Performance analysis of multistage high‐temperature heat pump cycle

High‐temperature heat pumps (HTHPs) that can supply heat at temperatures at and above 200°C have the potential to increase energy efficiency and decrease carbon dioxide (CO2) emissions in industrial processes. In this study, three reversed Rankine cycles using water vapor (R‐718) as the working medium, with different intercooling strategies, were proposed and their performance has been investigated. The thermodynamic performance was estimated under different operating conditions, and the optimal pressure ratio (PR) between compression stages was found to be where both compressors had the same PR. The thermodynamic efficiency, φ, and exergy efficiency, ηexergy, were also analyzed at the optimum PR. The cycles that employed an intercooler between the first and second compression stages (IC cycles) showed higher φ and ηexergy values compared with the spray‐injection cycle. Among the IC cycles, the IC‐in cycle, with an inward flow direction of heat sink to the IC, demonstrated higher efficiency and deliverable temperature, Tsink out, than the spray‐injection and IC‐out cycles. To assess the practical impact of the HTHP cycles on industrial CO2 reduction, the PR for each stage was limited to 2.5. Theoretically, the IC‐in cycle could achieve a coefficient of performance of 5.86 with a Tsink out of 200°C or higher when Tevap and Tcond were at 90°C and 150°C, respectively. Additionally, the study demonstrated that the proposed HTHP system has the potential to reduce CO2 emissions by 8.1% in 2030 for industrial heat supply at temperature up to 200°C, by replacing existing industrial fossil boilers with high‐efficiency HTHP.

For the past few decades, global greenhouse gas (GHG) emissions have been increasing steadily and finally reached 51,199 Mt CO 2 -eq of GHG in 2018 excluding agriculture, forestry, and other land uses (AFOLU).Specifically, carbon dioxide (CO 2 ) accounts for over 73%, of total GHG emissions. 1Among all sectors, the energy sector has the largest share of GHG emissions, followed by the industrial sector, which is responsible for 34.8% of global GHG emissions.With the constantly increasing decarbonization of the energy sector through renewable generation, the industrial sector is becoming increasingly important for reaching the climate goals of the European Union (EU). 2,3n 2019, 120,944 PJ were consumed in the industrial sector, and the fossil fuels share was over 58% (70,544 PJ). 4 While the EU has been concentrating on reducing energy consumption per unit for many years, the total energy usage did not greatly decrease. 5,6Heat supply is the dominant source of emissions in the industrial sector (73% of final energy consuming in 2015).Heat supply temperatures correlate with specific branches and the respective processes; for example, the largest share of heat in the food industry is delivered at temperatures below 100°C, between 100°C and 500°C for the chemical industry, and above 500°C for iron and steel production, respectively. 7,8In addition, process heat below 500°C is generally supplied in the form of steam and hot water, while process heat above 500°C is mainly connected to industrial furnaces. 91][12] Apart from power generation from high-temperature waste heat, an efficient option to upgrade and recycle waste heat is with industrial heat pumps and their combination with other renewable energy sources (solar, geothermal, and so on).Heat pumps are used in domestic applications and are currently a niche application in industrial processes.4][15][16][17][18] Many industrial heat pump systems have been developed with technological advancements in the working media, compressors, heat exchangers, and control concepts.However, most commercial heat pumps can deliver heat at a maximum temperature of 150°C, mainly because of component limitations. 19,20Despite this shortcoming, there are still several research and development efforts to push the sink temperature of industrial heat pumps to 200-250°C, and thus extending their availability for a larger proportion of industrial processes. 21,22lecting an appropriate working medium is also important for the development of high-temperature heat pump (HTHP) for industrial processes.Generally, working media with a global warming potential (GWP) of less than 150 are considered by the community, with the main focus being on using natural working media, [23][24][25][26][27] such as Water (R-718).Water has zero GWP and ozone depletion potential, and it is also easily available, nontoxic, nonflammable, nonexplosive, and chemically stable.As a working medium at high temperatures, water exhibits distinctive thermodynamic properties.Because of its high critical temperature (373.95°C),water is suitable for HTHP working at temperatures between 200°C and 250°C.A further advantage of water in heat pump applications is its high evaporation enthalpy (~2256 kJ/kg at 1 bar at 100°C).
The current work focuses on three methods to integrate the heat sink into the cycle of a two-stage water vapor reversed Rankine HTHP.Parameter studies are performed to find the optimum design solutions for each integration strategy and to compare the strategies with each other.To the knowledge of the authors, this is the first time, that the studied cycle architectures and integration concepts have been studied in the open literature.Furthermore, this study will serve as valuable fundamental research data for the development of the industrial HTHP system by our group, the DLR Institute of Low-Carbon Industrial Processes.The HTHP targets a higher heat sink temperature, above 150°C, compare to other conventional heat pump systems, and the practical validation will be carried out while the system is in operation.

