Heat Pump Performance Mapping for Energy Recovery from an Industrial Building

Abstract

Industrial buildings have numerous kinds of energy-losing equipment, such as engines, ovens, boilers and heat exchangers. Energy losses are related to inefficient energy use and lousy work conditions for the people inside the buildings. This work is devoted to the recovery of lost energy from industrial buildings. Firstly, the residual energy of the building is extracted to be used to warm water. Consequently, the work conditions of the people inside industrial buildings can be improved by maintaining the adequate temperature. The recovery of the energy is performed by a multipurpose heat pump system (HP system). The working fluid used in the HP system is R134a, which is a traditional and cheap working fluid. The thermophysical properties of R134a are obtained through the PC-SAFT equation of state. This work presents a performance mapping based on the intercepted areas framework to evaluate which working conditions are the optimal operating variables. The latter depends on several key parameters, such as compressor work, heat delivery, heat absorbed and exergetic efficiency. The results show that the optimal work conditions are found at different condenser and evaporator temperatures, and these may be limited by what the designer considers a sound performance of the heat pump system.

1. Introduction

The efficient use of energy is a trendy topic due to the high increase in energy demand and the search for more environmentally friendly energy sources [1,2,3]. Among the broad spectrum of possibilities for exploiting residual thermal energy, organic Rankine cycles (ORCs) are one of the most promising and investigated alternatives [4,5]. ORCs are one of the most popular and well-known technologies in this area for taking advantage of residual heat from processes, such as combustion and hot flows. However, the work production from ORCs requires significant energy from low-temperature thermal energy (LTTE) sources. Other technologies that may benefit from LTTE are thermal energy accumulators (TEAs) [6,7], drying technologies [8,9] and heat pumps (HPs) [10,11,12,13,14,15,16].

In most cases, mechanical work produces electric energy. TEAs accumulate LTTE for immediate or later use, such as the heating process. Drying technologies direct the LTTE to reduce the humidity of some materials, such as food, wood and clothes. HP technologies absorb LTTE for delivery to other places. All the mentioned technologies have in common that they work based on low-temperature thermal energy, i.e., under 200 °C [17,18]. Generally, energy sources near the ambient temperature are excluded from utilization in ORCs. The aforementioned sources can be exploited using heat pumps by correctly selecting the working fluids.

Industrial buildings use equipment that generates residual heat, such as engines, ovens, boilers and heat exchangers, to name a few; these buildings reach temperatures around 40 °C [19,20]. The heat generated by the mentioned equipment can change conditions and wellness inside an industrial building by increasing the temperature [21,22]. Therefore, the temperature and energy losses need to be controlled. On the one hand, the building’s interior temperature must be limited to a maximum of around 27 °C [23] to avoid a deterioration of the workers’ work conditions, generating health issues [24]. On the other hand, converting energy losses into useful sources laterally helps reduce energy consumption, reduce pollution and increase economic competitiveness.

Heat pumps may take advantage of very low temperatures where other technologies cannot operate [25,26]. In addition to using the LTTE to heat a place or substance, HPs can lower the temperature inside an industrial building [27,28]. The above involves investing electric energy in a compressor to multiply the heat absorbed and deliver it to a medium to increase its temperature [29]. As mentioned, the translated heat can be used to warm another fluid or for direct heating. In the first scenario, the most common requirement is hot-water production. Remarkably, water is always necessary. Despite this, water storage is not an economically desirable process [30]. To address the aforementioned issue, there have been proposals for innovative solutions to utilize this resource effectively [10,11,25,26,29,31,32,33].

Min et al. [29] deeply analyzed the heat pump performance and found it is severely degraded as the temperature of the heat source is decreased. This results in a serious mismatch of heat pump output and space heating demand for air source heat pumps. Zhao et al. [25] investigated the thermal performance of the water-source heat pump water heater system. The study used a prototype cycle in a heating mode. The influence of the vapor flows and the evaporator performance was established.

Esfahni et al. [26] present a novel approach for addressing the water and cooling demand in climate-change-vulnerable regions. The system includes a multi-effect system based on heat pumps. Oh et al. [31] use a dynamic process simulator to model different layouts of a heat pump system for a building’s water treatment. Pitarch et al. [32] analyze the critical equipment for improvement in these cycles, as well as the external conditions. Hervás-Blasco et al. [10] present the experimental results of a new water-to-water heat pump composed of the basic heat pump components for water. Stene et al. [33] test a carbon dioxide heat pump by a simulation in space heating and water heating scenarios, and both function simultaneously. Finally, Ammar et al. [11] present a complete review of heat recovery studies, including high- and low-grade temperature sources. Various aspects influencing the decision-making for low-grade heat recovery in the process industry are discussed.

