and Case ETC, respectively (Figure 10). In order to obtain a further increase of the ratio *Eel,self*/*Eel,LOAD*, an increase in the electric energy production by PV panels or ORC machine is needed because with the current installed electric capacity, the proposed renewable plant covers only 53% for Case PV and 44.2 % for Case ETC of the total electric energy demand (Figure 10).

Besides, the increase of LIB capacity leads to a limited worsening of the energy and environmental performance, for both the analyzed cases.

In Figure 11 the economic results are shown, in particular, Figure 11 (left) displays SPB, while Figure 11 (right) displays *Jtot* and Δ*C*. Figure 10 (left) also explains the economic results: by increasing the battery capacity, the values of electric energy sent/withdrawn to/from the grid initially decreases/increases but for capacity values higher than 113.9 kWh they become about constant (Figure 10). Consequently, the yearly economic savings initially increase and then become almost constant. In particular, for capacity values higher than 113.9 kWh, Δ*CCaseETC* and Δ*CCasePV* are equal to about 7.8 k€/year and to about 9.1 k€/year, respectively (Figure 11). By increasing the battery capacity from 22.11 kWh to 227.77 kWh, the capital cost hugely increases from 103.7 k€ and 101.7 k€ to 174.7 k€ and 172.7 k€, for Case ETC and Case PV, respectively. This is mainly due to the high cost of LIB. Consequently, SPB dramatically grows up: SPBCaseETC passes from 14.17 years to 22.25 years, and *PBCasePV* varies from 12.17 years to 18.82 years.

**Figure 11.** Parametric analysis: SPB (**left**) and capital cost and economic savings (**right**).

In conclusion, the LIB capacity increase causes a general reduction in the economic performance of the two studied cases.

#### 5.3.3. PV and ETC Area

The area of ETCs and PV panels varied from 5 m<sup>2</sup> to 85 m2. The energy and environmental results of this parametric analysis are displayed in Figures 12 and 13. In particular, Figure 12 (left) displays the electric energy produced by the ORC and the ORC efficiency, for both the studied cases, while Figure 12 (right) shows the electric energy withdrawn/sent from/to the grid, and the total electric energy produced by the proposed renewable power plants. Figure 13 (left) displays *PES* and Figure 13 (right) shows Δ*CO2*.

**Figure 12.** Parametric analysis: ORC performance (**left**) and electric energy performance (**right**).

The increase of ETCs area directly affects the ORC performance: the higher the ETCs area the higher the thermal energy provided to the ORC evaporator, and consequently, the higher the electric energy produced by the ORC. Conversely, the variation of PV field area obviously does not affect the ORC performance. Thus *Eel,ORC*,*CaseETC* increases, by passing from 43.28 MWh/year to 48.21 MWh/year, while *Eel,ORC*,*CasePV* remains constant (Figure 12).

Note that the growth of the ETCs area causes also an increase of η*ORC*, because for higher ETCs areas, higher inlet oil temperatures to the ORC evaporator are reached. In particular, η*ORC,CaseETC* passes from 6.49% to 7.15%, by varying ETCs area from 5 m2 to 85 m2 (Figure 12).

Anyway, by considering the whole plant, the increase of PV field area with respect to the increase of ETCs area leads to a more significant enhancement of the energy performance of the power plant. In fact, the increase of the PV field causes a remarkable increase in the electric energy production, due to PV field energy production, thus *Eel,renw* passes from 44.58 MWh/year to 66.09 MWh/year (Figure 12). This result affects the values obtained for *Eel,toGRID,CasePV*, significantly increasing from 1.96 MWh/year to 16.96 MWh/year (Figure 12).

Note that, although the electric energy production for Case PV significantly increases, the electric energy withdrawn from the grid exhibits a limited reduction. This is due to the selected LIB capacity (that is not able to store all the electric energy surplus), and because the electric load and production are not simultaneous. For all the reasons above explained, *PESCaseETC* values increase slightly, whereas *PESCasePV* values increase remarkably. In particular, *PESCaseETC* and *PESCasePV,* respectively, passes from 36.89% and 38.19% to 41.94% and 64.57% (Figure 13). The avoided CO2 emissions follow the same trend as *PES*. Finally, the increase of the solar fields area enhances the energy and environmental performance of the proposed plants.

**Figure 13.** Parametric analysis: *PES* (**left**) and avoided equivalent CO2 emissions (**right**).

Figure 14 displays the economic results, in particular this figure plots SPB (left) and *Jtot* and Δ*C* (right). *Eel,fromGRID*,*CaseETC* exhibits a limited reduction without significative increasing of *Eel,toGRID*,*CaseETC,* whereas *Eel,fromGRID*,*CasePV* exhibits a limited reduction but a remarkable increase in *Eel,toGRID*,*CasePV*. Therefore, Δ*CCaseETC* remains about constant, conversely, Δ*CCasePV* increases. In fact, Δ*CCaseETC* is averagely equal to about 7.73 k€/year, whereas Δ*CCasePV* passes from 7.73 k€/year to 9.44 k€/year. The capital cost of both the cases has a remarkable increase but *Jtot,CaseETC* is higher than *Jtot,CasePV* due to the higher capital cost of evacuated thermal solar collectors with respect to the PV panels.

Therefore, SPBCaseETC increases by passing from 13.69 years to 16.91 years. Conversely, SPBCasePV shows a limited decrease, by passing from 13.30 years to 12.27 years.

In conclusion, Case PV has better energy, environmental and economic performance. However, the increase of the ETCs and PV panels area leads to an enhancement of the energy and environmental performance of the proposed renewable power plans. Conversely, from the economic point of view, the better configuration suggests larger PV fields.

**Figure 14.** Parametric analysis: SPB (**left**) and capital and operative cost (**right**).

#### 5.3.4. Optimization

In conclusion, an optimization analysis is performed in order to detect the optimal configuration of each analyzed layout. Primary energy savings, avoided CO2 emissions and simple payback period are considered as object functions. For PV layout, the number of battery cells in parallel and the size of the PV field are simultaneously varied (Table 9). The results of these simulations are displayed in Figure 15. The best configuration achieves a PES equal to 107%, a ΔCO2 equal to 107% and a SPB equal to 8.60 years. This configuration consists of a PV field area equal to 200 m2 and a storage system capacity equal to 22.78 kWh. This layout exhibits the larger PV field and the smaller battery capacity. This trend is due to the high cost of the lithium-ion battery. Indeed, increasing the battery size the economic performance worsens. Figure 15 (left) displays the Pareto front for two objective functions: SPB and PES. Note that the higher the primary energy savings, the lower the payback period. These configurations are that in which the PV field is larger, and the battery capacity is smaller.


**Table 9.** Parameter varied during the optimization analysis, PV layout and ETC playout.

**Figure 15.** 2D Pareto frontier (**left**) and Optimal configuration research for Case PV (**right**).

For ETC layout, the number of the battery cells in parallel, the size of the ETC field and the specific tank parameter are simultaneously varied (Table 9). It is clear that the increase of the avoided CO2 emissions and primary energy savings lead to a remarkable increase of the payback period, reducing the economic feasibility of the ETC layout (Figure 16). This trend is related to the high cost of the ETCs, indeed increasing the ETCs field area PES and ΔCO2 increase while SPB worsens. Moreover, as deeply explained in the previous section, the increase in the ETC area leads to a not so significant improvement of the ORC efficiency. Therefore, the increase in the ETC area causes a huge rise in the capital cost and a limited increase in the yearly savings.

**Figure 16.** 2D Pareto frontier (**left**) and Optimal configuration research for Case ETC (**right**).

The optimal configuration, consisting of an ETC field equal to 5 m2, a specific tank parameter equal to 7.5 l/m<sup>2</sup> and a battery capacity equal to 22.78 kWh, achieves a payback period of 13.36 years, a ΔCO2 equal to 38.91% and a PES equal to 39.12% (Figure 16). Note that the system is not too sensitive to the variation of the specific tank parameter, in fact, the overlapped points (Figure 16) are due to the configurations among which varies only this parameter.

