Exergoeconomic performance comparison, selection and integration of industrial heat pumps for low grade waste heat recovery

Energy Conversion and Management 207 (2020) 112532

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Exergoeconomic performance comparison, selection and integration of industrial heat pumps for low grade waste heat recovery

T

Mengying Wanga, Chun Denga, , Yufei Wanga, Xiao Fengb ⁎

a b

State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing 102249, China School of Chemical Engineering & Technology, Xi’an Jiaotong University, Xi’an 710049, China

ARTICLE INFO

ABSTRACT

Keywords: Heat pumps Process integration Exergoeconomic Waste heat recovery

Mechanical heat pumps, absorption heat pumps, and absorption heat transformers are typical technologies for low-grade heat upgrading to save energy. However, there are few guidelines on the selection and integration of heat pumps in industrial processes, and different heat pumps need the input energy with several types or grades (i.e., mechanical work, high or medium grade heat), the coefficient of performance is not suitable to evaluate different heat upgrading technologies. In this work, an exergoeconomic criterion (i.e., exergy loss per total capital investment), measuring the exergy performance of each type of heat pumps and considers economic impact, is introduced to assist the screening of industrial heat pumps. The process models of heat pumps are developed using Aspen Plus. A systematic method for heat pump integration into an industrial process is presented, relying on Pinch Analysis of a given heat exchanger network. The impacts of different waste heat temperatures and temperature lifts on the selection of heat pumps are analyzed. A case study of a catalyst reforming unit in a petroleum refinery is used to demonstrate the applicability of the proposed method, and the energy-saving and economic performance of three types of heat pumps at different waste heat upgrading options are compared. Results show heat pump selection based on the exergoeconomic criterion can achieve better thermodynamic (exergy-based) and economic performance than that based on conventional one. The introduced guide map can simplify the heat pump integration process, and the proposed method of heat pump integration can be further extended to other industrial processes for low-grade waste heat recovery.

1. Introduction

rely on high global warming potential (GWP) refrigerants, like R22, R114, etc. Thus, one research area focuses on seeking refrigerants to meet the requirements of high critical temperature, low GWP, nonflammability, and being non-toxic [5]. Absorption heat pumps (AHPs) and absorption heat transformers (AHTs) work with eco-friendly natural refrigerants, mainly using waste heat and renewable energies such as solar and geothermal energy. AHPs and AHTs are thermally driven, and the entire absorber/generator system has the same effect as MHPs. An AHT can be regarded as a reversed AHP in which the evaporator and absorber operate at a higher pressure than the condenser and generator [5]. These three types of heat pumps have been widely developed for various applications in the industry [6], mainly for heating [7], cooling [8], desalination [9], and drying [10]. Many researchers focus on the selection and performance improvement of working fluids, operational optimization of a specific heat pump in industrial processes, and the improvement of heat pump configurations. Söylemez [11] presented a thermo economic optimization analysis to estimate the optimum

Energy efficiency remains low and is about 30% in China [1] at present, which indicates that 70% of the energy input is lost and cannot be reused. For industrial waste heat recovery, heat pumps are becoming more and more attractive due to increasing energy prices and concerns about energy conservation and significant reductions in greenhouse gas emissions [2]. In recent decades, heat pumps have been increasingly applied to improve the energy efficiency of industrial processes through low-grade waste heat recovery. Philipp et al. [3] reported that heat pumps provide the lowest emissions and highest primary energy efficiency for countries with low grid emissions factors. Chua et al. [4] reviewed the recent advances in heat pump technology to improve heat pump energy efficiency. Many types of industrial heat pumps are available, including mechanical heat pumps, absorption heat pumps, and absorption heat transformers. Mechanical heat pumps (MHPs) upgrade low-temperature waste heat to a higher temperature with the input of electric energy and

⁎

Corresponding author. E-mail address: [email protected] (C. Deng).

https://doi.org/10.1016/j.enconman.2020.112532 Received 3 October 2019; Received in revised form 20 January 2020; Accepted 21 January 2020 0196-8904/ © 2020 Elsevier Ltd. All rights reserved.

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Nomenclature C E Eloss Hγ OC Q W To T ΔT TCI TAC

MHP PRR

cost exergy exergy loss annual operating time operation cost heating load, kW work, kW environment temperature, °C temperature, °C temperature difference, °C total capital investment, M$ total annualized cost, M$

Subscripts abs c CU C comp cond ELECT evap gen H HU IE lift min p she UH

Abbreviations AHP AHT COP EPC GCC GWP

mechanical heat pump primary fuel recovery ratio

absorption heat pump absorption heat transformer coefficient of performance exergy loss per total capital investment grand composite curve global warming potential

absorber critical cooling utility cold stream compressor condenser electricity evaporator generator hot stream heating utility input energy upgrade minimum pump solution heat exchanger upgraded heat

compared the integration of mechanical heat pump and vapor compression into a cheese production plant. Liew and Walmsley [20] only considered the vapor compression system. However, the analyses on the comparison and selection of different heat pump types on various waste heat sources of processes are still quite a few. When a heat pump is selected and integrated into an industrial process for low-grade waste heat utilization, various criteria are proposed to evaluate the performance of heat pump systems. The COP is a widely used criterion, but it ignores the characteristics of different heat pump systems. The COP of MHPs is higher than that of AHPs and AHTs [21], although MHPs require higher grade electric energy than thermal energy needed in AHPs and AHTs. Oluleye et al. [22] proposed a system-oriented criterion, the primary fuel recovery ratio (PRR), which can only measure the savings in primary fuel from heat upgraded. However, the economic aspects were not considered. Philipp et al. [3] analyzed the most energy efficiency supply system structure and selected two criteria for comparison, carbon emissions, and primary energy efficiency. They also pointed out that the weakness of primary energy efficiency, which compares energy quantity at the same reference point but does not consider energy quality (e.g., exergy). Sozen et al. [23] used exergetic coefficient of performance to analyze the thermal performance of an absorption heat pump at different condenser, absorber, and evaporator temperatures [24]. For different types of heat pumps, exergetic coefficient of performance may be a better criterion to evaluate their thermal performances. However, industry engineers are concerned about the economic selection of heat pumps. Fonyo and Mizsey [25] proposed a simple heat pump selection method for preliminary economic analysis, which involved both vapor recompression and absorption heat pump schemes, but they provide very little information on the type of heat pump. Van de Bor and Infante Ferreira [26] defined an economic selection criterion, but this criterion cannot be associated with thermal performance. Generally, economic analysis for energy conversion technologies conventionally considers unit cost based on energy. When analyzing different energy technologies to achieve optimum designs, scientific disciplines (mainly thermodynamics) and economic disciplines (mainly cost consuming) are often combined. Feng et al. [27] introduced a critical COP for an economically feasible industrial heat pump application based on the price ratio between input energy and heating, the price ratio between equipment and energy, and the payback period. A preliminary