Zendehboudi et al. [12,13,14] aimed to improve cleaner production by improving the energy efficiency and control strategies of transcritical ${\mathrm{CO}}_2$ heat pumps. The above was achieved by evaluating the operational conditions and key parameters of the system, such as surrounding temperature, COP and discharge pressure. In addition, it evaluates the influence of different equipment in the HP system, such as internal heat exchangers (IHXs) and plate heat exchangers. These findings offer insights for designing and optimizing transcritical ${\mathrm{CO}}_2$ heat pumps for simultaneous space and water heating applications. Song et al. [16] studied and compared the performance of combined R134a/${\mathrm{CO}}_2$ and cascade R134a/${\mathrm{CO}}_2$ systems for space heating. Parameters such as water feed temperature, water supply temperature and ambient temperature were investigated. Results showed that the systems had different preferable application conditions. The cascade system performed better at low ambient temperatures, while the combined system performed better under high ambient temperature and high hot water temperature differences between the system inlet and outlet. Sun et al. [15] proposed a novel ternary refrigerant. The refrigerant was named RDR-a (ternary blend composed of R134a/RE170/R152a). Experiments were performed to compare the system performance of RDR-a and R134a for applications in the high-temperature heat pump (HTHP) system. RDR-a exhibited the capability of being applied directly to the R134a system. In addition, RDR-a achieved a GWP of 61.79% lower than R134a. The above is considered an important step toward reusing refrigerants, which are categorized as environmentally unfriendly.

This work is dedicated to analyzing the key parameters for determining the optimal operational conditions for a multipurpose HP system. This heat pump is used to preserve adequate work conditions in an industrial building and produce hot water. As a first approach to this novel equipment, R134a is utilized as the working fluid, and the analyzed parameters are the HP coefficient of performance (COP), the compressor energy demand, the heating capacity of the condenser and the heat absorbed by the evaporator. Additionally, the exergetic efficiency of the isobaric processes is evaluated as a measurement of the effectiveness of both critical aspects of the system. The optimal operation variables are established to fulfill the two purposes of the system: heating water on demand and promoting the health of the workers in an industrial building.

2. Methodology

2.1. Description of the System

Figure 1 shows a novel heat pump system (HP system) based on a vapor compression cycle. The main objective is to use the thermal residual energy from industrial buildings to heat water. Moreover, the system has a complementary objective. The above purpose is to lower the air temperature in industrial buildings to improve workers’ welfare. The HP system is composed of a compressor, a condenser, a valve expander and an evaporator. The compressor unit compresses the refrigerant, (1) to (2i), at the condenser pressure. The condenser unit delivers energy, from point (2i) to (3), to the water to raise its temperature. Then, the valve strangles the refrigerant pass, from (3) to (4), to the evaporator work pressure. The evaporator unit absorbs heat from (4) to (1v) from the industrial building.

Figure 2 shows the temperature vs. entropy diagram of a refrigerant detailing the system’s fundamental points. The points highlight the four main processes: (1) to (2) reversible compression process, (1) to (2i) irreversible compression process, (2) to (3) isobaric process heat delivery, (3) to (4) isoenthalpic expansion and (4) to (1v) isobaric heat absorption process. Additionally, Figure 2 shows the water heating profile in the blue line and the air cooling profile in the crimson line. Both temperature profiles, water (w) and air (a), show the inlet temperature (in), the middle temperature (m) and the outlet temperature (out). The middle temperature is defined as the minimum temperature necessary to promote heat transfer between the water and the refrigerant. These points are fundamental in the thermal and exergetic analysis of the system.

The coefficient of performance of a HP, ${\mathrm{COP}}_{\mathrm{HP}}$, is used to evaluate the performance of the system based on a vapor compression cycle. The heat pump COP is given by

$${\mathrm{COP}}_{\mathrm{HP}}={\displaystyle \frac{Q_{\mathrm{del}}}{W}}={\displaystyle \frac{W+Q_{\mathrm{abs}}}{W}}=\mathrm{COP}+1$$

(1)

where $Q_{\mathrm{del}}$ is the condenser heat, $Q_{\mathrm{abs}}$ is the evaporator heat, W is the compressor thermodynamic work, and COP is the coefficient of performance of a vapor compression cycle. Further, $Q_{\mathrm{del}}={\dot{Q}}_{\mathrm{del}}/\dot{m}$, and $W=\dot{W}/\dot{m}$, $\dot{m}$ being the mass or molar flow in the HP system.

Compressor power input and condenser heat delivery also can be expressed as enthalpy differences. For instance, the compressor power is given by

$${\displaystyle \frac{{\dot{W}}_{\mathrm{c}}}{\dot{m}}}={\tilde{H}}_{2\mathrm{i}}-{\tilde{H}}_1$$

(2)

while for the condenser heat delivery, the heat yields

$${\displaystyle \frac{{\dot{Q}}_{\mathrm{del}}}{\dot{m}}}={\tilde{H}}_3-{\tilde{H}}_{2i}={\displaystyle \frac{{\dot{m}}_{\mathrm{w}}}{\dot{m}}}\left({\tilde{H}}_{\mathrm{w},\mathrm{out}}-{\tilde{H}}_{\mathrm{w},\mathrm{in}}\right)$$

(3)

Correspondingly, the heat absorbed in the evaporator from the industrial building can be written as

$${\displaystyle \frac{{\dot{Q}}_{\mathrm{abs}}}{\dot{m}}}={\tilde{H}}_{1\mathrm{v}}-{\tilde{H}}_4={\displaystyle \frac{{\dot{m}}_{\mathrm{a}}}{\dot{m}}}\left({\tilde{H}}_{\mathrm{a},\mathrm{out}}-{\tilde{H}}_{\mathrm{a},\mathrm{in}}\right)$$

(4)

Now, considering an exergy approach, the flow-specific exergy [5] can be defined as

$${\psi }_k={\tilde{H}}_k-{\tilde{H}}_0-T_0\left({\tilde{S}}_k-{\tilde{S}}_0\right)$$

(5)

where the subscripts k concern the flow, while the subscript 0 represents the dead-point condition fixed at the surrounding temperature, which is given by 293.15 K.

