DESIGN AND ANALYSIS OF TRI-GENERATION PLANT FOR HEATING, COOLING AND POWER

A Thesis Presented By Dongchuan You to The Department of Mechanical and Industrial Engineering

in partial fulfillment of the requirements for the degree of

Master of Science in the field of Mechanical Engineering

Northeastern University Boston, Massachusetts

April 2021

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ACKNOWLEDGEMENTS

It is my extreme pleasure to thank Professor Metghalchi for his guidance, patience, encouragement, and inspiration that he provided generously during my whole master studies, not only throughout the thesis but also in his class. It has been my honor to be his student and learning under his instruction.

The author also would like to say thanks to his friends, Aobo Liu, Zhenyu Lu, Ziyu

Wang and others who give me a helping hand on my way of studying abroad. It is really an unforgettable happy time to study, communicating with each other and I will never forget the encouragement when I am confusing and frustrating.

Next, I must thank my parents sincerely, not only because of the financial support for my tuition and daily expenses, but also for their constant understanding, patience, encouragement during my whole master studies.

I also want to thank the department, the college of engineering, for their assistance for my study for the past two years. I would like to say thank you to all professors who taught me with their kindness and try their best effort to guide me.

Finally, please allow me to show my appreciation to all the people who have helped me in my master studies. It builds an impressive memory of my past time, an unforgettable journey on my learning road.

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ABSTRACT

A new tri-generation plant for heating, cooling and power has been designed and analyzed. Tri-generation system has been studied in recent years and its advantages like energy saving and environmental safety has been proved. Research on improving their performance has been increasing lately. In this thesis, a new tri-generation plant, consisted of a supercritical carbon dioxide (sCO2) recompression Brayton cycle and aqueous lithium bromide absorption refrigeration cycle, has been designed and its performance has been determined. Mass, energy, entropy and exergy balances have been used to model sCO2 recompression Brayton cycle, aqueous lithium bromide absorption refrigeration cycle and the tri-generation power plant. Parametric studies have been done in all three cycles to investigate effects of operating conditions on the performance of the system. Results show efficiency of sCO2 recompression Brayton cycle increases when pressure ratio and maximum temperature increase; the coefficient of performance of the absorption refrigeration system increases when generator exit temperature increases; the exergetic efficiency of the tri-generation plant increase when pressure ratio increases.

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TABLE OF CONTENTS 1 Introduction……………………………………………………………………….…….1 2 Supercritical Carbon Dioxide Recompression Cycle……………………………………3 2.1 Background………………………………………………………………………...3 2.2 Description of Recompression Cycle………………………………………………4 2.3 Method and Assumptions……………………………………………………….….6 2.4 Thermodynamic Model…………………………………………………………….7 2.5 Results…………………………………………………………………………….10 2.5.1 Model 1………………………………………………………………….….10 2.5.1.1 Effects of Pressure Ratio……………………………………...….…10 2.5.1.2 Effects of Split Fraction…………………………………………….13 2.5.1.3 Effects of Maximum Temperature……………………………….....14 2.5.2 Model 2……………………………………………………...……………...16 2.5.3 Model Comparison…………………………………………………….…...19 2.6 Conclusion………………………………………………………………………..20 3 Aqueous Lithium Bromide Absorption Refrigeration System………………………....22 3.1 Background………………………………………………….……………………22 3.2 Refrigerators Description…………………………………………………………24 3.3 Mathematical Model………………...……………………………………………27 3.3.1 Working Fluid Property Calculation……………………………………….27 3.3.2 Analysis of Single-effect Cycle…………………………………………….28 3.3.3 Analysis of Double-effect Cycle…………………………………………...31 3.3.4 Assumptions and Parameters…………………………………………….…35 3.4 Results and Discussion……………………………………………………………36 3.4.1 Single-effect Cycle…………………………………………………...…….36 iv

3.4.1.1 Effect of Cooling Loads………………………………….……….…36 3.4.1.2 Effect of Evaporator Exit Temperature………………….….………37 3.4.1.3 Effect of Condenser Exit Temperature…………………..……….…38 3.4.1.4 Effect of Absorber Exit Temperature…………………….…………39 3.4.1.5 Effect of Generator Exit Temperature………………….…….……..39 3.4.1.6 Effect of Solution Energy Exchanger Effectiveness…….…….……41 3.4.2 Double-effect Cycle……………………………….………………….…….42 3.4.2.1 Effect of Cooling Loads……………………………………….……42 3.4.2.2 Effect of Evaporator Exit Temperature……………………….…….42 3.4.2.3 Effect of Upper Condenser Exit Temperature………………..…….43 3.4.2.4 Effect of Absorber Exit Temperature……………………….….…..43 3.4.2.5 Effect of Upper Generator Exit Temperature……………….….…..45 3.4.2.6 Effect of Solution Energy Exchanger Effectiveness……….….……46 3.4.2.7 Effect of Lower Condenser Exit Temperature……………….….….47 3.5 Conclusion………………………………………………………………………..48 4 Tri-Generation System Analysis……………………………………………………….50 4.1 Model description………………………………………………………………...50 4.2 Thermodynamic Model…………………………………………………………..52 4.3 Assumptions and Parameters…………………………………………………….54 4.4 Results……………………………………………………………………………55 5 Conclusion and Recommendation………………………………………………….…61 5.1 Conclusion……………………………………………………………………..…61 5.2 Recommendation…………………………………………………………………62 References……………………………………………………………..…………………63 Appendices..…...…………………………………………………………………..……..72 v

Appendix Ⅰ MATLAB Code for sCO2 Recompression Cycle (Trial and Error)……..72

Appendix Ⅱ MATLAB Code for sCO2 Recompression Cycle (Newton-Raphson Iteration)………………………...………………………………………………….…75 Appendix Ⅲ MATLAB Code for Single-Effect Absorption Refrigeration System.....79 Appendix Ⅳ MATLAB Code for Double-Effect Absorption Refrigeration System…………...……………………………………………………………………81 Appendix Ⅴ MATLAB Code for Tri-Generation Plant………………………….…....83

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CHAPTER 1

INTRODUCTION

Tri-generation systems also known as combined cooling, heating and power (CCHP) systems, is becoming a major subject of research in order to improve energy efficiency of power generation, thermal energy needs of plants and refrigeration systems. Tri-generation systems include various new technologies, provide an alternative for the world to meet and solve energy-related problems such as energy shortages, energy supply security, emission control, conservation of energy, and energy economy [1]. Tri-generation systems mostly produce both electric and usable thermal energy on-site or near site and converts 75–80% of the fuel source into useful energy [2-3]. The research of tri-generation system has been heated up in recent years [4-8], covering analysis based on different energy source like solar power plant [9], geothermal energy [10-11], fuel cell [12-13]. Also, studies based on different types of cycles in the system, such as organic Rankine cycle [14], Kalina cycle

[15], have been reported.

The purpose of this thesis is to perform analysis of a given tri-generation consisted of supercritical carbon dioxide (sCO2) recompression cycle and aqueous lithium bromide refrigeration cycle. The effects of some operating variables, such us pressure ratio, generator exit temperature on energy effectiveness as well as exergetic efficiency have been evaluated. Chapter 2 covers complete design and analysis of a recompression super critical Brayton cycle based. Results of this chapter will be published in American Society of Mechanical Engineers (ASME) Journal of Energy Resources Technology (JERT).

Chapter 3 is the design and analysis of both single effect as well as double effect water 2 lithium bromide absorption refrigerator system. A paper based on the results of chapter 3 will be published in JERT too. Chapter 4 is a complete Tri-generation system combing results of chapters 2 and 3 and also developing thermal energy for use as needed. Chapter

5 is the conclusion and recommendation of this study.

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CHAPTER 2

SUPERCRITICAL CARBON DIOXIDE RECOMPRESSION CYCLE

In this chapter, parametric analysis of different variables such as pressure ratio, split fraction and maximum temperature of the sCO2 recompression cycle have been performed.

The effects of these variables on thermal efficiency as well as exergetic efficiency have been evaluated.

2.1 Background

Carbon dioxide has been studied as a working fluid in power plants for years due to favorable high efficiency of the plant using carbon dioxide [16] and environmental safety

[17]. Supercritical carbon dioxide can be used in different types of energy sources, such us nuclear [18], solar [19], coal fired [20,21] in topping cycles [22], bottom cycles [23] and power cycles [24]. Also, additional attributes of sCO2 Brayton cycle, such us impurities

[25], pinch point analysis [26], convective energy transfer coefficient [27] have been reported.

Ahn [28] wrote a review paper on the thermal efficiencies of sCO2 power conversion systems and applications with respect to the turbine inlet temperature. Geothermal, nuclear and solar power plants have excellent environmental attributes, but their most common efficiencies are less than 45% [29] because their turbine inlet temperature are mostly between 400-700 ℃, which are much lower than gas or steam turbine system. The sCO2

Brayton cycles, which have been studied in recent decades, can have higher thermal efficiency, about 5% higher while having lower turbine inlet temperature [28]. The main 4

advantage for the sCO2 Brayton cycle is that the working fluid is compressed near critical point which is incompressible and requires less energy for compression work. The carbon dioxide critical condition is 31.08 ℃ and 7.38 MPa [30] and becomes more incompressible near the critical point [31]. Also, there are fewer material issues at high turbine inlet temperature for sCO2 Brayton cycle [28].

Different types of sCO2 cycles such us reheating cycle [32], intercooling cycle [33], recompression cycle [34], turbine split flow cycle [35] and few others are described in references [36,37]. The most efficient layout of sCO2 cycle is generally agreed as recompression cycle [37] which was suggested by Feher [38] and Anglino [39]. An important characteristic of recompression sCO2 Brayton cycle is that in the recuperator, the specific heat of the cold side flow is two to three times higher than the hot side flow [28], and that makes recompression cycle important because of the unique thermal properties at supercritical condition [40]. Since compression work of the compressor is much lower in the sCO2 cycle and only part of the flow goes through energy loss device before the compressor, the efficiency of the cycle is high.

2.2 Description of Recompression Power Cycle

Figure 2.1 shows the schematic diagram of recompression sCO2 Brayton cycle. There are two compressors, one turbine, two recuperators, high temperature recuperator (HTR) and low temperature recuperator (LTR), a high temperature energy exchanger where energy is added to the plant, a mixing device and a low temperature energy exchanger where energy is removed from the system. High pressure carbon dioxide receives energy in the high temperature heater, process 7-8, where its temperature increases and then 5 generates power through the turbine, process 8-9. After the turbine. Carbon dioxide goes through the High Temperature Recurperator (HTR), process 9-10, where energy is transferred to low temperature carbon dioxide. Carbon dioxide, then, goes through the Low

Temperature Recuperator (LTR), process 10-11, where additional energy is transferred to low temperature carbon dioxide. At state 11, carbon dioxide splits into two parts: The main flow, at state 12 is cooled in a low temperature energy exchanger, process 12-1 and then compressed, process 1-2, before entering into LTR. The secondary flow, which starts at state 3, goes through the second compressor, process 3-4, and then is mixed with the main flow which has been heated in the LTR, process 2-5. Carbon dioxide leaves the mixing device at state 6. Temperature of carbon dioxide increases in the HTR before it goes to the high temperature energy exchanger and the cycle continues. Figure 2.2 shows a typical T- s diagram of this cycle when T1 = 32 ℃, P1 = 8 MPa, pressure ratio is 2.4, Tmax = 550 ℃ and split fraction (푚̇ 12/푚̇ 11) is 0.9. Carbon dioxide saturation curve is also shown in the figure and part of it is expanded and is shown in the upper left corner of the figure. The expanded saturation curve shows that state 1 has higher temperature and pressure than the critical state and is in supercritical condition.

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qin

wc1 wc2 wt

qout

Figure 2.1: Recompression sCO2 Brayton cycle

Figure 2.2: Temperature vs entropy of a recompression sCO2 cycle

2.3 Method and Assumptions

The thermodynamic and transport properties data of CO2 in this article is based on

REFPROP [41], developed by National Institute of Standards and Technology (NIST). 7

In the cycle, there is no pressure drop through energy exchangers, mixer, splitter and recuperators. The maximum temperature in the cycle (T8) is constant and two cases have been considered in these calculations. The following table is a list of parameters of the cycle.

