ENERGY, EXERGY AND ECONOMIC ANALYSIS OF A MICRO-CCHP SYSTEM

by

Ganesh Vinayak Doiphode

A thesis submitted to the Department of Mechanical and Civil Engineering of Florida Institute of Technology

in partial fulfillment of the requirements for the degree of

Master of Science in

Mechanical Engineering

Melbourne, Florida May, 2019

We the undersigned committee hereby approve the attached thesis, “ENERGY, EXERGY AND ECONOMIC ANALYSIS OF A MICRO-CCHP SYSTEM,” by

Ganesh Vinayak Doiphode.

_________________________________________________ Hamidreza Najafi, Ph.D. Assistant Professor Mechanical Engineering

_________________________________________________ Troy Nguyen, Ph.D., P.E., ESEP Associate Professor Civil Engineering

_________________________________________________ Gerald J. Micklow, Ph.D., P.E. Professor Mechanical Engineering

_________________________________________________ Ashok Pandit, Ph.D., P.E., F.ASCE Professor and Head Department of Mechanical and Civil Engineering

iii

Abstract

Title: ENERGY, EXERGY AND ECONOMIC ANALYSIS OF A MICRO-CCHP

SYSTEM

Author: Ganesh Vinayak Doiphode

Advisor: Hamidreza Najafi, Ph. D.

Combined cooling, heating and power generation (CCHP) systems can be

utilized for commercial or multi-family residential buildings as efficient and reliable

means to satisfy building power requirements and thermal loads. In the present study,

a CCHP system consist of a Bryton cycle, an Organic Rankine cycle (ORC) and an

absorption Ammonia-water cycle is considered. A detailed model is developed via

MATLAB to assess the performance of the considered cycle from energy, exergy

and economic perspectives. Appropriate ranges for inputs are considered and the first

law efficiency, second law efficiency and ECOP of the cycle are determined as

77.17%, 33.18% and 0.31 respectively for the given inputs. Exergy destruction rates

are found to be greatest primarily in the generator and the absorber of refrigeration

cycle followed by the combustion chamber. The total exergy destruction rate in the

system is found as 5311.51 kW. The exergoeconomic analysis is performed using

iv

SPECO approach to evaluate cost flow rate equations of the complete system and its

individual components. Summation of capital investment cost rates and cost rates

associated with the exergy destruction for the whole system is found as $18.245 per

hour. Energy based cost of useful products is $2.14 per kW-h. A parametric study is

also performed to provide an understanding on the effect of total pressure ratio and

turbine inlet temperature of ORC on the performance of the system. A multi-

objective optimization using Genetic Algorithm is performed to maximize plant

energy efficiency and minimize the total cost flow rate of the whole system. A pareto

front of all possible optimized operating points is obtained. A suitable operating point

can be chosen making a trade-off between the two objective functions.

v

Contents

Contents .................................................................................................................... v

List of Figures ........................................................................................................ vii List of Tables ........................................................................................................ viii List of Symbols & abbreviations ........................................................................... ix

Acknowledgement ................................................................................................ xiii Chapter 1 Introduction ............................................................................................ 1

Chapter 2 CCHP System ....................................................................................... 10 1. CCHP Cycle Diagram and Description .............................................................. 10

a. Brayton Cycle ...................................................................................................... 10 b. Organic Rankine Cycle ....................................................................................... 12 c. Ammonia-Water Absorption cycle .................................................................... 12

2. Assumptions Made in Study ................................................................................ 13

Chapter 3 Thermodynamic Analysis .................................................................... 16 1. Mass and Energy Balances .................................................................................. 16 2. Exergy Definitions and Balances ......................................................................... 17

a. Physical & Chemical Exergy Destruction Rates for Each Component of Cycle ....................................................................................................................... 18

3. 2nd Law Efficiency ................................................................................................. 22 4. Properties of Working Fluids .............................................................................. 22 5. Validation of Working Model .............................................................................. 23

Chapter 4 Economic Analysis ............................................................................... 26 1. SPECO Approach ................................................................................................. 26

a. Identification of Exergy Streams ....................................................................... 27 b. Defining Fuel (F) and Product (P) For Each Component ............................... 27 c. Cost equations ..................................................................................................... 27

2. Energy specific costing ......................................................................................... 30

Chapter 5 System Optimization ............................................................................ 33 1. Optimization algorithm ........................................................................................ 33 2. Objective functions ............................................................................................... 34 3. Decision variables ................................................................................................. 35

Chapter 6 Simulation Results and Discussion ..................................................... 37 1. System Performance ............................................................................................. 37 2. Exergy Analysis Results ....................................................................................... 42 3. Economic Analysis Results .................................................................................. 44

a. Exergoeconomic results ...................................................................................... 44 b. Energy Specific Results ...................................................................................... 46

vi

4. Parametric Studies ............................................................................................... 46 5. System Optimization Results ............................................................................... 52

Chapter 7 Conclusions ........................................................................................... 56

References ............................................................................................................... 58

vii

List of Figures

Figure 1: SCHEMATIC OF THE SYSTEM PROPOSED BY AMIN ET AL. [30]

.......................................................................................................................... 11

Figure 2: GENERAL STRUCTURE OF GENETIC ALGORITHM [43] .............. 34

Figure 3: EXERGY DESTRUCTION RATES FOR THE COMPONENTS OF

BRAYTON CYCLE ........................................................................................ 41

Figure 4: EXERGY DESTRUCTION RATES FOR THE COMPONENTS OF

ORGANIC RANKINE CYCLE ...................................................................... 42

Figure 5: EXERGY DESTRUCTION RATES IN THE COMPONENTS

REFRIGERATION CYCLE (EXERGY DESTRUCTION RATE FOR

GENERATOR AND ABSORBER HERE ARE 233.54 KW AND 232.27 KW

RESPECTIVELY) ........................................................................................... 43

Figure 6: EFFECT OF OVERALL PRESSURE RATIO OF BC ON ENERGY-

EXERGY PERFORMANCE PARAMETERS ............................................... 47

Figure 7: EFFECT OF OVERALL PRESSURE RATIO OF BC ON EXERGY-

ECONOMIC PERFORMANCE PARAMETERS .......................................... 48

Figure 8: EFFECT OF TIT OF ORC ON ENERGY- EXERGY PERFORMANCE

PARAMETERS ............................................................................................... 50

Figure 9: EFFECT OF TIT OF ORC ON EXERGY-ECONOMIC

PERFORMANCE PARAMETERS ................................................................. 51

Figure 10: PARETO FRONT OF THE MULTI-OBJECTIVE SYSTEM

OPTIMIZATION ............................................................................................. 52

Figure 11: IN DETAIL PARETO FRONT OF THE SYSTEM WITH SELECT

POINTS A AND B .......................................................................................... 54

viii

List of Tables

Table 1: CONSTANT PARAMETERS ASSUMED FOR THE CCHP SYSTEM

ANALYSIS ...................................................................................................... 14

Table 2: ENERGY RELATIONS USED FOR EACH COMPONENT OF THE

SYSTEM .......................................................................................................... 16

Table 3: COMPARISON BETWEEN OBTAINED RESULTS AND DATA IN

LITERATURE [34], [21] AND [36] ............................................................... 23

Table 4: OVERALL HEAT TRANSFER COEFFICIENT VALUES USED IN

THE ANALYSIS [48] ..................................................................................... 24

Table 5: COST FLOW RATE BALANCES AND AUXILIARY EQUATION

MATRICES TO EVALUATE COST FLOW RATES .................................... 32

Table 6: OPTIMIZATION VARIABLES AND THEIR RANGE .......................... 35

Table 7: THERMODYNAMIC PROPERTIES OF ALL THE STREAMS ............ 38

Table 9. TOTAL PERFORMANCE OF THE CCHP SYSTEM ............................. 40

Table 10: EXERGY AND EXERGOECONOMIC PARAMETERS FOR

COMPONENTS OF THE SYSTEM ............................................................... 45

Table 10: OPTIMIZED VARIABLES FOR DATA SET A AND B WITH

VARIABLES USED IN BASE CASE ............................................................ 55

ix

List of Symbols & abbreviations

𝑐𝑐 Unit cost of exergy ($/MJ)

𝑐𝑐𝑝𝑝 Specific heat at constant pressure (kJ/kg.K)

�̇�𝐶 Cost flow rate ($/s)

�̇�𝐶𝐷𝐷 Exergy destruction cost rate ($/s)

�̇�𝐶𝐿𝐿 Cost rate associated with exergy losses ($/s)

COP Coefficient of performance

𝐶𝐶𝐶𝐶𝐶𝐶 Capital recovery factor

𝑒𝑒𝑐𝑐ℎ0 Molar chemical exergy (kJ/mol)

𝑒𝑒𝑒𝑒 Specific exergy (kJ/kg)

ECOP Exergic coefficient of performance

𝐸𝐸𝑒𝑒 Total exergy (kJ)

𝐸𝐸�̇�𝑒𝐷𝐷 Exergy destruction rate (kW)

𝑓𝑓 Exergoeconomic factor

F Fuel (exergy point of view)

ℎ Specific enthalpy (kJ/kg)

𝑖𝑖 Interest rate (%)

�̇�𝑚 Mass flow rate (kg/s)

𝑀𝑀 Molar mass (g/mol)

x

𝑁𝑁 Number of operational hours

𝑃𝑃 Pressure (bar)