| Heat sink integration concepts
The three studied concepts to integrate the heat sink in a water vapor compression cycle are presented schematically and on the corresponding T-S diagrams in Figure 1.All cycles employ intercooling between the first and second compression stages to reduce the degree of superheating at the inlet of the second compression stage and also its efficiency.The target sink temperature is defined by the outlet pressure of the second compression stage.The intermediate pressure, the pressure between the two compression stages, is typically determined by the geometric mean of the total pressure ratio (PR) of the cycle, PR between condenser and evaporator. 28The current work focuses on three integration KIM ET AL.
| 3501 strategies of the heat sink in the heat pump cycle.The first two options, integrate the heat sink in the intercooler (IC) and are presented in Figure 1A,B.The IC cycles differ in the direction of the heat sink flow against the IC on the main heat pump cycle (IC-in and IC-out).The last option is a typical spray-injection cycle, Figure 1C with the heat sink solely connected to the condenser of the heat pump.

| Simulation process and methodology
The proposed HTHP cycles were modeled with EBSI-LON Professional 15 using IAPW-IF97 as the standard thermodynamic fluid library of water steam. 29The software is a steady-state simulation tool and is widely used in industry and research. 30,31The flowchart in Figure 2 depicts the calculation process of the multistage HTHP cycle, and the overall specifications of the HTHP model are provided in Table 1.The cumulative power consumption of the two compressors was fixed at 120 kW for all simulations.The pinch point between the main and secondary flows in the evaporator and condenser was assumed to be 10 K.The working medium temperature after the evaporator was set to 10 K above the saturation temperature and it had 10 K subcooling at the outlet of the condenser, points 1 and 5 in Figure 1.In addition, the pressure drop in the heat exchangers was neglected for simplicity.With regard to the heat sink flow, the inlet temperature of the heat sink was 15°C in the liquid state, point 7 in Figure 1, and pressure, P sink , was adjusted based on the pressure of the main flow at the end of the heat sink flow for heat exchange.The performance of the three different multistage cycles was studied and compared by varying the evaporation and condensation temperatures.Additionally, the intermediate pressure between the first and second compressor stages, P int , was also adjusted, as shown in Table 2.The effect of these changes on the heat sink flow (i.e., change in mass flow rate), the coefficient of performance (COP), the thermodynamic efficiency, φ, and exergy efficiency, η exergy , were then analyzed.The evaporation temperature was varied from 60°C to 110°C, while the condensation temperature was changed from 150°C to 250°C.The overall PR of the two compression stages was determined based on the temperature conditions, and the PR for each compression stage was adjusted sequentially during simulation.The increment of the evaporation and condensation temperature conditions was 5 K, and the intermediate pressure was varied by 0.5 bar each time.The mass flow rate of the main cycle, m main , was adjusted according to the total power consumption of two compressors, and the mass flow rate of heat sink, m sink , was controlled to satisfy the temperature constraints, T sub after condenser and T sup after IC of IC cycles.The injection mass flow, m inj , for the sprayinjection cycle, which is split from the main flow, was also determined to maintain a 10 K superheat before entering the second compression stage.