Parameter Value or range

Minimum temperature, T1 32 ℃

Minimum pressure, P1 8 MPa

Maximum temperature, T8 550 ℃ or 750 ℃ LTR effectiveness 86% [42] HTR effectiveness 86% [42] Turbine isentropic efficiency 90% Compressor isentropic efficiency 90% Pressure ratio 2-5

Table 2.1: Parameters of the sCO2 Recompression Cycle

2.4 Thermodynamic Model

The split fraction, at point 11 in figure, is defined as:

푚̇ 푥 = 12 (2.1) 푚̇ 11

The definition for turbine efficiency is:

ℎ8−ℎ9 휂푡 = (2.2) ℎ8−ℎ9𝑖

Where state 9i is the ideal exit condition from the turbine where:

푠8 = 푠9𝑖 (2.3)

For the main compressor: 8

ℎ2𝑖−ℎ1 휂푐 = (2.4) ℎ2−ℎ1

Where state 2i is the ideal exit condition of the compressor where:

푠1 = 푠2𝑖 (2.5)

It is the same for the second compressor:

ℎ4𝑖−ℎ3 휂푐 = (2.6) ℎ4−ℎ3

푠3 = 푠4𝑖 (2.7)

Energy balance for both LTR and HTR are:

푥(ℎ2 − ℎ5) + (ℎ10 − ℎ11) = 0 (2.8)

(ℎ6 − ℎ7) + (ℎ9 − ℎ10) = 0 (2.9)

Also, the effectiveness of LTR and HTR:

푥(ℎ5−ℎ2) 휀퐿푇푅 = (2.10) ℎ10−ℎ11′

ℎ7−ℎ6 휀퐻푇푅 = (2.11) ℎ9−ℎ10′

Where according to the definition of effectiveness of recuperator, h11’ is the enthalpy of CO2 when T11’=T2 and pressure is P11; h10’ is the enthalpy of CO2 when temperature is

T6 and pressure is P10.

Energy balance at the mixer:

ℎ6 = (1 − 푥)ℎ4 + 푥ℎ5 (2.12)

The energy input of the cycle is:

푞𝑖푛 = ℎ8 − ℎ7 (2.13)

The exergy input is:

푇0 푒푥 = 푞𝑖푛(1 − ) (2.14) 푇푠

Where the ambient temperature T0 is set as 25℃, the source temperature Ts is set as 9

800 ℃.

The net work of the cycle is:

푤푛푒푡 = (ℎ8 − ℎ9) − 푥(ℎ2 − ℎ1) − (1 − 푥)(ℎ4 − ℎ3) (2.15)

And the thermal efficiency of the cycle is

푤 휂 = 푛푒푡 (2.16) 푞𝑖푛

The exergetic (second law) efficiency is:

푤 휀 = 푛푒푡 (2.17) 푒푥

In this article, there are two different models based on the temperature differences between T4 and T5. Model 1 is that T4 and T5 are different. Model 2, like most studies Bai

[20], Sharama [40], will set temperatures at states 4,5 to be the same, which can reduce the exergy destruction in the mixing process.

The first part of this chapter shows the effects of varying pressure ratio and split fraction on performance of sCO2 Brayton cycle in model 1. In this part, with a given split fraction and pressure ratio, trial and error method is used to solve the governing equations.

The process starts with initial guess of T5 and calculates all the temperatures in the cycle, then checks if the answers satisfy equation (2.11). If not, the second iteration is developed.

The process continues till the correct value of temperature at state 5 is found.

The second part of this study is to determine effects of different pressure ratio and maximum temperature on thermal and exergetic efficiency of the cycle in model 2. In this model, the split fraction will take a specific number and it is unknown. In this model

Newton-Raphson iteration method has been used to solve all the governing equations together.

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2.5 Results

2.5.1 Model 1

Analysis have been done for recompression sCO2 cycle as shown of Figure 2.1 when T4 and T5 are different.

2.5.1.1 Effects of Pressure Ratio

Figure 2.3 shows the effect of varying pressure ratio on thermal efficiency of power plant for the maximum temperature of 550 ℃ and varying the split ratio from 0.7 to 0.9.

As it can be seen, the thermal efficiency increases as pressure ratio increases reaching a maximum value and then decreases.

Figure 2.3: Thermal efficiency vs pressure ratio in model 1 with different split fraction 11

when T8 = 550℃

Figure 2.4 shows the results of simulation for higher temperature of carbon dioxide entering the turbine. As it can be seen the same trend as figure 2.3 is observed, but efficiency is higher due to high temperature at the turbine inlet. As figures 2.3 and 2.4 show, when maximum temperature and split fraction are kept constant, for higher pressure ratio, efficiency first increases, and then decreases after reaching the highest point. This trend is the same as typical Brayton cycle with recuperator [43].

Figure 2.4: Thermal efficiency vs pressure ratio in model 1 with different split fraction when T8 = 750℃

Figures 2.5 and 2.6 show exergetic efficiency (second law efficiency) of the cycle for the two turbine inlet temperatures of 550℃ and 750℃. The results follow those of figures 12

2.3 and 2.4.

Figure 2.5: Exergetic efficiency vs pressure ratio for different split fraction and T8 = 550℃ 13

Figure 2.6: Exergetic efficiency vs pressure ratio vs in model 1 with different split fraction when T8 = 750℃

2.5.1.2 Effect of Split Fraction

The split fraction also plays an important role for the performance of the cycle. As figure 2.3, 2.4, 2.5 and 2.6 show with the increase of the split fraction, the thermal efficiency and exergetic efficiency of the cycle decrease. The main reason for this is flow rate through low temperature energy exchanger where energy is transferred to ambient there are more energy and exergy losses for higher splits.

The split fraction is restricted by the design of recuperator. To make a possible recuperator, the cold side outlet temperature should not be higher than the hot side inlet temperature, which means: 14

푇5 ≤ 푇10 (2.18)

The energy transfer from each side will be:

휕푣(푇,푝) 푞 = ∫ 푑ℎ = ∫ {푐 (푇, 푝)푑푇 + [푣(푇, 푝) − 푇 ]푑푝} (2.19) 푝 휕푇

Assuming no pressure drops in recuperator, above equation becomes:

푇5 ℎ5 − ℎ2 = ∫ 푐푝 푑푇 = (푇5 − 푇2)푐̅̅푝̅̅̅ (2.20) 푇2 퐻 퐻

푇10 ℎ10 − ℎ ′ = ∫ 푐푝 푑푇 = (푇10 − 푇2)푐̅̅푝̅̅ (2.21) 11 푇2 퐿 퐿

Where the subscript H and L for specific heat represent the higher pressure and lower pressure.

Substitute equations (2.20) and (2.21) into equation (2.10),

푥(푇5−푇2)푐̅̅푝̅̅̅̅ 휀 = 퐻 (2.22) 퐿푇푅 ̅̅̅̅̅ (푇10−푇2)푐푝퐿

Consider equation (18) and actual condition that T2 will be less than T5 and T10, then:

푐̅̅̅̅̅ 푥 ≥ 휀 푝퐿 퐿푇푅 ̅̅̅̅̅̅ (2.23) 푐푝퐻

It turns out the ratio of the two specific heats in equation (2.23) is always less than 1 setting up a minimum value of the split.

2.5.1.3 Effects of Maximum Temperature

Figure 2.7 shows thermal efficiency as a function of pressure ratio when split fraction is 0.7. The same trends are found when split fraction changes to 0.8 and 0.9. It can be seen that the higher the maximum temperature, the higher the thermal efficiency of the cycle. 15

Figure 2.7: Thermal efficiency vs pressure ratio in model 1 with different maximum temperature when x = 0.7

Figure 2.8 shows exergetic efficiency as a function of pressure ratio when split fraction is 0.7. The same trends are found when split fraction changes to 0.8 and 0.9. It is obvious that the higher the maximum temperature, the higher the exergetic efficiency of the cycle. 16

Figure 2.8: Exergetic efficiency vs pressure ratio in model 1 with different maximum temperature when x = 0.7

2.5.2 Model 2

Analysis have been done for recompression sCO2 cycle for cases where T4 and T5 are the same. For this case, split fraction becomes a specific value for a given pressure ratio that needs to be determined. Figure 2.9 shows how split fraction changes as a function of pressure ratio. The split fraction of the cycle keeps decreasing when pressure ratio increases.

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Figure 2.9: Split fraction in the cycle as a function of pressure ratio in model 2

Figure 2.10 shows thermal efficiency of the cycle as a function of pressure ratio. As it can be seen, thermal efficiency increases as pressure ratio increases. The thermal efficiency of the cycle first increases to reach a highest point and then decrease while the pressure ratio keeps rising. 18

Figure 2.10: Thermal efficiency of the cycle as a function of pressure ratio in model 2

Figure 2.11 shows the exergetic efficiency as a function of pressure ratio. The same as model 1, the higher the maximum temperature, the higher the exergetic efficiency of the cycle. For higher pressure ratio, efficiency first increases, and then decreases after reaching the highest point. 19

Figure 2.11: Exergetic efficiency of the cycle as a function of pressure ratio in model 2

2.5.3 Model Comparison

Figure 2.12 (a) shows the thermal efficiency of the cycle in model 1 and 2 when the maximum temperature is 750℃. As it can be seen, the thermal efficiency is higher in model

1 and it is mainly due to having a smaller split fraction reducing energy losses in the low temperature energy exchanger. Figure 2.12 (b) shows the split fractions in two models. It can be noticed as the pressure ratio increases, the split fraction in model 2 approaches to that of model 1 and approaching its thermal efficiency. 20

Figure 2.12: (a) Thermal efficiency and (b) split fraction of the cycle as a function of pressure ratio in model 1 and 2 when T8 = 750℃

2.6 Conclusion

Supercritical CO2 recompression cycle has been modeled and parametric analyses have been done with two different maximum temperatures and range of pressure ratios.

Two different cases have been used and the effect of split on performance of the cycle has been determined. The followings are conclusions of this study:

1) The cycle shows some typical Brayton cycle with regeneration features. With the

increase of pressure ratio, thermal efficiency and exergetic efficiency of the cycle

increase, and then decrease. With the increase of maximin temperature, the thermal

efficiency and exergetic efficiency of the cycle also rise. 21

2) When T4 and T5 are not the same, the increase of split fraction causes the decrease of

cycle performance. This is due to increase of energy loss when split increases. So,

the highest efficiency should be for the lowest the split fraction when the system can

run properly.

3) Comparing the efficiency of cycle between model 1 and model 2, setting T4 and T5

the same does not increase the thermal efficiency and exergetic efficiency of the cycle

for the range of pressure ratios studied. But, as the pressure ratio increases thermal

efficiency of model 2 approaches to the results of model 1.

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CHAPTER 3

AQUEOUS LITHIUM BROMIDE ABSORPTION REFRIGERATION

SYSTEM

This chapter focuses on the modeling of single-effect and parallel flow double-effect absorption refrigeration system, seeking for the relationship between the performance of the cycle and different parameter such us cooling load, evaporator exit temperature, condenser exit temperature, (upper) generator exit temperature, absorber exit temperature and solution energy exchanger effectiveness.

3.1 Background

Over the past decades, there have been significant growth in the demands for refrigeration, cooling and air conditioning devices to fulfill various needs. Vapor compression refrigeration systems (VCRS), as a conventional cycle in cooling and refrigeration, consume one-fifth of all the electricity generated worldwide, according to the

International institute of refrigeration [44]. Large volumes of greenhouse gases have been generated by consuming enormous amount of energy to power conventional VCRS [44].

In addition, conventional refrigerants, such us hydrochlorofluorocarbons (HCFCs), chlorofluorocarbons (CFCs), may cause notable depletion in ozone layer. In October 2000, the European Commission adopted a resolution to prohibit all HCFCs [45,46].