operating conditions of the heat pump used in drying applications. The simple method of economic analysis is significant for energy savings and economic growth, but it ignores the selection of heat pumps. Besides, this method is only suitable for a mechanical heat pump. In industrial processes, hydrocarbons such as propane and isobutene are mainly used as refrigerants of heat pump because they are easily available and can generate high system efficiency. Energy performance of heat pump and safety issues are equally important in heat pump systems [12]. Heat pump cycles can be extended to two-stage or multistage systems to achieve higher energy performance, and the investment in system equipment will increase accordingly. Ma et al. [13] found that the coefficient of performance (COP) of different thermodynamic cycles increases with the increasing number of compression cycle stages. Chaturvedi et al. [14] proposed two-stage heat pump systems for hightemperature applications in the range of 60–90 °C and compared them with the single-stage system. Although the two-stage system improved the thermal performance significantly, the required initial cost is higher than that of the single-stage system at the same temperature levels. Huang et al. [15] compared the heating tower heat pump and the airsource heat pump based on a simulation study to investigate the performance. Although several heat pumps have been extensively developed and examined, optimal integration of these technologies remains a major challenge for industrial processes. Therefore, there is still much room for improvement of heat upgrading technologies. Process Integration is an effective technique that is widely used to optimize industrial processes by improving energy efficiency and reducing the consumption of resources and harmful environmental emissions. Pinch Analysis, which is an essential and common used method for heat integration, can be applied for the optimal integration and placement of an industrial heat pump. Pinch Analysis enables engineers to determine the potential heat recovery [16], and the integration of a proper heat pump can increase energy savings and reduce emissions. Walmsley et al. [17] investigated the adequate placement of an open cycle heat pump in vapor recompression for the milk industry, but the type of heat pump technology was determined before integration. Kapustenko et al. [18] analyzed heat pump integration for cheese production in Ukraine with a pre-selected heat pump technology. Generally, the appropriate integration of heat pumps should consider the optimal type of heat pump. Becker et al. [19] analyzed and 2

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This paper consists of seven sections. Three models of heat pumps are developed in Section 2. Section 3 introduces the method of this work, evaluation criterion for heat pump selection is proposed in Section 3.1, and then Section 3.2 addresses heat pump integration procedure. Section 4 illustrates the selection of heat pumps at different waste heat temperatures and temperature lifts. The proposed method is highlighted by a case study in Section 5 for an industrial process. Section 6 discusses and analyzes the results. Finally, Section 7 draws the conclusions.

assessment can be conducted using the critical COP whether an industrial heat pump is economically feasible, but it still cannot evaluate which type of heat pump is suitable for industrial processes with different waste heat sources and sinks. Also, many researchers have recommended that costs are better distributed among outputs if the economic analysis is based on the exergy. Because a systematic correlation appears to exist between capital cost and exergy loss, but not between capital cost and energy loss [28]. And exergy-based economic analysis methodologies exist (e.g., exergoeconomics, thermoeconomics) [29]. Rosen et al. [28] applied the ratio of exergetic losses and capital costs for the design of electrical generating stations. However, this ratio has never been used for the selection of heat pumps. An economically installed heat pump may not recover process waste heat efficiently to achieve stepwise energy utilization at the cost of using higher-grade energy, but releasing large amount of waste heat into the environment. For example, when upgrading the same heat in the same quantities for the same heat sink, AHPs can produce the most amount of higher-grade heat consuming steam; next comes MHPs but requiring the highestgrade energy (electricity); the amount of upgraded heat is the lowest for AHTs and only low-grade heat is required. Therefore, thermodynamic and economic characteristics are needed to be considered simultaneously. It is believed that a sensible criterion can help industries to select and integrate heat pumps into processes. To obtain the performance of heat pumps with different working fluids under different operating parameters conveniently, this work considers the real performance of various heat pumps by developing the process models of mechanical heat pumps, absorption heat pumps, and absorption heat transformers using Aspen Plus. An exergoeconomic criterion is used for the selection of heat pumps in industrial processes. This criterion EPC (exergy loss per total capital investment) measures the available energy performance of each type of heat pumps based on the second law of thermodynamics and considers economic impacts (i.e., investment cost), to correlations between specific second-lawbased thermodynamic destruction and capital investment. The effect of waste heat temperatures and temperature lifts on the correlations between thermodynamic and economic performances of different heat pumps will be analyzed. The results of such correlations can help industries to know the merits of exergy analysis for heat pump integration. Besides, a pinch-based systematic method is developed for the integration of different heat pumps in an industrial process. A case study of a unit in a petroleum refinery will be carried out to demonstrate the proposed method. The final goal of this paper is to generate a guide map and a systematic procedure for the selection of mechanical heat pump, absorption heat pump, and absorption heat transformer, considering different waste heat conditions, making the best use of lowgrade waste heat.

2. Models of heat pumps The ideal performance of heat pumps is usually used to evaluate heat pump systems [22]. However, this method ignores the inefficiencies of the cycle and the non-ideal behavior of working fluid. To obtain accurate results and determine operating parameters more conveniently, the process models of mechanical heat pumps, absorption heat pumps, and absorption heat transformers are developed using Aspen Plus. 2.1. Mechanical heat pumps Mechanical heat pumps mainly consist of four parts: the evaporator, compressor, condenser, and expansion valve. For closed-loop systems, low-grade waste heat is required in the evaporator at state point 2 (see Fig. 1a) to protect the compressor by ensuring that the fluid is fully evaporated. The vapor is compressed by means of electric energy to a higher pressure and, therefore, the higher temperature in the compressor, and higher-grade heat is released to the heat sink in the condenser at state point 4. Finally, the high-pressure working fluid is expanded in the expansion valve and the cycle is then repeated. MHPs work best when temperature lift is low, and the heat source and heat sink are latent heat, which leads to less heat loss. In multistage heat pump systems, higher temperature lifts can be achieved. Worthy of mentioning, the heat pump performance decreases with the increase of temperature lift. In this work, single-stage heat pumps are only considered. Fig. 1b shows the schematic diagram of the mechanical heat pump. The COP can be determined by Eq. (1).