P Product (exergy point of view)

�̇�𝑄 Heat transfer rate (kW)

𝑟𝑟𝑝𝑝 Pressure ratio

𝑠𝑠 Entropy (kJ/kg.K)

T Temperature (C)

�̇�𝑊 Work done (kW)

𝑒𝑒 Concentration (kg/kg)

�̇�𝑋 Exergy flow rate (kW)

𝑑𝑑 𝑑𝑑𝑑𝑑

Differential operator

𝑍𝑍 Capital investment cost ($)

�̇�𝑍 Capital investment cost rate ($/s)

Greek Symbols

𝛾𝛾 Specific heat ratio

𝜂𝜂 Efficiency (%)

𝜖𝜖 Effectiveness of heat exchanger

𝜙𝜙 Maintenance factor

Subscript

a Air

xi

𝑐𝑐𝑐𝑐 Combustion chamber

𝑐𝑐ℎ Chemical

𝑒𝑒 exit

𝑓𝑓 Fuel

𝑔𝑔 Combustion gases

𝑖𝑖 inlet

𝑗𝑗 Counting number

𝑘𝑘𝑘𝑘 Kinetic

𝑝𝑝ℎ Physical

𝑝𝑝𝑑𝑑 Potential

𝑤𝑤 Water

𝑑𝑑, T Turbine

0 ambient

1-36 Fluid state numbers

ABS

Absorber

BC Brayton cycle

C1 Compressor 1 of BC

C2 Compressor 2 of BC

CC Combustion chamber

xii

CV Control volume

CD1 Condenser of organic Rankine cycle

CD2 Condenser of absorption cycle

EV Evaporator in absorption cycle

G Generator

GT Gas turbine cycle

𝐻𝐻2O Water

𝐿𝐿𝐻𝐻𝐿𝐿 Lower heating value (kJ/kg)

LMTD Log mean temperature difference

𝑁𝑁𝐻𝐻3 Ammonia

ORC Organic Rankine cycle

P1 Pump in ORC

P2 Pump in absorption cycle

𝑟𝑟𝑒𝑒𝑓𝑓 Refrigeration

R Recuperator

T1 Turbine in BC

T2 Turbine in ORC

V Throttle valve

VG Vapor generator

xiii

Acknowledgement

Thesis journey was a mix of intellect, fun, frustration and hard work but all that

made research super interesting. First and foremost, I would like to thank my thesis

advisor, Dr. Hamidreza Najafi at Florida Institute of Technology. He was there to

help me at every hurdle that I faced in research and writing. He steered me in the

right direction whenever I was deviating into the lost. He encouraged me not just to

do the research but to publish the research even before I graduate. He always insisted

me to attend conference, meet industry people and interact with them. Upon Dr.

Najafi’s recommendation, getting involved in ASHRAE activities and Brevard

Public School’s energy auditing program proved really stimulating. I learnt a great

value from his interpersonal skills. I would also like to thank the Mechanical and

Civil Engineering department to provide me some financial support to complete my

thesis.

Finally, I must express my profound gratitude to my parents and my sisters for

believing in me. Me being in a different country, they constantly provided me

unfailing support and encouragement. I would also like to thank my girlfriend for

being there during mental breakdowns. Lastly, I would like to thank my late best

friend who always knew I have something in me.

1

Chapter 1 Introduction

Combined cooling, heating and power generation (CCHP) systems, owing to

their desirable characteristics, have been attracting a lot of attentions over the last

several years. Micro CCHP systems in particular are becoming more popular in

commercial and even residential sectors rapidly as they offer a reliable source of

energy to the building managers and end users. Micro CCHP systems improve

reliability in the event of natural disasters when long power outage episodes are

likely. In the state of Florida, where hurricane menace is expected, the power from

grid may be unavailable for days. In such cases, many critical facilities like old age

housing facilities, hospitals may find it very difficult to operate and may lose lives.

Presence of an in-house power generation system along with cooling and heating

capabilities can make the system self-reliant of such needs from the grid and can

sustain emergency power situations.

Many researchers studied various configuration of CCHP systems with the

ultimate goal of maximizing the performance and minimizing the cost of the system.

Different approaches have been also employed such as intercooling, reheating

2

turbine inlet air cooling and more in order to achieve a cost-effective design for the

system.

Ebaid and Al-hamdan [1] showed supplementary reheating decreases the

combined cycle efficiency, on the other hand supplementary heating significantly

increases the steam turbine cycle efficiency. Also, gas turbine pre-cooling improves

the gas turbine performance, but it has a less significant effect on the combined cycle

efficiency and the combined specific work output. Javanshir et al. [2] compared the

effect of working fluid properties on the combined Brayton/ORC cycle. They

considered twelve different working fluids and conclude that working fluids with

higher specific heat capacity produce higher net power output in a subcritical region.

Also, their economic analysis showed combined cycle requires significantly lower

total capital investment and levelized cost of electricity (LCOE) compared to the

regenerative Brayton cycle. Najjar and Abubaker [3] optimized thermo-economic

performance of cascade waster heat recovery system. They showed when the total

cost rate is minimized to 1.715 US$/s, net power and thermal efficiency decreased to

27,135 kW and 28.34% respectively.

A thorough assessment of a thermodynamic cycle requires both energy and

exergy analysis. While first law efficiency can provide an understanding of the

current performance of the system, the second law efficiency sheds light on the

irreversibilities and possible improvement opportunities. Several studies have been

conducted on the exergy and energy analysis of different types of CCHP systems.

3

Tuma et al. [4] formulated and discussed the equations for overall energy and

exergy efficiencies of a combined gas steam cycle plant with cogeneration. Bilgen

[5] developed an algorithm to carry out thermodynamic first and second law analyses

and engineering evaluation based on the levelized cost methodology and payback

period for the gas turbine cogeneration system. Huang et al. [6] formulated in detail

exergy balance equations for all the components of the combined system of STIG

cogeneration and forward-feed triple-effect evaporation process and showed that

exergy destruction is significant in the combustion chamber and maximum exergy

loss takes place in the stack. Authors concluded that with the vapor recompression,

system thermal efficiency of a combined system of STIG cogeneration and forward-

feed triple-effect evaporation process, is better than a system without vapor

recompression for a given steam injection ratio and feedstock mass flow rate. Pak et

al. [7] evaluated exergy flows of three different cogeneration systems to improve

power generation efficiency and concluded that increase in turbine inlet temperature

reduces exergy destruction in combustion chamber, also incorporating regenerator

reduces exergy destruction in waste heat boiler. Additionally, for a low heat demand,

highest exergetic power generation efficiency is achieved when dual-fluid cycle is

incorporated.

Some researchers incorporated the economic aspects of the CCHP cycles in their

analysis. Bejan et al. [8] showed that a true representative economic analysis must

be based on exergy and not energy. This is because energy analysis by itself does not

4

provide any information about usefulness of the energy transfers. Xia et al. [9]

performed thermo-economic analysis and optimization of CCP system consisting of

CO2 Brayton cycle (BC), an ORC and an ejector refrigeration cycle that produced

both power and refrigeration simultaneously to recover energy from engine waste

heat. Their Exergoeconomic analysis showed, increasing the BC turbine inlet

temperature, the ORC turbine inlet pressure and the ejector primary flow pressure,

lower average cost per unit of exergy product for combined system can be obtained.

However, increase in compressor pressure and compressor inlet temperature,

increases the average cost per unit of exergy product for combined system.

Guarinello Jr. et al. [10] performed exergy based thermoeconomic analysis to

determine the production cost of electricity and steam in STIG cogeneration system

located in industrial district Cabo (Pernambuco, Brazil) to provide thermal and

electrical needs. Thermodynamic exergy analysis performed on combined cycle

power plants in [11], [12], [13], [14], concluded that more than 80% of exergy

destruction takes place in combustion chamber and heat recovery steam generator.

Vandani et al. [15] performed comprehensive exergetic, economic and

environmental analysis for a combined cycle power plant that used natural gas and

diesel as fuels to show former fuel has better performance in terms of environmental

impact, contaminants, total annual cost of plant and exergy efficiency. Mohtaram et

al. [16] optimized exergy and thermal efficiencies using genetic algorithm and

performed parametric analyses of a combined absorption refrigeration and Rankine

5

cycle with ammonia-water as working fluid. Yang and Yeh [17] evaluated thermo-

economic performance optimization of an Organic Rankine Cycle utilizing exhaust

gas of a diesel engine, they showed raising turbine inlet temperature results in higher

optimal thermodynamic and economic performances. Also, compared optimal

economic conditions for refrigerants R245fa, R600, R600a, and R1234ze; and

concluded that R245fa performs most satisfactorily. Zhang et al. [18] presented novel

CHP system coupling biomass partial gasification and ground source heat pump

along with gas and steam turbine power generation. Authors studied exergetic and

exergoeconomic performance of the system and also performed parametric study on

several variables. Calise et al. [19] presented exergetic and exergoeconomic analyses

of solar-geothermal poly-generation system that provides electrical, thermal, cooling

energy, and producing fresh desalinized water from multi-effect distillation unit from

sea water. Xu et al. [20] compared two absorption-compression refrigeration cycles

with novel evaporator-subcooler and conventional evaporator-condenser, based on

energy, exergy, economic and environmental perspectives.