In an adiabatic heat exchanger system with two flows, the exergy supplied is the decrease in the hot-flow exergy. In contrast, the exergy recovered is the increase in the cold-flow exergy, as long as it is not at a lower temperature than the surroundings [5,6]. Therefore, the exergetic efficiency between the condenser as a heater and the water yields

$${\eta }_{\mathrm{II},\mathrm{c}}={\displaystyle \frac{{\dot{m}}_{\mathrm{w}}\left({\psi }_{\mathrm{w},\mathrm{in}}-{\psi }_{\mathrm{w},\mathrm{out}}\right)}{\dot{m}\left({\psi }_{2\mathrm{i}}-{\psi }_3\right)}}$$

(6)

where ${\dot{m}}_{\mathrm{w}}$ is water mass flow, and $\dot{m}$ is working fluid mass flow.

Moreover, the exergetic efficiency between the evaporator as a cooler and the air industrial building yields

$${\eta }_{\mathrm{II},\mathrm{e}}={\displaystyle \frac{\dot{m}\left({\psi }_{1\mathrm{v}}-{\psi }_4\right)}{{\dot{m}}_{\mathrm{a}}\left({\psi }_{\mathrm{a},\mathrm{in}}-{\psi }_{\mathrm{a},\mathrm{out}}\right)}}$$

(7)

where $\dot{m_{\mathrm{a}}}$ is air mass flow.

As expected, the evaporator temperature is lower than the ambient temperature. Consequently, the previously selected reference cannot be used as the dead-point temperature. For this reason, a second reference is defined to evaluate the exergetic efficiency of the evaporator, ${\eta }_{\mathrm{II},\mathrm{e}}$. This second dead-point temperature is defined as a temperature 5 K lower than the evaporator temperature in each scenario of analysis.

2.2. Case of Study

This study employs the SECOP compressor model SC10GHH as a compressor unit for the HP system.

Table 1. Input parameters and boundary conditions considered in this study.

	Value	Range
	HP system compressor technical conditions
Displaced volume	10.29 ${\mathrm{cm}}^3$	–
Revolutions per minute	2900.00 rpm	2900.00 to 3500.00 rpm
Pressure operation maximum	1600.00 kPa	–
Temperature operation maximum	330.15 K	–
Isentropic performance	–	60 to 100%
	General boundary and limit conditions
Condenser temperature	–	313.15 to 330.15 K
Evaporator temperature	–	263.15 to 293.15 K
Initial water temperature	293.15 K	–
Initial industrial building temperature	313.15 K	–
Comfort industrial building temperature	297.15 K	–

shows the technical characteristics of the SECOP compressor that limit this study [34]. The displaced volume of the compressor, $V_d$, is fixed. The compressor has a revolution per minute limit range for its use, depending on the motor [35]. For this study, 2900 rpm is considered (motor with a pair of poles, 50 Hz).

On the one hand, the compressor operation is operationally limited by the saturation temperature and pressure. On the other hand, a performance range is determined by both the compressor’s lifetime and spoilage. Finally, to determine the refrigerant mass flow that can move the compressor, a technical-mathematical expression is used [36], which is given by

$$\dot{m}=V_d{R}_v{\rho }_1$$

(8)

The latter expression considers $V_d$ in ${\mathrm{m}}^3$ ${\mathrm{h}}^{-1}$, the volumetric performance, $R_v$, and the working fluid density in the compressor inlet, ${\rho }_1$. Further, $R_v$ is a function of the compression relation $r_c$ as

$$r_c={\displaystyle \frac{P_{2\mathrm{i}}}{P_1}}$$

(9)

$$R_v=1-0.03r_c$$

(10)

Table 1 shows the condenser and evaporator temperature limit conditions. Additionally, Table 1 displays the water’s initial and air temperatures. The limit condition of the compressor determines the condenser temperature. The evaporator temperature is given by the operating temperature of a compressor that can be used for high back pressure application, HBP [37]. HBP applications, such as heat pump systems, should be used for high evaporation temperatures. The SECOP compressor, categorized as an HBP compressor, should operate for an evaporator temperature between −10 and 20 °C [37]. The above is considered a regular use of the turbomachine [34,37].

2.3. Modelling

The water to be heated begins at an initial temperature, ${\mathrm{T}}_{\mathrm{w},\mathrm{in}}=$ 20 °C. The temperature reached by the water, ${\mathrm{T}}_{\mathrm{w},\mathrm{out}}$, is determined by the delivery heat by the HP system. The water properties are obtained by the IAPWS multiparametric equation [38].