COPMHP =

Qcond Wcomp

Tlift _MHP = Tcond

(1)

Tevap

(2)

Preselected working fluids in this work are listed in Table 1. The thermodynamic properties are extracted from Aspen Plus. Table 2 shows the validation of the Aspen Plus model with experimental thermodynamic design data for ammonia (NH3) [30]. The simulation

Fig. 1. (a) Temperature-entropy diagram and (b) schematic diagram of MHP. 3

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Table 1 Preselected working fluids and their critical properties. Working fluid

Chemical formula

Tc (°C)

Pc (MPa)

n-butane i-butane ammonia propane propylene water

n-C4H10 i-C4H10 NH3 C3H8 C3H6 H2O

151.97 134.65 132.50 96.68 91.70 373.95

3.796 3.640 11.28 4.248 4.600 22.06

Table 2 Validation of MHP simulation in Aspen Plus. Tcond

Tevap

COP(reference)

COP(Aspen

120 120 120 120

10 30 50 70

1.9137 2.2855 2.8934 4.0222

1.8564 2.2342 2.8415 3.9558

Plus)

% error 2.99 2.25 1.80 1.65

results are in good agreement with the data in reference [30]. Due to the high specific volumes of water vapor in the corresponding temperature range, water is applied to the situation with higher evaporation temperature, but it would require extensive and expensive compressors [21]. The real COP can be used to determine the best working fluid considering evaporation and condensation temperatures. Similarly, at the same evaporation temperature of 55 °C, the best working fluid can be determined for different temperature lifts defined in Eq. (2), as shown in Fig. 2a. For different cycle evaporation temperatures, working fluids with the highest COP are shown in Fig. 2b. 2.2. Absorption heat pumps A single-stage absorption heat pump mainly includes seven parts: the generator, condenser, throttle, evaporator, absorber, solution heat exchanger, and pump. Kurem and Horuz [31] concluded that waterlithium bromide (LiBr) solution showed better performance than ammonia-water solution. The absorbent is a LiBr solution, and the refrigeration fluid is pure water. The working principle is the same as the absorption refrigeration cycle [8], but the user demands are different. The schematic diagram of the single AHP is presented in Fig. 3a. The refrigeration vapor is removed from the lean LiBr solution by the driving heat source in the generator at state point 8. After condensing the vaporized refrigerant in the condenser, the refrigeration fluid is evaporated at state point 11 in the evaporator by a low-grade heat source at lower pressure. The steam from the evaporator dissolves and reacts with the rich solution from the generator that flows into the

Fig. 3. Schematic diagram of (a) the single AHP and (b) AHT.

absorber through the throttle, the lean solution is pressurized in the solution pump, returns back to the generator again, and finishes a cycle. Solution heat exchanger is placed between the pump and generator. In the solution heat exchanger, the cold rich solution from the absorber is heated by the hot lean solution coming from the generator at state point

Fig. 2. Working fluid selection for MHPs: (a) at the same evaporation temperature of 55 °C, (b) at different evaporation temperatures. 4

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5. Additional useful heat is released in the condenser and absorber, and the temperature is higher than that of the low-grade heat in the evaporator but lower than that of the driving heat in the generator. Therefore, the AHP can utilize low-grade heat in the evaporator, which is provided from low temperature waste heat sources. Then, mediumgrade heat is produced in the condenser and absorber. The heat quantity is increased because the heat supplied to the generator and evaporator is converted into the upgraded heat side [32]. The COP can be calculated using Eq. (3).

Qabs + Qcond Qgen

(3)

Qabs = Qevap + Qgen

(4)

COPAHP = COPAHT

Tlift _AHP = Tcond Tlift _AHT = Tabs

Tevap Tevap

(6) Condensation temperature in the AHT is set at 30 °C; (7) Solution heat exchange efficiency is specified as 0.64. 3. Method In the section, a novel evaluation criterion for the selection of different heat pumps and a procedure for heat pump integration using Pinch Analysis are presented. 3.1. Evaluation criterion The coefficient of performance (COP) is widely used to evaluate and compare different heat upgrading technologies, but it neglects the energy grade differences, only considers the energy efficiency based on the first law of thermodynamics. Because MHPs, AHPs, and AHTs utilize the driving energy of several types of grades (e.g., electricity, high or medium-temperature heat) to upgrade the temperature of low-grade waste heat sources, the COP is not suitable to evaluate heat upgrading systems. The advantages of absorption heat upgrade systems compared with mechanical heat pumps cannot be assessed only using the COP. Although an economic analysis can assist the determination of what kind of heat pumps can be used to recover cost-effectively waste heat, it is a complicated process to compare different heat pumps at different waste heat potentials, and it is mostly based on energy but not exergy. Exergy is typically used for the comparisons of energy with different grades, i.e., thermal energy, mechanical work. And it can quantify the usefulness of diverse types of energy streams in an industrial system. Associated with exergy analysis, the exergoeconomic criterion for heat pump selection that is defined as exergy loss per total capital investment (EPC) is proposed, which is given by Eq. (7) and based on Rosen et al. [28]. The criterion can show correlations between the exergy loss (i.e., specific second-law-based thermodynamic destruction) and capital investment of different types of heat pumps, appropriately balancing the thermodynamic (exergy-based) and economic performances of the process and heat pump technologies.