The previous studies showed the effectiveness of CCHP systems. One of the most

promising configurations for CCHP system consists of a main gas turbine cycle

followed by is using an organic Rankine cycle and an absorption refrigeration cycle.

An energetic analysis is performed on such a cycle by by Amin et al. [21]. Authors

found the energy efficiency of the plant to be around 77%. While the high energy

efficiency of the system makes it a promising configuration, no exergetic or

6

economic analysis have been conducted on the cycle to date. Furthermore, a

comprehensive optimization of the cycle is necessary in order to obtain the optimal

parameters for the cycle.

In the present study, a thorough energetic, exergetic and economic analysis is

performed on a micro CCHP system consist of a Brayton cycle, an Organic Rankine

cycle and an absorption-refrigeration cycle. The system is capable of generating

power, cooling effect and hot water and therefore is a good candidate to be used for

commercial and large residential buildings. The previous works on this particular

cycle have been focused on the energy aspect, however, the cost has not been

considered as a determining factor. Given the fact that the cost of the system can

make a significant impact on decision making process regarding implementation of

the system, in this thesis, an exergoeconomic study is performedto provide a clear

picture of the performance of the system to the designer or the end user. The results

of the exergetic analysis allows identifying irreversibilities and potential

improvement opportunities through the system. Exergoconomic analysis is used to

estimate the cost of each component of the system and also the cost of operation of

the whole cycle.

While maximizing the output and efficiency of the system is of great importance,

the system parameters must be set to minimize the cost simultaneously. Thus, an

optimization must be performed to achieve optimal system parameters. In past

decade, many researchers have studied co-generation systems and optimized it using

7

various optimization algorithms. Kavvadias and Maroulis [22] optimized a tri-

generation plant for economical, energetic and environmental performance using

multi-objective evolutionary algorithm. Wang et al. [23] constructed and maximized

a weighted objective function measuring energetic, economic and environmental

benefits of building cooling heating and power system using particle swarm

optimization algorithm. Ghaebi et al. [24] optimized tri-generation system for the

cost of total system product and found that objective system modification by 15%

after optimization. Hu and Cho [25] developed a probability constrained stochastic

multi-objective optimization model to optimize CCHP operation strategy for five

different cities namely Columbus, Minneapolis, San Francisco, Boston and Miami.

Wang et al. [26] optimized biomass BCHP system with thermal storage unit and

hybrid cooling system to minimize annual total cost using GA and combined it to the

case study in Harbin, China.

Najafi et al. [27] modelled solid oxide fuel cell- gas turbine hybrid system with

a multi-stage desalination unit and performed multi-objective optimization to

maximize exergy efficiency and minimize total cost rate of the system using genetic

algorithm. Authors found the optimal solution that led to exergy efficiency of 46.7%

and total cost of 3.76 USD/yr. Boyaghchi and Heidarnejad [28] performed single and

multi-objective optimization of a micro solar CCHP for summer and winter seasons

with objective functions being thermal efficiency, exergy efficiency and total product

cost rate. Authors found optimal results for summer as 28%, 27% and 17% for the

8

objective functions respectively, and in winter as 4%, 13%, and 4%. Many researcher

lately reviewed multi-objective optimization methods in tri, poly-generation CCHP

systems in power plant as well as in buildings applications.

Given the fact that any effort to increase the energy efficiency of the system will

result in higher total cost of the system, optimization of the system with respect to a

single objective will not provide a clear perspective regarding the optimal

performance of the system. Therefore, a multi-objective optimization has to be

performed. In this study, the CCHP system under consideration is optimized for

maximizing the first law efficiency and minimizing the total cost rate of the working

plant. A multi-objective optimization is performed using Genetic Algorithm and

Pareto front is generated which includes a series of optimal solutions each of which

is a tradeoff between the cost and the energy efficiency. The compiled results of this

thesis can be used to understand the complete system performance, from energy,

exergy and economic standpoints. The structure of this thesis document is briefly

reviewed as below.

Chapter 2 discussed the details of the system under observation. Necessary

system parameter values assumed to initiate the simulation and assumptions made in

the study are provided. Chapter 3 elaborates the thermodynamic modeling of the

system that includes energy and exergy relations used. The model is then validated

with the data available in the literature. Chapter 4, discusses the economic analysis

of the system. Details of SPECO approach and the necessary cost relating equations

9

are discussed in this chapter. Chapter 5 contains discussions on the optimization

algorithm used, the objective functions and the system variables under observation.

Simulation results and corresponding discussions are presented in Chapter 6.

Energy, exergy and the economic performance of the system is evaluated and

presented in this chapter. The results of the parametric study and optimization of the

system are also discussed in detail. Lastly, Chapter 7 enlists the important

conclusions drawn from the complete analysis.

Outcome of this thesis can be a value addition to the deeper understanding of

CCHP systems, importance of exergy and economic analysis and system

optimization in the design and decision-making process of micro-CCHP systems.

10

Chapter 2 CCHP System

The considered thermodynamic cycle as well as the components of the system

are described in this section.

1. CCHP Cycle Diagram and Description

Figure 1 shows the schematic diagram of the system proposed by Amin et al.

[15]. Complete system consists of three major parts, namely a Brayton cycle, an

Organic Rankine Cycle and an absorption refrigeration cycle.

a. Brayton Cycle

Ambient air gets pressurized in compressor 1, cools down through the intercooler

and flows into the compressor 2 where it gets further pressurized before flowing into

the combustion chamber. The intercooler is simply a heat exchanger which captures

heat content of the compressed air and transfer it to water that may be used for

domestic hot water applications. The combustion occurs in the combustion chamber

and high temperature and high-pressure combustion gases will rotate the turbine

which in turn rotates a generator and produce power. The flue gases that leaves the

Brayton cycle are at lower pressure and temperature but still has significant energy

content that can be harnessed to improve overall efficiency of the system.

11

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12

b. Organic Rankine Cycle

The flue gases that left the gas turbine flow through a heat recovery steam

generator (HRSG) which captures the remaining heat content of the flue gases and

evaporates the organic fluid. Toluene is used as the organic fluid for this study owing

to its desirable characteristics within the range of the operation of the considered

cycle. The HRSG consists of an economizer, an evaporator and a superheater.

Expansion of superheated steam in turbine produces power and turbine outlet stream

condenses in the condenser accordingly. The liquid Toluene is then pumped back to

the vapor generator. Even after expansion in the steam turbine, the ORC turbine

outlet temperature is marginally high, a recuperator placed before the condenser

boosts the efficiency of the plant and reduces the condenser load.

c. Ammonia-Water Absorption cycle

In order to provide cooling effect, a binary mixture of ammonia- water is used in

an absorption refrigeration cycle. The remaining energy of the flue gases that left the

HRSG is imparted to ammonia-water solution in the generator. In high temperature,

ammonia as the more volatile component of the mixture vaporizes and flows to the

condenser and liquid water returns to the absorber. The high-pressure ammonia loses

its high energy content in the condenser and its pressure regulates down through the

expansion valve. The low-pressure liquid ammonia flows in the evaporator where it

absorbs heat from the surrounding and produces cooling effect as chilled water. After

13

evaporation, saturated liquid ammonia reaches to the absorber where recombines

with water to produce the aqua ammonia solution. The strong ammonia-water

solution is pumped to the generator and the cycle repeats. Water is used for cooling

in the absorber and the condenser which gets preheated and may be used for domestic

hot water applications.

2. Assumptions Made in Study

Following are the important assumptions implemented in the analysis:

• All processes are assumed to be steady state.

• Both air and flue gases in Brayton cycle are considered as an ideal gas

mixture.

• Natural gas is used as fuel in the combustion chamber.

• All processes in Brayton cycle are adiabatic, except the combustion chamber.

• A constant isentropic efficiency is assumed for both compressors and turbine

of Brayton cycle.

• Condenser pressure in ORC is selected in a way that water can be used as

cooling agent.

• A constant isentropic efficiency is assumed for turbine and pump in ORC.

• All processes are considered adiabatic in ORC.

• Generator and evaporator outlet in refrigeration cycle are assumed to be

saturated vapor ammonia.

14

• Condenser outlet is assumed to be saturated liquid ammonia.

• Pressure losses in the pipes and all heat exchangers are negligible.

• All components are adiabatic in refrigeration cycle.

• A constant isentropic efficiency is considered for refrigeration pump and

pump in ORC.

Important parameters utilized to evaluate performance of the CCHP system

are listed in Table 1.

Table 1: CONSTANT PARAMETERS ASSUMED FOR THE CCHP SYSTEM ANALYSIS

Parameter Value unit Ambient Temperature 25 C Ambient pr. 1.01325 Bar Total pr. ratio 10 - Air mass flow rate 0.1 Kg/s BC compressor isentropic efficiency 85 % CC efficiency 95 % BC turbine isentropic efficiency 90 % BC TIT 800 C LHV 48,000 kJ/kg Intercooler pr. drop in BC 1 % ORC Pinch 10 C ORC TIT 350 C ORC TIP 25 Bar ORC condenser pr. 0.1 Bar ORC turbine isentropic efficiency 80 % ORC pump isentropic efficiency 70 % Recuperator Pinch 10 C Pr. drop in economizer 1 % Pr. drop in evaporator 1 % Pr. drop in superheater 1 % Pr. drop in recuperator 1 % Generator temperature 90 C Condenser temperature 40 C

15

Absorber temperature 20 C Evaporator temperature 2.5 C HX effectiveness 80 % Water temp rise in absorber 5 C

16

Chapter 3 Thermodynamic Analysis

1. Mass and Energy Balances

Mass and energy balance relations for each component of the cycle can be used

based on the first law of thermodynamics, as listed in Table 2.