#### **6. Conclusions**

In this work, two innovative micro renewable polygeneration plants, both consisting of a micro organic Rankine cycle, single-stage H2O/LiBr absorption chiller, geothermal well, biomass auxiliary heater and lithium-ion battery are presented. The main aim of this work is the thermoeconomic comparison of two alternative solar technologies integrated as auxiliary systems into two polygeneration plants, namely the evacuated solar collectors and photovoltaic panels. Both plants produce power for, heat and cool a small bar, located in Naples (South Italy), in a weather zone famous for its volcanic activity and high solar availability. Plant layouts are dynamically simulated in the TRNSYS environment, by developing comprehensive models suitable for evaluating the transient energy performance (temperatures, heat, power and efficiency) of all the plant components on hourly, daily, weekly, monthly and yearly time basis. A parametric analysis of the design parameters of the key units of the plant is also performed. The main findings of the simulations are summarised in the following:


• From the economic point of view the better configuration suggests larger photovoltaic fields and smaller evacuated solar collectors fields due to the higher capital cost of evacuated solar collectors than photovoltaic panels and the achievable economic saving for the higher amount of selling electric energy.

Finally, an optimization analysis is carried out for both the analyzed layouts, the main findings are listed in the following:


**Author Contributions:** Conceptualization, F.C., F.L.C., M.D.d. and M.V.; Methodology, F.C., F.L.C., M.D.d. and M.V.; Software, F.C., F.L.C., M.D.d. and M.V.; Writing—review and editing, F.C., F.L.C., M.D.d. and M.V. All authors have read and agreed to the published version of the manuscript.

**Funding:** It is important to stress that this work is developed in the framework of the project "GEOGRID", aiming at adopting suitable technologies and methods in order to use efficiently the geothermal energy of the Campania Region (South Italy). This project is funded by POR CAMPANIA FESR 2014/2020.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Nomenclature**



#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Energy, Environmental, and Economic Analyses of Geothermal Polygeneration System Using Dynamic Simulations**

#### **Francesca Ceglia 1, Adriano Macaluso 2,\*, Elisa Marrasso 1, Carlo Roselli <sup>1</sup> and Laura Vanoli <sup>2</sup>**


Received: 18 June 2020; Accepted: 31 August 2020; Published: 4 September 2020

**Abstract:** This paper presents a thermodynamic, economic, and environmental analysis of a renewable polygeneration system connected to a district heating and cooling network. The system, fed by geothermal energy, provides thermal energy for heating and cooling, and domestic hot water for a residential district located in the metropolitan city of Naples (South of Italy). The produced electricity is partly used for auxiliaries of the thermal district and partly sold to the power grid. A calibration control strategy was implemented by considering manufacturer data matching the appropriate operating temperature levels in each component. The cooling and thermal demands of the connected users were calculated using suitable building dynamic simulation models. An energy network dedicated to heating and cooling loads was designed and simulated by considering the variable ground temperature throughout the year, as well as the accurate heat transfer coefficients and pressure losses of the network pipes. The results were based on a 1-year dynamic simulation and were analyzed on a daily, monthly, and yearly basis. The performance was evaluated by means of the main economic and environmental aspects. Two parametric analyses were performed by varying geothermal well depth, to consider the uncertainty in the geofluid temperature as a function of the depth, and by varying the time of operation of the district heating and cooling network. Additionally, the economic analysis was performed by considering two different scenarios with and without feed-in tariffs. Based on the assumptions made, the system is economically feasible only if feed-in tariffs are considered: the minimum Simple Pay Back period is 7.00 years, corresponding to a Discounted Pay Back period of 8.84 years, and the maximum Net Present Value is 6.11 M€, corresponding to a Profit Index of 77.9% and a maximum Internal Rate of Return of 13.0%. The system allows avoiding exploitation of 27.2 GWh of primary energy yearly, corresponding to 5.49·10<sup>3</sup> tons of CO2 avoided emissions. The increase of the time of the operation increases the economic profitability.

**Keywords:** heating and cooling network; polygeneration system; geothermal energy community; ORC; geothermal energy; energy district

#### **1. Introduction**

Industrialization has promoted the use of oil, natural gas, coal, and other conventional energy sources causing the risks of stock depletion and environmental pollution [1]. Thus, the environmental emergency is a priority on the policy agenda of different countries. Indeed, in the framework of the Conference of the Parties in Paris [2], a group of countries has signed and ratified different documental acts with the common aim to solve the climate change problems [3]. Moreover, the European Commission developed the model to convert the energy and production economic panorama

into a low-carbon model within 2050 [4]. The crucial topic of these legislations is the necessity to obtain a climate-friendly European economy encouraging renewable energy against long-term energy consumption.

The concerns regarding global warming and well-being targets allowed defining the elementary energy objectives to be reached [5], such as the almost exclusive use of renewable energy sources (RESs) and, in particular, the increase of local RESs exploitation. The objective of a completely renewable energy production panorama cannot disregard adoptable city strategies to enhance their sustainability to a globally competitive level [6,7].

Different studies [8,9] about energy districts fed by local energy sources demonstrate that the development of energy systems depends on the reciprocal connection of all the energy vectors such as the electric, heating, and cooling. Thus, the correct combination in energy polygeneration model permits to obtain a territorial energy planning strategy to optimize the use of the local energy resources and satisfy the energy needs of a defined territory [10,11].

Ecological policies, aimed to define energy-independent areas by use of the availability of RESs in the area, have increasingly become a branding factor of cities [12]. Avant-garde cities such as the Danish capital of Copenhagen, the Swedish city of Malmö, and the German city of Freiburg have all invested significant resources into the development of a green image via ambitious sustainability policies [13]. These cities attract thousands of foreign politicians interested in learning about ways to optimize the concept of a common green economy. Finally, a "green image" is often associated with a high degree of livability [14], which can attract new citizens [15]. Therefore, a requalification of a zone through a green imagine could be a way to develop and recover an interesting area with the promotion of social acceptability of renewable plants by encouraging citizenship in both social and economic aspects [16].

Sometimes the employment of renewable energy is limited by the uncertainty of RESs with higher impact of diffusion (such as solar or wind energy). The possible strategy can be the use of higher stable RESs such as geothermal and biomass. In addition, to reach energy independence, the use of local RESs is incentivized to obtain energy districts and communities [17]. In this context, the use of RESs to satisfy the energy requirements of an entire area of a city is crucial for achieving the energy and environmental targets associated with ecological policies. In worldwide panorama, the geothermal power plants represent the higher reliable RESs in terms of operating hours (this value is averagely the 62% of total yearly hours) [18]. The use of geothermal reservoirs could be a good solution to obtain a more flexible and stable energy system. In 2016, renewable energy was used to meet 13.7% of the worldwide electricity demand, and only 4.3% was covered by geothermal sources [19]. Concerning geothermal power plants, in 2014, the total worldwide installed capacity was 12.6 GWel. Among the World's countries, the United States had the largest installed capacity (3.5 GWel, 28% of the world total), followed by the Philippines (1.9 GWel, 15%), Indonesia (1.4 GWel, 11%), and New Zealand (1 GWel, 8%) [20]. Although geothermal power generation accounted for only 0.3% of the total electricity production, it increased significantly in 2014, representing a substantial proportion of the total electricity generation in countries such as Kenya (32%), Iceland (30%), El Salvador (25%), and New Zealand (17%) [20].

As regards thermal direct geothermal applications, the installed geothermal power is ~107,727 MWth worldwide, with an annual increment of 8.73% from 2015. Geothermal energy is mainly exploited in ground-source heat pumps (58.8%), bathing and swimming (18.0%), and space heating (16.0%); only 3.50% is employed in greenhouse heating and 3.70% for all the other applications. China, Iceland, Turkey, France, and Germany are the best countries for geothermal district heating exploitation [21]. District heating systems coupled with renewable energy sources can save fossil fuels and reduce greenhouse gas emissions. Indeed, the interest in RES based-district heating and cooling systems has increased during the last years and different applications can be found worldwide. In [22], an application based on low-temperature geothermal district heating feeding the municipality of Aalborg has been analyzed. The simulation results highlighted that RES was not able to cover the

total space heating request for the municipality. In Germany, during 2017 geothermal plants provided 1.3 TWh of heat on yearly based, which was generally used for district heating purposed [23]. Moreover, in [24], it was compared a district heating system based on deep geothermal energy with a conventional district heating system based on natural gas. The innovative RES system was able to increase the exergy efficiency by ~12% and to reduce heating costs by ~25%.