(5) (6)

2.3. Absorption heat transformers The schematic diagram of the single AHT is shown in Fig. 3b. Note that the AHT has the same components and use the same working fluid (water is used as refrigerant and LiBr-H2O as an absorption pair) as the AHP cycle, but it requires driving heat sources of different grades. The generator and evaporator are supplied with waste heat at the same temperature, leading to upgraded heat that can be obtained in the absorber [33]. Low/mediate-temperature waste heat at state point DH1 and at state point MH1 is used as driving heat in the generator and evaporator to vaporize the refrigerant. The refrigerant vapor at state point 8 is absorbed by the refrigerant-absorbent solution that enters the absorber at strong state point 11 and leaves weak at state point 1, delivering an amount of heat at a higher temperature. Next, the weak solution returns to the generator, where some refrigerant vapor at state point 5 is generated, and then a strong solution comes out and enters the absorber. The vaporized refrigerant at state point 5 is condensed in the condenser by cooling water. The refrigerant leaving the condenser is pumped to the evaporator where it is evaporated by the waste. The evaporated refrigerant at state point 8 is then absorbed in the absorber at a higher temperature heat. Finally, a cycle is done and repeated. Contrary to the AHP, the generator and condenser are located on the low-pressure side of the AHT, while the absorber and evaporator are located on the high-pressure side of the AHT, and the COP of the AHT is lower than that of the AHP. Thus, the AHT can upgrade the low/ medium-grade of the heat source in the generator and evaporator to the high-temperature of useful heat in the absorber. The COP can be calculated by Eq. (4). The simulation of MHP is done in Aspen Plus, using the Peng Robinson Equation of State. The property method ‘ELECNRTL’ is selected for the process simulation of AHP and AHT via Aspen Plus [34], as H2O-LiBr belongs to electrolytes. The models for each component and the calculated parameters in each block are given in Tables A1–A3 in the Appendix. To simplify the calculation of these three heat pumps, some basic assumptions are made as listed below [35].

EPC (kW M $) =

Eloss E EUH = IE TCI TCI

Eloss, MHP = (Eevap + W )

Econd

Eloss, AHP = (Eevap + Egen)

(Econd + Eabs )

Eloss, AHT = (Eevap + Egen )

Eabs

(7) (8) (9) (10)

where EUH refers to the exergy of the upgraded heat, EIE denotes the exergy of the input energy of heat pumps, which is low-grade waste heat and mechanical work for MHPs, low- and high-grade heat sources used in AHPs, and medium/low-grade heat sources used in AHTs, respectively. TCI represents the total capital investment of heat pump technologies. The exergy loss of MHPs, AHPs, and AHTs can be identified in Eqs. (8)–(10). Besides, the exergy flow of heat can be calculated via Eq. (11):

E= 1

T0 Q T

(11)

where T is the temperature of input and output flows in MHPs (i.e., WH1 and H2 in Fig. 1b), AHPs (i.e., LH1, MH1, and DH2 in Fig. 3a) and AHTs (i.e., H1, MH1, and DH2 in Fig. 3b). Note that the exergy of mechanical work consuming in MHPs is equal to the quantity of work. The criterion allows energy and economic comparison of different types of heat pumps. The principal reason that total capital investment is used here is that the use of the total annualized cost (TAC) term will increase the complexity of the heat pump selection process since many other economic details (interest rates, energy prices, etc.) must be fully known. There are two main justifications for this simple term [36]. Firstly, total capital investment is the most important component of TAC, which can closely approximate the results of TAC. Secondly,

(1) The heat pump system is in the steady flow; pressure losses and heat losses are ignored; (2) The electricity consumption of the pump is negligible in the AHP and AHT; (3) The solutions leaving the generator and absorber are both saturated; (4) Working fluid leaving the evaporator and condenser is saturated vapor and liquid, respectively; (5) The isentropic efficiency of the pump and compressor is assumed to be 75% [22]; 5

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Fig. 4. Appropriate placement of heat pumps in GCC: (a) MHPs; (b) AHPs; (c) AHTs.

Operation cost in TAC is often proportional to capital investment. To calculate the EPC (kW/M$) in Eq. (7), the total capital investment of different heat pump systems is given in Eqs. (12)–(14). Eqs. (15)–(17) show the saved operation cost for each heat pump, which can be used for further economic evaluation after heat pump selection.

TCIMHP = 0.000417Qcond

(12)

TCIAHP = 0.000332(Qabs + Qcond )

(13)

TCIAHT = 0.00045Qabs

(14)

OCsaved, MHP = HY (CHU QH + CCU QC

(15)

CELECT W )

OCsaved, AHP = HY (CHU Qcond + CCU Qevap

CHU Qgen)

OCsaved, AHT = HY (CHU Qabs + CCU (Qevap + Qgen

Qcond ))

(16) (17)

HY : 8, 000 h , CELECT : 26300 M $ MJ , CHU : 8300M $ MJ , CCU : 27170 M $ t where HY , CELECT , CHU and CCU represent annual operating time, the unit cost of electric energy, the unit cost of heating utility (low-pressure steam), and unit cost of cooling utility, respectively. TCIMHP denotes total capital investment of MHP [37]. TCIAHP and TCIAHT represent the total capital investment of AHP and AHT, respectively [37]. 3.2. Heat pump integration procedure Heat pump integration considers both the process streams and multiple types of heat pumps. Before applying heat pumps into industrial processes, Pinch Analysis is required to determine the energy and cost targets. Given a temperature difference (ΔTmin), the grand composite curve (GCC) can be plotted, and it shows the minimum hot and cold utility. Then the benefit of heat pump integration can be evaluated. Townsend and Linnhoff [38] first introduced the correct and incorrect placement of heat pumps in the process. Bakhtiari et al. [39] illustrated a simple case of the correct placement of diverse types of heat pumps. Generally, the proper placement of a heat pump is across the Pinch point where the heat pump can upgrade waste heat to a higher temperature level [38]. Fig. 4 illustrates the appropriate placement of MHPs, AHPs, and AHTs, and the GCC graphically represents the feasible cascade of net heat flow needed at specific temperature intervals shifted for a given ΔTmin to ensure a necessary temperature driving force in the heat transfer process [40]. The temperature of the evaporator, condenser, generator, and absorber can be conveniently shown in Fig. 4. The detailed procedure to determine the operating conditions of these three types of heat pumps and perform the Pinch Analysis is presented in Fig. 5. At first, collect operating data of the process, including heat loads and temperature for all of the utilities and process streams. Secondly, set ΔTmin and conduct the Pinch Analysis to obtain the grand composite curve. The grand composite curve can show the Pinch temperature, the heating, and cooling requirements. The heat below the Pinch is the process waste heat, which can be recovered by waste heat technologies. Thirdly, determine the evaporation temperature of heat pumps. The evaporation temperature is constrained by the Pinch temperature and ΔTmin. The condensation temperature of MHPs and AHPs, the absorption temperature of AHTs should be ΔTmin higher than the temperature of the heat sink above the Pinch. Next, the temperature lift of MHP, AHP, and AHT is determined via Eqs. (2), (5) and (6), respectively. Once the operating conditions can meet the requirement of each type of heat pump, the proper temperature lift (i.e., the condensation

Fig. 5. Procedure for Pinch Analysis and determination of operation conditions for heat pumps. 6

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Fig. 7. The variation of EPC at different temperature lifts and evaporation temperatures (Q = 1 MW): (a) MHP and AHP, (b) MHP and AHT.