Table 2: ENERGY RELATIONS USED FOR EACH COMPONENT OF THE SYSTEM

GT: Energy balances

Compressor 1 (C1)

𝑇𝑇2 = 𝑇𝑇1 �1 + 1𝜂𝜂𝑐𝑐�𝑟𝑟𝑝𝑝

𝛾𝛾𝑎𝑎−1𝛾𝛾𝑎𝑎 − 1��

𝑊𝑊𝑐𝑐1̇ = 𝑚𝑚𝑎𝑎̇ 𝑐𝑐𝑝𝑝𝑎𝑎(𝑇𝑇2 − 𝑇𝑇1) Intercooler (IN) 𝑚𝑚�̇�𝑤(ℎ8 − ℎ9) = 𝑚𝑚𝑎𝑎̇ 𝑐𝑐𝑝𝑝𝑎𝑎(𝑇𝑇2 − 𝑇𝑇3)

Compressor 2 (C2) 𝑇𝑇4 = 𝑇𝑇3 �1 + 1𝜂𝜂𝑐𝑐�𝑟𝑟𝑝𝑝

𝛾𝛾𝑎𝑎−1𝛾𝛾𝑎𝑎 − 1��

𝑊𝑊𝑐𝑐2̇ = 𝑚𝑚𝑎𝑎̇ 𝑐𝑐𝑝𝑝𝑎𝑎(𝑇𝑇4 − 𝑇𝑇3)

Combustion Chamber (CC) 𝑚𝑚𝑎𝑎̇ 𝑐𝑐𝑝𝑝𝑎𝑎𝑇𝑇4 + �̇�𝑚𝑓𝑓𝐿𝐿𝐻𝐻𝐿𝐿 = 𝑚𝑚𝑔𝑔̇ 𝑐𝑐𝑝𝑝𝑔𝑔𝑇𝑇5 + �1 − 𝜂𝜂𝑐𝑐𝑐𝑐��̇�𝑚𝑓𝑓𝐿𝐿𝐻𝐻𝐿𝐿

Turbine (T1) 𝑇𝑇6 = 𝑇𝑇5 �1 − 𝜂𝜂𝑑𝑑 �1 − �

𝑃𝑃5

𝑃𝑃6�

1−𝛾𝛾𝑔𝑔𝛾𝛾𝑔𝑔 ��

𝑊𝑊𝑇𝑇1̇ = 𝑚𝑚𝑔𝑔̇ 𝑐𝑐𝑝𝑝𝑔𝑔(𝑇𝑇5 − 𝑇𝑇6)

ORC: Energy Balances

Vapor Generator (VG) 𝑚𝑚𝑔𝑔̇ 𝑐𝑐𝑝𝑝𝑔𝑔(𝑇𝑇6 − 𝑇𝑇18) = �̇�𝑚𝑂𝑂𝐶𝐶𝐶𝐶(ℎ10 − ℎ17) 𝑚𝑚𝑔𝑔̇ 𝑐𝑐𝑝𝑝𝑔𝑔(𝑇𝑇18 − 𝑇𝑇19) = �̇�𝑚𝑂𝑂𝐶𝐶𝐶𝐶(ℎ17 − ℎ16) 𝑚𝑚𝑔𝑔̇ 𝑐𝑐𝑝𝑝𝑔𝑔(𝑇𝑇19 − 𝑇𝑇7) = �̇�𝑚𝑂𝑂𝐶𝐶𝐶𝐶(ℎ15 − ℎ16)

ORC Turbine (T2) 𝑇𝑇11 = 𝑇𝑇10 �1 − 𝜂𝜂𝑑𝑑𝑂𝑂𝐶𝐶𝐶𝐶 �1 − �𝑃𝑃10

𝑃𝑃11�

1−𝛾𝛾𝑑𝑑𝛾𝛾𝑑𝑑 ��

17

�̇�𝑊𝑇𝑇𝑂𝑂𝐶𝐶𝐶𝐶 = �̇�𝑊𝑇𝑇2 = 𝑚𝑚𝑂𝑂𝐶𝐶𝐶𝐶̇ (ℎ10 − ℎ11) Recuperator (R) �̇�𝑚𝑂𝑂𝐶𝐶𝐶𝐶(ℎ11 − ℎ12) = �̇�𝑚𝑂𝑂𝐶𝐶𝐶𝐶(ℎ15 − ℎ14) Condenser (CD 1) �̇�𝑚𝑂𝑂𝐶𝐶𝐶𝐶(ℎ12 − ℎ13) = �̇�𝑚𝑤𝑤(ℎ21 − ℎ20) Pump (P1) �̇�𝑊𝑝𝑝𝑝𝑝𝑚𝑚𝑝𝑝 = �̇�𝑊𝑃𝑃1 = 𝑚𝑚𝑂𝑂𝐶𝐶𝐶𝐶̇ (ℎ14 − ℎ13)

Absorption Refrigeration: Mass, concentration and energy balances

Generator (G) �̇�𝑚25 = �̇�𝑚26 + �̇�𝑚29

�̇�𝑚25𝑒𝑒25 = �̇�𝑚26𝑒𝑒26 + �̇�𝑚29 �̇�𝑚25ℎ25 + �̇�𝑚7ℎ7 = �̇�𝑚26ℎ26 + �̇�𝑚29ℎ29 + �̇�𝑚33ℎ33

Heat exchanger (HX) 𝑇𝑇27 = 𝜖𝜖𝑇𝑇24 + (1 − 𝜖𝜖)𝑇𝑇26 �̇�𝑚24(ℎ25 − ℎ24) = �̇�𝑚26(ℎ26 − ℎ27)

Pump (P 2) �̇�𝑊𝑝𝑝𝑝𝑝𝑚𝑚𝑝𝑝,𝑟𝑟𝑒𝑒𝑓𝑓 = �̇�𝑊𝑃𝑃2 = 𝑚𝑚23̇ (ℎ24 − ℎ23) Throttle valve 1 (V1) ℎ27 = ℎ28 Absorber (ABS) �̇�𝑚32ℎ32 + �̇�𝑚34ℎ34 + �̇�𝑚28ℎ28 = �̇�𝑚23ℎ23 + �̇�𝑚35ℎ35 Evaporator (EV) �̇�𝑚31ℎ31 − �̇�𝑚32ℎ32 = �̇�𝑄𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑖𝑖𝑘𝑘𝑔𝑔 Throttle valve 2 (V2) ℎ30 = ℎ31 Condenser (CD 2) �̇�𝑚29ℎ29 + �̇�𝑚35ℎ35 = �̇�𝑚30ℎ30 + �̇�𝑚36ℎ36

2. Exergy Definitions and Balances

Exergy of a system is defined as the maximum theoretical useful work done by

the system to attain an equilibrium with the specified reference environment stated

by its temperature, pressure and chemical composition. Thus, the value of exergy can

at least be zero but cannot be negative. Exergy is a thermodynamic property

connecting both system and its environment. Second law of thermodynamics

explains the entropy generation due to irreversibility present in the system. Exergy

is an extensive property of the system, linked to second law and in combination with

the first law can help analyze energy system with a high accuracy. In an irreversible

18

process, exergy is always destroyed, and it is conserved only when all the processes

taking place between the system and surrounding are reversible. In this section, the

relations to calculate exergy for each component of the system are discussed.

a. Physical & Chemical Exergy Destruction Rates for Each Component of Cycle

Total exergy of a system is comprised of physical exergy, kinetic exergy,

potential exergy and chemical exergy [29],

𝐸𝐸𝑒𝑒 = 𝐸𝐸𝑒𝑒𝑝𝑝ℎ + 𝐸𝐸𝑒𝑒𝑘𝑘𝑘𝑘 + 𝐸𝐸𝑒𝑒𝑝𝑝𝑝𝑝 + 𝐸𝐸𝑒𝑒𝑐𝑐ℎ (1)

Kinetic exergy and potential exergy in most cases can be neglected so that total

exergy becomes combination of physical exergy and chemical exergy. Specific

physical exergy for a 𝑗𝑗𝑝𝑝ℎstate can be expressed as [30],

𝑒𝑒𝑒𝑒𝑝𝑝ℎ,𝑗𝑗 = �ℎ𝑗𝑗 − ℎ0� - 𝑇𝑇0�𝑠𝑠𝑗𝑗 − 𝑠𝑠0� (2)

where T0 and P0 represent the temperature and pressure of the reference environment

state. Specific chemical exergy can be written as [31]:

𝑒𝑒𝑒𝑒𝑐𝑐ℎ = ��𝑒𝑒

𝑀𝑀𝑁𝑁𝑁𝑁3� 𝑒𝑒𝑐𝑐ℎ,𝑁𝑁𝑁𝑁3

0 + �1 − 𝑒𝑒𝑀𝑀𝑁𝑁2𝑜𝑜

� 𝑒𝑒𝑐𝑐ℎ,𝑁𝑁2𝑜𝑜0 � (3)

where M, x and 𝑒𝑒𝑐𝑐ℎ0 represent molar mass, the ammonia concentration in ammonia-

water mixture and standard specific chemical exergy, respectively. The standard

specific chemical exergy for ammonia and water are 336.5 kJ/mol and 0.045

kJ/mol, respectively [32]. Specific exergy of gaseous fuel can be calculated by [15],