Furthermore, the geothermal reservoirs allow the cascade use of geothermal hot fluids [25,26] to provide different energy vectors such electricity and heat exchanging fluids to meet space heating and cooling, as well as domestic hot water (DHW) demands. From literature analysis about the future employment of geothermal uses, it has been calculated that this source could satisfy 5% of the global heating demand by 2050 [27].

Despite the encouraging data, the geothermal reservoirs are often not used in many areas such as Italy [28]. The employing of the geothermal source is threatened by the impossibility to generalize the plant configuration that strictly depends on chemical, enthalpy, deep, and quantity of geothermal site availability. In addition, to define a basic model compatible with all sites, a limit is the social acceptability of geothermal plants by citizens often caused by incomplete and inaccurate environmental information [29]. In the actual RESs, world panorama America and Asia exhibit the largest geothermoelectric installed capacity, followed by Europe. Italy is the leading country in Europe, with installed geothermal power plants around 916 MW, but all these plants are in Toscana. The Italian electricity generation from geothermal sources amounts to 5.9% of the total renewable-based electricity production, and up to 0.9% of thermal energy produced from renewables is from geothermal sources [30,31]. The usage of geothermal sites in electric applications in Italy regards the higher temperature sources (T > 150 ◦C) by traditional Rankine or Kalina Cycle. These plants are not suitable for the exploitation of the most widespread low/medium temperature reservoirs. To use the low/medium geothermal energy sources in power plants the literature considers the employment of Organic Rankine Cycle (ORC). This technology represents one of the most satisfying strategies to exploit renewable energies and low/medium temperature thermal cascades that permits in addition to electricity the thermal energy recovering if opportunely designed [32,33]. The ORC module consists of a Rankine cycle in which the water was replaced by an organic fluid that, despite the cons represented by high cost, toxicity, and flammability, it presents the vantages such as low critical temperature, low latent heat of evaporation, positive slope of the vapor saturation curve and high molecular weight.

The share of ORC installations in geothermal applications worldwide is 19% of the total number of ORC plants for all feeding typologies, but they cover 74.8% of the installed ORC capacity owing to their high size availability (typically under set of ten MWel) [34]. In many zones, ORC installations at low/medium temperatures are available, allowing the use of the well-known ORC technology, which is particularly suitable for these applications. The renewed interest in the academic study of the ORC is due to its growing technological adoption in the energy conversion of thermal sources at low/medium temperatures ranging from 80 to 300 ◦C [35]. The results of ORC applications in this field are very promising [36] when coupled with different renewable sources as solar, geothermal, and biomass [27,37], but its diffusion is nowadays complexed because of the high specific cost of investment, low conversion efficiencies, high production costs, and maintenance cost linked to aggressivity of geothermal fluids [38].

Currently, only large power plants can compensate for the technological concerns in exploiting low-temperature heat sources for electricity production [39]. Globally, only 16.0% of geothermal power plants use ORC technology [39].

Typically, the ORC modules are suitable for large power range applications in particularly those with low/medium enthalpy, e.g., geothermal reservoirs, biomass combustion, industrial waste heat, waste heat from reciprocating engines [40–42] and gas turbines [43], biomass gasification [44,45], concentrated solar radiation [46–48], exploiting the recovery of residual heat from diesel engines [49], and drying [50,51]. Simulation studies on geothermal ORC plants indicated that the first-law efficiency for the ORC ranges from 7 to 15% with a geothermal source temperature of 160 ◦C. Sometimes to improve the system the integrations with solar collectors are considered to keep the working fluid

under the desired conditions at the turbine inlet. In addition to trigeneration use, the geothermal brine sometimes could be used for the desalinization of water [52–54].

In the present study, an ORC module for geothermal applications was designed and simulated to supply the energy demand of a district in Monterusciello, a district of Pozzuoli (Naples), in the geothermal area of Phlegraean Fields, South Italy. The ORC module uses a geothermal source in cascade application to supply thermal demands for space heating and cooling and domestic hot water demands of the district in a polygeneration application; otherwise, the electric output energy is partly used to supply the energy request of thermal network and the remaining part is sold to electric national grid. The selection of organic fluids is based on a literature analysis and depends on the thermophysical, economic, and environmental properties [55,56]. An appropriate selection of the working fluid of the cycle is crucial for optimizing the efficiency of the binary plant, to maximize the conversion efficiency or to determine the best configuration for a given plant capacity. The selection of the working fluid also significantly affects the costs of the heat exchanger.

Considering the previous literature [57], the choice of the working fluid depended on the source temperature and critical temperature of the fluid. The working fluid must satisfy the general technological and environmental criteria, which have been widely discussed in the literature, for example, suitable thermodynamic fluid properties, no toxicity, no or low flammability, low cost, a low Global Warming Potential, and no Ozone Depletion Potential impact.

By using the previous analysis [58–60], the organic fluid R245fa was selected because of its environmental and thermodynamic efficiency in the case of heat sources with temperatures close to 150 ◦C for geothermal applications and/or other renewable sources for ORC applications. The use of R245fa is also effective for temperatures below 170 ◦C [61]. Other studies that optimize the ORC efficiency, consider the zeotropic mixtures such as the combination of 70% R245fa and 30% R125a [62].

The analyzed polygenerative plant application in Monterusciello is used to satisfy the thermal loads of a small local energy community through a mini-grid system. The geothermal district was inspired by energy community based on geothermal activity in Japanese real cases [63]. Its simulative model is created to evaluate the economic and social benefits of a district energy system as suggested in the literature [64], getting closer to meet economic and environmental needs. The study wants to encourage the energy district diffusion. It defines the limits and advantages of small independent energy districts fed by renewables reservoirs.

The keys for comprehensively developing such district contexts and making them economically profitable are the integration of different sources, the simultaneous production of different energy vectors (polygeneration), and the "load plant sharing" approach, which maximizes the source exploitation. In this context, a pre-feasibility study cannot be neglected. The authors propose a district system based on the exploitation of geothermal sources integrated with an auxiliary biomass backup system for the simultaneous production of electricity, heating, and cooling for domestic air conditioning (using a district heating and cooling network (DHCN) and domestic hot water network (DHWN). The plant system was simulated in TRNSYS environment [65], and all the heat exchangers and the ORC were first developed by previous analysis in the AspenEDR [66] and AspenONE [66] environments, respectively. AspenEDR allows a detailed and in-depth design; according to its simulation results, the heat-exchanger geometry is developed in the TRNSYS environment, creating user-defined components.

Because the ORC built-in model is absent in the TRNSYS library, it was first developed and simulated in AspenONE to extrapolate working maps as functions of the inlet heat source temperature and mass flow rate and after inserted in TRNSYS environment to create a user-defined component following the approach adopted in [52–54]. A control strategy is developed in this study to manage the layout and the simultaneous production of multiple energy vectors.

The dynamic model of the entire system includes a typical building configuration in the real considered residential district realized by TRNBUILD (a TRNSYS tool).

The novelty of the study is related to defining a possible geothermal energy district in a not yet used geothermal field. In particular, a combination of two flexible and stable RESs is considered (biomass and geothermal energy). A sustainable energy district in load sharing configuration is analyzed by using low-temperature geothermal source, to requalify a district of Naples by improving the local energy sources and the local energy network. Moreover, a sensitivity analysis is performed by varying the depth of the geothermal well, to take into account the uncertainty related to the depth where a suitable geothermal source temperature is available. An economic analysis, which is the most central aspect of the pre-feasibility study and based on accurate market surveys, is performed by taking into account different scenarios of the Italian market for electricity production (with and without feed-in tariffs).

#### **2. Area of Interest**

This study should be referred to the improvement of geothermal reservoirs exploitation in Italy. Considering the general Italian geothermal context, it has been highlighted from the geothermal maps (available at depths of 1000, 2000, and 3000 m) that the areas of interest concerning the temperature and geothermal flow are located in Tuscany, Aeolian Islands, and Neapolitan area [67,68]. In [69,70], it is demonstrated that the geothermal anomalies also in different Italian areas such as the Alps, Sicily, and the central Tyrrhenian and the Mediterranean Sea with a heat flux of 80, 40, and higher than 150 mW/m2, respectively.