Because of the environmental problems caused by conventional VCRSs, an alternative green technology to replace the conventional refrigeration systems is highly 23 demanded. Different types of low-grade energy, such us solar energy [47-52], geothermal energy [53-54], waste energy from industrial processes [55], can be utilized to operate the absorption refrigeration systems [56].

Various pairs of absorbent-refrigerant in the absorption refrigeration system are possible and have been discussed and studied [47]. Among all the pairs, water/lithium bromide (LiBr), a most suitable pair for air-conditioning [47], because of its physical property, and ammonia/water, which has been used for refrigeration process mostly [47], are the most common match ups. Water/lithium bromide designs have higher coefficient of performance (COP) than those of ammonia/water chillers and do not have working fluid toxicity issues [57], which is the working fluid in this paper.

Researchers have put significant effort to improve the absorption systems’ performance [58-59]. It has been found out that the coefficient of performance (COP) will rise remarkably from single-effect to triple-effect [56]. However, it has also been reported that multi-effect systems are very complex and need higher operating temperature and cost more [60].

Many papers focus on aqueous lithium bromide double-effect absorption cycle [61-

62]. There are different flow patterns, such us series, parallel and reverse parallel [44,63].

Some research [64-66] compared many patterns and found out that the parallel flow layout has the highest performance.

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3.2 Refrigerators Description

In this paper, both single-effect aqueous lithium bromide absorption refrigeration system and parallel flow double-effect aqueous lithium bromide absorption refrigeration system have been analyzed and parametric analyses have been made. Figure 3.1 shows diagram of single-effect aqueous lithium bromide absorption refrigeration system. The solid lines show flow directions and dotted lines show energy transfers. In the system, there are one condenser, one evaporator, one absorber and one generator. The weak solution exits absorber at state l and is pressurized in the pump. The solution pressure is increased, state 2, and then it is heated in the solution energy exchanger to state 3. The solution enters the generator and splits into water vapor, state 7, and strong solution, state 4, after receiving energy from an energy source. The water vapor condenses and becomes saturated liquid water, state 8, expands through the valve, state 9, and enters the evaporator. Water leaves evaporator as saturated vapor at state 10 and then enters the absorber. The strong solution at state 4, is cooled in the solution energy exchanger reducing it temperature. After that, the strong solution enters the absorber, mixes with the water vapor, releases energy and weak solution exits at state 1.

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Figure 3.1: Single-effect aqueous Lithium Bromide absorption refrigeration system

Figure 3.2 shows the diagram of double-effect parallel flow aqueous lithium bromide absorption refrigeration system. In the system, there are two condensers, one evaporator, one absorber and two generators. Weak solution leaves absorber at state 1 and is directed into a pump. Solution pressure is increased and then is heated in the solution energy exchanger. Solution leaves at state 3 and splits into two flows. One part goes to the lower generator at state 20 and the other part is pressurized in the second pump. Solution leaves the pump at state 12, enters the upper solution energy exchanger and leaves at higher temperature, state 13. Then, the solution enters the upper generator where it is heated. Part of water is evaporated, state 17, leaves the generator toward the condenser and the remaining leaves the generator as strong solution, at state 14.

The strong solution is cooled in the upper solution energy exchanger, state 15, its pressure is reduced in the valve, state 16, and then enters the lower generator, mixing with solution at state 20 and absorbs energy from the upper condenser. The solution exits the 26 lower generator at state 4 and water vapor exits at state 7. The solution at state 4 cools again in the lower solution energy exchanger and it goes through an isenthalpic process in a valve where its pressure is reduced and then enters the absorber.

The water vapor exits the upper generator at state 17, first cools down and condenses in the upper condenser, pressure reduction in the valve and then mixes with water vapor at state 7 in the lower condenser. Saturated liquid water leaves the condenser at state 8, goes through a valve and enters the evaporator. The cooling load is applied in the evaporator and saturated water vapor leaves the evaporator.

Figure 3.2: Double-effect aqueous lithium bromide absorption refrigeration system in parallel flow

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3.3 Mathematical Model

3.3.1 Working Fluid Property Calculation

The enthalpy of aqueous Lithium Bromide in this article is based on 2017 ASHRAE

Handbook [67]. The equation is

4 푛 4 푛 2 4 푛 ℎ(푡, 푥) = ∑0 퐴푛푥 + 푡 ∑0 퐵푛푥 + 푡 ∑0 퐶푛푥 (3.1)

where t is the solution temperature in Celsius and x % is the mass fraction of Lithium bromide in the solution. In this article, the pressure effect in enthalpy and entropy of solution are ignored since there are very low [57]. Equation (3.1) is valid when t is between

15℃ and 165 ℃, x is larger than 40 and lower than 70. The parameters in equation (3.1) are listed in the Table 3.1.

n A B C 0 -2024.33 18.2829 -3.7008214*10-2 1 163.309 -1.1691757 2.8877666*10-3 2 -4.88161 3.248041*10-2 -8.1313015*10-5 3 6.302848*10-2 -4.034184*10-4 9.9116628*10-7 4 -2.913705*10-4 1.8520569*10-6 -4.4441207*10-9

Table 3.1: Parameters in equation (3.1)

the relation between mass fraction x % and molar fraction y is:

푦∙푀 푥 % = 퐿𝑖퐵푟 (3.2) 푦∙푀퐿𝑖퐵푟+(1−푦)∙푀퐻2푂

Where MLiBr and MH2O are the molar mass of lithium bromide and water.

Equation (3.3) shows the relation of saturated solution temperature as a function of its mass fraction of lithium bromide in the solution: 28

3 푛 ′ 3 푛 푡 = ∑0 퐷푛푥 + 푡 ∑0 퐶푛푥 (3.3) Where t is the temperature of the solution in Celsius, x % is the mass fraction of lithium bromide in the solution, t′ in the equation represents the temperature of pure statured water at the same pressure as the solution. The parameters in the equation are listed in Table 3.2.

n C D 0 -2.00755 124.937 1 0.16976 -7.71649 2 -3.133362*10-2 0.152286 3 1.97668*10-2 -7.95090*10-4

Table 3.2: Parameters in equation (3.3)

The density of aqueous lithium bromide in this article is based on the article written by Patek and Klomfar [68]:

푇 , 2 푚𝑖 푡𝑖 휌(푇, 푦) = (1 − 푦)휌 (푇) + 휌푐 ∑𝑖=1 푎𝑖푥 ( ) (3.4) 푇푐 In equation (3.4), 휌,(푇) is the density of pure saturated liquid water at temperature T, where T is in Kelvin and y is the mole fraction of lithium bromide in the solution. Tc is the

3 critical temperature of H2O, 647.096 K. 휌푐 is the density at the critical state , 17873 mol/m .

The unit of density in equation (3.4) is also mol/m3. Table 3.3 shows the parameters in equation (3.4).

i m t a 1 1 0 1.746 2 1 6 4.709

Table 3.3: Parameters in equation (3.4)

3.3.2 Analysis of Single-effect Cycle 29

For single-effect cycle, as the evaporator exit temperature (T10) is given, the pressure

(P10) and enthalpy (h10) at state 10 can be determined according to the steam table. It is also the same for P8 and h8 since the condenser exit temperature (T8) is given and h8 and h9 are the same. Mass flow rate of water vapor can be calculated using equation (3.5).

푄̇ 퐸 푚̇ 10 = (3.5) ℎ10−ℎ9

The pressure at state 1 is the same as P10, the mass fraction at state 1 can be determined by solving the following function about x1:

3 푛 ′ 3 푛 푡1 = ∑0 퐷푛푥1 + 푡1 ∑0 퐶푛푥1 (3.6)

Where t1’ is determined by steam table for saturated liquid water at P1. With the given temperature and mass fraction, the enthalpy at state 1 can also be calculated. The work required by the pump from state 1 to 2 is:

1 푝2 푝2−푝1 푤푝 = ∫ 푣1푑푝 = (3.7) 휂 푝1 휌1휂

Where 휂 is the efficiency of the pump, which is assumed to be 90%, P1 is the same as P10 and P2 is the same as P8. Enthalpy at state 2 can be calculated using equation (3.8).

ℎ2 = ℎ1 + 푤푝 (3.8)

And t2 satisfies the following equation:

4 푛 4 푛 2 4 푛 ℎ2 = ∑0 퐴푛푥2 + 푡2 ∑0 퐵푛푥2 + 푡2 ∑0 퐶푛푥2 (3.9)

Where x2 is the same as x1 in equation (3.9). Also, the mass fraction of lithium bromide at state 4 satisfies the following equation:

3 푛 ′ 3 푛 푡4 = ∑0 퐷푛푥8 + 푡4 ∑0 퐶푛푥8 (3.10)

Where t4′ is determined by steam table for saturated liquid at P4, which is the same as P8. With the given temperature and mass fraction, enthalpy of solution at state 4 can also 30 be calculated.

Enthalpy of steam at state 7 is also known with the given temperature t7 and pressure

P7 = P4.

For mass balance of the generator, there are two equations:

푚̇ 7 + 푚̇ 4 = 푚̇ 3 (3.11)

푚̇ 4푥4 = 푚̇ 3푥3 (3.12)

In the above equations, 푚̇ 7 is the same as 푚̇ 10, x3 is equal to x1. So, 푚̇ 4 and 푚̇ 3 can be solved.

Effectiveness of solution energy exchanger is defined as:

푚̇ (ℎ −ℎ ) 휀 = 3 3 2 (3.13) 푚̇ 4(ℎ4−ℎ(푡2,푥4))

Therefore, h3 can be calculated with the given effectiveness, and t3 can be determined from equation (3.14):

4 푛 4 푛 2 4 푛 ℎ3 = ∑0 퐴푛푥3 + 푡3 ∑0 퐵푛푥3 + 푡3 ∑0 퐶푛푥3 (3.14)

Energy balance of solution energy exchanger is:

푚̇ 3(ℎ3 − ℎ2) = 푚̇ 4(ℎ4 − ℎ5) (3.15)

h5 can be determined by equation (3.5) and t5 can also be calculated since x5 is the same as x4. Energy required in the generator can be calculated by equation (3.16).

푄̇퐺 + 푚̇ 3ℎ3 = 푚̇ 4ℎ4 + 푚̇ 7ℎ7 (3.16)

Coefficient of performance (COP), is calculated by equation (3.17):

푄̇ 퐶푂푃 = 퐸 (3.17) 푄̇ 퐺+푤̇ 푝

The exegetic efficiency ECOP, defined as:

퐶푂푃 퐸̇ 퐸퐶푂푃 = = 푥퐸 (3.18) (퐶푂푃)푟푒푣푒푟푠𝑖푏푙푒 푐푦푐푙푒 퐸̇푥퐺+푤̇ 푝 31

In equation (3.18), 퐸̇푥퐸 is the exergy of 푄̇퐸, which is defined as the minimum work required to transfer energy from low temperature of the room, (TR), at 293 K in this case to the environment at T0 = 298 K. It can be calculated by the following equation:

푇0 퐸̇푥퐸 = −푄̇퐸(1 − ) (3.19) 푇푅

퐸̇푥퐺 in equation (3.18) is the exergy of 푄̇퐺, which is defined as maximum work that can be developed from the source, Ts2 :

푇0 퐸̇푥퐺 = 푄̇퐺(1 − ) (3.20) 푇푠2

In this chapter, the source temperature is 20 ℃ higher than the generator temperature.