19

𝑒𝑒𝑒𝑒𝑓𝑓 = 1.06 ∗ 𝐿𝐿𝐻𝐻𝐿𝐿 (4)

The most general form of exergy rate balance for a stream entering and exiting a

control volume (C.V) is given by equation 5: time rate of change in exergy of the

control volume is equal to the rates of exergy transfers taking place across the CV

boundaries plus the rate of exergy destruction [8]:

𝑑𝑑𝐸𝐸𝑒𝑒𝐶𝐶𝐶𝐶𝐷𝐷𝑑𝑑

= ��1 −𝑇𝑇0𝑇𝑇𝑗𝑗� �̇�𝑄𝑗𝑗

𝑗𝑗

− ��̇�𝑊𝐶𝐶𝐶𝐶 − 𝑃𝑃0𝑑𝑑𝐿𝐿𝐶𝐶𝐶𝐶𝐷𝐷𝑑𝑑

� + ��̇�𝑚𝑖𝑖𝑒𝑒𝑒𝑒𝑖𝑖𝑖𝑖

−��̇�𝑚𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 𝑒𝑒

− 𝐸𝐸�̇�𝑒𝐷𝐷

(5)

where subscripts i and e stand for an inlet and an outlet of the CV. For steady state,

equation (5) can be expressed as,

0 = ��1 −𝑇𝑇0𝑇𝑇𝑗𝑗� �̇�𝑄𝑗𝑗

𝑗𝑗

− �̇�𝑊𝐶𝐶𝐶𝐶 + ��̇�𝑚𝑖𝑖𝑒𝑒𝑒𝑒𝑖𝑖𝑖𝑖

−��̇�𝑚𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒

− �̇�𝐸𝑒𝑒𝐷𝐷 (6)

In terms of total exergy rates equation (6) becomes,

0 = ��̇�𝐸𝑒𝑒𝑞𝑞,𝑗𝑗𝑗𝑗

− �̇�𝑊𝐶𝐶𝐶𝐶 + ��̇�𝐸𝑒𝑒𝑖𝑖𝑖𝑖

−��̇�𝐸𝑒𝑒𝑒𝑒𝑒𝑒

− �̇�𝐸𝑒𝑒𝐷𝐷 (7)

�̇�𝐸𝑒𝑒𝑞𝑞,𝑗𝑗 is the exergy transfer rate for the associated rate of heat transfer �̇�𝑄𝑗𝑗 at the

location on the boundary with instantaneous temperature 𝑇𝑇𝑗𝑗. Exergy destruction rates

can be calculated for each component of the system using equation (8). Equations

(9) – (12) represent exergy destruction rates for the gas turbine Brayton cycle

20

components, compressors, intercooler, combustion chamber and turbine

respectively.

0 = ��1 −𝑇𝑇0𝑇𝑇𝑗𝑗� �̇�𝑄𝑗𝑗

𝑗𝑗

− �̇�𝑊𝐶𝐶𝐶𝐶 + ��̇�𝑚𝑖𝑖𝑒𝑒𝑒𝑒𝑖𝑖𝑖𝑖

−��̇�𝑚𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒

− �̇�𝐸𝑒𝑒𝐷𝐷 (8)

�̇�𝐸𝑒𝑒𝐷𝐷,𝐶𝐶1 = �̇�𝑊𝐶𝐶1 + �̇�𝐸𝑒𝑒1 − �̇�𝐸𝑒𝑒2

�̇�𝐸𝑒𝑒𝐷𝐷,𝐶𝐶2 = �̇�𝑊𝐶𝐶2 + �̇�𝐸𝑒𝑒3 − �̇�𝐸𝑒𝑒4 (9)

�̇�𝐸𝑒𝑒𝐷𝐷,𝐼𝐼𝑁𝑁 = �̇�𝐸𝑒𝑒2 + �̇�𝐸𝑒𝑒8 − �̇�𝐸𝑒𝑒1 − �̇�𝐸𝑒𝑒9 (10)

�̇�𝐸𝑒𝑒𝐷𝐷,𝐶𝐶𝐶𝐶 = �̇�𝐸𝑒𝑒4 + �̇�𝐸𝑒𝑒𝑓𝑓 − �̇�𝐸𝑒𝑒5 (11)

�̇�𝐸𝑒𝑒𝐷𝐷,𝑇𝑇1 = �̇�𝐸𝑒𝑒5 − �̇�𝐸𝑒𝑒6 − �̇�𝑊𝑇𝑇1 (12)

For Organic Rankine cycle, exergy destruction rates are calculated in similar fashion.

Equations (13) - (17) represent exergy destruction rates of the components of ORC.

�̇�𝐸𝑒𝑒𝐷𝐷,𝐶𝐶𝑉𝑉 = �̇�𝐸𝑒𝑒6 + �̇�𝐸𝑒𝑒15 − �̇�𝐸𝑒𝑒7 − �̇�𝐸𝑒𝑒10 (13)

�̇�𝐸𝑒𝑒𝐷𝐷,𝑇𝑇2 = �̇�𝐸𝑒𝑒10 − �̇�𝐸𝑒𝑒11 − �̇�𝑊𝑇𝑇2 (14)

�̇�𝐸𝑒𝑒𝐷𝐷,𝑅𝑅 = �̇�𝐸𝑒𝑒11 + �̇�𝐸𝑒𝑒14 − �̇�𝐸𝑒𝑒12 − �̇�𝐸𝑒𝑒15 (15)

�̇�𝐸𝑒𝑒𝐷𝐷,𝐶𝐶𝐷𝐷1 = �̇�𝐸𝑒𝑒12 + �̇�𝐸𝑒𝑒20 − �̇�𝐸𝑒𝑒13 − �̇�𝐸𝑒𝑒21 (16)

21

�̇�𝐸𝑒𝑒𝐷𝐷,𝑃𝑃1 = �̇�𝑊𝑃𝑃1 + �̇�𝐸𝑒𝑒13 − �̇�𝐸𝑒𝑒14 (17)

Exergy destruction rates for the binary Ammonia- Water fluid absorption

refrigeration cycle can also be obtained implementing fundamental equations 2 and2

23. Exergy destruction rates for the generator and absorber are given by equations

(18) and (19),

�̇�𝐸𝑒𝑒𝐷𝐷,𝑉𝑉 = �̇�𝐸𝑒𝑒7 + �̇�𝐸𝑒𝑒25 − �̇�𝐸𝑒𝑒33 − �̇�𝐸𝑒𝑒26 − �̇�𝐸𝑒𝑒29

𝑐𝑐𝑟𝑟

�̇�𝐸𝑒𝑒𝐷𝐷,𝑉𝑉 = �1 − 𝑇𝑇0𝑇𝑇𝑔𝑔� �̇�𝑄𝑔𝑔𝑒𝑒𝑘𝑘 + �̇�𝐸𝑒𝑒25 − �̇�𝐸𝑒𝑒26 − �̇�𝐸𝑒𝑒29

(18)

�̇�𝐸𝑒𝑒𝐷𝐷,𝐴𝐴𝐴𝐴𝐴𝐴 = �̇�𝐸𝑒𝑒32 + �̇�𝐸𝑒𝑒34 + �̇�𝐸𝑒𝑒28 − �̇�𝐸𝑒𝑒23 − �̇�𝐸𝑒𝑒35

𝑐𝑐𝑟𝑟

�̇�𝐸𝑒𝑒𝐷𝐷,𝐴𝐴𝐴𝐴𝐴𝐴 = �̇�𝐸𝑒𝑒32 + �̇�𝐸𝑒𝑒28 − �̇�𝐸𝑒𝑒23 − �̇�𝑄𝑎𝑎𝑎𝑎𝑎𝑎 �𝑇𝑇0𝑇𝑇𝑔𝑔− 1�

(19)

The exergy rate balances across heat exchanger, condenser and yields following

exergy destruction rates across respective components,

�̇�𝐸𝑒𝑒𝐷𝐷,𝑁𝑁𝐻𝐻 = �̇�𝐸𝑒𝑒26 + �̇�𝐸𝑒𝑒24 − �̇�𝐸𝑒𝑒27 − �̇�𝐸𝑒𝑒25 (20)

�̇�𝐸𝑒𝑒𝐷𝐷,𝐶𝐶𝐷𝐷2 = �̇�𝐸𝑒𝑒29 + �̇�𝐸𝑒𝑒35 − �̇�𝐸𝑒𝑒30 − �̇�𝐸𝑒𝑒36 (21)

Exergy destruction rates for pump and throttle valves of the refrigeration cycle are

given by equations (22) and (23) respectively.