The area of interest in this study is the Neapolitan area (Phlegraean Fields), which (similar to numerous wells already surveyed in the 1980s) has a highly aggressive geothermal fluid and temperatures of approximately 100 ÷ 150 ◦C at the land surface [71–73]. Interest in the geothermal area of Naples started in 1930 and grew rapidly in the mid-1980s. A total of 117 geothermal wells were investigated, with a maximum depth of 3046 m. The results were particularly encouraging for the Phlegraean Fields [74] and Ischia, where high geothermal gradients have been recorded, owing to the presence of localized high enthalpy fluids (T > 150 ◦C) at low depths (hundreds of meters), and both steam and water dominated [75–77].

In the Neapolitan contest, the Phlegraean Fields represent the area of greatest interest. According to the previous investigation for some reservoirs of these sites, the average geothermal gradient is 0.170 ◦C/m (average reference value of 0.03 ◦C/m) [68] and the average geothermal flow is 149 mW/m2 (average reference value of 63.0 mW/m2) [68]. In this area, buildings with different intended uses (such as residential, commercial, and also industrial buildings) can be found and they all can be connected by a thermal grid fed by geothermal sources.

In the past, the local geothermal applications in the Neapolitan area provided to direct use of the source in thermal employment using available reservoir sites in medium-low enthalpy. Nowadays, the technological maturity of the ORC component and the large diffusion of polygeneration systems to define energy district can be made usable these low/medium enthalpy sources. This study analyses the possibility to employ the large low/medium temperature geothermal sources available in Phlegraean Fields in polygeneration approach to satisfy the energy loads of a district. In addition, this work focuses on the replacement of pre-existent wells realized from 1930 until 1985, during which a large amount of data were collected firstly by the SAFEN Company and successively in ENEL-AGIP Joint Venture for geothermal exploration [77].

In a previous study about Monterusciello [78], it was analyzed only a system, without ORC module, meeting thermal loads using geothermal fluid at a temperature of 50 ◦C available at a depth of 100 m. In the current analysis, the geothermal fluid could be obtained from two wells of extraction (really investigated from the previous AGIP campaigns [77]) at the desired temperature and flow rate. In this upgrade study, an analysis of the existing geothermal wells of Phlegraean Fields was conducted as reported in Table 1. According to geological maps, the geothermal analyzed wells are collected and geolocated. For each well, the geothermal gradient is estimated by considering a linearity approximation as reported in the last column of the table. For Monterusciello, the gradient considered is 0.1 ◦C/m in the simulation at depth of 1500 m that guarantees a geothermal brine temperature

of 150 ◦C. This value represents a possible real gradient in the Monterusciello by considering the near wells.


**Table 1.** Collection data of wells in Phlegraean Fields.

#### **3. Buildings and Heating and Cooling Network Characterization**

A previous analysis for the building modeling was performed based on a field investigation to define both for the envelope characteristics and users/consumers typologies. The definition and modeling of the building are set up using a tool of TRNSYS software (TRNBUILD). Each building of the district, which is an ensemble of social housing, consists of four floors and eight apartments and is in a residential zone. In the SKETCHUP environment [79], the rendering of the building is represented in Figure 1. Each building consists of four floors with eight thermal zones of 198 m<sup>2</sup> and two apartments for each thermal zone; such a configuration was implemented by considering, on one hand, a plausible reproducibility of the considered context and, on the other hand, the computational burden of such a complex layout. The building model reproduces the typical council housing of 1960s. The stratigraphy respects the Italian building regulations for its specific age of construction [80]. All 90 buildings of the district led to a total of 1440 apartments and 1980 habitants, covering ~6% of the Monterusciello population. The opaque and transparent building envelope characteristics and the geometrical parameters for each building are reported in Table 2. The transmittance of windows is referred to a single glass component with aluminum frame. Space heating and cooling loads were evaluated considering an occupancy schedule, represented in Figure 2, based on four different cases (a, b, c, and d):


**Figure 1.** Single building representation in the SKETCHUP [79] environment.


**Table 2.** Building envelope and geometric parameters.

**Figure 2.** Schedule occupation.

Each one of these schedules refers to two apartments of each considered building.

For the domestic hot water, load is defined as a normalized hourly profile for different months of the year [81] and a daily volume consumption of 50 L per district resident [79].

According to Italian normative [82], the heating period for Naples in climate zone C goes from 15 November to 31 March. While the cooling period is from 1 June to 30 September. The maximum number of heating and cooling systems operating hours is established to 10 h per day.

All the electric energy produced by the plant is sold to the power grid excluding the part needed for auxiliaries of the thermal district network.

While during the winter period the heating load depends on the desired comfort condition (indoor temperature at 20 ◦C) required in the whole apartment, during the summer season the energy delivered by cooling network depends by activation of terminal cooling units that commonly serve only the rooms of the apartment effectively occupied. The yearly trends of heating and cooling load for the whole building are presented in Figure 3. The 1-year simulation was based on the weather file available in Trnsys library, which refers to [83].

**Figure 3.** Yearly trend of the building load.

The buildings of the Monterusciello District area, modeled through TRNBUILD tools and based on the previous information, are connected by means of two energy networks: DHCN and DHWN.

The district area is divided by considering the constraints of the DHCN and DHWN network installation. Figure 4 reports the pipelines segments (in light blue color) running along the main roads, the spatial distribution of the buildings and a viable energy conversion system plant location (in red color). The pipelines segment are labeled as "A" or "B", referring to different blocks of the district or "MAIN". The lengths of the pipeline are consequently calculated by considering the real building location and the plausible location of the plant. The diameters sizing takes into account the thermal demand distribution and a fluid velocity of 2.0 m/s is considered. The DHWN sizing was performed similarly to the DHCN one. The geometric features of piping are listed in Table A1 in Appendix. The DHCN considers a time operation of ten hours (from 10 a.m. to 8 p.m.). A parametrical analysis was also conducted to consider the cases in which DHCN is turned off 2 and 4 h later than the base case (10 p.m. and 12 p.m.). The DHW is guaranteed for all 24 h. The set point of DHW temperature is ensured by the biomass boiler. The overall head and thermal losses of the distribution networks takes into account the ones related to the DHCN and the one related to the DHWN.

**Figure 4.** DHCN layout. Map data © 2019 Google.

#### **4. System Configuration and Layout**

The simplified system layout is shown in Figure 5, where the main components are presented but the DHCN and the DHWN are omitted. For simplicity of the scheme, only one production well is represented, even if such an analysis two production wells are supposed to be exploited.

**Figure 5.** System layout.

First, geofluid powers an ORC module through a heat exchanger (GHE1) heating the hot water (HWORC); the HWORC heats the ORC working fluid in the evaporator.

The ORC is calibrated to ensure a constant power production; it is condensed with cooling water (CW), which is cooled through the cooling tower (CTORC) and whose mass flow rate is adjusted using a variable speed pump to keep the temperature difference at the condenser constant. The ORC module is intended to operate under steady-state conditions with stable evaporation and condensation pressures. This condition at the evaporator is guaranteed by fixed temperature and flow rate of geothermal brine. While to assure the stationary condition at the condenser a variable cooling water flow rate from the water supply net is considered.

A little part of the electricity available from the ORC plant is used to cover the network auxiliaries (pumps, etc.), while the most is sold to the national grid. After delivering thermal energy at ORC evaporator the geothermal fluid is used to provide space heating, cooling, and DHW by means of DHCN and DHWN. A brief description of the system operation and the control strategy is presented herein following a previous study [78].

The Hot Water (HW, red line in the layout) feeding tanks (TK1 and TK3) are produced through the GHE2 heat exchanger. One part of HW is stored in a tank (TK1) to recover thermal energy for space heating and cooling. Through a control strategy, HW is alternatively sent to storage tank TK3, and it is used to store and heat the DHW. Then, a dedicated subsystem is used to ensure a constant temperature.

GHE2 is designed to provide a suitable HW mass flow rate basing on the temperature approach. If the temperature of the HW is higher than that of the geothermal source entering GHE2, the thermostatic valve (through D1/M1) diverts the HW bypassing GHE2, to prevent heat dissipation.