3.3.3 Analysis of Double-effect Cycle

The analysis of double-effect cycle follows that of the singe cycle with few modifications. The evaporator exit temperature (t10), lower condenser exit temperature (t8) and upper condenser exit temperature (t18) are given, the pressure and enthalpy at state 10

(P10, h10), state 8 (P8, h8) and state 18 (P18, h18) can be determined using steam table. Since the processes are isenthalpic in the valve, h8 = h9 and h18 = h19. Mass flow rate of refrigerant

(water vapor) is:

푄̇ 퐸 푚̇ 10 = (3.21) ℎ10−ℎ9

Pressure at state 1 is the same as P10 , mass fraction at state 1 is determined by equation (3.22):

3 푛 ′ 3 푛 푡1 = ∑0 퐷푛푥1 + 푡1 ∑0 퐶푛푥1 (3.22)

Where t1′ is determined by steam table for saturated liquid at P1. Enthalpy at state 1 can be calculated knowing temperature and mass fraction. Mass concentration at state 14 32 satisfies the following equation:

3 푛 ′ 3 푛 푡14 = ∑0 퐷푛푥14 + 푡14 ∑0 퐶푛푥14 (3.23)

’ Where t14 is determined by steam table for saturated liquid at P14, which is the same as P18. Enthalpy at state 14 can be calculated knowing temperature and mass fraction. Since x4 is the same as x14, and with the known pressure P4, which is same as P8, then temperature at state 4 scan be calculated using equation (3.24)

3 푛 ′ 3 푛 푡4 = ∑0 퐷푛푥4 + 푡4 ∑0 퐶푛푥4 (3.24)

’ Where t4 is determined by steam table for saturated liquid at P4, which is the same as P8. Enthalpy at state 4 can be determined by knowing temperature and mass fraction.

Enthalpy of steam at state 7 is also known with the given temperature t7 and pressure P7

(the same as P8). There are two mass balance relations in the absorber:

푚̇ 10 + 푚̇ 6 = 푚̇ 1 (3.25)

푚̇ 6푥6 = 푚̇ 1푥1 (3.26)

Solution exits the absorber at state 1, pumps up at state 2 and then heats up to state

3:

푚̇ 1 = 푚̇ 2 = 푚̇ 3 (3.27)

푥1 = 푥2 = 푥3 (3.28)

1 푝2 푝2−푝1 푤푝1 = ∫ 푣1푑푝 = (3.29) 휂 푝1 휌1휂

ℎ2 = ℎ1 + 푤푝1 (3.30)

Where 휂 is 0.9, P1 is the same as P10 and P2 is the same as P8. Solution at state 3 separates into two parts of states 20 and 11.

푚̇ 3 = 푚̇ 20 + 푚̇ 11 (3.31)

푥3 = 푥20 = 푥11 (3.32) 33

푡3 = 푡20 = 푡11 (3.33)

ℎ3 = ℎ20 = ℎ11 (3.34)

Solution at state 11 pumps up to state 12 and then heats up to state 13:

푚̇ 11 = 푚̇ 12 = 푚̇ 13 (3.35)

푥11 = 푥12 = 푥13 (3.36)

1 푝12 푝12−푝11 푤푝2 = ∫ 푣11푑푝 = (3.37) 휂 푝11 휌11휂

ℎ12 = ℎ11 + 푤푝2 (3.38)

Where 휂 is 0.9, P11 is the same as P8 and P12 is the same as P18. Mass balance at the upper and lower generators:

푚̇ 7 + 푚̇ 4 = 푚̇ 20 + 푚̇ 16 (3.39)

푚̇ 4푥4 = 푚̇ 20푥20 + 푚̇ 16푥16 (3.40)

푚̇ 13푥13 = 푚̇ 14푥14 (3.41)

푚̇ 13 = 푚̇ 17 + 푚̇ 14 (3.42)

Solution at state 14 goes through solution energy exchanger and valve:

푚̇ 14 = 푚̇ 15 = 푚̇ 16 (3.43)

푥14 = 푥15 = 푥16 (3.44)

ℎ15 = ℎ16 (3.45)

Energy balance and the effectiveness of the upper solution energy exchanger are:

푚̇ 14(ℎ14 − ℎ15) = 푚̇ 12(ℎ13 − ℎ12) (3.46)

푚̇ (ℎ −ℎ ) 휀 = 13 13 12 (3.47) 푚̇ 14(ℎ14−ℎ(푡12,푥14))

And for the lower solution energy exchanger:

푚̇ 4(ℎ4 − ℎ5) = 푚̇ 3(ℎ3 − ℎ2) (3.48) 34

푚̇ (ℎ −ℎ ) 휀 = 3 3 2 (3.49) 푚̇ 4(ℎ4−ℎ(푡2,푥4))

Solution leaves lower generator at state 4, cools down at the solution energy exchanger and then its pressure decreases through the valve:

푚̇ 4 = 푚̇ 5 = 푚̇ 6 (3.50)

푥4 = 푥5 = 푥6 (3.51)

ℎ5 = ℎ6 (3.52)

Energy analysis for both generators are:

푄̇퐺2 − 푚̇ 17ℎ17 + 푚̇ 13ℎ13−푚̇ 14ℎ14 = 0 (3.53)

푄̇퐺1 − 푚̇ 7ℎ7 + 푚̇ 20ℎ20−푚̇ 4ℎ4 + 푚̇ 16ℎ16 = 0 (3.54)

Based on the design, the energy source for lower generator is from the upper condenser:

푄̇퐺1 = 푄̇퐶2 (3.55)

푄̇퐶2 = 푚̇ 17(ℎ17 − ℎ18) (3.56)

The coefficient of performance (COP) is defined as:

푄̇ 퐶푂푃 = 퐸 (3.57) 푄̇ 퐺2+푤̇ 푝1+푤̇ 푝2

The exegetic efficiency ECOP, defined as:

퐶푂푃 퐸̇ 퐸퐶푂푃 = = 푥퐸 (3.58) (퐶푂푃)푟푒푣푒푟푠𝑖푏푙푒 푐푦푐푙푒 퐸̇푥퐺2+푤̇ 푝1+푤̇ 푝2

In equation (3.58), 퐸̇푥퐸 is the exergy of 푄̇퐸, which is defined as the minimum work required to transfer energy from low temperature of the room, (TR) at 293 K in this case to the environment at T0 = 298 K. It can be calculated by the following equation:

푇0 퐸̇푥퐸 = −푄̇퐸(1 − ) (3.59) 푇푅

퐸̇푥퐺2 in equation (3.58) is the exergy of 푄̇퐺, maximum work that can be developed 35

from the source, Ts :

푇0 퐸̇푥퐺2 = 푄̇퐺2(1 − ) (3.60) 푇푠

In this article, the source temperature is 20 ℃ higher than the generator temperature.

3.3.4 Assumptions and Parameters

In the systems there is no pressure drop through pipes, absorber , energy exchangers and generators.

The required inputs are:

1) Either quantity of energy input in the generator or desired cooling load

2) The evaporator pressure or exit temperature

3) Condenser and absorber exit temperatures

4) Generator exit temperature.

For all cycles, the solution is at saturated condition at the exit of absorber and generator. The temperature of vapor and solution at the exit of generators are the same. The primary inputs of single-effect cycle are listed in Table 3.4.

Parameters Primary input value Solution temperature at exit of absorber (t1) 26 ℃ Solution temperature at exit of upper generator (t4) 85 ℃ Evaporator exit temperature (t10) 1 ℃ Condenser exit temperature (t8) 37 ℃

Desired Cooling load (푄̇퐸) 200 KW Solution energy exchanger effectiveness 65% [57]

Table 3.4: Parameters of single-effect absorption refrigeration cycle

36

The primary inputs of double-effect cycle are listed in Table 3.5.

Parameters Primary input value Solution temperature at exit of absorber (t1) 30 ℃ Solution temperature at exit of upper generator (t14) 144 ℃ Evaporator exit temperature (t10) 5 ℃ Lower Condenser exit temperature (t8) 37 ℃ Upper Condenser exit temperature (t18) 88 ℃ Desired Cooling load (푄퐸̇ ) 200 KW Solution energy exchangers effectiveness 65% [57]

Table 3.5: Parameters of double-effect absorption refrigeration cycle

3.4 Results and Discussion

Both single-effect and double-effect lithium bromide absorption refrigeration systems have been analyzed using above mathematical models. The following variables: cooling load, evaporator temperature, absorber exit temperature, generator exit temperature, solution energy exchanger effectiveness and condensers exit temperatures, have been varied one at a time to determine its effect on coefficient of performance and exergetic efficiency. The results of these analyses for both single-effect and double-effect systems are discussed next.

3.4.1 Single-effect Cycle

3.4.1.1 Effect of Cooling Loads

It is obvious that changing cooling loads does not affect the COP and ECOP, since the temperature and pressure at each state remain the same. The only change in the cycle is the mass flow rate, which effects the size and cost of the system. 37

3.4.1.2 Effect of Evaporator Exit Temperature

Evaporator temperatures has been changed from 1 ℃ to 15 ℃ and results are shown in figure 3.3. As it can be seen in figure 3.3, the increase of evaporator exit temperature increases both COP and ECOP. When evaporator temperature increases, the pressures at state 10 and state 1 also increase, which causes the concentration of lithium bromide at state 1 to decrease significantly. Since the mass fraction at state 4, is kept constant, the ratio of x1 to x4 decreases, which leads to the reduction of the mass flow rate at state 3, 4 and 7, and that causes the reduction of 푄̇퐺. Since 푄̇퐸 is constant in our model, COP and ECOP increase when evaporator temperature rises.

Figure 3.3: Coefficient of performance (COP) and exergetic efficiency (ECOP) versus evaporator exit temperature in a single-effect absorption refrigeration system

38

3.4.1.3 Effect of Condenser Exit Temperature

Condenser exit temperature has been varied from 37 ℃ to 52 ℃ and its effect on coefficient of performance and exergetic efficiency has been determined. Figure 3.4 shows the increase of condenser exit temperature decreases coefficient of performance and exergetic efficiency. Increasing condenser temperature increase the pressure at state 4, which decreases mass fraction at state 4 significantly. Since x1 is kept constant, the ratio of x1 to x4 increase. That causes the increase of mass flow rate at state 3,4 and 7, which leads to a significant increase of 푄̇퐺. With the 푄̇퐸 is kept unchanged in our model, the COP and

ECOP decreases as the condenser exit temperature increases.

Figure 3.4: Coefficient of performance (COP) and exergetic efficiency (ECOP) versus condenser exit temperature in a single-effect absorption refrigeration system

39

3.4.1.4 Effect of Absorber Exit Temperature

Figure 3.5 shows the effect of absorber exit temperature on coefficient of performance and exergetic efficiency when it is varied from 20 ℃ to 40 ℃. As it can be seen in figure 3.5, the increase of absorber exit temperature decreases the COP and ECOP.

When the absorber temperature increases while pressure at state 1 is constant, the mass fraction of the lithium bromide at state 1 increases and ratio of x1 to x4 increases. The increase of the ratio leads to the increase of mass flow rate at state 3, 4 and 7, and causes the rise of 푄̇퐺 , declining of COP and ECOP.

Figure 3.5: Coefficient of performance (COP) and exergetic efficiency (ECOP) versus absorber exit temperature in a single-effect absorption refrigeration system

3.4.1.5 Effect of Generator Exit Temperature 40

Figure 3.6 shows effect of generator exit temperature on coefficient of performance and exergetic efficiency when it is changed from 70 ℃ to 100 ℃. This range of temperature has been chosen because the energy input will be the waste energy from some other systems.

The increase of generator solution exit temperature increases COP. Coefficient of performance first increases, reaches a peak and then it reduces slightly. At first, when generator temperature increases between 70 ℃ to about 85 ℃, the x4 increases significantly, reducing ratio of x1 to x4 causing reduction of mass flow rate and 푄̇퐺. As the temperature increases above 85 ℃ increase of x4 reduces and so does the mass flow rates. With the increase of enthalpy of state 4 and 7 because of the increase of temperature, 푄̇퐺, which is calculated by equation (3.16), reaches to a stable value because of the balancing of the drop of mass flow rate and the rise of enthalpy. In this range the COP is almost constant.

Exergertic efficiency first increases and then decreases as generator temperature increases. This is because when the generator temperature increases, the maximum COP, or the COP of reversible cycle, keeps rising. Since COP of the cycle is almost constant, the

ECOP decreases after it reaches to the highest point. 41

Figure 3.6: Coefficient of performance (COP) and exergetic efficiency (ECOP) versus generator exit temperature in a single-effect absorption refrigeration system

3.4.1.6 Effect of Solution Energy Exchanger Effectiveness

Figure 3.7 shows the effect of effectiveness of solution energy exchanger range from

0.5 to 0.9 on coefficient of performance and exergetic efficiency. As it is obvious increasing the effectiveness of energy exchanger improves both coefficient of performance and exergetic efficiency. 42

Figure 3.7: Coefficient of performance (COP) and exergetic efficiency (ECOP) versus solution energy exchanger effectiveness in a single-effect absorption refrigeration system

3.4.2 Double-effect Cycle

3.4.2.1 Effect of Cooling Loads

It is obvious that only changing cooling loads does not affect the COP and ECOP, since the temperature and pressure at all states remain the same. The only change in the cycle is the mass flow rate, which influences the system size and cost.