22

�̇�𝐸𝑒𝑒𝐷𝐷,𝑃𝑃2 = �̇�𝑊𝑃𝑃2 + �̇�𝐸𝑒𝑒23 − �̇�𝐸𝑒𝑒24 (22)

�̇�𝐸𝑒𝑒𝐷𝐷,𝐶𝐶1 = �̇�𝐸𝑒𝑒27 − �̇�𝐸𝑒𝑒28

�̇�𝐸𝑒𝑒𝐷𝐷,𝐶𝐶2 = �̇�𝐸𝑒𝑒30 − �̇�𝐸𝑒𝑒31

(23)

3. 2nd Law Efficiency

Efficiency is a measure that considers the resource utilization. Efficiency calculated

using exergy terms provide a measure of an approach to an ideal or theoretical upper

limit [32]. Second law efficiency or exergy efficiency for the multi-generation

system considered can be given by the following equation,

𝜂𝜂𝑒𝑒𝑒𝑒 = �̇�𝑊𝑘𝑘𝑒𝑒𝑝𝑝 + ��1 − 𝑇𝑇0

𝑇𝑇𝑒𝑒� �̇�𝑄𝑒𝑒�+ ��̇�𝐸𝑒𝑒9 − �̇�𝐸𝑒𝑒8� + ��1 − 𝑇𝑇0

𝑇𝑇𝑔𝑔� �̇�𝑄𝑔𝑔𝑒𝑒𝑘𝑘�

�̇�𝐸𝑒𝑒𝑓𝑓 (24)

4. Properties of Working Fluids

Thermodynamic properties of Air, combustion gases, organic fluid namely

Toluene and ammonia-water solution are obtained using REFPROP [33], a database

developed by NIST for the thermodynamic and transport properties of fluids.

23

5. Validation of Working Model

To validate the model developed, Table 3 shows comparison between

simulations generated data with the data present in the literature. Each of the three

sub-systems is compared separately.

Brayton cycle and Organic Rankine cycle is compared with the data

presented in References [34] and [21] respectively with very little deviation. Da-

Wen Sun compared the performances of absorption refrigeration systems [35]

and presented the optimum design maps for such systems [36]. The model in the

Table 3: COMPARISON BETWEEN OBTAINED RESULTS AND DATA IN LITERATURE [34], [21] AND [36]

Cycle Comparison Parameter

Present Study

Reference Error (%)

BC

Required compressor power for unit 1 (MW) [34]

162.12 162.17 0.03

Net power output for unit 1 (MW) [34] 115.43 115.49 0.05

OR

C

Economizer inlet temp (C) [30] 180.24 180.26 0.01

Mass flow rate (kg/s) [30] 0.0354 0.0360 1.53

ORC net power output (kW) [30] 7.143 7.161 0.25

Ref

riger

atio

n COP [35] 0.70 0.71 1.41

Evaporator load (kW) [35] 18.75 18.59 0.74

24

present study determined a COP of 0.70 which is very close to 0.71 value that

was obtained by Sun.

It should be noted that for the simulation the values of overall heat transfer

coefficient for the heat exchangers are considered as shown in Table 4. MATLAB

model comprising isentropic relations and energy balances are utilized to

evaluate the Brayton cycle component state points and loads. Mass and energy

balances across vapor generator gives the mass flow rate of organic fluid in the

ORC. Ammonia-water refrigeration cycle operates on the exhaust gas heat

content imparted to the generator. Based on the operating temperatures of

generator, absorber, condenser, evaporator and generator load, the two operating

pressures are calculated first. Unknown weak solution concentration is then

calculated using the algorithm described in reference [37] .

A separate algorithm is implemented to evaluate the rest of the states of

ammonia- water cycle. An initial guess is made for the generator inlet

temperature 𝑇𝑇25 and strong solution concentration is evaluated in the same way

as for weak solution concentration. Mass, concentration and energy balance

Table 4: OVERALL HEAT TRANSFER COEFFICIENT VALUES USED IN THE ANALYSIS [48]

Components 𝑼𝑼 (𝑾𝑾/𝒎𝒎𝟐𝟐𝑲𝑲) Intercooler 30 Vapor Generator 65 Recuperator 200 Heat exchanger (ref) 200 Absorber 500

25

across the generator yields the mass flow rates in the cycle. Temperature 𝑇𝑇27 is

obtained using heat exchanger effectiveness relation. Finally, the equality of

energy balance across the heat exchanger is compared to confirm the assumed

generator inlet temperature otherwise 𝑇𝑇25 is adjusted until the equality achieved

under sufficiently acceptable limit. Once all the state points are obtained, the

system then undergoes Exergetic and Exergoeconomic analysis. Table 7 that

appears in the later section lists the thermodynamic properties and mass flow

rates of all the stream points present in the entire cycle.

26

Chapter 4 Economic Analysis

Thermoeconomics is an engineering branch that combines thermodynamic

analysis and economic principles of a system to provide a clear picture of not only

energy aspects but also cost of the system. When the thermodynamic aspect is given

by an exergy analysis, it becomes exergoeconomic analysis which provides a very

powerful tool for the study and optimization of energy systems and thermodynamic

cycles. The type and amounts of actual exergy destruction and exergy losses are

determined in the exergy analysis. Economic analysis allows calculating the share of

the cost associated with exergy insufficiencies in the total cost of the system under

consideration. Individual cost related to every component of a system can be

analyzed, and the system can be optimized to reduce the total cost. Thermoeconomic

analysis also helps to understand cost formation process and flow of costs in the

system.

The main goal of this study is to evaluate cost of exergy destruction and losses

in each individual component of the system as well as for the complete system.

1. SPECO Approach

SPECO approach in evaluating Exergoeconomics is explained in [8], [18], [38], [39],

[40]. Lazzaretto and Tsatsaronis [41] proposed general methodology for defining and

27

calculating exergic efficiencies and exergic costing called, Specific Exergy Costing

(SPECO) in details. SPECO approach is mainly composed of three steps,

a. Identification of Exergy Streams

Exergy flows of the system under consideration need to be determined properly.

Combining several components into one and taking exergy changes across the bunch

can lead to a deviated result than real. Bejan et al. [8] explained the importance of

taking account of all individual components and not aggregating them together. In

an aggregated system, important information related to the actual production process

may differ and hence an actual quality of cost formation process within the system

may be misleading.

b. Defining Fuel (F) and Product (P) For Each Component

The product of any component contains the exergy at the outlets, exergy of

energy generated in the component and exergy of the actual purpose of component

[41]. Similarly, the fuel contains exergy supplied at the inlets, exergy removal from

the material stream and exergy addition to the stream for not intended by the

component [42].

c. Cost equations

Developing the cost balance equations for each component of the system. Also,

for the heat input and the work extracted from the system, evaluating their respective

cost rates can enable users to analyze the overall and individual component cost in

28

the complete system. For each component of the cogeneration cycles, the cost

equation or cost flow rate ($/𝑠𝑠) balance is written using equation (24) [31],

��̇�𝐶𝑒𝑒,𝑗𝑗𝑒𝑒

+ �̇�𝐶𝑤𝑤,𝑗𝑗 = �̇�𝐶𝑞𝑞,𝑗𝑗 + ��̇�𝐶𝑖𝑖,𝑗𝑗𝑖𝑖

+ �̇�𝑍𝑗𝑗 (25)

where �̇�𝑍𝑗𝑗 is the capital investment cost rate of 𝑗𝑗𝑝𝑝ℎ component. �̇�𝐶𝑤𝑤 and �̇�𝐶𝑞𝑞 are the cost

rates associated with the work and heat transfer respectively. 𝑖𝑖 and 𝑒𝑒 represent usual

inlet and outlet flows. Capital investment cost rate is connected to capital investment

cost, 𝑍𝑍𝑗𝑗, via following equation [30],

�̇�𝑍𝑗𝑗 = 𝑍𝑍𝑗𝑗 ∗ 𝐶𝐶𝐶𝐶𝐶𝐶 ∗ 𝜙𝜙𝑁𝑁 ∗ 3600

(26)

where 𝜙𝜙 and 𝑁𝑁 are the maintenance factor and number of operational hours per year

respectively. Values of Capital recovery factor [31] is given by equation (26) in

which 𝑖𝑖 and 𝑘𝑘 are the interest rate and lifetime of the system in years respectively.

1.06, 7446, 1.06 and 20 are the numerical values used in the analysis for 𝜙𝜙, 𝑁𝑁, 𝑖𝑖 and

𝑘𝑘 respectively.

𝐶𝐶𝐶𝐶𝐶𝐶 = 𝑖𝑖(1 + 𝑖𝑖)𝑘𝑘

(1 + 𝑖𝑖)𝑘𝑘 − 1 (27)

Cost flow rate of each component is connected to exergy rate and unit cost of exergy

𝑐𝑐 using the following equation,

�̇�𝐶𝑗𝑗 = 𝑐𝑐𝑗𝑗 �̇�𝐸𝑒𝑒𝑗𝑗 (28)

29

To evaluate exergoeconomic parameters in each component, we must solve all the

cost balance equations. In order to solve such equations, auxiliary equations are

formed for each component. Table 5 is the essence of economic analysis that entails

the system of equations composing cost balances and auxiliary equations. The goal

here is to find cost flow rates matrix��̇�𝐶𝑗𝑗�. This system of equation can be represented

by following matrix equation,

�𝐶𝐶𝑓𝑓𝑓𝑓� ∗ ��̇�𝐶𝑗𝑗� = [𝐶𝐶𝐻𝐻𝑅𝑅] (29)

�𝐶𝐶𝑓𝑓𝑓𝑓� = Green text [39×39] coefficient matrix present in Table 5.

[𝐶𝐶𝐻𝐻𝑅𝑅] = Blue text [39×1] matrix present in Table 5.

��̇�𝐶𝑗𝑗�𝑇𝑇= Red text [1×39] matrix present in Table 5.