| Energy and thermodynamic efficiencies
The COP is the first parameter used to evaluate heat pump performance.The COP is the ratio of the useful heat transferred in the heat sink, Q sink , to the power consumed by the compressors, W comp , Equation (1).
In addition, the thermodynamic efficiency, φ, was introduced to compare the system performance with that of an ideal cycle, Equation ( 2).The Carnot efficiency, COP carnot , is the maximum energy efficiency of an ideal process converting power to heating between two different temperatures, T L and T H , Equation (3). 32

| Exergetic efficiency
In comparison with conventional energy analysis, exergy analysis can quantitatively characterize and localize thermodynamic losses in a process, and define the subprocesses that require most attention.The specific exergy, ε, the difference between the flow availability of a stream and that of the same stream at its restricted dead state, is given by Equation ( 4) when ignoring chemical, potential, and kinetic exergy terms. 33 where h 0 and s 0 are the enthalpy and entropy values of the working medium at the reference states, P 0 = 1 atm, T 0 = 25°C (298.15K).The exergy of heat, E Q , that contains heat, Q, at temperature, T, is obtained using Equation ( 5), and the values were obtained from the main cycle.The exergy efficiency, η exergy , is defined as the ratio of the total outgoing exergy, E out , to the total incoming exergy, E in , of the heat pump system, Equation (6).
To investigate the effect of cycle architecture on performance, an exergy analysis was carried out.The total exergy input, E in , of the heat pumps is given by Equation (7).Because the number of utilizing heat exchangers is different between IC cycles and sprayinjection cycles, total outgoing exergy, E out , for both cycles are defined by Equations ( 8) and ( 9), respectively.
where T m is the logarithmic mean temperature difference (LMTD) and it was adopted to calculate the representative temperature in an IC.The main flow in the IC is not associated with the phase change, and the LMTD method can represent nonlinear temperature changes across the heat exchanger from entrance to exit effectively.
3 | RESULTS AND DISCUSSION

| Simulation results of multistage water vapor compression cycle
In this section, the performance of the proposed HTHP cycles is evaluated for different combinations of evaporation temperature, T evap , condensation temperature, T cond , and intermediate pressure, P int .The mass flow rate and outlet temperature of heat sink, m sink and T sink out , are investigated initially as these parameters are directly related to the heat demand.To evaluate the impact on cycle performance, the pressure ratio, PR = PR 1 /PR 2 , between the first and second compression stages is varied under specified evaporation and condensation temperature conditions, T evap and T cond , as outlined in Table 2.
To satisfy the cycle constraint that maintains a temperature difference of 10 K between the main cycle and heat sink, T main − T sink out = 10 K, it is necessary to adjust the mass flow rate of heat sink.This parameter is affected by the main cycle temperature, discharge temperature for IC-in and spray-injection cycles, and intermediate temperature for IC-out cycle.The results show that the m sink of the IC-in and spray-injection cycles increase with PR, while the value of the IC-out cycle decreases for all temperature conditions.From Figure 3A,B, it was observed that the mass flow rate of the heat sink, m sink , is strongly correlated with the temperature lift value, T lift = T cond − T evap .Overall, the mass flow rate increases as T lift decreases, with no specific observed from varying T evap and T cond .For instance, the cycle with the lowest T lift , 100-150 in Figure 3A, exhibits the highest m sink , while graphs with T lift = 60°C, 100-160 in Figure 3A and 90-150 in Figure 3B, show similar m sink values despite representing different temperature conditions.In particular, the sprayinjection cycle has a slightly lower m sink than the IC-in cycle, because the heat sink flow passes only through the condenser, to control the superheating degree of the main cycle.
The heat sink outlet temperature, T sink out , shows a similar trend to the mass flow rate, Figure 3C,D.The ICin and spray-injection cycles have the same outlet temperature, while the IC-out cycle has different results.The temperature of the IC-out cycle increases with PR because this value is linked to the intermediate temperature, T int , while the T sink out of the IC-in and spray-injection cycles decrease.The temperature lift condition also has more effect on T sink out than changes in T evap and T cond .T sink out value increase with increasing T lift contrary to the case of m sink .Especially, all of the proposed HTHP cycles exhibit a heat sink outlet temperature that exceeds 200°C, which is the target of this study, except for IC-out cycle at low PR.
Figure 4 depicts the relationship between COP and PR between the first and second compression stages for different temperature conditions.The results show that as temperature lift values decrease, COP values increase, similar to the behavior observed for m sink .Additionally, it was found that cycles with the same T lift exhibit a similar range of COP, and COP values are more strongly influenced by temperature lift values than by evaporation and condensation temperature.
The IC cycles demonstrate higher COP than the spray-injection cycle because of their ability to utilize two heat exchangers.Detailed analysis revealed that the IC-in cycle has the same T sink out but higher m sink across the entire range of PR due to its architectural advantages of using an IC and condenser.Similarly, the IC-out cycle has higher m sink and T sink out at low and high PR, respectively, as shown in Figure 3.These results suggest that the use of two heat exchangers and architectural advantages of IC-in and IC-out cycles led to a higher COP for both cycles.
The COP values show a rapid increase when the first compression stage has a low, PR 1 /PR 2 < 0.5.The highest COP values were achieved when the PR of both compressors were equal, PR 1 /PR 2 = 1.0, under all temperature conditions.