3.4.2.2 Effect of Evaporator Exit Temperature

Evaporator temperature has been changed from 1 ℃ to 15 ℃ and results are shown in figure 3.8. As it can be seen in figure 3.8, the increase of evaporator exit temperature 43 causes the increase of COP and ECOP. When evaporator temperature increases, the pressures at state 10 and state 1 also increase, reducing concentration of lithium bromide at state 1. Since mass fraction at state 14 is constant, the ratio of x1 to x14 decreases, which leads to the remarkable reduction of the mass flow rate at state 13, 14 and 17, and that causes reduction of 푄̇퐺2. Since 푄̇퐸 is constant in our model, COP and ECOP increase when evaporator temperature increases.

Figure 3.8: Coefficient of performance (COP) and exergetic efficiency (ECOP) versus evaporator exit temperature in double-effect absorption refrigeration system

3.4.2.3 Effect of Upper Condenser Exit Temperature

Figure 3.9 shows effect of upper condenser exit temperature on coefficient of performance and exergetic efficiency when it varies between 80 ℃ to 100 ℃. As the figure

3.9 shows, the increase of upper condenser exit temperature reduces COP and ECOP. 44

Increasing upper condenser temperature increases pressure at state 14, which decreases mass fraction of lithium bromide in the mixture at state 14 significantly. Since x1 is constant, the ratio of x1 to x14 increases. The increase of ratio of x1to x14 causes the increase of mass flow rate at state 13, 14 and 17, which leads to a significant increase of 푄̇퐺2. With the 푄̇퐸 to be unchanged in our model, COP and ECOP decrease when the upper condenser exit temperature increases.

Figure 3.9: Coefficient of performance (COP) and exergetic efficiency (ECOP) versus upper condenser exit temperature in a double-effect absorption refrigeration system

3.4.2.4 Effect of Absorber Exit Temperature

Absorber exit temperature has been changed from 20 ℃ to 40 ℃ and results are shown in figure 3.10. As the figure 3.10 shows, the increase of absorber exit temperature causes the decrease of COP and ECOP. When the absorber temperature increases while 45

pressure at state 1 is constant, mass fraction at state 1 increases and the ratio of x1 to x14 increases. The increase of the ratio leads to increase of mass flow rate at state 13, 14 and

17, and causes the increase of 푄̇퐺, reducing COP and ECOP.

Figure 3.10: Coefficient of performance (COP) and exergetic efficiency (ECOP) versus absorber exit temperature in double-effect absorption refrigeration system

3.4.2.5 Effect of Upper Generator Exit Temperature

Exit temperature of the upper generator has been changed from 124 ℃ to 154 ℃ and its effect on coefficient of performance and exergetic efficiency has been determined as shown in figure 3.11. The increase of upper generator solution exit temperature increases

COP, but its rate of increase reduces as temperature increases. At first, when generator temperature increases from 124 ℃ to about 134 ℃, the x14 increase significantly, decreasing ratio of x1 to x14 reducing mass flow rate and 푄̇퐺2. As a result, coefficient of 46

performance increases. At about 134 ℃, rate of increase of x14 reduces and so does the mass flow rate. Resulting a very slow increase of COP. Exergetic efficiency, ECOP, increases at first and then decreases after it reaches its maximum value. The reason for this is exactly the same as for single effect system.

Figure 3.11: Coefficient of performance (COP) and exergetic efficiency (ECOP) versus upper generator exit temperature in double-effect absorption refrigeration system

3.4.2.6 Effect of Solution Energy Exchanger Effectiveness

Figure 3.12 shows the effect of effectiveness of solution energy exchangers range from 0.5 to 0.9 on coefficient of performance and exergetic efficiency. As it is obvious increasing the effectiveness improves both coefficient of performance and exergetic efficiency. 47

Figure 3.12: Coefficient of performance (COP) and exergetic efficiency (ECOP) versus solution energy exchangers effectiveness in double-effect absorption refrigeration system

3.4.2.7 Effect of Lower Condenser Exit Temperature

Figure 3.13 shows effect of lower condenser exit temperature on coefficient of performance and exergetic efficiency when it varies between 20 ℃ to 40 ℃. As the figure

3.13 shows, the increase of lower condenser exit temperature causes the decrease of COP and ECOP. Increasing lower condenser temperature increases the enthalpy at state 8 and 9, and that leads to increase of mass flow rate at state 10 since the cooling load and the enthalpy at state 10 are unchanged. With fixed value of ratio of x1 to x14, the mass flow rates at state 13, 14 and 17 increase, which leads to the increase of 푄̇퐺2. With the 푄̇퐸 being constant, the COP and ECOP decrease when the lower condenser exit temperature increases. 48

Figure 3.13: Coefficient of performance (COP) and exergetic efficiency (ECOP) versus lower condenser exit temperature in double-effect absorption refrigeration system

3.5 Conclusion

Both single-effect and double-effect refrigeration systems have been modeled and parametric analyses have been done with different values of cooling load, evaporator exit temperature, condenser exit temperature, (upper) generator exit temperature, absorber exit temperature and solution energy exchanger effectiveness. The followings are conclusions of this study:

1) It is obvious that double-effect absorption refrigeration system has a higher COP

than single-effect cycle. In both systems ratio of the mass fraction of lithium

bromide for weak and strong solution is an important factor on how COP and

ECOP change. 49

2) Cooling load does not have any effect on coefficient of performance and

exergetic efficiency.

3) For single-effect and double-effect absorption refrigeration systems, the increase

of solution energy exchanger effectiveness and evaporator exit temperature leads

to the increase of both coefficient of performance and exergetic efficiency.

4) For single effect and double effect absorption refrigeration systems, the increase

of absorber exit temperature and (upper) condenser exit temperature causes

reduction of both coefficient of performance and exergetic efficiency.

5) For single effect and double effect absorption refrigeration systems, the increase

of (upper) generator solution exit temperature increases coefficient of

performance, but its rate of increase reduces as temperature increases. The

exergetic efficiency increases first and then it decreases as the COP of the

reversible system increases.

6) For double effect absorption refrigeration system, the increase of lower

condenser exit temperature decreases both coefficient of performance and

exergetic efficiency of the system, but its effect is not as significant as other

variables.

50

CHAPTER 4

TRI-GENERATION SYSTEM ANALYSIS

This chapter focuses on the modeling a tri-generation consisted by sCO2 recompression Brayton cycle and double-effect parallel flow aqueous lithium bromide refrigeration cycle. Parametric studies have been performed and will be presented. Effects of variables such as pressure ratio and generator exit temperature on the performance of the whole tri-generation system will be presented.

4.1 Model Description

Figure 4.1 shows the design of the tri-generation system. The black lines (upper cycle) show the flow of sCO2. High pressure carbon dioxide receives energy in the high temperature heater, process 7-8, where its temperature increases and then generates power through the turbine, process 8-9. After the turbine, carbon dioxide goes through the high temperature recurperator (HTR), process 9-10, where energy is transferred to low temperature carbon dioxide. Before it enters the LTR, process 10-11, Carbon dioxide enters the upper generator providing the energy needed for the absorption chiller. Carbon dioxide, then, goes through the Low Temperature Recuperator (LTR), process 11-12, where additional energy is transferred to low temperature carbon dioxide. At state 12, carbon dioxide splits into two parts: The main flow, at state 13 is cooled in a low temperature energy exchanger, process 13-1, which is one of the heating parts in the system to provide energy for heating purposes, and then, it is compressed, process 1-2, before entering into

LTR. The secondary flow, which starts at state 3, goes through the second compressor, process 3-4, and then is mixed with the main flow which has been heated in the LTR, 51 process 2-5. Carbon dioxide leaves the mixing device at state 6. Temperature of carbon dioxide increases in the HTR before it goes to the high temperature energy exchanger and the cycle continues.

The red lines show the flow in the absorption refrigeration cycle. Weak solution leaves absorber at state 20 and is directed into a pump. Solution pressure is increased and then is heated in the solution energy exchanger. Solution leaves at state 22 and splits into two flows. One part goes to the lower generator at state 23 and the other part is pressurized in the second pump. Solution leaves the pump at state 25, enters the upper solution energy exchanger and leaves at higher temperature, state 26. Then, the solution enters the upper generator where it is heated by the energy from the sCO2 Brayton cycle. Part of water is evaporated, state 27, leaves the generator toward the condenser and the remaining leaves the generator as strong solution, at state 14.

The strong solution is cooled in the upper solution energy exchanger, state 15, its pressure is reduced in the valve, state 16, and then enters the lower generator, mixing with solution at state 23 and absorbs energy from the upper condenser. The solution exits the lower generator at state 17 and water vapor exits at state 33. The solution at state 17 cools again in the lower solution energy exchanger and it goes through an isenthalpic process in a valve where its pressure is reduced and then enters the absorber.

The water vapor exits the upper generator at state 27, first cools down and condenses in the upper condenser, pressure reduction in the valve and then mixes with water vapor at state 33 in the lower condenser. Saturated liquid water leaves the condenser at state 30, goes through a valve and enters the evaporator. The cooling load is applied in the evaporator and saturated water vapor leaves the evaporator. 52

Figure 4.1: A tri-generation system consists of a sCO2 recompression Brayton cycle and aqueous lithium bromide absorption refrigeration cycle

4.2 Thermodynamic Model

The calculation process is similar with the models mentioned in previous chapters.

Some differences are listed below:

The energy balance in the upper generator is:

푚̇ 10(ℎ10 − ℎ11) = 푄̇퐺2 (4.1)

푄̇퐺2 + 푚̇ 26ℎ26 = 푚̇ 14ℎ14 + 푚̇ 17ℎ17 (4.2)

The net work from the plant is : 53

푤̇ 푛푒푡 = 푤̇ 푡 − 푤̇ 푐1 − 푤̇ 푐2 − 푤̇ 푝1 − 푤̇ 푝2 (4.3)

The heating load of the system is :

푄̇ℎ = 푄̇ℎ1 + 푄̇ℎ2 (4.4)

푄̇ℎ1 = 푚̇ 1(ℎ13 − ℎ10) (4.5)

푄̇ℎ2 + 푚̇ 30ℎ30 = 푚̇ 33ℎ33 + 푚̇ 29ℎ29 (4.6)

The cooling load of the system is:

푄̇퐸 = 푚̇ 32(ℎ32 − ℎ31) (4.7)

The energy effectiveness of the system is:

푤̇ +푄̇ +푄̇ 퐸퐹퐹 = 푛푒푡 퐸 ℎ (4.8) 푄̇ 𝑖푛

The exergetic efficiency of the system is:

푤̇ +퐸̇ +퐸̇ 퐸푋 = 푛푒푡 푥퐸 푥ℎ (4.9) 퐸̇푥𝑖푛

The exergy input is:

푇0 퐸̇푥𝑖푛 = 푞𝑖푛(1 − ) (4.10) 푇푠

Where T0 is the 298 K, the reservoir temperature. Ts is the energy source temperature,

800 ℃.