(4) Select proper working fluid for MHPs, according to Fig. 2. (5) Determine the operating parameters for different heat pumps. (6) Calculate and compare different heat pumps based on the new exergoeconomic criterion. 4. Performance analysis Hammond et al. [2] summarized the required conditions on the surplus heat source for the examined technologies, but they did not analyze the temperature range of waste heat sources and heat demands or sinks that are suitable for different types of heat pump technologies. The main selection criteria of the appropriate heat pump system are the heat source, the heat pump technology, and the heat demand or sink. These factors should be considered to enable heat pump integration into an industrial process. In this section, MHPs, AHPs, and AHTs are utilized to recover waste heat at different temperatures under different evaporation temperatures. The waste heat duties (1 MW and 10 MW) are considered. The simulation conditions for MHPs, AHPs, and AHTs at different waste heat temperatures under waste heat duty of 1 MW are shown in Tables A4–A6 in the Appendix. Finally, the performance evaluation of three heat pumps for different waste heat sources and sinks is compared and analyzed, which can assist in determining the appropriate heat pump technology for different waste heat conditions. It should be noted that since there are different application ranges of useful heat and upgraded heat temperatures for AHP and AHT, their comparison is not conducted.

Fig. 6. The variation of COP at different temperature lifts and evaporation temperatures (Q = 1 MW): (a) MHP, (b) AHP, (c) AHT.

temperature, absorption temperature) is determined. Then different heat pumps are compared and selected. As the required driving forces in heat pumps are different, a proper heat pump cannot be roughly selected for an industrial process only according to the reduction in both hot and cold utility and the COP of different heat pumps. It is critical to propose a suitable heat pump selection guidance based on the exergoeconomic criterion first and then make final decisions based on economic evaluation. The procedure to select and integrate the heat pump into process systems is summarized as follows: (1) Perform Pinch Analysis of a given industrial process. (2) Extract the data of heat source and heat sink (i.e., temperature intervals and heat duties). (3) Select proper process streams recovered by different types of heat pumps and corresponding heat sinks.

4.1. Performance comparison based on the coefficient of performance The COP is defined based on the first law of thermodynamics, which 7

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Fig. 8. The variation of (a) COP and (b) EPC at the evaporation temperature of 50 °C for MHP and AHP, 55 °C for MHP and AHT (Q = 1 MW).

MHP decreases with the rise of the temperature lift at the same evaporation temperature. At different temperature lifts, COPs of MHP are the highest at the evaporation temperature of 55 °C. Therefore, MHP is suitable to recover waste heat at low temperature with low-temperature lift. For AHP and AHT, the variations of COP with the temperature lifts and evaporation temperatures under waste heat duty of 1 MW are determined, as shown in Fig. 6b and Fig. 6c. Note that the evaporation temperature and temperature lift of AHP cannot be higher than 50 °C because of the crystallization of the working fluid [41]. Obviously, the COP of AHP is higher than 1, but the COP of AHT is < 1. The COP of AHT changes slightly at different temperature lifts and evaporation temperatures, and it is within the range of 0.4–0.6. The COP can be used to determine the performance of a certain type of heat pump at different waste heat conditions. However, because the driving energy source is of different types or grades, and the ranges of values for COP of these three heat pumps at different heat conditions are obviously diverse, so the COP is not suitable for the selection of different heat pumps.

Fig. 9. Guide map for the selection of MHP, AHP and AHT at different waste heat conditions. Table 3 Stream data of the process. Streams

Tin (°C)

Tout (°C)

Heat load (kW)

H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11 H12 H13 C1 C2 C3 C4 C5 C6 C7 C8 C9

503.9 366.1 366.1 303.3 76.7 232.2 79.4 112 67.2 157.2 43.3 92 107 66.1 232.2 36.7 112 157.2 92 370.6 452.6 480.6

366.1 178.9 253.9 36.7 26.7 112.2 32.2 23.9 27.2 32.2 26.3 65 32.2 370.6 247.2 125.6 112.8 163.9 97.2 495.6 497.2 496.1

9285 712.7 2928 16840 1228 1813 1878 65.02 3022 988.1 81.14 47.87 573.8 23180 2929 1812 2006 716.4 202.7 11760 4751 1768

4.2. Performance comparison based on exergy loss per total capital investment Waste heat upgraded by different heat pumps requires the energy of diverse types or grades (e.g., mechanical work, high or medium-grade heat source). According to the previous analysis, it is impossible to guide the selection of heat pumps when using the COP as an evaluation criterion. Associated with exergy analysis, exergy loss per total capital investment (EPC) is introduced, which is given by Eq. (6). As mentioned in the Introduction, economic analysis for energy conversion technologies conventionally considers unit cost based on energy. Many researchers have combined exergy and economic disciplines to achieve the appropriate allocation of economic resources for process optimization, economic feasibility, and profitability of a system. They consequently assign costs and/or prices to exergy-related variables [28]. According to the simulation and calculating results, the variation of EPC of MHP, AHP, and AHT at different temperature lifts and evaporation temperatures are determined as shown in Fig. 7. As for MHP and AHP shown in Fig. 7a, the variation trend of EPC is opposite to that of COP with different temperature lifts in Fig. 6a and b. It implies the EPC can be used as an indicator to evaluate the thermodynamic performance of each heat pump at different heat conditions, and the comparison results of MHP and AHP at different heat conditions are different. As shown in Fig. 7a, at the evaporation temperature of 30 °C and 40 °C, the EPC of MHP is lower than that of AHP when the temperature lift is lower than 26 °C and 24 °C, respectively. It indicates that upgrading waste heat to satisfy a heat sink with lower temperature should be prior to a heat sink with higher temperature using an MHP. However, AHP is better for a higher temperature lift. When the

has been widely used in the performance evaluation of heat pump technologies. The COP of MHP, AHP, and AHT are determined via Eq. (1), (3) and (4). For MHPs, working fluids should be selected using Fig. 2 according to the operating parameters. Next, the variation of COP of MHP with the temperature lifts and evaporation temperatures under waste heat duty of 1 MW is determined, as shown in Fig. 6a. The COP of 8

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Fig. 10. Grand composite curve of (a) the total process, (b) the process of heat pump integration potential.