| Thermodynamic performance at the optimized PR
On the basis of the results in Section 3.1, where the highest COP was confirmed when both compressors had the same pressure ratio, PR 1 /PR 2 = 1.0, was selected as the optimized PR for the HTHP cycles.Therefore, the thermodynamic performances of the HTHP cycles at the optimized PR were evaluated in this section.
Figure 5A illustrates the optimized COP change with respect to the evaporation and condensation temperatures (T evap = 60-110°C, T cond = 150-250°C).As the temperature lift decreases, COP values increase exponentially from around 1.94 to 8.97.Both IC-in and IC-out cycles exhibit the same COP as shown in Figure 4A.Although IC-in has a higher T sink out value than the ICout cycle at optimized PR as shown in Figure 3C,D, the IC-out cycle has a higher m sink at that point as shown in Figure 3A,B.On the other hand, the spray-injection cycle shows 2.07%-7.68%lower COP than the IC cycles.Basically, the spray-injection cycle has a higher mass flow rate on the main cycle, m main , than IC cycles at the same temperature conditions because a certain amount of m main should be used for injection flow to cool down T int to near the condensation temperature.However, after splitting with injection flow, the spray-injection cycle has a lower mass flow rate for evaporation, m evap , that exchange the thermal energy with heat source.Additionally, m sink is low owing to the architectural features of the spray-injection cycle.These low values of m evap and m sink result in a low COP for the sprayinjection cycle.
The result of the exergy efficiency, η exergy , showed a similar trend as the COP analysis, Figure 5B.The IC cycles had the same η exergy , and these values, which gradually increased with decreasing T lift .Consistent with the COP analysis at an optimized PR, the IC cycles had η exergy values ranging from 0.81 to 0.96, while the injection cycle had 0.88%-6.75%lower values.Further analysis revealed that the spray-injection cycle had a lower m evap resulting in 1.5%-2.7%lower exergy input, E in in Equation ( 7), compared with the IC cycles.Regarding the exergy out, E out in Equations ( 8) and ( 9), the spray-injection cycle had a higher Q cond value than the IC cycles due to the higher m main in the condenser.However, accounting for the thermal energy exchange in the IC, Q IC , the IC cycles exhibited 2.4%-8.2%higher E out .In conclusion, the results indicate that the IC cycles are more efficient in terms of exergy efficiency than the spray-injection cycle under the studied conditions.
Figure 6 shows the variation in thermodynamic efficiency, φ, which is the ratio of the actual COP to the Carnot COP, with respect to the T evap , T cond , and T lift at the optimized pressure ratio, PR 1 /PR 2 = 1.0.Generally, it can be observed that the value of φ increases with T evap , Figure 6A, and it decreases with increasing T cond or T lift , Figure 6B,C The difference in φ between the IC and sprayinjection cycles varied with temperature conditions.When T evap is 60°C, the IC cycle had a φ of 0.79-0.81,while the spray-injection cycle had a φ that was 4.76%-6.17%lower, 0.74-0.77.As T evap increased to 110°C, the difference in φ decreased to 2.07%-3.82%;IC cycles had a φ of 0.82-0.85and the spray-injection cycle had a φ of 0.79-0.83, Figure 6A.When T evap has fixed values, the discrepancy between the IC and sprayinjection cycles increased with T cond as shown in Figure 6B.Specifically, the difference between the IC and spray injection increased from 2.60%-4.76% to 6.28%-7.68%as T cond increased from 150°C to 250°C.It is important to note that T evap and T cond have different impacts on thermodynamic efficiency; increasing T evap has a positive impact, while increasing T cond results in a decline in φ.In other words, the thermodynamic efficiency value is dependent on T lift .
Figure 6C comprehensively presents the results of the above mentioned φ analysis.It is observed that not only does φ decreases with T lift , but the discrepancy between IC and spray-injection cycles are also increases from 2.70% to 6.17% as T lift changes from 40°C to 130°C.This change in discrepancy comes from the variation in the ratio of m inj to m main for the spray-injection cycle.Similar to the other cycles, the main mass flow rate, m main , of the spray-injection cycle decreases significantly with increasing T lift .However, m inj does not change significantly with increasing T lift .This is because while the higher T lift cycle has low m main , the required heat for cooling at intermediate stage increases with T lift .Therefore, as T lift increases, the ratio of m inj that is not involved in heat exchange with the heat source at evaporator relatively.This increase in the m inj ratio induces a further decline in the φ of the spray-injection cycle compared with the IC cycles.
The change in exergy efficiency, η exergy , showed a similar tendency to that of the thermodynamic efficiency, φ, Figure 7.The IC cycles had the same η exergy , and the | 3507 spray-injection cycle showed lower values.Similar to the results of the φ analysis, the overall η exergy decrease as T lift increases.
The η exergy difference between the IC cycles and spray-injection change is also like that in the φ analysis.When the cycle has a T evap of 60°C, the IC cycles have an η exergy of 0.85-0.88 and the spray-injection cycle has 4.61%-6.79%lower exergy efficiency, and this difference has been reduced to 0.88%-1.97%with increasing T evap to 110°C, Figure 7A.In addition, the discrepancy increased from 1.35%-4.61% to 3.89%-6.75%during T cond increasing from 150°C to 250°C, Figure 7B.In terms of the η exergy changes according to the temperature lift, Figure 7C, the differences between IC and sprayinjection cycles are smaller compare to φ analysis.This difference was due to different evaluation subjects.While the φ analysis focused on the heat sink flow and its direct connection to demand, η exergy analysis was conducted for the main cycle to evaluate the completeness of proposed heat pump cycles.The results of both analyses showed that IC cycles had higher COP and η exergy values compared with the spray-injection cycle, indicating that IC cycles exhibit higher efficiency and systemic perfection.