퐸̇푥퐸 is the exergy of 푄̇퐸, which is defined as the minimum work required to transfer energy from low temperature of the room, (TR) at 293 K in this case, to the environment at

T0 = 298 K. It can be calculated by the following equation:

푇0 퐸̇푥퐸 = −푄̇퐸(1 − ) (4.11) 푇푅

퐸̇푥ℎ is the exergy of 푄̇ℎ, which can be calculated by the following equations:

퐸̇푥ℎ = 퐸̇푥ℎ1 + 퐸̇푥ℎ2 (4.12)

퐸̇푥ℎ1 = 푚̇ 1[(ℎ13 − ℎ1) − 푇0(푠13 − 푠1)] (4.13) 54

퐸̇푥ℎ2 = (푚̇ 33ℎ33 + 푚̇ 29ℎ29 − 푚̇ 26ℎ26) − 푇0(푚̇ 33푠33 + 푚̇ 29푠29 − 푚̇ 26푠26)

(4.14)

4.3 Assumptions and Parameters

The assumptions in the tri-generation plants are same as the assumptions mentioned in the previous chapters. In the cycle, there is no pressure drop through energy exchangers, mixer, splitter, pipes, recuperators, absorber and generators.

In the absorption refrigeration system, the solution is at saturated condition at the exit of absorber and generator. The temperature of vapor and solution at the exit of generators are the same.

The parameters are listed below:

Parameter Value or range

Minimum temperature, T1 32 ℃

Minimum pressure, P1 8 MPa

Maximum temperature, T8 550 ℃ LTR effectiveness 86% HTR effectiveness 86% Turbine isentropic efficiency 90% Compressor isentropic efficiency 90% Pressure ratio 2.4 ; 3.2 ; 4.0 Maximum flow ratio 1 kg/s Split fraction 0 .7

Generator exit temperature (T11) 383-423 K

Table 4.1: Parameters of the sCO2 Recompression Cycle

55

Parameters Primary input value

Solution temperature at exit of absorber (t20) 20 ℃

Solution temperature at exit of upper generator (t14) 144 ℃

Evaporator exit temperature (t32) 9 ℃

Lower Condenser exit temperature (t30) 30 ℃

Upper Condenser exit temperature (t28) 80 ℃ Solution energy exchangers effectiveness 65%

Table 4.2: Parameters of the aqueous absorption refrigeration system

In order to determine the performance of the system, the generator exit temperature(T11) needs to be known since the effectiveness of the generator is not defined in this thesis. Varying T11, performance of the system changes. For this reason, the relation between the system’s performance and the T11 is discussed.

4.4 Results

The tri-generation system has been analyzed using above mathematical models. The following variables: pressure ratio, generator exit temperature (T11), have been varied one at a time to determine its effect on net work output, cooling load, heating load, energy effectiveness and exergetic efficiency of the tr-generation system. The results of these analyses are discussed next.

Figure 4.2 shows how net work per unit mass flow rate of carbon dioxide changes with different T11 and pressure ratio. As the figure shows, net work of the system is almost constant as T11 increases. It is because though T11 is increasing, the temperature of states 56

1,2,3,4,8 and 9 do not change significantly. Net work of the cycle increases as pressure ratio increases, which is the same as Brayton cycle.

Figure 4.2: Net work output of the system versus generator exit temperature (T11) with different pressure ratios

Figure 4.3 and 4.4 show how cooling load and heating load change with different T11 and pressure ratios. As the figures show, with the increase of T11, the heating load and cooling load decrease. It is because when T11 is increases, the temperature difference between 10 and 11 decreases which means a significant decrease of energy transfer from the Brayton cycle to the absorption chiller. That leads to the decrease of the mass flow rate in the refrigeration cycle, which causes the decrease of heating and cooling load of the tri- generation. 57

For the constant T11, increasing pressure ratio causes the rise of the energy transfer from the Brayton cycle to the absorption chiller. That leads to the increase of the mass flow rate in the refrigeration cycle, which leads to the increase of heating and cooling load of the tri-generation.

Figure 4.3: Cooling load versus generator exit temperature (T11) with different pressure ratios

58

Figure 4.4: Heating load versus generator exit temperature (T11) with different pressure ratios

Figure 4.5 shows how energy effectiveness changes with different generator exit temperature (T11) and pressure ratio. Keeping pressure ratio constant and increasing T11, both heating load and cooling load decrease and while net work is constant, leads to the energy effectiveness decrease.

When T11 is constant, the increase of the pressure ratio causes the remarkable increase of the heating load and cooling load which leads to the increase of heating and cooling load of the tri-generation. 59

Figure 4.5: Energy effectiveness versus generator exit temperature (T11) with different pressure ratios

Figure 4.6 shows the relation between exergetic efficiency and generator exit temperature (T11) for different pressure ratios. As for sCO2 Brayton cycle, the exergetic efficiency of the tri-generation system increases when pressure ratio increases for the given range of operation. Since the exergy of both heating and cooling loads are low, they don’t play any role in the calculation of exergetic efficiency of the tri-generation system. The same reasoning is true for change of exergetic efficiency as a function of T11. The exergy of the sCO2 Brayton cycle increases when T11 increases since less energy has been transferred to absorption chiller and since the exergy of heating and cooling load is small 60

because of their low temperature, the exergy of the tri-generation plant increases when T11 increases.

Figure 4.6: Exergetic efficiency versus generator exit temperature (T11) with different pressure ratios

61

CHAPTER 5

CONCLUSION AND RECOMMENDATION

5.1 Conclusion

In this thesis, an analysis of a given tri-generation system consisted of sCO2 recompression cycle and aqueous lithium bromide refrigeration cycle has been performed.

The effects of some operating variables, such us pressure ratio, generator exit temperature on energy effectiveness as well as exergetic efficiency have been evaluated. The following are the conclusions:

1) The sCO2 recompression cycle shows some typical Brayton cycle with

regeneration features. With the increase of pressure ratio, thermal efficiency and

exergetic efficiency of the cycle increase, and then decrease. With the increase of

maximin temperature, the thermal efficiency and exergetic efficiency of the cycle

also rise. The highest efficiency should be for the lowest the split fraction when

the system can run properly.

2) For single-effect and double-effect absorption refrigeration systems, the increase

of solution energy exchanger effectiveness and evaporator exit temperature leads

to the increase of both coefficient of performance and exergetic efficiency; the

increase of absorber exit temperature and (upper) condenser exit temperature

causes reduction of both coefficient of performance and exergetic efficiency; the

increase of (upper) generator solution exit temperature increases coefficient of

performance, but its rate of increase reduces as temperature increases. The

exergetic efficiency increases first and then it decreases as the COP of the

reversible system increases. 62

3) For tri-generation system, the increase of pressure and the generator exit

temperature in the Brayton cycle leads to the increase of exergetic efficiency of

the plant but causes the decrease of the heating cooling load and energy

effectiveness.

5.2 Recommendation

Additional research needs to be done to develop an optimum tri-generation

(Combined cooling, heating and power) system. The additional research could include:

1) Design modification such as having multi-staged compression and expansion.

2) Operating conditions play an important role on the performance of the tri-

generation system. Since there are many independent variables in the system, a

multi-optimization analysis needs to be developed to find the optimum operating

condition.

3) Economic analysis, in parallel, is also very important, which is recommended.

63

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72

APPENDICES

Appendix Ⅰ MATLAB Code for sCO2 Recompression Cycle (Trial and

Error)

The code is:

T1=32+273; T8=273+700; pr=2;% p1=8000000; p2=p1*pr; p5=p2; p4=p2; p6=p5; p7=p6; p8=p7; p9=p8/pr; p10=p9; p11=p10; p3=p11; p12=p11; ec=0.9; er1=0.86; et=0.9; x=0.7; h1=refpropm('H','T',T1,'P',p1/1000,'CO2') s1=refpropm('S','T',T1,'P',p1/1000,'CO2') for T2i=T1:0.001:1000; s2i=refpropm('S','T',T2i,'P',p2/1000,'CO2'); if abs(s2i-s1)/s1<0.00001%; break; else; end; end; h2i=refpropm('H','T',T2i,'P',p2/1000,'CO2') h2=(h2i-h1)/ec+h1; for T2=T1:0.001:1000; h2c=refpropm('H','T',T2,'P',p2/1000,'CO2'); if abs(h2c-h2)/h2<0.00001%; break; else; end; end; h8=refpropm('H','T',T8,'P',p8/1000,'CO2'); s8=refpropm('S','T',T8,'P',p8/1000,'CO2'); for T9i=T8:-0.001:T1 s9i=refpropm('S','T',T9i,'P',p9/1000,'CO2'); if abs(s9i-s8)/s8<0.00001 break; else; 73

end; end; h9i=refpropm('H','T',T9i,'P',p9/1000,'CO2'); h9=h8-et*(h8-h9i); for T9=T9i:0.001:T8; h9c=refpropm('H','T',T9,'P',p9/1000,'CO2'); if abs(h9c-h9)/h9<0.00001%; break; else; end; end; for T5=477.2:0.05:700.4;%¼ÙÉè h5=refpropm('H','T',T5,'P',p5/1000,'CO2'); hmin1=refpropm('H','T',T2,'P',p10/1000,'CO2'); h10=x*(h5-h2)/er1+hmin1; for T10=T5:0.001:T8; h10c=refpropm('H','T',T10,'P',p10/1000,'CO2'); if abs(h10c-h10)/h10<0.0001%; break; else; end; end; h11=x*(h2-h5)+h10; for T11=T2:0.001:T10; h11c=refpropm('H','T',T11,'P',p11/1000,'CO2'); if abs(h11c-h11)/h11<0.00001%; break; else; end; end; T3=T11; h3=refpropm('H','T',T3,'P',p3/1000,'CO2') s3=refpropm('S','T',T3,'P',p3/1000,'CO2') for T4i=T3:0.001:1000; s4i=refpropm('S','T',T4i,'P',p4/1000,'CO2'); if abs(s4i-s3)/s3<0.00001%; break; else; end; end; h4i=refpropm('H','T',T4i,'P',p4/1000,'CO2') h4=(h4i-h3)/ec+h3; for T4=T3:0.001:1000; h4c=refpropm('H','T',T4,'P',p4/1000,'CO2'); if abs(h4c-h4)/h4<0.00001%; break; else; end; end; h6=x*h5+(1-x)*h4; a=(T5-T4)/50000; for T6=T4:a:T5; h6c=refpropm('H','T',T6,'P',p6/1000,'CO2'); if abs(h6c-h6)/h6<0.00001%; 74

break; else; end; end; hmin2=refpropm('H','T',T6,'P',p10/1000,'CO2'); h7=h6+h9-h10; er2=(h7-h6)/(h9-hmin2) if abs(er2-er1)/er1<0.00013 break; else; end end for T7=T6:0.001:T8; h7c=refpropm('H','T',T7,'P',p7/1000,'CO2'); if abs(h7c-h7)/h7<0.00001%; break; else; end; end; qin=h8-h7; wnet=h8-h9-((1-x)*(h4-h3)+x*(h2-h1)); e=wnet/qin T0=25+273; Ts=800+273; qinx=qin*(1-T0/Ts); ex=wnet/qinx;

75

Appendix Ⅱ MATLAB Code for sCO2 Recompression Cycle (Newton-

Raphson Iteration)