Diverter D2 diverts the HW flow to keep TK1 and TK3 thermally loaded, giving priority to TK1. Different opportune set temperatures on the top of the tanks are provided for both the heating and cooling operation modes. A thermostatic valve (through D3/M3) ensures a constant temperature (45 ◦C) of the DHW for the networks.

A thermostatic valve (through D4/M4) ensures a constant temperature of the HWDHCN for the DHCN, which is sent directly to the network during the heating operation while it is sent to the adsorption chiller (ADS) during the cooling operation. The HW temperature is set to 50.0 ◦C during the heating operation and 100 ◦C during the cooling operation for feeding the ADS. If the set point temperatures cannot be ensured, the biomass boiler (BB) fed with wood chip, is activated until the indicated temperature is reached and until the thermal storage TK1 is thermally loaded. Similarly, if the DHWN set point temperature cannot be ensured, the DHW flow is diverted to the biomass boiler trough thermostatic valve D7/M7.

During the cooling operation, the ADS is activated (by cooling tower, CTADS), and the chilled water (ChWADS) produced is sent to storage tank TK2, where the water ChWDHCN is stored at 10.0 ◦C and is sent to the DCHN.

To fed DHCN and DHWN the GHE2 is designed to provide a suitable mass flow rate of HW in a temperature range of 40 ÷ 75 ◦C.

The modeling of the plant has considered an ad hoc defined flow rate for geothermal fluid and a recommended minimum rejection temperature of 70.0 ◦C as the literature suggestions [84,85]. This value represents a good compromise for avoiding excessive depletion of the geothermal source and moderately mitigating problems involving scaling at the heat exchangers and the mechanical apparatus of the rejection process. Once the geothermal source is set, according to the mass flow rate and temperature range, the available thermal energy is calculated, and the entire system is calibrated accordingly. The ORC is calibrated to ensure constant power production. It is intended to operate under steady-state conditions of working fluid (R245fa); the evaporation and condensation pressures are stable.

#### **5. Models**

The development of the whole simulation model has been carried out in three steps, namely, the development of the ORC module in AspenPlus environment, the heat exchanger in AspenEDR environment, and the dynamic simulation model in TRNSYS environment. The TRNSYS library does not include the ORC module; the ORC was implemented in AspenPlus software and simulated by varying the inlet temperature of the source; there were obtained working maps reporting the main output parameters as a function of the inlet temperature of the thermal source, given a constant mass flow rate.

These functions have been implemented in TRNSYS environment adding a user-defined component. The entire dynamic simulation model also includes the ORC heat exchangers modules (evaporator and condenser) and geothermal heat exchangers (GHE1 and GHE2) designed, as previously defined in the introduction section, in the AspenPlus and AspenEDR environments, respectively.

All the heat exchangers of the plant have been developed and designed in AspenEDR environment.

After this, the geometry and suitable heat transfer coefficient correlations have been implemented in TRNSYS software to create a user-defined component: this approach is more rigorous with respect to using the built-in ones since it takes into account the real instant operation of the heat exchanger in terms of overall heat transfer coefficient and efficiency. In the Table A2 in Appendix A all the input parameters of the dynamic model are listed for ORC, working fluid, and heat exchangers. In particular, the heat exchanger GHE1 and GHE2 are simulated considering shell and tube heat exchanger model in titanium material. The resulted characteristics of GHE1 and GHE2 show an external diameter of tubes of 19.05 mm, thickness of tube of 1.2 mm, pitch of 23.8 mm. For the ORC module, the isentropic efficiencies are fixed: 70% and 85% for the pump and turbine, respectively. The ORC pinch point temperature differences are 7 and 5 ◦C respectively at the evaporator and the condenser. The working fluid used for the ORC plant is the R245fa. The evaporator and condenser for ORC module are two AISI306 shell and tube heat exchangers. The output parameters of the heat-exchanger design and the ORC module obtained as results are presented in Tables A3 and A4, respectively. In the ORC evaporator (not showed in the layout figure), the inlet and outlet temperatures of R245fa are, respectively, 51.08 and 120.1 ◦C at 19.35 bar, while at the condenser, they are 66.05◦C for the inlet and 50 ◦C in the outlet section at 3.43 bar. The thermal power exchanged in the evaporator and condenser is 4698 and 3835 kW, respectively.

The nomenclature used to define each parameter in Tables A2–A4 is referred to system layout scheme represented in Figure 5.

The ORC is calibrated considering a nominal power production of 500 kWel. All the heat exchangers are simulated by calculating the outlet streams' conditions using the heat and mass balances and the surface area. The inlet and the outlet temperatures of the condensation process are fixed. The mass flow rate is determined accordingly.

Once the cycle is completely defined and simulated in the AspenONE environment, the evaporator and the condenser are designed in AspenEDR.

Both the geothermal heat exchangers (GHE1 and GHE2) are designed by considering plausible values from an ORC market survey of the cold-side mass flow rate for feeding the ORC module, a plausible value of the cold-side temperature difference, and a hot inlet–cold outlet temperature approach. The correlations adopted for the overall heat-transfer coefficient to define heat exchangers parameters are based on the fully developed laminar flow inside the duct with an isothermal wall [86] and the fully developed turbulent flow inside the duct with an isothermal wall [87].

The calibration of the overall system is based on a preventive dynamic simulation of the building equipped with a plausible number of fan coils per apartment, which are also implemented in the TRNSYS environment. Then, according to the simulation results, the heat-exchanger geometry is developed in the TRNSYS environment (with the creation of user-defined components using macros and Calculator blocks) to dynamically simulate the real heat-transfer performance with regard to the instant value of the overall heat-transfer coefficient, efficiency, and number thermal Unit (NTU).

The simulation model of the building is linked to the simulation model of the fan coil in the same TRNSYS environment. The calibration of the fan-coil simulation model is based on a market survey.

The seasonal data about fan coil are listed in the Table 3, such as the nominal power of fan coil (Pnom,fc), flow rate water and air of fan coil (mfc,w, mfc,a), the comfort temperature set (Tset,amb), and the ratio between sensible and total thermal power (Pth,sens/Pth,TOT).


**Table 3.** Fan coils data set.

This approach allows us to determine the effective thermal and cooling loads under dynamic operating conditions and then take into account variable weather conditions, the thermal inertia of the building envelope, and the variability of the space occupation.

Once the time-dependent thermal and cooling loads are extrapolated and the maximum thermal energy available from the geothermal source is considered, it is possible to determine the maximum number of apartments served by the system.

Finally, the variable parameters are calibrated in the TRNSYS environment such as mass flow rates, set point temperatures, and characteristics of components under nominal conditions.

The system plant simulation model is linked to the DHCN one, which takes into account the heat losses occurring in the network piping. In turn, the DHCN simulation model is linked to the thermal and cooling loads, allowing the return water conditions to be determined.

#### **6. Methodologies**

The system described in the previous sections has been analyzed from an economic an environmental point of view according to the following methodology.

As regards to economic analysis, the total plant investment cost, ZTOT, is given by the sum of the costs of all the modules composing the plant, the cost of the distribution networks, and the BOP (Balance of the Plant) cost ZBOP, to take into account all the auxiliary systems and supporting components of the plant. Table 4 reports the parameters used in the economic analysis, as well as the main parameters of the reference scenarios for each energy vector and emission factor. The performances of the renewable ORC coupled with DHCN system are evaluated by assessing the energetic and economic savings, and by comparing the proposed system (PS) with the reference one (RS). In particular, in case of the reference scenario


The same space heating and cooling terminal units (fan coils) are adopted both in case of PS and RS.

All the electricity prices (for the cases with and without feed-in tariffs) are based on the Italian real market trends from January 2018 to August 2019 [31]. Different prices are provided for the three time-dependent partitions of the Italian market (F1, F2, and F3). The prices of heating and cooling energy are based on market surveys.

The ZBOP is calculated as 3.00% of the overall plant cost. An economic analysis is performed by taking into account two different scenarios for electricity sales: with and without feed-in tariffs provided by the Italian market [31].