| Practical performance of the HTHP cycles and CO 2 saving potential
The technical feasibility of the Rankine cycle using steam compression equipment is demonstrated for HTHPs, and turbo compressors are considered to be a promising solution. 22,34To understand the practical performance of the proposed HTHP cycles, the COP and T sink out were investigated, Figure 8.The PR per compression stage of the turbo compressor using water vapor is expected to reach up to 3.5. 35,36However, considering its efficiency, the practical PR was assumed to <2.5.
The analysis revealed that the available temperature lift is limited to approximately 60-65 K when PR < 2.5 for each stage.Specifically, the IC-in cycle was found to demonstrate higher COP and T sink out values compared with the spray-injection cycle and IC-out cycle, respectively, due to its cycle architectural characteristics as previously discussed.The IC-in cycle was able to achieve a COP of 5.86, equivalent to 720 kW, and a T sink out of over 200°C when the cycle's T evap and T cond are set to 90°C and 150°C.
On the basis of the above results, it is possible to estimate the amount of energy saving and the reduction in CO 2 emissions achieved through the application of the proposed HTHP system.According to data from 2012, the final energy consumption in the industrial sector of EU28 was 3200 TWh, with process heating accounting for 60% of this total (1920 TWh).In addition, the target temperature range of this study is 100-200°C, which corresponds to approximately 16% (512 TWh) of the total energy demand.This energy is mostly required by the pulp and paper industry, and other nonclassified subsectors. 7he GHG emission intensity for different fossil boilers and electricity generation in Europe, along with the CO 2 saving potential are listed in Table 3. Conventional fossil boilers have CO 2 emission intensities of ~250 g CO 2 -eq/ kWh th , while electricity generation in the EU had an emission intensity of 275.0 g CO 2 -eq/kWh el in 2021, which is projected to reduce to 118.0 g CO 2 -eq/kWh el by 2030. 37,38y substituting existing fossil boilers with a highly efficient HTHP system, there will be a significant reduction in total energy consumption.The HTHP showed a COP of 5.86 with T sink out exceeding 200°C under 90-150 conditions in Figure 8.This result indicates that electrification can significantly reduce the amount of CO 2 emission from industrial processes operating between 100°C and 200°C.The CO 2 emission intensity is estimated to decrease from approximately 128 to 24.0 Mt/year in 2021, and further decrease to 10.3 Mt by 2030.The HTHP system for industrial processes has the potential to reduce net GHG emissions by up to 8.1% in 2030, compared with conventional fossil boilers (~250 g CO 2 -eq/kWh th ).Overall, the HTHP system is a promising option for reducing energy consumption in industrial processes and decreasing CO 2 emissions in various ways.HTHP cycles with three different intercooling strategies have been proposed to supply high-temperature thermal energy (>200°C) for industrial processes.These include two IC cycles with different directions of heat sink flow and one spray-injection cycle.
As the temperature lift increases, there is a decrease in the overall COP and m sink values, accompanied by an increase in T sink out values.The IC-in cycle exhibits the higher COP and T sink out values compare to the sprayinjection and IC-out cycles, respectively.The highest COP was observed when both compressors had the same PR per stage, PR 1 /PR 2 = 1.0, which was defined as the optimized PR.From the thermodynamic and exergy efficiency analysis at the optimized PR, it was confirmed that the overall φ and η exergy increased as the temperature lift decreased.The spray-injection cycle consistently showed lower φ and η exergy values than the IC cycles due to limitations in cycle architecture.Especially, the IC-in cycle, with a T evap of 60°C and T cond of 150°C, achieved a COP of approximately 5.86 and T sink out of over 200°C when the practical PR per stage (PR < 2.5) was applied.
In conclusion, the proposed multistage HTHP cycles have the potential to provide high-temperature thermal energy (>200°C) for industrial processes with high efficiency.Moreover, its application is expected to reduce CO 2 emissions from industrial processes up to 200°C by 91.9% compared with conventional fossil boilers in 2030.The HTHP systems can significantly contribute to achieving Low-Carbon Industrial Processes and a sustainable energy transition.