The air that is to be cooled begins at a fixed initial temperature, ${\mathrm{T}}_{\mathrm{a},\mathrm{in}}=$ 40 °C, and the desired temperature in the industrial building also is fixed, ${\mathrm{T}}_{\mathrm{a},\mathrm{out}}=$ 27 °C. The air is modelled using the standard air assumptions [39]. The enthalpy and entropy are fundamental to evaluating ${\dot{Q}}_{\mathrm{abs}}$ and evaporator exergetic efficiency. Then, to calculate the air enthalpy and entropy, a second-order polynomial is fitted to render the air data, which is given by

$${\tilde{H}}_{\mathrm{a}}-{\tilde{H}}_{\mathrm{r}}={\beta }_{1,0}+{\beta }_{1,1}T+{\beta }_{1,2}{T}^2$$

(11)

and

$${\tilde{S}}_{\mathrm{a}}-{\tilde{S}}_{\mathrm{r}}={\beta }_{2,0}+{\beta }_{2,1}T+{\beta }_{2,2}{T}^2$$

(12)

where the constants of Equations (11) and (13) are presented in the

Table 2. Constants for the air enthalpy, Equation (11), and entropy, Equation (12).

i	${\mathit{\beta }}_{\mathit{i},1}$	${\mathit{\beta }}_{\mathit{i},2}$	${\mathit{\beta }}_{\mathit{i},3}$
1	J ${\mathrm{kg}}^{-1}$	J ${\mathrm{kg}}^{-1}$ ${\mathrm{K}}^{-1}$	J ${\mathrm{kg}}^{-1}$ ${\mathrm{K}}^{-2}$
	5.8341 $\times {10}^3$	9.6110 $\times {10}^2$	6.6642 $\times {10}^{-2}$
2	J ${\mathrm{kg}}^{-1}$ ${\mathrm{K}}^{-1}$	J ${\mathrm{kg}}^{-1}$ ${\mathrm{K}}^{-2}$	J ${\mathrm{kg}}^{-1}$ ${\mathrm{K}}^{-3}$
	0.4713 $\times {10}^3$	4.9931 $\times {10}^1$	−2.9897 $\times {10}^{-3}$

. The subscript r concerns an arbitrarily selected value for the enthalpy or entropy.

The working fluid used in this study is R134a. R134a is the most popular refrigerant used on a global level [40,41]. R134a is used as the working fluid for the heat pump. The aforementioned working fluid is the most popular refrigerant worldwide [40,41]. For the accurate modelling of the R134a properties, the PC-SAFT equation of state (EOS) is utilized [42,43]. PC-SAFT EOS is one of the most used versions of the SAFT-family EOS [44,45] and is highly recognized for its versatility and accuracy. Many different working fluids have been successfully modelled with this approach [46,47,48]. In a general form, these EOSs are expressed as a sum of different contributions to the residual Helmholtz energy of a specific compound, ${\tilde{A}}^{\mathrm{r}}$. For a simple compound, this construction is reduced to

$${\tilde{A}}^{\mathrm{r}}={\tilde{A}}^{\mathrm{hc}}+{\tilde{A}}^{\mathrm{disp}}$$

(13)

the superscripts in Equation (13) concern hard-chain and dispersive contributions, respectively [42]. The total Helmholtz energy function is the sum of the residual contribution and the ideal contribution, i.e., $\tilde{A}={\tilde{A}}^{\mathrm{r}}+{\tilde{A}}^{\mathrm{i}}$, where the ideal contribution is given by

$${\displaystyle \frac{{\tilde{A}}^{\mathrm{i}}}{RT}}=-\ln \tilde{v}-{\displaystyle \frac{1}{RT}}\int \int {\displaystyle \frac{C_P^{\mathrm{i}}-R}{T}}d{T}^2+\ln {\displaystyle \frac{R{T}^{\Theta }}{P^{\Theta }}}+{\tilde{A}}^{\mathrm{i}\Theta }$$

(14)

in Equation (14), R is the universal gas constant, and $T^{\Theta }$ and $P^{\Theta }$ are the thermodynamic temperature and pressure of a reference state, $\Theta$, respectively. Meanwhile, ${\tilde{A}}^{\mathrm{i}\Theta }$ corresponds to the value of the Helmholtz energy function of the perfect gas at the same reference. Additionally, $C_P^{\mathrm{i}}$ is the isobaric heat capacity of the perfect gas. The isobaric heat capacity is usually expressed in a polynomial form as

$${\displaystyle \frac{C_P^{\mathrm{i}}}{R}}={\alpha }_0+{\alpha }_{1}T+{\alpha }_2{T}^2+{\alpha }_3{T}^{-2}$$

(15)

Table 3. Parameter for the reference EOS and the perfect-gas isobaric heat capacity [49].

R134a	m	$\mathit{\sigma }$	$\mathit{\epsilon }/{\mathit{k}}_{\mathit{B}}$
Residual		${\mathrm{m}}^{-10}$	K
	3.2483	3.0157	170.60
Ideal gas	${\alpha }_0$	${\alpha }_1$	${\alpha }_2$	${\alpha }_3$
		$T^{-1}$	$T^{-2}$	$T^2$
	7.4912	0.01707	−6.0249$·{10}^5$	−115,348.62

summarizes the parameter for the reference EOS and for the perfect-gas isobaric heat capacity.

Furthermore, to simplify the analysis, the system is considered to have steady-state conditions in all components, and the heat and friction losses in the system are neglected.

3. Results

3.1. Validation

Table 4. Validation of the predicted R134a properties with the PC-SAFT model from –10 to 57 °C.