In Table 5,

C_ (…) represents cost flow rates at numbered state/component;

W_ (…) represents work on/by a component;

Z_ (…) represents capital investment cost rate of a component;

X (…) represents exergy at numbered state.

Parameters such as exergoeconomic factor (𝑓𝑓𝑗𝑗 ), exergy destruction cost rate

( �̇�𝐶𝐷𝐷,𝑗𝑗 ) are evaluated to obtain the performance of the cogeneration system.

Exergoeconomic factor shows relative importance of capital cost rate of the

component to the exergy destruction cost rate of that component.

30

𝑓𝑓𝑗𝑗 = �̇�𝑍𝑗𝑗

�̇�𝑍𝑗𝑗 + �̇�𝐶𝐷𝐷,𝑗𝑗 + �̇�𝐶𝐿𝐿,𝑗𝑗 (30)

�̇�𝐶𝐷𝐷,𝑗𝑗 = 𝑐𝑐𝐹𝐹,𝑗𝑗 �̇�𝐸𝑒𝑒𝐷𝐷,𝑗𝑗 (31)

where 𝑐𝑐𝐹𝐹,𝑗𝑗 is the average unit cost of fuel exergy.

2. Energy specific costing

Exergy related costing has been discussed in earlier section. In general costing is

based on energy terms. To compare the performance of simulated system with an

existing plant, the comparison can be made in terms of dollars per kW-h.

Considering the fact that the system under consideration is a tri-generation

system (electricity, cooling and heating), in order to provide a clear picture of the

system energy value, the output hot water and cooling effect are also converted to

equivalent electrical power. In other words, the amount of electricity that will be used

to produce hot water and cooling effect through conventional systems is evaluated.

For the system under consideration, the total power in produced in terms of

electrical power is given by,

�̇�𝑊𝑒𝑒𝑒𝑒𝑒𝑒𝑐𝑐𝑝𝑝𝑒𝑒𝑖𝑖𝑐𝑐 = �̇�𝑊𝑘𝑘𝑒𝑒𝑝𝑝 + �̇�𝑄𝑐𝑐𝑜𝑜𝑜𝑜𝑒𝑒𝑖𝑖𝑘𝑘𝑔𝑔𝐶𝐶𝑂𝑂𝑃𝑃𝑒𝑒𝑒𝑒𝑓𝑓

+�̇�𝑄ℎ𝑜𝑜𝑝𝑝 𝑤𝑤𝑎𝑎𝑝𝑝𝑒𝑒𝑒𝑒

𝜂𝜂ℎ𝑒𝑒𝑎𝑎𝑝𝑝𝑒𝑒𝑒𝑒 (32)

𝐶𝐶𝑂𝑂𝑃𝑃𝑒𝑒𝑒𝑒𝑓𝑓 is taken to be 3 and efficiency of water heater (𝜂𝜂ℎ𝑒𝑒𝑎𝑎𝑝𝑝𝑒𝑒𝑒𝑒) is taken high as 90%.

The energy based cost (EBC) becomes,

31

𝐸𝐸𝐸𝐸𝐶𝐶 ($/𝑘𝑘𝑊𝑊ℎ) =𝑇𝑇𝑐𝑐𝑑𝑑𝑎𝑎𝑐𝑐 𝑐𝑐𝑐𝑐𝑠𝑠𝑑𝑑 𝑐𝑐𝑓𝑓 𝑠𝑠𝑠𝑠𝑠𝑠𝑑𝑑𝑒𝑒𝑚𝑚 ($/ℎ)

�̇�𝑊𝑒𝑒𝑒𝑒𝑒𝑒𝑐𝑐𝑝𝑝𝑒𝑒𝑖𝑖𝑐𝑐 (𝑘𝑘𝑊𝑊) (33)

32

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33

Chapter 5 System Optimization

Modeling a system with particular requirements is always a primary step in any

design process. When the system is ready, the next step is to optimize the system

parameters for the desired outcomes otherwise experimenting to find the desired

operating point may become expensive.

1. Optimization algorithm

The system model consists of multiple variables that are bounded in given ranges

and multiple non-linear objective functions. These factors necessitate the use of

evolutionary algorithms, such as Genetic Algorithm, as an effective tool for

optimizing the cycle. Genetic algorithm has been successfully used in the

optimization of several thermodynamic cycles particularly CCHP configurations that

have been discussed in Chapter 1. Few researchers converted multiple objectives into

single using weighted functions and then evaluated the system as a single objective

optimization.

Genetic algorithm (GA) is a bio-inspired algorithm which replicates the natural

selection process. The basic structure of GA can be seen in Figure 2. Selection is

contribution of individuals (parents) to the population at the next generation.

Selection determines the individual that are chosen for mating/recombination and

34

number of offspring each selected individual produces. In crossover step,

recombination produces new individuals i.e., two parents are combined to form

children for the next generation. Mutation is the step that makes random changes to

the individual parents to form children. Over successive generations, weak children

are dropped to evolve a global optimal solution.

Figure 2: GENERAL STRUCTURE OF GENETIC ALGORITHM [43]

2. Objective functions

The first law efficiency/energy efficiency and total cost of the system are

considered as objective functions for the optimization study. The goal is to maximize

the first law efficiency and minimize the total cost of the system.

Objective(1) = 100 ×�̇�𝑊𝑘𝑘𝑒𝑒𝑝𝑝 + �̇�𝑄𝑐𝑐𝑜𝑜𝑜𝑜𝑒𝑒𝑖𝑖𝑘𝑘𝑔𝑔 + �̇�𝑄ℎ𝑜𝑜𝑝𝑝 𝑤𝑤𝑎𝑎𝑝𝑝𝑒𝑒𝑒𝑒 + �̇�𝑄𝑔𝑔𝑒𝑒𝑘𝑘

�̇�𝑚𝑓𝑓 𝐿𝐿𝐻𝐻𝐿𝐿 (34)

35

Objective(2) = �̇�𝐶𝐷𝐷𝑗𝑗,𝑎𝑎𝑠𝑠𝑠𝑠 + �̇�𝑍𝑗𝑗,𝑎𝑎𝑠𝑠𝑠𝑠 (35)

Objective (1) is to be maximized and objective (2) is to be minimized.

3. Decision variables

The main parameters/ variables under observation and their corresponding ranges

are listed in Table 6. GA chooses the optimal value for each of these parameters

within the given ranges.

Table 6: OPTIMIZATION VARIABLES AND THEIR RANGE

Parameter/ Variable Range Unit

Total pressure ratio of BC (𝐶𝐶𝑝𝑝) {7-11} Bar

TIT of BC {780-850} C

TIT of ORC {320-360} C

Turbine inlet pressure of ORC {2-2.8} Bar

ORC pinch temperature {8-14} C

Generator temperature (𝑇𝑇𝑔𝑔) {80-100} C

Evaporator temperature (𝑇𝑇𝑒𝑒) {1-6} C

Effectiveness of HX (ref) {70-90} %

The result of this multi-objective optimization is a plot called ‘Pareto-front’ that

gives a set of optimal solutions. Each data set in the pareto-front is an optimized

value of the corresponding objective function. Each optimized set is a trade-off

36

between the plant energy efficiency and the total cost rate of the plant. Based on the

interest, designer/user can choose the corresponding operating point.

37

Chapter 6 Simulation Results and Discussion

1. System Performance

Ambient air is assumed to behave as an ideal gas and its composition is taken as

[34],

𝑁𝑁2 = 77.6812%, 𝑂𝑂2 = 20.8395%, 𝐴𝐴𝑟𝑟 = 0.9292%, 𝐶𝐶𝑂𝑂2 = 0.0312%, and

𝐻𝐻2𝑂𝑂 =0.5159%

The reaction of Natural gas and air in combustion chamber results in combustion/

flue gases that have molar concentrations mentioned in [44]. The inlet temperature

of second compressor 𝑇𝑇3 is set to 40 𝐶𝐶𝑜𝑜 so as to quantify the daily hot water

production rate. Also, the extreme exit of the flue gases, stream 33, is fixed to have

temperature of 50 𝐶𝐶𝑜𝑜. In order to proceed for the economic analysis, areas of various

components have been calculated using log-mean temperature difference (LMTD)

method and for that suitable overall heat transfer coefficients used are listed in Table

4. To calculate area of evaporator, its effectiveness is taken as 0.9. For the sake of

simplicity economizer, evaporator and superheater in the ORC is collectively taken

as Vapor Generator (VG) and are not evaluated separately.