In the case of feed-in tariffs, the revenue related to electricity sales Rel,feed-in is defined as follows,

$$R\_{\text{el,feed-in}} = E\_{\text{el}} \mathbf{c}\_{\text{el,feed-in}} \tag{1}$$

where Eel represents the amount of yearly electricity produced, and cel,feed-in represents the price of electricity under feed-in tariff market conditions. In the case where no feed-in tariffs are provided, a guarantee minimum price tariff system is assumed: regardless of the effective electricity market price, the plant always sells energy above a certain threshold price established by the GSE (Gestore dei Servizi Energetici, i.e., Italian energy services management institution).

Moreover, three selling prices are considered based on the hourly partition of the time-dependent tariff system. Given the uncertainty of the results due to the variability of prices, a plausible range of the revenue (i.e., Rel,min and Rel,max) is calculated according to the minimum and maximum values of the sale price. The minimum and maximum sale price values are established with consideration of the real price trend from January 2018 to August 2019 (reported in Figure A1 in Appendix A).

Then, the minimum and the maximum revenues are calculated as follows,

$$\mathcal{R}\_{\text{el,min}} = \mathcal{E}\_{\text{el}} \mathbf{f}\_{\text{F1}} \mathbf{c}\_{\text{el,F1,min}} + \mathcal{E}\_{\text{el}} \mathbf{f}\_{\text{F2}} \mathbf{c}\_{\text{el,F2,min}} + \mathcal{E}\_{\text{el}} \mathbf{f}\_{\text{F3}} \mathbf{c}\_{\text{el,F3,min}} \tag{2}$$

$$R\_{\rm el,max} = E\_{\rm el} f\_{\rm F1} \mathbf{c}\_{\rm el,F1,max} + E\_{\rm el} f\_{\rm F2} \mathbf{c}\_{\rm el,F2,max} + E\_{\rm el} f\_{\rm F3} \mathbf{c}\_{\rm el,F3,max} \tag{3}$$

where the subscript Fi indicates the specific partition of the time-dependent tariff system and the subscript fFi indicates the yearly fraction of the hours belonging to the specific Fi partition.

The revenue related to the selling of thermal energy for space heating Rth is calculated as follows,

$$\mathbf{R\_{th}} = \mathbf{E\_{th}} \mathbf{c\_{th}} \tag{4}$$

where Eth represents the amount of thermal energy provided to the network yearly, and cth represents the price of thermal energy based on an Italian market survey.

Similarly, the revenue related to the selling of cooling energy Rcool is defined as

$$R\_{\rm cool} = E\_{\rm cool} \mathfrak{c}\_{\rm cool} \tag{5}$$

where Ecool represents the amount of cooling energy provided to the network yearly, and ccool represents the price of cooling energy based on an Italian market survey.

The simple payback (SPB) is defined as follows,

$$\text{SPB} = \frac{Z\_{\text{TOT}}}{\text{CFS}} \tag{6}$$

where CFS represents the yearly cash-flow statement, which is defined as

$$\text{CFS} = \text{R}\_{\text{TOT}} - \text{C}\_{\text{TOT}} \tag{7}$$

RTOT represents the sum of all the revenues, and CTOT represents the sum of the yearly maintenance cost CO&M and the yearly operational cost COp, which are defined as follows,

$$\mathbf{C\_{O\&M}} = 0.05 \times \mathbf{Z\_{TOT}} \tag{8}$$

$$\mathsf{C}\_{\mathsf{op}} = \frac{\mathsf{P}\_{\mathsf{AUX}, \mathsf{TOT}}}{\mathsf{LHVV}\_{\mathsf{biom}}} \times \mathsf{c}\_{\mathsf{biom}} \tag{9}$$

where PAUX,TOT represents the total thermal energy provided by the auxiliary boiler, LHVbiom represents the lower heating value of the biomass (wood chips), and cbiom represents the unit cost of the biomass.

Finally, the main economic indicators are calculated to assess the economic profitability of the system, i.e., the discounted payback period (DPB), net present value (NPV), profit index (PI), and internal rate of return (IRR):

$$\text{DPB} = \frac{\ln(1 - \text{SPBa})}{\ln(1 + \text{a})} \tag{10}$$

$$\text{NPV} = (\text{CFS} \times \text{AF}) - Z\_{\text{TOT}} \tag{11}$$

$$\text{PI} = \frac{\text{NPV}}{\overline{\text{Z}\_{\text{TOT}}}} \tag{12}$$

where *a* represents the discount rate, AF represents the annuity factor, and N represents the service life.

$$\text{AF} = \frac{1}{\text{a}} \times (1 - \frac{11}{\left(1 + \text{a}\right)^{\text{N}}}) \tag{13}$$

Regarding the environmental analysis, the saved primary energy source (PE) is calculated by considering a specific reference scenario for each produced energy vector (electric energy and thermal energy for air conditioning).

Then, the PE is calculated as follows,

$$\text{PE} = \frac{\text{E}\_{\text{el}}}{\eta\_{\text{grid}}} + \frac{\text{E}\_{\text{th}}}{\eta\_{\text{bol,ref}}} + \frac{\text{E}\_{\text{cool}}}{\text{COP}\_{\text{ref,HP}}\eta\_{\text{grid}}} \tag{14}$$

where ηboil,ref. represents the reference value for the efficiency of the traditional natural gas boiler, and COPref,HP represents the reference value for the coefficient of performance (COP) of a traditional chiller.

Finally, the avoided CO2 emissions EMCO2 are calculated as follows,

$$\rm{EC\_{CO2}} \left( \rm{E\_{el}} + \frac{\rm{E\_{cool}}}{\rm{COP\_{ref,HP}}} \right) \times \rm{EF\_{grid}} + \frac{\rm{E\_{th}}}{\eta\_{boil,ref} + \rm{LHV\_{nat,gas}}} \rm{EF\_{rat,gas}} \tag{15}$$

where EFgrid represents the emission factor related to the national grid and EFnat,gas represents the emission factor of the natural gas.

The implemented economic model calculates the investment and the operating costs of both PS and RS. The cost functions adopted for PS and RS components are taken from scientific and technical literature. The cost of GHE1 and GHE2 are obtained by previous literature studies as a function of the heat exchanger area [51]. The tank cost is a function of occupied volume [90]. The cost of line networks for DHCN and DHWN is the functions of diameters and length of pipes [91]. The cost of pumping depends on flow rates which cross the pumps [92].


**Table 4.** Main input parameters for the economic and environmental analysis.

The study realizes a parametric analysis with different depths of the geothermal well. The depth of the geothermal well affects both the operation of the system plant and economic performance. The aim of the analysis is the prefeasibility study by considering the uncertainty related to the depth where the geothermal source is available and assessing a range for each main performance indicator where the system can be considered feasible and profitable.

A second parametric analysis is performed with different operation times of the DHCN, without changing the operation time of the DHWN; this ensured a constant temperature of 45 ◦C.

When the DHCN operation time is reduced, a larger amount of electric energy is available, because all the auxiliaries of the DHCN subsystem are off. Consequently, higher revenue related to electricity production is expected.

Additionally, the DHWN subsystem is forced to use the auxiliary biomass boiler to ensure the appropriate temperature of the DHWN; thus, a higher operational cost related to boiler fuel (wood chip) is expected.

The objective is to evaluate the effects of the production strategy on profitability and to determine the optimum operation point.

#### **7. Results**

#### *7.1. Thermodynamic Analysis*

First, the daily results are presented and discussed through two days representative of the system functioning for each operation mode: one for heating (winter day) and one for cooling (summer day).

Figures 6 and 7 show the main system outputs, respectively, for the winter day where the nomenclature and numeration refer to Figure 5.

(**b**)

**Figure 6.** Main system temperatures: winter day (30 January). from T1 to T8 (**a**); from T10 to T26 (**b**).

**Figure 7.** Main system powers: winter day (30 January). . Qgeo, . QNET.req, . QTK1,in and . QBB (**a**); . QDHW, . QNET.supply, . Qloss,tot and . Pel,net (**b**).

Figure 6 presents the temperatures of the geothermal system for the winter day. T1 and T2 are not reported on the figure. T1 is constant at 150 ◦C, according to the input parameters, and T2 is constant at 122 ◦C due to the steady working conditions of the ORC module. T3 varies depending on the time operation of the DHCN and the operation of TK1.

When the DHCN is off, T3 coincides with T2, whereas it continuously varies depending on the inlet condition of the cool side at GHE2, i.e., T10.