AARE of the Equilibrium Properties/%
Pressure	Liquid Density	Vapor Density	Enthalpy Difference	Entropy Difference
$\mathit{P}$	${\mathit{\rho }}_{\mathit{l}}$	${\mathit{\rho }}_{\mathit{v}}$	$\Delta \tilde{\mathit{H}}$	$\Delta \tilde{\mathit{S}}$
0.0800	0.3299	3.3205	3.5697	3.5706

shows the validation of the equilibrium properties used in this study. The above is through calculating the Average Absolute Relative Error (AARE) between the predicted properties by PC-SAFT and the experimental data obtained from NIST [50]. The above can be written as

$${\mathrm{AARE}}_X={\displaystyle \frac{100}{n}}\sum _{i=1}^n\left|{\displaystyle \frac{X_{\mathrm{PC}-\mathrm{SAFT},i}-X_{exp,i}}{X_{exp,i}}}\right|$$

(16)

where X is the key parameter, the subscripts $exp$ and “PC-SAFT” denote the experimental data and the equilibrium properties calculated with the PC-SAFT model (n = 62).

The AARE of both the pressure, P, and liquid density, ${\rho }_l$, are predicted to be less than 1%. Moreover, the AARE vapor density, ${\rho }_v$, phase change enthalpy, $\Delta \tilde{H}$, and phase change entropy, $\Delta \tilde{S}$, are less than 5%.

The proposed PC-SAFT model and HP system are validated by comparing key parameters reported experimentally in the works of Carrington [20] and Linton et al. [19]. The compared parameters are heat delivery, COP and compression relation, $r_c$.

Table 5. Validation of the predicted properties with PC-SAFT EOS from 10 to 70 °C) [19].

AARE of the Equilibrium Properties/%
Pressure	Liquid Density	Vapor Density	Enthalpy Difference	Entropy Difference
$\mathit{P}$	${\mathit{\rho }}_{\mathit{l}}$	${\mathit{\rho }}_{\mathit{v}}$	$\Delta \tilde{\mathit{H}}$	$\Delta \tilde{\mathit{S}}$
0.1057	0.5328	4.0941	4.6929	4.6935

shows the validation of the equilibrium properties in the temperature range reported [19] (temperature range from 10 to 70 °C, n = 60). The AARE of the pressure and liquid density prediction is not higher than 1%. In addition, the AARE vapor density, phase change enthalpy and phase change entropy are not higher than 5%.

The border condition reported by Linton [19] is established to validate the HP system. The refrigerant temperature is constant and maintained at 70 °C. The evaporating temperatures were varied over a range from 11 to 34 °C. The reported refrigerant mass flow and compressor power were input parameters to determine the key parameters.

Table 6. Validation of the key parameters calculated with the PC-SAFT model.

AARE of the Key Parameters/%
Heat Delivery	Coefficient of Performance	Compression Relation
${\dot{\mathit{Q}}}_{\mathit{del}}$	$\mathbf{COP}$	${\mathit{r}}_{\mathit{c}}$
3.8219	3.7433	1.3864

shows the key parameters’ validation in the reported temperature range. It can be seen that the AARE of both of the ${\dot{Q}}_{\mathrm{del}}$ and $\mathrm{COP}$ are less than 4%. Moreover, the AARE of the $r_c$ is less than 2%.

3.2. HP-System Behavior

Figure 3 shows the three key parameters: compressor power input, delivery heat by the condenser to the water and COP. The parameters are calculated for three different compressor performances, i.e., 100, 80 and 60%. The above is for evaluating the compressor performance during a standard compressor life cycle. Moreover, the key parameters are calculated as a function of the evaporator’s and condenser’s saturation temperatures.

The contour plots presented in Figure 3 highlight the optimization direction of each variable with the arrows in their margins. For instance, the compressor power grows as the condenser and evaporator temperatures increase. In this case, the optimization path is opposite to the arrow because consuming less energy in the compression stage is desirable. In the case of the delivered heat, this variable increases with the evaporator temperature and decreases with the condenser temperature.

A compressor that uses a lower amount of energy to perform the same compression labor is more beneficial. Figure 3a shows the compressor power input for the design volumetric flow of the equipment. Figure 3a also illustrates the temperature range of the condenser and evaporator for different compressor efficiency values where the lower compression power is reached. As expected, a lower compression power is reached for higher compressor efficiency. Moreover, lower compressor power is located in the lower condenser and evaporator temperatures. Underlining the crucial role of the condenser in a heat pump, its objective is to deliver a significant amount of energy to a substance, in this case, water.

Figure 3b illustrates the condenser’s heat delivery to the water. The temperature range of the condenser and evaporator for different performance compressor values, where the heat delivery is maximized, is also illustrated in Figure 3b. It is noticeable that a lower heat delivery is achieved for a higher compressor performance. Furthermore, significant heat delivery is found at a lower condenser temperature and higher evaporator temperatures, as indicated by the two arrows that guide the direction of this significant heat delivery.

As mentioned, the ${\mathrm{COP}}_{\mathrm{HP}}$ represents the ratio between the heat delivery and the amount of energy consumed by the compressor. Therefore, a larger ${\mathrm{COP}}_{\mathrm{HP}}$ denotes better performance. Figure 3c shows the ${\mathrm{COP}}_{\mathrm{HP}}$ at the three selected efficiencies. As expected, greater ${\mathrm{COP}}_{\mathrm{HP}}$ can be found for higher compressor performance. As in the case of heat delivery, the parameter is more sensitive to the changes in the evaporator temperature than those in the condenser. This fact is expected as both variables are narrowly related.

As shown in Figure 3, compressor power, heat delivery and COP vary with the compressor efficiency.