FF I G U R E 2
I G U R E 1 Schematic and ideal T-S diagrams of the heat pump cycles studied: (A) IC-in, (B) IC-out, and (C) spray injection.IC, intercooler.Flowchart of the calculation of multistage HTHP cycle.HTHP, high-temperature heat pump; IC, intercooler.

F
I G U R E 3 m sink and T sink out changes by pressure ratio, PR 1 /PR 2 : (A, C) with fixed evaporation temperature, T evap , and (B, D) with fixed condensation temperature, T cond .IC, intercooler; PR, pressure ratio.F I G U R E 4 COP changes by pressure ratio, PR 1 /PR 2 : (A) with fixed evaporation temperature, T evap , and (B) with fixed condensation temperature, T cond .COP, coefficient of performance; IC, intercooler; PR, pressure ratio.
. Both IC-in and IC-out cycles exhibit the same φ, while the spray-injection cycle has F I G U R E 5 Performance of the HTHP cycles at optimized pressure ratio: (A) COP and (B) η exergy .COP, coefficient of performance; HTHP, high-temperature heat pump; IC, intercooler.a lower φ than the IC cycles due to its different architectural characteristics as previously explained in Section 3.1.

F I G U R E 6
Thermodynamic efficiency, φ, changes according to (A) evaporation temperature, T evap , (B) condensation temperature, T cond , and (C) temperature lift, T lift .IC, intercooler.KIM ET AL.

F I G U R E 7
Exergy efficiency, η exergy , changes according to (A) evaporation temperature, T evap , (B) condensation temperature, T cond , and (C) temperature lift, T lift .IC, intercooler.

F I G U R E 8
Estimated practical performance of the HTHP cycles by considering practical pressure ratio: (A) COP and (B) T sink out by T evap .COP, coefficient of performance; HTHP, high-temperature heat pump; IC, intercooler.T A B L E 3 CO 2 emission intensities for different energy sources and CO 2 savings potential.
Specifications of the considered HTHP cycle.
T A B L E 1Abbreviation: HTHP, high-temperature heat pump.T A B L E 2 Variable parameters for HTHP cycle simulation.Abbreviation: HTHP, high-temperature heat pump.