The program is listed below: pr=3.2; T1=305; T8=550+273; ec=0.9; er=0.86; et=0.9; pl=8000000; T2=336.768; T9=685.315; ph=pl*pr; syms t T3 T4 T7 T10 T4i m1=@(t,T3,T4,T7,T10,T4i)+t* refpropm('H','T',T2,'P',ph/1000,'CO2')- t* refpropm('H','T',T4,'P',ph/1000,'CO2')+ refpropm('H','T',T10,'P',pl/1000,'CO2')- refpropm('H','T',T3,'P',pl/1000,'CO2'); m2=@(t,T3,T4,T7,T10,T4i)+t* refpropm('H','T',T4,'P',ph/1000,'CO2')- t* refpropm('H','T',T2,'P',ph/1000,'CO2')-er* refpropm('H','T',T10,'P',pl/1000,'CO2')+er*refpropm('H','T',T2,'P',p l/1000,'CO2'); m3=@(t,T3,T4,T7,T10,T4i)-refpropm('H','T',T7,'P',ph/1000,'CO2')+ refpropm('H','T',T4,'P',ph/1000,'CO2')+ refpropm('H','T',T9,'P',pl/1000,'CO2')- refpropm('H','T',T10,'P',pl/1000,'CO2'); m4=@(t,T3,T4,T7,T10,T4i)+refpropm('H','T',T7,'P',ph/1000,'CO2')- refpropm('H','T',T4,'P',ph/1000,'CO2')-er* refpropm('H','T',T9,'P',pl/1000,'CO2')+er* refpropm('H','T',T4,'P',pl/1000,'CO2'); m5=@(t,T3,T4,T7,T10,T4i)+refpropm('S','T',T3,'P',pl/1000,'CO2')- refpropm('S','T',T4i,'P',ph/1000,'CO2'); m6=@(t,T3,T4,T7,T10,T4i)+ec* refpropm('H','T',T4,'P',ph/1000,'CO2')- ec* refpropm('H','T',T3,'P',pl/1000,'CO2')- refpropm('H','T',T4i,'P',ph/1000,'CO2')+ refpropm('H','T',T3,'P',pl/1000,'CO2'); m11=@(t,T3,T4,T7,T10,T4i)+refpropm('H','T',T2,'P',ph/1000,'CO2')- refpropm('H','T',T4,'P',ph/1000,'CO2'); m12=@(t,T3,T4,T7,T10,T4i)-refpropm('C','T',T3,'P',pl/1000,'CO2') m13=@(t,T3,T4,T7,T10,T4i)-t*refpropm('C','T',T4,'P',ph/1000,'CO2') m14=@(t,T3,T4,T7,T10,T4i)-0 m15=@(t,T3,T4,T7,T10,T4i)+refpropm('C','T',T10,'P',pl/1000,'CO2') m16=@(t,T3,T4,T7,T10,T4i)-0 m21=@(t,T3,T4,T7,T10,T4i)-refpropm('H','T',T2,'P',ph/1000,'CO2')+ refpropm('H','T',T4,'P',ph/1000,'CO2'); m22=@(t,T3,T4,T7,T10,T4i)-0; m23=@(t,T3,T4,T7,T10,T4i)+t*refpropm('C','T',T4,'P',ph/1000,'CO2') m24=@(t,T3,T4,T7,T10,T4i)-0; m25=@(t,T3,T4,T7,T10,T4i)-er* 76 refpropm('C','T',T10,'P',pl/1000,'CO2') m26=@(t,T3,T4,T7,T10,T4i)-0; m31=@(t,T3,T4,T7,T10,T4i)-0; m32=@(t,T3,T4,T7,T10,T4i)-0; m33=@(t,T3,T4,T7,T10,T4i)+refpropm('C','T',T4,'P',ph/1000,'CO2'); m34=@(t,T3,T4,T7,T10,T4i)-refpropm('C','T',T7,'P',ph/1000,'CO2'); m35=@(t,T3,T4,T7,T10,T4i)-refpropm('C','T',T10,'P',pl/1000,'CO2'); m36=@(t,T3,T4,T7,T10,T4i)-0; m41=@(t,T3,T4,T7,T10,T4i)-0; m42=@(t,T3,T4,T7,T10,T4i)-0; m43=@(t,T3,T4,T7,T10,T4i)- refpropm('C','T',T4,'P',ph/1000,'CO2')+er*refpropm('C','T',T4,'P',pl /1000,'CO2'); m44=@(t,T3,T4,T7,T10,T4i)+refpropm('C','T',T7,'P',ph/1000,'CO2'); m45=@(t,T3,T4,T7,T10,T4i)-0 m46=@(t,T3,T4,T7,T10,T4i)-0; m51=@(t,T3,T4,T7,T10,T4i)-0; m52=@(t,T3,T4,T7,T10,T4i)+refpropm('C','T',T3,'P',pl/1000,'CO2')/T3; m53=@(t,T3,T4,T7,T10,T4i)-0; m54=@(t,T3,T4,T7,T10,T4i)-0; m55=@(t,T3,T4,T7,T10,T4i)-0; m56=@(t,T3,T4,T7,T10,T4i)- refpropm('C','T',T4i,'P',ph/1000,'CO2')/T4i; m61=@(t,T3,T4,T7,T10,T4i)-0; m62=@(t,T3,T4,T7,T10,T4i)-ec*refpropm('C','T',T3,'P',pl/1000,'CO2')+ refpropm('C','T',T3,'P',pl/1000,'CO2'); m63=@(t,T3,T4,T7,T10,T4i)+ec*refpropm('C','T',T4,'P',ph/1000,'CO2') m64=@(t,T3,T4,T7,T10,T4i)-0; m65=@(t,T3,T4,T7,T10,T4i)-0; m66=@(t,T3,T4,T7,T10,T4i)-refpropm('C','T',T4i,'P',ph/1000,'CO2') T0=0.7 T30=400 T40=499 T70=605 T100=400 T4i0=380 for i=1:300 a11=m11(T0,T30,T40,T70,T100,T4i0); a12=m12(T0,T30,T40,T70,T100,T4i0); a13=m13(T0,T30,T40,T70,T100,T4i0); a14=m14(T0,T30,T40,T70,T100,T4i0); a15=m15(T0,T30,T40,T70,T100,T4i0); a16=m16(T0,T30,T40,T70,T100,T4i0); a21=m21(T0,T30,T40,T70,T100,T4i0); a22=m22(T0,T30,T40,T70,T100,T4i0); a23=m23(T0,T30,T40,T70,T100,T4i0); a24=m24(T0,T30,T40,T70,T100,T4i0); a25=m25(T0,T30,T40,T70,T100,T4i0); a26=m26(T0,T30,T40,T70,T100,T4i0); a31=m31(T0,T30,T40,T70,T100,T4i0); a32=m32(T0,T30,T40,T70,T100,T4i0); a33=m33(T0,T30,T40,T70,T100,T4i0); a34=m34(T0,T30,T40,T70,T100,T4i0); a35=m35(T0,T30,T40,T70,T100,T4i0); 77

a36=m36(T0,T30,T40,T70,T100,T4i0); a41=m41(T0,T30,T40,T70,T100,T4i0); a42=m42(T0,T30,T40,T70,T100,T4i0); a43=m43(T0,T30,T40,T70,T100,T4i0); a44=m44(T0,T30,T40,T70,T100,T4i0); a45=m45(T0,T30,T40,T70,T100,T4i0); a46=m46(T0,T30,T40,T70,T100,T4i0); a51=m51(T0,T30,T40,T70,T100,T4i0); a52=m52(T0,T30,T40,T70,T100,T4i0); a53=m53(T0,T30,T40,T70,T100,T4i0); a54=m54(T0,T30,T40,T70,T100,T4i0); a55=m55(T0,T30,T40,T70,T100,T4i0); a56=m56(T0,T30,T40,T70,T100,T4i0); a61=m61(T0,T30,T40,T70,T100,T4i0); a62=m62(T0,T30,T40,T70,T100,T4i0); a63=m63(T0,T30,T40,T70,T100,T4i0); a64=m64(T0,T30,T40,T70,T100,T4i0); a65=m65(T0,T30,T40,T70,T100,T4i0); a66=m66(T0,T30,T40,T70,T100,T4i0); a18=- m1(T0,T30,T40,T70,T100,T4i0)+m11(T0,T30,T40,T70,T100,T4i0)*T0+m12(T0 ,T30,T40,T70,T100,T4i0)*T30+m13(T0,T30,T40,T70,T100,T4i0)*T40+m14(T0 ,T30,T40,T70,T100,T4i0)*T70+m15(T0,T30,T40,T70,T100,T4i0)*T100+m16(T 0,T30,T40,T70,T100,T4i0)*T4i0; a28=- m2(T0,T30,T40,T70,T100,T4i0)+m21(T0,T30,T40,T70,T100,T4i0)*T0+m22(T0 ,T30,T40,T70,T100,T4i0)*T30+m23(T0,T30,T40,T70,T100,T4i0)*T40+m24(T0 ,T30,T40,T70,T100,T4i0)*T70+m25(T0,T30,T40,T70,T100,T4i0)*T100+m26(T 0,T30,T40,T70,T100,T4i0)*T4i0; a38=- m3(T0,T30,T40,T70,T100,T4i0)+m31(T0,T30,T40,T70,T100,T4i0)*T0+m32(T0 ,T30,T40,T70,T100,T4i0)*T30+m33(T0,T30,T40,T70,T100,T4i0)*T40+m34(T0 ,T30,T40,T70,T100,T4i0)*T70+m35(T0,T30,T40,T70,T100,T4i0)*T100+m36(T 0,T30,T40,T70,T100,T4i0)*T4i0; a48=- m4(T0,T30,T40,T70,T100,T4i0)+m41(T0,T30,T40,T70,T100,T4i0)*T0+m42(T0 ,T30,T40,T70,T100,T4i0)*T30+m43(T0,T30,T40,T70,T100,T4i0)*T40+m44(T0 ,T30,T40,T70,T100,T4i0)*T70+m45(T0,T30,T40,T70,T100,T4i0)*T100+m46(T 0,T30,T40,T70,T100,T4i0)*T4i0; a58=- m5(T0,T30,T40,T70,T100,T4i0)+m51(T0,T30,T40,T70,T100,T4i0)*T0+m52(T0 ,T30,T40,T70,T100,T4i0)*T30+m53(T0,T30,T40,T70,T100,T4i0)*T40+m54(T0 ,T30,T40,T70,T100,T4i0)*T70+m55(T0,T30,T40,T70,T100,T4i0)*T100+m56(T 0,T30,T40,T70,T100,T4i0)*T4i0; a68=- m6(T0,T30,T40,T70,T100,T4i0)+m61(T0,T30,T40,T70,T100,T4i0)*T0+m62(T0 ,T30,T40,T70,T100,T4i0)*T30+m63(T0,T30,T40,T70,T100,T4i0)*T40+m64(T0 ,T30,T40,T70,T100,T4i0)*T70+m65(T0,T30,T40,T70,T100,T4i0)*T100+m66(T 0,T30,T40,T70,T100,T4i0)*T4i0; A0=[a11 a12 a13 a14 a15 a16;a21 a22 a23 a24 a25 a26;a31 a32 a33 a34 a35 a36;a41 a42 a43 a44 a45 a46;a51 a52 a53 a54 a55 a56;a61 a62 a63 a64 a65 a66]; A1=[a18 a12 a13 a14 a15 a16;a28 a22 a23 a24 a25 a26;a38 a32 a33 a34 a35 a36;a48 a42 a43 a44 a45 a46;a58 a52 a53 a54 a55 a56;a68 a62 78 a63 a64 a65 a66]; A2=[a11 a18 a13 a14 a15 a16;a21 a28 a23 a24 a25 a26;a31 a38 a33 a34 a35 a36;a41 a48 a43 a44 a45 a46;a51 a58 a53 a54 a55 a56;a61 a68 a63 a64 a65 a66]; A3=[a11 a12 a18 a14 a15 a16;a21 a22 a28 a24 a25 a26;a31 a32 a38 a34 a35 a36;a41 a42 a48 a44 a45 a46;a51 a52 a58 a54 a55 a56;a61 a62 a68 a64 a65 a66]; A4=[a11 a12 a13 a18 a15 a16;a21 a22 a23 a28 a25 a26;a31 a32 a33 a38 a35 a36;a41 a42 a43 a48 a45 a46;a51 a52 a53 a58 a55 a56;a61 a62 a63 a68 a65 a66]; A5=[a11 a12 a13 a14 a18 a16;a21 a22 a23 a24 a28 a26;a31 a32 a33 a34 a38 a36;a41 a42 a43 a44 a48 a46;a51 a52 a53 a54 a58 a56;a61 a62 a63 a64 a68 a66]; A6=[a11 a12 a13 a14 a15 a18;a21 a22 a23 a24 a25 a28;a31 a32 a33 a34 a35 a38;a41 a42 a43 a44 a45 a48;a51 a52 a53 a54 a55 a58;a61 a62 a63 a64 a65 a68]; t=det(A1)/det(A0) T3=det(A2)/det(A0) T4=det(A3)/det(A0) T7=det(A4)/det(A0) T10=det(A5)/det(A0) T4i=det(A6)/det(A0) T0=t T30=T3 T40=T4 T70=T7 T100=T10 T4i0=T4i end