Table 7. Variation of the key parameters when the compressor efficiency is equal to 100%.

${\mathit{V}}_{\mathit{X}}$ of the Key Parameters/%
Temperature Increase	Compressor Power/${\dot{\mathit{W}}}_{\mathit{c}}$		Heat Delivery/${\dot{\mathit{Q}}}_{\mathbf{del}}$		Coefficient of Performance/COP
	${\mathit{\eta }}_{\mathit{c}}$ = 80%	${\mathit{\eta }}_{\mathit{c}}$ = 60%	${\mathit{\eta }}_{\mathit{c}}$ = 80%	${\mathit{\eta }}_{\mathit{c}}$ = 60%	${\mathit{\eta }}_{\mathit{c}}$ = 80%	${\mathit{\eta }}_{\mathit{c}}$ = 60%
Condenser	25.000	66.670 (o)	5.960	15.892 (+)	15.232	30.465 (−)
Evaporator	25.000	66.670 (o)	3.332	8.884 (−)	17.335	34.670 (+)

shows the key parameter variation average depending on both the condenser and evaporator temperature increments, using as a reference the key parameter value obtained for a compressor efficiency of 100%. The above can be expressed as

$${\mathrm{V}}_X={\displaystyle \frac{100}{n}}\sum _{i=1}^n\left|{\displaystyle \frac{X_{100\%,i}-X_{\%,i}}{X_{100\%,i}}}\right|$$

(17)

where X is the key parameter, the subscript 100% denotes the key parameter value calculated with a 100% of compressor efficiency, and the subscript % is the key parameter value calculated with a 80% or 60% of compressor efficiency (n = 18). In addition, Table 7 uses three symbols, “+”, “−” and “o”, to point out the behavior variation in the key parameter with the increasing condenser or evaporator temperature. If the number in Table 7 is accompanied by “+”, the key parameter variation increases with the increasing condenser or evaporator temperature. If the number in Table 7 is accompanied by “−”, the key parameter variation decreases with the increasing condenser or evaporator temperature. If the number in Table 7 is accompanied by “o”, the key parameter variation is constant with the increasing condenser evaporator temperature.

It can be seen that the compressor power variation is constant for the increase in both condenser and evaporator temperatures. Moreover, the compressor power variation increases significantly with the decreasing compressor efficiency (from 25 to 66%). The above means the compressor power input increases drastically with the compressor efficiency loss. On the one hand, the heat delivery variation increases with the increase in condenser temperature. On the other hand, the heat delivery variation decreases while the evaporator temperature increases. Furthermore, heat delivery variation increases with the compressor efficiency loss. When the variation in compressor power is compared to the variation in heat delivery, it can be seen that the variation in compressor power is higher than the variation in heat delivery. Therefore, the improvement observed in the heat delivery to invest a higher amount of compressor power given the compressor efficiency loss could be more convenient from the energy point of view. The above can be seen in the COP variation. COP variation decreases with the increase in condenser temperature. The COP variation increases with the evaporator temperature increase. Furthermore, the COP variation increases with the compressor efficiency loss, but the COP variation is more uniform than the compressor power and heat delivery variation. Moreover, COP variation relates to compressor power and heat delivery variation. Consequently, it is the first signal of the HP system’s optimal operational conditions. The above is a higher value of COP and minor COP variation. This condition is located at a lower condenser temperature and higher evaporator temperature.

Figure 4 shows the absorbed heat by the HP evaporator, the refrigerant mass flow and the refrigerant inlet density of the compressor. As in Figure 4, the contour plots are a function of the evaporator’s and condenser’s saturation temperatures. None of the aforementioned parameters change with the compressor’s isentropic efficiency.

One of the goals of this heat pump is to absorb a significant amount of heat from industrial buildings. This process is crucial for the efficient operation of the system. Figure 4a visually represents the condenser and evaporator’s temperature range where the most heat is absorbed. It is important to note that greater heat absorption occurs at a lower condenser temperature and higher evaporator temperatures, as indicated by the two arrows that guide the direction of greater heat absorption.

The mass flow is a function of $V_d$, $R_v$ and ${\rho }_1$, considering that $V_d$ is fixed by the compressor’s technical characteristic. Therefore, the mass flow is directly proportional to ${\rho }_1$ and $R_v$. A greater ${\rho }_1$ value means moving more refrigerant mass in a specified volume is possible. The straightforward functionality of $R_v$ shows that decreasing the compression ratio yields an increase in $R_v$. Therefore, there is a larger refrigerant flow in the system. It is essential to point out that a greater mass flow generates greater delivery and absorption of heat. However, it also generates a greater consume compressor power input. Particularly, the evaporator temperature impacts the density of the compressor suction. In contrast, the condenser temperature does not affect this variable, as seen in Figure 4b. The absorbed heat and refrigerant mass flow are softly sensitive to the condenser temperature, with the evaporator temperature being their major influence.

The compressor outlet temperature is a critical parameter when evaluating the water outlet temperature. This temperature represents the higher temperature reached by the heat pump. Figure 5a depicts the compressor outlet temperature at the same variables as the previous analysis. As expected, two points are observed in these figures. Firstly, the temperature is stable depending on the evaporator and condenser temperatures, with the condenser temperature being the most sensitive variable. With less isentropic compression, the evaporator temperature becomes more important, and the temperature can reach higher temperatures. However, the efficiency loss in compression can cause other handicaps in the process [51].