Fig. 11. Temperature regions and intervals on the (a) heat source profile, (b) heat sink profile. Table 4 Heat source profile temperature intervals and heat duties. Heat source shifted temperature (°C)

Heat duty (kW)

71.1 60 41.7

96 1556 3642

Table 6 Evaporation temperatures and temperature lifts for different options for heat pump integration. Option

Tevap (°C)

ΔTlift (°C)

Available heat pump type

1

41.7 60 41.7 60 41.7 60

55.3 27 55.3 47.2 55.3 57.8

MHP/AHP MHP/AHT MHP/AHP MHP/AHT MHP/AHP MHP/AHT

2 3

Table 5 Heat sink profile temperature intervals and heat duties. Heat sink shifted temperature (°C)

Heat duty (kW)

87 107.2 117.8 130.6

192 586 2115 132

Table 7 Operating parameters for MHP in case study.

evaporation temperature is 50 °C, the EPC of AHP is lower than that of MHP in the whole ranges of temperature lifts. In Fig. 6c, the COP of AHT changes slightly with the temperature lift, but the EPC reduces as the temperature lift increases shown in Fig. 7b. It indicates that there is less exergy loss per capital investment, and the stepwise utilization of energy is more reasonable at higher temperature lift. This is because energy performance has stronger impacts on overall performance than economic performance at lower temperature lifts. The EPC of AHT is the lowest at the evaporation temperature of 75 °C, showing the best performance. Therefore, when only integrating an AHT to a process, the best operating parameters can be found. For MHP and AHT shown in Fig. 7b, the variation tendency of EPC with the waste heat conditions is obviously different. At lower temperature lift, the EPC of AHT is higher than that of MHP at different evaporation temperatures (ΔTlift < 35 °C

Working fluid

Tevap (°C)

Tcond (°C)

ΔTlift (°C)

QUH (kW)

QRH (kW)

n-butane n-butane n-butane ammonia

41.7 60 60 60

87 87 107.2 107.2

45.3 27 47.2 57.8

192 192 586 2115

160 170 488 1510

at Tevap = 55 °C and 65 °C; ΔTlift < 34 °C at Tevap = 75 °C; ΔTlift < 32 °C at Tevap = 85 °C). However, increasing the temperature lift makes AHT as competitive as MHP. That is, the EPC of AHT is lower than that of MHP at high temperature lift. The performances evaluated using COP and EPC of these three heat pumps at one selected evaporation temperature are represented in Fig. 8, which shows that the differences of the EPC of these three heat pumps are more obvious at different temperature lifts than their COPs. Comparing the results at different evaporation temperatures, the EPC is more proper for heat pumps comparison than the conventional COP. To determine whether 9

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Table 8 Operating parameters for AHP and AHT in case study. Heat pump type

Mass fraction (LiBr)

Tevap (°C)

Tcond (°C)

Tgen (°C)

Tabs (°C)

ΔTlift (°C)

QUH (kW)

QRH (kW)

AHP AHT AHT AHT

0.607 0.4985 0.5989 0.6398

41.7 60 60 60

87 30 30 30

160 60 80 100

87 87 107.2 117.8

45.3 27 47.2 57.8

192 192 586 1907

96 429 549 1556

temperature lift. For a waste heat source in the temperature range of 60 °C–95 °C, the AHT is especially competitive in application with higher temperature lifts. The guide map for heat pump selection presented in this work can be utilized to develop a ranking of heat pumps based on the waste heat conditions and help to determine the temperature lifts, which will be investigated in detail in the case study section. 5. Case study The proposed criterion and systematic procedure for the selection and integration of heat pumps in industrial processes are applied to a catalyst reforming unit of a petroleum refinery. This case is taken from Fraser et al. [42], and the process stream data is listed in Table 3. At first, the heat recovery potential between hot and cold streams is identified. Given the temperature difference ΔTmin (in this case 10 °C), Pinch Analysis for the heat exchanger network is conducted, and the corresponding minimum hot and cold utility are determined as 8791 kW and 18450 kW. The GCC of the total process is shown in Fig. 10a, and the Pinch temperature is 74.4 °C. In order to recover the waste heat by using heat pump technologies, the GCC of the process only consuming LP is shown in Fig. 10b. Based on the rules of heat pump placement, a heat pump can be integrated to upgrade heat from below the Pinch for heat sink usage above the Pinch. In the second and third steps, the heat source and sink profiles are divided into temperature intervals in Fig. 11 to select proper heat pump technologies for the process. The temperature intervals are selected based on the output and input temperatures of the streams; beginning from the highest output temperature ensures that high-temperature heat is recovered before low-temperature heat [22]. The heat source and heat sink temperatures and duties that have the potential for heat pump integration from Fig. 11a and b are shown in Tables 4 and 5. In the case study, three types of heat pumps, MHP, AHP, and AHT are considered. The operation parameters of these three heat pumps are determined in the fourth and fifth steps. According to Fig. 11a and b, there are different options for heat pump applications. For heat source shifted temperature at 41.7 °C with a heat duty of 3642 kW, it can only be upgraded to 87 °C (ΔTlift = 55.3 °C) because the temperature lift is not higher than 60 °C. For heat source shifted temperature at 60 °C with a heat duty of 1556 kW, it can be upgraded to 87 °C, 107.2 °C or 117.8 °C. Since the heat duty of heat source shifted temperature at 71.1 °C is only 96 kW, and there is not much potential for heat recovery. As a result, there are three options of the heat sources and sinks for heat pump integration, which are listed in Table 6. For each option, the models of the MHP, AHP, and AHT are simulated via Aspen Plus. The detailed operating parameters, upgraded, and recovered heat duties of these three types of heat pumps are shown in Tables 7 and 8. It should be noted that the selection of working fluid for MHPs is based on Section 2.1. That is, given a temperature lift and an evaporation temperature, the working fluid of the MHP can be determined through Fig. 2b. It shows that at the temperature interval of 41.7 °C, applying MHP and AHP can both meet the demand of heat sink at 87 °C. Only when integrating an AHT to upgrade the heat source at a temperature

Fig. 12. Coefficient of performance of the MHP, AHP, and AHT.