79

Appendix Ⅲ MATLAB Code for Single-Effect Absorption

Refrigeration System

The code is listed below: t10=1; t8=37; qe=200; t1=26; e=0.65; t4=85; t7=t4; p10=XSteam('psat_T',t10); h10=XSteam('hV_T',t10); p8=XSteam('psat_T',t8); h8=XSteam('hL_T',t8); h9=h8; m10=qe/(h10-h9); syms a; x1=vpasolve(twater(t1,a)==t10,[40 75]); h1=hlibr(t1,x1); syms a; x4=vpasolve(twater(t4,a)==t8,[40 75]); h4=hlibr(t4,x4); m4=m10/(x4-x1)*x1; m1=m10+m4; w1=wlibr(x1); molar1=wmolarlibr(w1); v1=vlibr(t1+273,w1); ep=0.9; p2=p8; p1=p10; wp=v1*(p2-p1)/ep*100/molar1; h2=h1+wp; x2=x1; syms a; t2=vpasolve(hlibr(a,x2)==h2,[15 75]); h3=m4*(h4-hlibr(t2,x4))*e/m1+h2; x3=x1; syms a; t3=vpasolve(hlibr(a,x3)==h3,[40 100]); h5=h4-(h3-h2)*m1/m4; x5=x4; syms a; t5=vpasolve(hlibr(a,x5)==h2,[15 75]); p7=p8; h7=XSteam('h_pT',p7,t7); m7=m10; m3=m1; qd=m4*h4+m7*h7-m3*h3; cop=qe/(qd+wp) 80

T0=298; tes=20; tgs=20+t4; exqe=-qe*(1-T0/(tes+273)); exqd=qd*(1-T0/(tgs+273)); ecop=exqe/(exqd+wp);

81

Appendix Ⅳ MATLAB Code for Double-Effect Absorption

Refrigeration System

The code is listed below: t10=9; t18=80; t8=30; qe=200; t1=20; t14=144; t17=t14; e=0.65; p10=XSteam('psat_T',t10); h10=XSteam('hV_T',t10); p18=XSteam('psat_T',t18); h18=XSteam('hL_T',t18); p8=XSteam('psat_T',t8); h8=XSteam('hL_T',t8); h9=h8; m10=qe/(h10-h9); syms a x1=vpasolve(twater(t1,a)==t10,[40 70]); syms a x14=vpasolve(twater(t14,a)==t18,[40 70]); x6=x14; x4=x14; m1=m10/(x6-x1)*x6; m6=m1/x6*x1; x4=x14; syms a t4=vpasolve(twater(a,x4)==t8,[40 100]); t7=t4; h4=hlibr(t4,x4); h14=hlibr(t14,x14); h1=hlibr(t1,x1); w1=wlibr(x1); molar1=wmolarlibr(w1); v1=vlibr(t1+273,w1); ep=0.9; p2=p8; p1=p10; wp1=v1*(p2-p1)/ep*100/molar1; h2=h1+wp1; x2=x1; syms a; t2=vpasolve(hlibr(a,x2)==h2,[15 75]); m4=m6; h3=m4*(h4-hlibr(t2,x4))*e/m1+h2; x3=x1; syms a; 82 t3=vpasolve(hlibr(a,x3)==h3,[40 100]); h5=h4-(h3-h2)*m1/m4; x5=x4; syms a; t5=vpasolve(hlibr(a,x5)==h5,[15 155]); h20=h3; m3=m1; p7=p8; h7=XSteam('h_pT',p7,t7); x11=x1; w11=wlibr(x11); molar11=wmolarlibr(w11); t11=t3; v11=vlibr(t11+273,w11); ep=0.9; p12=p18; p11=p8; wp2=v11*(p12-p11)/ep*100/molar11; h11=hlibr(t11,x11); h12=h11+wp2; x12=x11; syms a; t12=vpasolve(hlibr(a,x12)==h12,[15 155]); x13=x1; h13=x13*e*(h14-hlibr(t12,x14))/x14+h12; syms a; t13=vpasolve(hlibr(a,x13)==h13,[15 150]); h15=-x14/x13*(h13-h12)+h14; x15=x14; syms a; t15=vpasolve(hlibr(a,x15)==h15,[15 155]); h16=h15; p17=p18; h17=XSteam('h_pT',p17,t17); A=m4*(h4-h16)-m10*(h17-h18); B=h20-(1-x1/x4)*(h17-h18)-h16*x1/x4-h7*(1-x1/x4); m20=A/B; m16=m4-m20*x1/x4; m7=m20*(1-x1/x4); m17=m10-m7; m14=m16; m13=m14*x14/x13; qd=-m13*h13+m14*h14+h17*m17; cop=qe/(qd+wp1+wp2) T0=298; tes=20; tgs=20+t14; exqe=-qe*(1-T0/(tes+273)); exqd=qd*(1-T0/(tgs+273)); ecop=exqe/(exqd+wp1+wp2);

83

Appendix Ⅴ MATLAB Code for Tri-Generation Plant

The code is:

T1=32+273; T8=273+700; pr=2;% p1=8000000; p2=p1*pr; p5=p2; p4=p2; p6=p5; p7=p6; p8=p7; p9=p8/pr; p10=p9; p11=p10; p3=p11; p12=p11; ec=0.9; er1=0.86; et=0.9; x=0.7; T11=383; h1=refpropm('H','T',T1,'P',p1/1000,'CO2') s1=refpropm('S','T',T1,'P',p1/1000,'CO2') for T2i=T1:0.001:1000; s2i=refpropm('S','T',T2i,'P',p2/1000,'CO2'); if abs(s2i-s1)/s1<0.00001%; break; else; end; end; h2i=refpropm('H','T',T2i,'P',p2/1000,'CO2') h2=(h2i-h1)/ec+h1; for T2=T1:0.001:1000; h2c=refpropm('H','T',T2,'P',p2/1000,'CO2'); if abs(h2c-h2)/h2<0.00001%; break; else; end; end; h8=refpropm('H','T',T8,'P',p8/1000,'CO2'); s8=refpropm('S','T',T8,'P',p8/1000,'CO2'); for T9i=T8:-0.001:T1 s9i=refpropm('S','T',T9i,'P',p9/1000,'CO2'); if abs(s9i-s8)/s8<0.00001 break; else; end; end; h9i=refpropm('H','T',T9i,'P',p9/1000,'CO2'); h9=h8-et*(h8-h9i); 84 for T9=T9i:0.001:T8; h9c=refpropm('H','T',T9,'P',p9/1000,'CO2'); if abs(h9c-h9)/h9<0.00001; break; else; end; end; p11=p1; h11=refpropm('H','T',T11,'P',p11/1000,'CO2') h5=refpropm('H','T',T5,'P',p5/1000,'CO2'); hmin1=refpropm('H','T',T2,'P',p10/1000,'CO2'); h5=er1*(h11-hmin1)/x+h2; for T5=T2:0.001:T8; h10c=refpropm('H','T',T5,'P',p5/1000,'CO2'); if abs(h10c-h10)/h10<0.0001%; break; else; end; end; h12=x*(h2-h5)+h11; for T12=T2:0.001:T11; h12c=refpropm('H','T',T11,'P',p11/1000,'CO2'); if abs(h12c-h12)/h12<0.00001%; break; else; end; end; T3=T12; h3=refpropm('H','T',T3,'P',p3/1000,'CO2') s3=refpropm('S','T',T3,'P',p3/1000,'CO2') for T4i=T3:0.001:1000; s4i=refpropm('S','T',T4i,'P',p4/1000,'CO2'); if abs(s4i-s3)/s3<0.00001%; break; else; end; end; h4i=refpropm('H','T',T4i,'P',p4/1000,'CO2') h4=(h4i-h3)/ec+h3; for T4=T3:0.001:1000; h4c=refpropm('H','T',T4,'P',p4/1000,'CO2'); if abs(h4c-h4)/h4<0.00001%; break; else; end; end; h6=x*h5+(1-x)*h4; a=(T5-T4)/50000; for T6=T4:a:T5; h6c=refpropm('H','T',T6,'P',p6/1000,'CO2'); if abs(h6c-h6)/h6<0.00001%; break; else; end; 85 end; hmin2=refpropm('H','T',T6,'P',p10/1000,'CO2'); h7=h6+h9-h10; er2=(h7-h6)/(h9-hmin2) if abs(er2-er1)/er1<0.00013 break; else; end end for T7=T6:0.001:T8; h7c=refpropm('H','T',T7,'P',p7/1000,'CO2'); if abs(h7c-h7)/h7<0.00001%; break; else; end; qin=h8-h7; w1=h8-h9-((1-x)*(h4-h3)+x*(h2-h1)); e=wnet/qin T0=25+273; Ts=800+273; qinx=qin*(1-T0/Ts); qh1=t*(h3-h1); t32=9; t28=80; t30=30; qe=200; t20=20; t14=144; t17=t14; e=0.65; p32=XSteam('psat_T',t32); h32=XSteam('hV_T',t32); p28=XSteam('psat_T',t28); h28=XSteam('hL_T',t28); p30=XSteam('psat_T',t30); h30=XSteam('hL_T',t30); h31=h30; m32=qe/(h32-h31); syms a x20=vpasolve(twater(t20,a)==t32,[40 70]); syms a x14=vpasolve(twater(t14,a)==t28,[40 70]); x19=x14; x17=x14; m20=m32/(x19-x20)*x19; m19=m20/x19*x20; x17=x14; syms a t17=vpasolve(twater(a,x17)==t30,[40 100]); t7=t17; h17=hlibr(t17,x17); h14=hlibr(t14,x14); h20=hlibr(t20,x20); w20=wlibr(x20); 86 molar20=wmolarlibr(w20); v20=vlibr(t20+273,w20); ep=0.9; p21=p30; p20=p32; wp1=v20*(p2-p20)/ep*100/molar20; h21=h20+wp1; x21=x20; syms a; t21=vpasolve(hlibr(a,x21)==h21,[15 75]); m17=m19; h3=m17*(h17-hlibr(t21,x17))*e/m20+h21; x3=x20; syms a; t22=vpasolve(hlibr(a,x22)==h22,[40 100]); h18=h17-(h22-h21)*m20/m17; x18=x17; syms a; t18=vpasolve(hlibr(a,x18)==h18,[15 155]); h20=h22; m22=m20; p33=p30; h33=XSteam('h_pT',p33,t33); x24=x20; w24=wlibr(x24); molar24=wmolarlibr(w24); t24=t22; v24=vlibr(t24+273,w24); ep=0.9; p25=p28; p24=p30; wp2=v24*(p25-p24)/ep*100/molar24; h24=hlibr(t24,x24); h25=h24+wp2; x25=x24; syms a; t25=vpasolve(hlibr(a,x25)==h25,[15 155]); x26=x1; h26=x26*e*(h14-hlibr(t25,x14))/x14+h25; syms a; t26=vpasolve(hlibr(a,x26)==h26,[15 150]); h15=-x14/x26*(h26-h25)+h14; x15=x14; syms a; t15=vpasolve(hlibr(a,x15)==h15,[15 155]); h16=h15; p27=p28; h27=XSteam('h_pT',p27,t27); A=m17*(h17-h16)-m32*(h27-h28); B=h20-(1-x20/x17)*(h27-h28)-h16*x20/x17-h33*(1-x20/x17); m20=A/B; m16=m17-m20*x23/x17; m33=m23*(1-x23/x17); m27=m32-m33; 87 m14=m16; m26=m14*x14/x26; qd=-m26*h26+m14*h14+h27*m27; cop=qe/(qd+wp1+wp2) T0=298; tes=20; tgs=20+t14; por=1*(h10-h11)/qd; qex=-qe*(1-T0/(tes+273))*por; wnet=w1-(wp1+wp2)*por; qea=qe*por; qh2=por*(m29*h29-m30*h30+m33*h33); qh=qh1+qh2; qh1x=x*(h13-h1)-x*(s13-s1)*T0; qh2x=por*(qh2-m29*s29-m30*s30+m33*s33); qhx=qh1x+qh2x; eff=(wnet+qea+qh)/qin; extr=(wnet+qex+qhx)/qinx;