Calefaction and sanitary water lie in a temperature range of around 35.0 to 55.0 °C [10]. The temperature that the water can reach is shown in Figure 5b. It is expected that fewer efficiencies in the compressor will give warmer water. However, as mentioned above, compression efficiency is not a variable in established equipment. Moreover, the water temperature distribution depends almost exclusively on the condenser temperature. The arrows in Figure 5b help to find the maximum water temperature. The latter is located at a larger condenser temperature and lower evaporator temperature. It considers the water application temperature range mentioned previously. It can be said that from a condenser temperature of 42.5 °C, for any evaporator temperature and any compressor performance, water temperatures can be found useful for water calefaction and sanitary application.

The heat exchange in the condenser, as a main aim of the process, is essential. For this reason, the exergetic efficiency of this process is analyzed and depicted in Figure 5c following Equation (6). The condenser temperature drives the exergetic production. The above is related to the temperature reached by the compressor outlet and the similarity between the profiles of the water and the working fluid in the superheated zone of the refrigerant. Furthermore, less efficiency in the compression yields a decrease in the exergetic efficiency.

In Figure 5, the compressor temperature, water outlet temperature and heater exergetic efficiency vary with compressor efficiency.

Table 8. Variation of the key parameters with respect to the compressor efficiency being equal to 100%.

${\mathit{V}}_{\mathit{X}}$ of the Key Parameters/%
Temperature Increase	Compressor Outlet Temperature/${\mathit{T}}_{\mathbf{2}\mathit{i}}$		Water Outlet Temperature/${\mathit{T}}_{\mathit{w},\mathit{out}}$		Heater Exergetic Efficiency/${\mathit{\eta }}_{\mathit{II},\mathit{c}}$
	${\mathit{\eta }}_{\mathit{c}}$ = 80%	${\mathit{\eta }}_{\mathit{c}}$ = 60%	${\mathit{\eta }}_{\mathit{c}}$ = 80%	${\mathit{\eta }}_{\mathit{c}}$ = 60%	${\mathit{\eta }}_{\mathit{c}}$ = 80%	${\mathit{\eta }}_{\mathit{c}}$ = 60%
Condenser	17.780	47.340 (−)	3.053	8.142 (+)	3.106	5.264 (+)
Evaporator	13.078	34.775 (−)	1.269	3.383 (−)	1.339	1.879 (−)

shows the key parameter variation average depending on the condenser and evaporator temperature increment using as reference the key parameter value obtained for a compressor efficiency of 100%.

The compressor temperature variation decreases with the condenser and evaporator temperatures increase. Moreover, the compressor temperature variation increases strongly with the efficiency loss of the compressor. The more significant compressor temperature variation is produced by decreases in the condenser temperature for both compressor efficiencies, i.e., 17.78 and 47.34 for ${\eta }_c$ = 80% and ${\eta }_c$ = 60%. The growth in the water outlet temperature is produced by the increase in the condenser temperature and the decrease in the evaporator temperature. Moreover, the outlet temperature variation of the water increases with the compressor efficiency loss. However, when comparing the compressor and water outlet temperature variation, it becomes clear that the latter is negligible. The above means that increasing the compressor outlet temperature is inconvenient since the water outlet temperature will stay constant. Therefore, it is convenient to keep the compressor efficiency nearer to 100% since there will not be a significant gain in the water temperature outlet by the compressor temperature increase produced by the power input increase. Finally, the heater’s exergetic efficiency variation is similar to the water outlet temperature variation. This parameter increases with the condenser temperature and the compressor efficiency loss. Further, the increase in the evaporator temperature reduces the exergetic efficiency. Notably, the heater’s exergetic efficiency variation remains stable with the variation in the condenser temperatures, demonstrating the system’s reliable energy delivery across all operational ranges considered in this study.

The water quantity is as important as its temperature. Clearly, both parameters are linked because the heat source has a limit for the heat source. Furthermore, it is also related to the number of possible services to use hot water [52]. Figure 6a shows the heated water flow obtained by the HP system. The compressor efficiency of Figure 6a is 80%. The selection is made given that the water flow is not sensitive to the efficiency of the turbomachinery. The volume of water significatively varies with both temperatures. The optimal point of operation for heated water production is decreasing the evaporator and condenser temperature.

One of the most crucial variables in the HP’s design is the airflow that can be cooled from the industrial building. This airflow plays a pivotal role in maintaining the desired temperature within the building, making it a key factor in the overall system design. Additionally, a higher capacity to cool an air volume is related to the time the system takes to reach the comfortable industrial building temperature, as seen in Table 1.

Figure 6b shows the HP cooling capability, as in the case of Figure 6a, this variable is independent of the compressor efficiency, and it is fixed at 80%. The behavior of this variable is similar to that of the hot water supply. However, the dependence on the condenser temperature is more prominent. Furthermore, the exergetic efficiency in the cold air supply is displayed in Figure 6c. The greater exergetic efficiency is reached at high temperatures of the evaporator and independent of the condenser temperature. The above yield optimization opportunities, setting the best combination of the evaporator and condenser temperature to operate an HP.