T3 never decreases to 70.0 ◦C, due to the calibration of the overall system and the control strategy.

T10 and T8 exhibit the trends of TK1 to and from GHE2, respectively; T11 and T21 represent the trends of the water temperatures to and from the DHCN, respectively. The system can ensure a constant temperature of 50.0 ◦C to the DHCN and the set point temperature of the fan coils installed in the apartments taking into account the small heat losses occurring in the piping.

Moreover, the system is capable to give the DHW at a constant temperature value of 45.0 ◦C, as shown in Figure 6, independently by the load, shown in Figure 7.

From 6:00 to 10:00, the geothermal source is mainly employed to thermally load TK3, which belongs to the DHW subsystem. From 10:00 to 20:00, the source is mainly employed to thermally load TK1, which belongs to the DHCN.

Simultaneously, the geothermal source is constantly employed to feed the ORC module.

The foregoing is clearly shown in Figure 7, which presents the main system powers.

When the DHCN is off, the amount of achievable thermal power by the geothermal fluid is equivalent approximately to 4.50 MW, whereas it increases to 13.0 MW when the load required by the network is maximized.

The ORC net power production depends on the operation time of the DHCN. When the DHCN is off, the ORC power (approximately 430 kWel) is employed for geothermal fluid pumping and the ORC cooling tower auxiliaries, and the remaining part is sent to the grid.

When the DHCN is on, ORC power is employed to feed all the system auxiliaries (pumps and the overall control and monitoring system). Then, the net power sent to the grid decreases to 380 kWel.

Figures 8 and 9 show the main system temperatures for the characteristic representative summer day, and Figure 10 presents the main system powers.

**Figure 8.** Main system temperatures: summer day (21 July—A). from T1 to T8 (**a**); from T10 to T26 (**b**).

**Figure 9.** Main system temperatures: summer day (21 July—B).

(**a**)

**Figure 10.** Main system powers: summer day (21 July). . Qgeo, . QNET.req, . QTK1,in, . QTK2,out and . QBB (**a**); . QDHW, . QNET.supply, . Qchill, . Qloss,tot and . Pel,net (**b**).

(**b**)

In particular, Figure 9 indicates the temperature trend of TK3 (T15, T16, T19, T20) and the ADS module (T13, T14, T15, T16, T17, T18). As shown, the feed temperature T13 of the ADS module is constant at 100 ◦C, except at the initial time, where no cooling load is observed (Figure 10) and the feed water is available at 120 ◦C. Moreover, the results indicate that the system is perfectly capable of ensuring a constant temperature T19 (10.0 ◦C) of the cooled water to be sent to the network, which corresponds (taking into account the losses in the network piping) to the set temperature of the fan coil in the cooling mode.

Table 5 presents the main results of the thermodynamic analysis on a monthly and yearly basis.


**Table 5.** Main results of the thermodynamic analysis (on a monthly and yearly basis).

As shown, the system is perfectly capable of ensuring the temperature levels in each subsystem and it is perfectly capable of covering the total network load required (sum of thermal total power required by DHCN and DHWN) and the losses occurring in the network.

During the heating season, the overall thermal energy provided by the system for district heating, ESUPPLIED,DHCN, is higher than the thermal energy required, Ereq,WINT,DHCN; the difference is caused by the losses occurring at the network piping.

Moreover, the sum given by the thermal energy exiting the TK1, ETK1,out, and the one coming from the auxiliary boiler for the DHCN, EAUX,DHCN, is higher than ESUPPLIED,DHCN: this is due to the thermal losses occurring at the plant piping.

Thermal losses occurring at the thermal storages are given by the difference between the thermal energy entering and exiting the tanks.

What has just been discussed can be referred to the domestic hot water production system.

During the cooling season, the overall cooling energy provided by the system for district cooling, ESUPPLIED,DHCN is higher than the cooling energy required Ereq.SUMM,DHCN; even in this case the difference is caused by the losses occurring at the network piping.

Similarly to the heating season, during the cooling season the cooling energy exiting the TK2 ETK2,out is higher than the supplied one ESUPPLIED,DHCN because of the losses occurring at the system plant.

The gross amount of electricity produced, Pel,ORC, remains constant throughout the year, and Pel,net, which represents the amount of electricity produced and sold to the grid, is lower during the cooling

operation than during the heating operation. This is because the entire ADS subsystem, which is off during the heating operation, must be powered.

The constant average first-law efficiency of the ORC is 10.6%, owing to the steady working condition of the module.

The ADS, whose COP is 0.700 under nominal conditions (temperature of the feed hot water equal to 100 ◦C, the temperature of chilled water equal to 7 ◦C, and temperature of the cooling water equal to 22 ◦C), operates during the year with an average COP of 0.660: this is due to fluctuations in operating conditions (in terms of the feed water temperature, cooling water temperature, load), which move the module from the optimum point of operation.

#### *7.2. Environmental and Economic Data Analysis*

In this section, the main results of the economic and environmental analyses are presented and briefly discussed. The costs of the components are presented in Table 6, along with the cost function adopted. The total investment cost takes into account three different values of the depth of the geothermal well: the base case at 1500 m and the case of higher depth at 2000 and 2500 m by considering two production and one reinjection wells. Globally, the total investment cost (ZTOT) ranges between 7.84 and 8.21 M€.


**Table 6.** Component plant costs.

Table 7 presents the detailed yearly economic analysis results for each well depth and the different scenarios of the electricity market (with and without feed-in tariffs).

In the case of no feed-in tariffs, the total revenue RTOT ranges from 1.09 to 1.18 M€. With a total operational and maintenance cost CTOT of approximately 0.40 M€, the CFS ranges between 0.69 and 0.78 M€ per year.

All the economic indicators are negatively affected by the low CFS, and the system appears to be unprofitable.


**Table 7.** Main results of the economic analysis (on a yearly basis).

The SPB period exhibits a minimum value of 10.0 years and a maximum value of 11.9 years. These are far higher than the acceptable range of 5.00 to 7.00 years for private investments.

With a discount rate of 5.00%, the DPB period increases (minimum value of 14.3 years and maximum value of 18.5 years).

The NPV exhibits low values ranging between 0.388 and 1.88 M€, corresponding to a PI ranging between 4.73% and 24.0%. Acceptable values of the PI are between 60.0% and 70.0%.

Finally, the IRR exhibits low values between 5.51% and 7.64%

The economic profitability is improved in the case of the feed-in tariffs for electricity selling.

In fact, given the constant revenues related to the thermal and cooling energy for air conditioning, Rth, and Rcool, as well as the constant operational and maintenance costs CTOT, in correspondence of

CFS value of 1.12 M€ the higher revenue related to power production Rel are equal to 0.631 M€. Consequently, acceptable values of the SPB and DPB are obtained.

The SPB period ranges between 7.00 and 7.33 years, and the DPB period ranges between 8.84 and 9.36 years.

The NPV is increased to values between 5.74 and 6.11 M€, corresponding to PIs of 69.9% and 77.9%, respectively.

Finally, the IRR ranges between 12.2% and 13.0%.

Globally, as shown in Table 8, such a renewable system allows avoiding the employment of 27.2 GWh of primary energy and (depending on the reference scenario adopted for the energy and material outputs) avoiding 5.49 <sup>×</sup> 103 tons of CO2 emissions.


**Table 8.** Saved primary energy and CO2 emissions.

The main results of the thermodynamic and economic analyses performed by varying the operation time of the DHCN are presented from Tables A5–A9 in Appendix A. In detail, the data about electricity production (Rel), the CFS, the SPB, the NPV, and the PIs in the case of feed-in tariffs (green) and the cases of the minimum and maximum selling prices of electricity are reported.

Longer operation time of the DHCN subsystem corresponds to higher economic profitability: all the economic indices are affected by lower DHCN operation time.

In fact, in the case of the longest time of operation, a slightly lower amount of electricity is sold to the grid because the auxiliaries are on, and the revenue related to electricity is lower as well.

On the other hand, a higher amount of thermal energy is available from the geothermal source, then avoiding the use of biomass and reducing the operational cost of the biomass boiler to supply the DHW.