Fig. 13. Exergy loss per total capital investment of the MHP, AHP, and AHT.

the heat pump selection is related to the waste heat duty, heat pump selection under waste heat duty of 10 MW was also performed, and the results are identical with those under waste heat duty of 1 MW. To find out the suitable applications for these three heat pumps, two factors, heat source temperature and temperature lift as defined in Eqs. (2), (5) and (6) are considered to show the feature of heat conditions. The heat source temperature for a mechanical heat pump refers to the temperature of waste heat to be upgraded. For absorption systems, the heat temperature required in the evaporator in AHP, and the temperature of the driving energy required in the generator and evaporator in AHT are defined as the heat source temperature. In this way, a guide map can be developed to show a suitable area for the MHP, AHP, and AHT, as shown in Fig. 9. When the heat source temperature is lower than 60 °C, the AHP is the best choice at higher temperature lift, but the MHP is economically and thermally more advantageous with a lower

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– 0.070 – 0.172 – 0.486 – 0.14 – 0.14 – 0.92 – 31.31 + 88.44 – 31.31 + 89.93 – 31.31 + 121.19 – 1.990 + 8.605 – 1.997 + 0.448 – 1.997 + 0.543 0.16 – 0.32 – 0.96 – 87.19 + 88.44 – 87.19 + 91.25 – 87.19 + 296.98 –

Fig. 14. Comparison results of TCI and OCsaved of three options based on COP and EPC.

interval of 60 °C–117.8 °C, waste heat is totally recovered (2115 kW). Finally, the performance evaluation of these three options for heat pump integration is conducted. The COP and proposed exergoeconomic criterion, EPC are used as heat pump selection criteria, respectively. The economic comparison of these three options based on different selection criteria is investigated.

54 22 129 – 637 –

6.089 + 8.605 – 6.089 + 6 – 6.089 + 3.493 –

0.067 – 0.120 – 0.151 –

COP TCI (M$) EPC (kW/M$) COP

6. Results and discussion

330 362 649 183 1670 143

384 288 778 682 2307 2003

Figs. 12 and 13 show the calculated results of the COP and EPC, which can be used to select the heat pump for different heat sources and sinks. Results of energy and economic performances based on different selection criteria COP and EPC are shown in Table 9. The comparison results of TCI and OCsaved based on COP and EPC of three options for heat pump integration are shown in Fig. 14a and b. As shown in Table 9, Fig. 14a and b, based on selection criterion COP, the COPs of three options are higher than those based on selection criterion EPC. But the EPCs and TCIs of options 1–3 are lower, and OCsaveds are higher, which implies heat pump selection based on EPC can achieve a better economic performance than based on conventional COP. As shown in Fig. 12, MHPs are selected for these three options because of the highest COP. However, an AHP and an AHT are selected using the EPC, saving operation cost 0.003 M$, 0.052 M$, and 0.335 M$ more than using the COP for option 1–3, respectively. The option 3 for heat pump integration has a maximum potential for waste heat recovery, and applying an AHP and an AHT to upgrade the heat in option 3 can save the highest operation cost, saving heating and cooling utilities 143 kW and 2003 kW, respectively. In Figs. 12, 13, and Table 9, the three heat pump types are compared based on the COP and EPC. The heat upgraded for the heat sink temperature of 87 °C, 107.2 °C, and 117.8 °C are 192 kW, 586 kW, and 2115 kW, respectively. For the same heat source temperature, the EPC of mechanical heat pumps increases with an increase in temperature lift. But the difference in the EPC for the heat pump is different at

3

2

Highest COP Lowest EPC Highest COP Lowest EPC Highest COP Lowest EPC 1

MHP + MHP AHP + MHP MHP + MHP AHP + AHT MHP + MHP AHP + AHT

Heating utility saved (kW) Cooling utility saved (kW) Heat pump type Selection criterion Option

Table 9 Energy and economic performances of different options of heat pump integration.

Power required (kW)

Based on COP

OCsaved (M $)

Based on EPC

EPC (kW/M$)

TCI (M$)

OCsaved (M $)

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than 60 °C, the absorption heat pump is the best selection at higher temperature lift, but the mechanical heat pump is economically and thermally more advantageous with a lower temperature lift at different evaporation temperatures. However, for a waste heat source in the temperature range of 60 °C–95 °C, the absorption heat transformer is better at higher temperature lifts. The results of COP and EPC both show that mechanical heat pumps are more sensitive to temperature lifts, so in practical applications, higher temperature lifts for mechanical heat pumps should be avoided as much as possible. The heat-driven heat pumps are particularly competitive in applications with high temperature lifts, according to the EPC. These results are also in agreement with those based on economic selection criterion [26]. The proposed method is applied to a case study of a catalyst reforming unit in a petroleum refinery. Heat pump selection is based on the exergoeconomic criterion first, then the energy-saving and cost-effectiveness of three types of heat pumps at different heat conditions are compared. Results show that absorption heat pump and absorption heat transformer have the highest potential to save operation cost compared to mechanical heat pump for different waste heat upgrading options. The exergy loss per total capital investment of the AHP and AHT in option 3 are 31.31 kW/M$ and 121.19 kW/M$, saving operation cost by 0.486 M$, which is 0.335 M$ higher than 0.151 M$ (the saved operation cost based on COP). The benefit of using an AHT is that the system is powered by a low-grade heat source instead of higher-grade mechanical power required in an MHP. The introduced guide map for the heat pump selection at different waste heat temperatures and temperature lifts can provide a preliminary reference for heat pump selection and further insights into heat pump technologies and exergoeconomic analysis. The proposed method of heat pump integration can be further extended to other industrial processes for low-grade waste heat recovery.