Nine of the twelve analyzed variables are displayed in Figure 7. The parameters are evaluated as a deviation given by

$$P_X=100\left|{\displaystyle \frac{X_{\mathrm{ref}}-X_i}{X_{\mathrm{ref}}}}\right|$$

(18)

where X is the key parameter, the subscript, ref, denotes the reference parameter, and the subscript (i) the ith key parameter. The reference value is selected depending on the variable at the minimum or maximum value presented in the range of the studied temperatures.

Figure 7 shows the deviation, P, of the critical parameters. Some of the selected parameters effectively vary as the compressor efficiency changes. However, the variation is slight, and an isentropic efficiency of 80% is selected as in previous cases. The arrows in the figures help locate the maximum deviation of the parameters. Therefore, the good performance of an HP can be limited by a contour of a mixed percentage. For example, a limit variation of 70% could be established as a good performance of the HP system. Figure 7 shows the deviation, P, of the critical parameters. Some of the selected parameters effectively vary as the compressor efficiency changes. However, the variation is slight, and an isentropic efficiency of 80% is selected as in previous cases. The arrows in the figures help locate the maximum deviation of the parameters. Therefore, the good performance of an HP can be limited by a contour of a mixed percentage. For example, a limit variation of 70% could be established as a good performance of the HP system. Figure 7a show that the good performance area for the compressor work is located in all evaporator temperature ranges up to a condenser temperature equal to 48 °C. and in all condenser temperature ranges up to an evaporator temperature equal to 0 °C. In addition, Figure 7b depicts that the superior performance area for the heat delivery is located in all condenser temperature ranges from an evaporator temperature close to 0 °C and 5 °C for condenser temperatures of 40 and 57 °C, respectively.

Figure 8 shows the overlapping of each acceptable performance area generated by key parameters related to a variation less than 70%. The above allows for visualizing the generation of sub-areas associated with the number of overlapping good performance areas. In this figure, if more areas overlap, more key parameters will meet the acceptable performance. Figure 8a shows the key parameter quantity contained in the areas generated by the overlapping (Roman numerals). Moreover, Figure 8b shows the key parameter types contained in the areas generated by the overlapping (see Figure 7). It is important to mention that heat and cooler exergetic efficiencies are not included in Figure 8 because the cited parameters never reach deviations over 70%. Only one area contains all key parameters (IX). However, the major quantity of key parameters is located at greater evaporator temperatures. The areas that contain fewer key parameters are located at lower evaporator temperatures.

Finally, the results obtained by applying the overlapping areas method show the behavior of the critical parameters in the area containing a major number of sub-areas, i.e., Area IX. It has been mentioned that the optimal operation of the HP system is located at greater evaporator and lower condenser temperatures. The above working conditions maintain the compressor relation at their minimum values concerning all possible values. The compression ratio is moved between 1.8 and 2.5, considering a maximum of 8.0, using an input pressure from 0.20 MPa to 0.56 MPa. The above contributes to the compressor’s useful life and minimizes the power input of the HP system. These ranges also take care of the compressor lifespan and help to maintain the compressor’s efficiency. The compressor power input is limited to 350 W in Area IX, and the condenser can obtain a maximum heat delivery of around 2000 W. Although the water temperature is low for calefaction purposes, this temperature helps to reach higher values with minor thermal jumps. The above is related to the working fluid’s phase change enthalpy since the vaporization enthalpy is larger for lower temperatures. The COP establishes the relationship between the delivery heat and compressor power input, which is always superior to 6 for the mentioned area. The obtained water outlet temperature is around 40 °C, and the minimum volumetric water flow is 80 L ${\mathrm{h}}^{-1}$. The HP system could be complementary equipment, and the above applies to the air conditioning of industrial buildings. Considering the previous and the optimal operation area mentioned, the HP system allows for reaching air conditioning of at least 300 ${\mathrm{m}}^3$ ${\mathrm{h}}^{-1}$ of the industrial building from 40 to 27 °C.

4. Conclusions

This work has been dedicated to a profound analysis of an HP system’s performance, a crucial aspect of energy efficiency. The primary goal is to recover residual thermal energy from industrial buildings, a task of significant importance. This study focuses on two key objectives: the recovery of energy for heating water and industrial building air conditioning, both of which play a vital role in energy conservation.

A set of key parameters was analyzed to evaluate the HP system’s performance. The above gives a reference frame concerning the operational conditions of the condenser and evaporator, where it is possible to find the optimal values for the analyzed parameters.

Additionally, this work presents an approach based on areas associated with a fixed value. Results show that the optimal operational condition is high evaporator and low condenser temperatures. In a general vision, many areas are encountered near high evaporator temperatures, while the condenser temperatures lie in a wide range. The above also allows moving in considerable ranges of water temperatures associated with several applications and requirements. In addition, it contributes to the industrial building’s air conditioning to promote good work conditions.

The application of the overlapping map of the global performance to different working fluids with low GWP and zero ODP is proposed as a powerful tool for analyzing and optimizing a variety of HP configurations. On the one hand, the working fluids that stand out are some hydrocarbons (n-propane, n-butane and n-pentane), four-generation refrigerants (R1234yf, R1243zf and R1233zd) and natural refrigerant (ammonia, water and ${\mathrm{CO}}_2$). On the other hand, several configurations of the HP system are related to the addition of equipment to improve the HP system’s performance. The above work seeks to combine theoretical and experimental approaches to contribute to developing efficient and environmentally friendly technological processes.