In case of the shortest time of operation, a higher amount of electricity is available (auxiliaries are off) for the selling. At the same time, any load from DHW network is cover by the biomass boiler, and a higher operational cost related to boiler fuel is obtained.

The higher operational cost of the biomass boiler prevails on the higher revenue related to electricity when the time of operation is reduced and the global profitability decreases.

The revenues related to space heating and cooling are constant.

It is worth noticing that, despite the analysis was carried out with the greatest possible precision, the results strictly depend on the specific case study analyzed and on the considered market context; moreover, they are affected by unavoidable uncertainty given by


#### **8. Conclusions**

A thermodynamic, economic, and environmental analysis of a renewable polygeneration system connected to a DHCN was performed.

The system is designed for a suburban area of the metropolitan city of Naples (South of Italy) and it is powered by geothermal sources and biomass, producing electricity, thermal energy for space heating and cooling, and DHW production.

The entire dynamic simulation model (which includes an organic Rankine cycle module, an ADS, an auxiliary biomass boiler, geothermal heat exchangers, thermal storage tanks, the DHCN, residential systems of space conditioning including terminals, and a suitable model of the building envelope) was developed and implemented in AspenONE and TRNSYS environments.

The layout and the control strategy were implemented to match the appropriate operating temperature levels for each component and to prevent the temperature of the geothermal fluid reinjected into the wells from decreasing below 70.0 ◦C.

The overall component calibration and the economic analysis were based on manufacturer data and market surveys.

The economical returns are estimated by considering the electric power sold to the national grid. Differently, the thermal energy for heating and cooling is employed to satisfy the thermal yearly load of the whole district.

An analysis was performed with different depths of geothermal wells where the source is available considering a geothermal temperature gradient of 0.1 ◦C/m.

An economic analysis was performed for two different electricity purchase scenarios: with and without feed-in tariffs.

The system, whose investment cost ranges between 7.84 and 8.02 M€, is economically feasible only under feed-in tariff conditions.

*Energies* **2020**, *13*, 4603

In fact, without feed-in tariffs, economic indicators suggest that the system is unprofitable: the minimum SPB period is 10.1 years (corresponding to a DPB period of 14.3 years if a discount rate of 5.00% is applied), and the maximum NPV is 1.88 M€ (corresponding to a maximum PI of 24.0%).

Finally, the maximum IRR is 7.64%.

Conversely, if feed-in tariffs are considered, the economic indicators suggest that for the specific case study analyzed, the system is attractive.

The minimum SPB period is 7.00 years, corresponding to a DPB period of 8.84 years.

The maximum NPV is increased to 6.11 M€, corresponding to a PI of 77.9%. The maximum IRR is 13.0%.

The system allows avoiding exploitation of 27.2 GWh of primary energy yearly, corresponding to 5.49 <sup>×</sup> <sup>10</sup><sup>3</sup> tons of CO2 emissions avoided yearly.

The keys to making the small-medium scale systems powered with geothermal sources feasible and attractive are the polygeneration and the load-sharing, which aim at maximizing the source exploitation by diversifying the energy and material vectors produced and by obtaining loads and requests that are distributed over time to the greatest extent possible.

In future studies, different typologies of final users and different energy vectors could be considered using the sources availability 24 h/24 h to feed the plant.

**Author Contributions:** Conceptualization, F.C., A.M., E.M., C.R. and L.V.; methodology, F.C., A.M., E.M., C.R. and L.V.; software, F.C., A.M. and E.M.; formal analysis, F.C., A.M. and E.M.; investigation, F.C., A.M. and E.M.; resources, C.R. and L.V.; data curation, F.C., A.M. and E.M.; writing—original draft preparation, F.C., A.M. and E.M.; writing—review and editing, F.C., A.M. and E.M.; visualization, F.C., A.M. and E.M.; supervision, C.R. and L.V.; project administration, C.R. and L.V.; funding acquisition, C.R. and L.V.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the GeoGrid project POR Campania FESR 2014/2020 CUP B43D18000230007.

**Acknowledgments:** The authors gratefully acknowledge the financial support of provided through the GeoGrid project POR Campania FESR 2014/2020 CUP B43D18000230007. Nicola Massarotti gratefully acknowledges the local program of the University of Napoli "Parthenope" for the support of individual research.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Nomenclature**



*Energies* **2020**, *13*, 4603


#### **Appendix A**

*Appendix A.1. Input Parameters*

**Table A1.** Lengths and diameters of the main line and of the pipes of the subdistrict.



**Table A2.** Main thermodynamic and design input parameters.

\* Under nominal conditions. \*\* Rated power.


**Table A3.** Geothermal heat exchanger output parameters.



\* Under nominal conditions.

**Table A4.** Main ORC output parameters.


**Figure A1.** Electricity price from January 2018 to August 2019 for every partition (F1, F2, and F3) of the time-dependent tariff.

#### *Appendix A.2. Cost Functions*

In the following are the cost functions used in the economic analysis; it is also indicated the reference the function was taken from.

The cost of the well zwell, which is divided into three different segments, is a function of the diameter and depth of each segment. In this work, two production well and one reinjection well were supposed.

$$\begin{aligned} \text{z}\_{\text{well}} &= 2 \left( 37.974 \times \text{e}^{(0.0079 \times \text{D}\_{\text{wall}})} \times \text{H}\_{\text{wall},1} + 37.6 \times \text{e}^{(0.0039 \times \text{D}\_{\text{wall},2})} \times \text{H}\_{\text{wall},2} \right. \\ &+ 37.6 \times \text{e}^{(0.0039 \times \text{D}\_{\text{wall},3})} \times \text{H}\_{\text{wall},3} \\ \text{D}\_{\text{wall},1} &= 0.600 \text{ m}; \text{ H}\_{\text{wall},1} = 10.0 \text{ m} \\ \text{D}\_{\text{wall},2} &= 0.600 \text{ m}; \text{ H}\_{\text{wall},2} = 10.0 \text{ m} \\ \text{D}\_{\text{wall},3} &= 0.600 \text{ m}; \text{ H}\_{\text{wall},3} = 10.0 \text{ m} \end{aligned} \tag{A1}$$

$$\mathbf{z}\_{\text{goopump}} = 107.26 \times \dot{\mathbf{P}}\_{\text{pumpling}}^{0.7176} \tag{A2}$$

zORC = <sup>3000</sup> <sup>×</sup> P´ ORC (A3)

$$\mathbf{z}\_{\rm HE} = 150 \times \left(\frac{\mathbf{A}\_{\rm HE}}{0.093}\right)^{0.78} \tag{A4}$$

$$\mathbf{z}\_{\rm{ADS}} = 126 \times \mathbf{\hat{Q}}\_{\rm{ADS}} \tag{A5}$$

$$\text{R\\_zo}\_{\text{biómaas,}\text{boill}} = 8000 \times \text{Q\\_bis}\_{\text{biómaas,}\text{boill}[\text{kW}]} \tag{A6}$$

$$\mathbf{z\_{TK}} = 167.19 \times \mathbf{V\_{TK}} \tag{A7}$$

$$\text{m}\_{\text{pump}} = \text{\textdegree 389} \times \ln(\text{\textdegree 3.6}) - \text{\textdegree 289} \tag{A8}$$

$$Z\_{\rm CT} = \; 8815 \times \ln \text{( $\dot{P}\_{\rm cool, CT} \times 3600$ )} - 174 \tag{A9}$$

$$\mathbf{z}\_{\text{substat\'on\'ee}} = 1850/\text{unit} \tag{A10}$$

$$\mathrm{L}\_{\mathrm{plipings}} = \left(349.63 + 2472.37 \times 2472.37 \times \mathrm{D\_{plpa}}\right) \times \mathrm{L}\_{\mathrm{plpa}}\tag{A11}$$

#### *Appendix A.3. Main Results of Thermodynamic Analysis*




**Table A6.** Main results of the thermodynamic analysis (stop time of the DHCN at 22:00).

#### *Appendix A.4. Main Results of Economic Analysis*

**Table A7.** Main results of the economic analysis (on a yearly basis; stop time of the DHCN at 20:00).



**Table A8.** Main results of the economic analysis (on a yearly basis; stop time of the DHCN at 22:00).

**Table A9.** Main results of the environmental analysis (on a yearly basis).


#### **References**


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