different quantities of useful heat upgraded, which is small at low demand for heat upgraded but more remarkable with the increase of heat upgraded. When the temperature lifts and waste heat source temperatures are determined, the criterion EPC and the guide map Fig. 9 are applicable for heat pump selection. For example, in the case study, the temperature lifts are 55.3 °C and 27 °C at the evaporation temperature of 41.7 °C and 60 °C for option 1, an AHP and an MHP are selected to recover the waste heat finally according to the criterion EPC. If using the proposed guide map shown in Fig. 9, at the heat source shifted temperature of 41.7 °C with a temperature lift of 55.3 °C, an AHP is selected. An MHP is chosen at the heat source shifted temperature of 60 °C with a temperature lift of 27 °C. Likewise, Table 9 gives the same results on heat pump selection for the other two options if using the guide map (i.e., Fig. 9). Besides, proper temperature lift should be determined based on the grand composite curve and the waste heat load of the practical process. After heat pump selection for different waste heat conditions of a process, an economic evaluation can be further carried out to determine the best heat pump option for the process. Therefore, the guide map can simplify the heat pump selection process in real applications. The method of heat pump integration applied in the case study can be further extended to other industrial processes for low-grade waste heat recovery. 7. Conclusion In this work, the exergoeconomic criterion EPC (i.e., exergy loss per total capital investment) is applied to heat pump selection. The criterion can appropriately balance the thermodynamic (exergy-based) and economic performances of the process and heat pump technologies, showing correlations between specific second-law-based thermodynamic destruction and capital investment, which can be more suitable for screening and selecting heat upgrading technologies. The process models of mechanical heat pumps, absorption heat pumps, and absorption heat transformers are developed using Aspen Plus. Besides, a systematic guideline on heat pump integration in industrial processes is introduced. The proper heat sources and heat sinks are selected from the given streams for different heat pumps. The performance analysis results show that heat pump selection at different waste heat conditions is different. The EPC for mechanical heat pumps decreases with the increase of temperature lift. The EPCs for absorption heat pumps and absorption heat transformers tend to decrease with the increase of temperature lift. When the heat source temperature is lower than 60 °C, the absorption heat pump is the best selection at higher temperature lift, but the mechanical heat pump is economically and thermally more advantageous with a lower temperature lift at different evaporation temperatures. The performance analysis results show that heat pump selection at different waste heat conditions is different. The EPC for mechanical heat pumps increases with the increase of temperature lift. The EPCs for absorption heat pumps and absorption heat transformers tend to decrease with the increase of temperature lift. When the heat source temperature is lower

CRediT authorship contribution statement Mengying Wang: Methodology, Software, Writing - original draft, Data curation. Chun Deng: Writing - review & editing, Formal analysis, Project administration, Supervision. Yufei Wang: Software, Validation. Xiao Feng: Conceptualization, Supervision. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The authors acknowledge financial support provided by the National Natural Science Foundation of China (21576286) and Science Foundation of China University of Petroleum, Beijing (No. 2462018BJC003). Sponsorship from China Scholarship Council (201806440077) is also gratefully acknowledged.

Appendix

Table A1 Simulation model of each component of MHP. Component

Block

Calculated parameters

Compressor VLV Evaporator Condenser

Compressor Valve Heat Exchanger Cooler

Pressure requirement, temperature, enthalpy, and entropy of State 3 are calculated. Temperature and entropy of State 1 are calculated. Heat duty of Evaporator, temperature, enthalpy, and entropy of State 2 and WH2 are calculated. Heat duty of Condenser, temperature, enthalpy, and entropy of State 4 are calculated.

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Table A2 Simulation model of each component of AHP. Component

Block

Calculated parameters

Pump SOLV REFV Solution Heat Exchanger Condenser Evaporator Absorber

Pump Valve Valve Heater + Heater Heater + Heater Heater + Heater Mixer+ (Heater + Heater)

Generator

HeatX + Flash2

Power requirement, temperature, enthalpy, and entropy of State 2 are calculated. Temperature and entropy of State 7 are calculated. Temperature and entropy of State 10 are calculated. Temperature of State 6, heat duty of Solution Heat Exchanger, enthalpy, and entropy of State 3 are calculated. Heat duty of Condenser, temperature, enthalpy, and entropy of State 9 and MH3 are calculated. Heat duty of Evaporator, temperature, enthalpy, and entropy of State 11 and LH2 are calculated. Mass flow, enthalpy, and entropy of State 12 are calculated. Heat duty of Absorber, temperature, enthalpy and entropy of MH2 are calculated. Heat duty of Generator, temperature, pressure, enthalpy, and entropy of State 5 and 8 are calculated.

Table A3 Simulation model of each component of AHT. Component

Block

Calculated parameters

Pump 1 and 2 SOLV Solution Heat Exchanger Condenser Evaporator Absorber

Pump Valve Heater + Heater Heater + Heater Heater + Heater Mixer+ (Heater + Heater)

Generator

HeatX + Flash2

Power requirement, temperature, enthalpy, and entropy of State 7 and 10 are calculated. Temperature and entropy of State 3 are calculated. Temperature of State 2, heat duty of Solution Heat Exchanger, enthalpy, and entropy of State 11 are calculated. Heat duty of Condenser, temperature, enthalpy, and entropy of State 6 and CW2 are calculated. Heat duty of Evaporator, temperature, enthalpy, and entropy of State 8 and MH2 are calculated. Mass flow, enthalpy, and entropy of State 12 are calculated. Heat duty of Absorber, temperature, enthalpy, and entropy of H2 are calculated. Heat duty of Generator, temperature, pressure, enthalpy, and entropy of State 5 and 9 are calculated.

Table A4 Simulation conditions for MHP. Tevap (°C)

Working fluid

Tcond (°C)

30 40 50 55 55 55 65 65 65 75 85

n-butane n-butane n-butane n-butane ammonia n-butane n-butane ammonia n-butane n-butane n-butane

50, 60, 70, 80 60, 70, 80, 90 70, 80, 90, 100 85, 95 105, 115, 125 135 95, 105 115, 125 135 105, 115, 125, 135 115, 125, 135

Table A5 Simulation conditions for AHP. Mass fraction (LiBr)

Tevap (°C)

Tcond (°C)

Tabs (°C)

Tgen (°C)

0.4730 0.5400 0.5930 0.4650 0.5320 0.5840 0.4588 0.5235 0.5755

30 30 30 40 40 50 60 50 50

50 60 70 60 70 80 70 80 90

50 60 70 60 70 80 70 80 90

110 110 130 110 120 140 110 130 150

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Table A6 Simulation conditions for AHT. Mass flow (kg/s)

Mass fraction (LiBr)

Effectiveness of solution heat exchanger

Tevap (°C)

Tcond (°C)

Tgen (°C)

Tabs (°C)

7.165 7.165 7.165 7.165 7.12 7.12 7.12 7.12 7.07 7.07 7.07 7.07 7.02 7.02 7.02 7.02

0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58

0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64

55 55 55 55 65 65 65 65 75 75 75 75 85 85 85 85

30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30

75 75 75 75 75 75 75 75 75 75 75 75 85 85 85 85

85 95 105 115 95 105 115 125 105 115 125 135 115 125 135 145

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