38

Table 7: THERMODYNAMIC PROPERTIES OF ALL THE STREAMS

# Fluid P (bar)

T (C)

�̇�𝒎 (kg/s) 𝒉𝒉 (kJ/kg) 𝒔𝒔

(kJ/kg K) �̇�𝑿 (kW)

1 Air 0.101 25.0 0.1 305.75 6.87 0

2 Air 0.320 162.0 0.1 444.51 6.92 12.34

3 Air 0.317 40.0 0.1 320.44 6.59 9.82

4 Air 1.003 184.7 0.1 467.31 6.64 22.90

5 Flue gas 1.003 800.0 0.102 1277.22 7.50 66.16

6 Flue gas 0.105 389.9 0.102 798.23 7.61 13.99

7 Flue gas 0.102 217.9 0.102 610.51 7.28 4.96

8 Water 0.101 34.6 0.084 144.93 0.50 0.05

9 Water 0.101 70.0 0.084 293.12 0.96 1.08

10 Toluene 2.500 350.0 0.031 766.35 1.50 10.58

11 Toluene 0.010 227.9 0.031 560.46 1.60 3.21

12 Toluene 0.010 56.6 0.031 291.83 0.95 0.86

13 Toluene 0.010 45.3 0.031 -123.11 -0.35 0.03

14 Toluene 2.602 46.6 0.031 -118.73 -0.35 0.13

15 Toluene 2.576 180.2 0.031 149.91 0.35 2.02

16 Toluene 2.550 279.9 0.031 404.56 0.86 -

17 Toluene 2.525 279.8 0.031 588.25 1.19 -

18 Flue gas 0.104 340.9 0.102 743.99 7.51 -

19 Flue gas 0.103 289.8 0.102 688.05 7.42 -

20 Water 0.101 25.0 0.308 104.92 0.37 0

21 Water 0.101 35.0 0.308 146.72 0.51 0.21

22 Toluene 0.010 45.3 0.031 -123.11 -0.35 0.03

23 𝑁𝑁𝐻𝐻3 − 𝐻𝐻2𝑂𝑂 0.471 20.0 0.028 152.83 1.28 379.61

39

24 𝑁𝑁𝐻𝐻3 − 𝐻𝐻2𝑂𝑂 1.555 31.8 0.028 155.59 1.28 379.69

25 𝑁𝑁𝐻𝐻3 − 𝐻𝐻2𝑂𝑂 1.555 58.2 0.028 293.21 1.71 379.93

26 𝑁𝑁𝐻𝐻3 − 𝐻𝐻2𝑂𝑂 1.555 90.0 0.016 320.46 1.74 144.52

27 𝑁𝑁𝐻𝐻3 − 𝐻𝐻2𝑂𝑂 1.555 43.4 0.016 87.28 1.06 144.02

28 𝑁𝑁𝐻𝐻3 − 𝐻𝐻2𝑂𝑂 0.471 43.6 0.016 87.28 1.06 144

29 Ammonia 1.555 90.0 0.012 1784.75 6.08 4.62

30 Ammonia 1.555 40.0 0.012 536.12 2.13 3.80

31 Ammonia 0.471 2.5 0.012 536.12 2.17 3.64

32 Ammonia 0.471 2.5 0.012 1610.09 6.07 2.6

33 Flue gas 0.101 50.0 0.102 433.22 6.84 0.22

34 Water 0.101 25.0 0.769 104.92 0.37 0

35 Water 0.101 30.0 0.769 125.82 0.44 0.13

36 Water 0.101 34.6 0.769 144.93 0.50 0.49

40

The simulation results, i.e., overall system performance can be seen in Table 8.

Operating on same pressure ratios, C2 requires 0.81 𝑘𝑘𝑊𝑊 more power than C1 due to

increase in the specific volume of the compressed air. The Brayton cycle gas turbine

Table 8. TOTAL PERFORMANCE OF THE CCHP SYSTEM Parameter Value Units

Power consumed by C1 13.88 𝑘𝑘𝑊𝑊

Power consumed by C2 14.69 𝑘𝑘𝑊𝑊

Power generated by T1 48.8 𝑘𝑘𝑊𝑊

Power generated by T2 6.39 𝑘𝑘𝑊𝑊

Power consumed by P1 0.14 𝑘𝑘𝑊𝑊

Power consumed by P2 0.07 𝑘𝑘𝑊𝑊

Net power output of system 26.42 𝑘𝑘𝑊𝑊

Cooling Capacity of the plant 12.66 𝑘𝑘𝑊𝑊

Hot water production 7.22 Ton/day

COP 0.70

Energy Efficiency of system 77.14 %

ECOP 0.31

Exergy efficiency of the system 33.19 %

Total exergy destruction rate of the system 529.89 𝑘𝑘𝑊𝑊

Cost per unit exergy of useful products 9.6 $/𝑀𝑀𝑀𝑀

Energy based cost of useful products 2.14 $/kW-h

Summation of capital investment cost rates

and cost rates associated with the exergy

destruction of all components of the system

95.58

$/ℎ𝑟𝑟

41

delivers 48.8 𝑘𝑘𝑊𝑊 power. It is augmented by 6.38 𝑘𝑘𝑊𝑊 of power produced in ORC

turbine. Subtracting the power required by compressors and pumps, the net power

obtained from the whole CCHP system is about 26.42 𝑘𝑘𝑊𝑊. Ammonia-water

absorption cycle produced 12.66 𝑘𝑘𝑊𝑊 of cooling power. The system can also produce

7.22 𝑑𝑑𝑐𝑐𝑘𝑘𝑠𝑠 𝑑𝑑𝑎𝑎𝑠𝑠⁄ of 70 𝐶𝐶𝑜𝑜 hot water as an intentional by-product.

The COP of the refrigeration system is obtained as 0.70 and the energy efficiency

of the whole system is 77.14% which is substantial for a big system. From the exergic

perspective, the ECOP of chiller is 0.31 and corresponding exergy efficiency of the

plant is just 33.19%. This suggests there is a lot of scope in improving the exergic

and corresponding economic performance of the whole system.

Figure 3: EXERGY DESTRUCTION RATES FOR THE COMPONENTS OF BRAYTON CYCLE

42

2. Exergy Analysis Results

Figure 3, Figure 4 and Figure 5 show the actual exergy destroyed in the Organic

Rankine Cycle, Brayton cycle and absorption cycle respectively. Owing to the fact

with the simulation initial data assumed, calculated mass flow rate of the fuel is

0.0019 𝐾𝐾𝑔𝑔 𝑠𝑠⁄ which in turn gives low fuel exergy and hence low exergy destruction

rate in the combustion chamber, accounts for only 9.85 % of the total exergy

destruction rates of all components of the system which is 529.89 𝑘𝑘𝑊𝑊. On the other

hand, the share of exergy destruction rate of combustion chamber is 87.92% in the

total of Brayton cycle alone. The contributions of summation of exergy distribution

rates of ORC to the combined cycle is negligible. Refrigeration cycle component

exergies in total take up 88.42% of the total cycle component exergies.

Figure 4: EXERGY DESTRUCTION RATES FOR THE COMPONENTS OF ORGANIC RANKINE CYCLE

43

Comparatively higher mass flow rates and chemical exergies aid to this larger

contribution.

In refrigeration cycle, the rate at which exergies are destroyed at the generator

and at the absorber almost weigh same (49.86% and 49.58% respectively) in terms

of the percentage of total exergy destruction rate in the cycle.

Figure 5: EXERGY DESTRUCTION RATES IN THE COMPONENTS REFRIGERATION CYCLE (EXERGY DESTRUCTION RATE FOR

GENERATOR AND ABSORBER HERE ARE 233.54 KW AND 232.27 KW RESPECTIVELY)

44

3. Economic Analysis Results

a. Exergoeconomic results

Exergies of each stream point can be found in Table 7. Using this data and

component capital cost rates ( �̇�𝑍𝑗𝑗 ), cost flow rate equations and corresponding

auxiliary equations were obtained using relations described in [31], [45] and [46].

Using equation (27) unit cost of exergy for each stream was obtained. Capital

recovery factor calculated is 0.1175. For each component, exergy related to fuel and

to product were calculated. Unit cost of exergy related to fuel (𝑐𝑐𝐹𝐹,𝑗𝑗 ) for each

component is then related to exergy destruction cost rate (�̇�𝐶𝐷𝐷,𝑗𝑗) using equation (28).

Cost rate related to exergy destructions are listed in Table 9.

Exergy destruction cost rate for refrigeration heat exchanger and absorber are

amongst the highest values of 8.45 and 10.4 $/ℎ respectively. Very small values

present in the table can be neglected. While calculating the exergoeconomic factor,

cost rate related to losses ( �̇�𝐶𝐿𝐿,𝑗𝑗) have been fairly neglected by appropriately selecting

the system boundaries [47]. Exergoeconomic factor is lower for the components with

high exergy destruction rates.

45

Table 9: EXERGY AND EXERGOECONOMIC PARAMETERS FOR COMPONENTS OF THE SYSTEM

Components �̇�𝑬𝒙𝒙𝑫𝑫 (𝒌𝒌𝑾𝑾)

�̇�𝑪𝑫𝑫 ($/𝒉𝒉)

�̇�𝒁𝒋𝒋 ($/𝒉𝒉)

𝒇𝒇 (%)

GT:

Compressor 1 (C1) 1.538 0.062 0.0062 9.13

Intercooler (IN) 1.491 0.068 0.0042 5.86

Compressor 2 (C2) 0.795 0.032 0.0062 16.27

Combustion Chamber

(CC) 52.3 0.89 0.383 30.11

Turbine (T1) 3.36 0.122 0.0627 33.94

ORC:

Vapor Generator (VG) 0.47 0.017 0 1.77

ORC Turbine (T2) 0.98 0.041 0.241 85.35

Recuperator (R) 0.46 0.019 0 17.64

Condenser (CD1) 0.007 0.03 0.001 75.36

Pump (P1) 0.038 0.00 0.005 30.31

Absorption cycle:

Generator (G) 234.012 0.003 0.004 1.15

Heat exchanger (HX) 0.26 8.45 0.01 5.28

Pump (P2) 0 0.07 0.004 100

Throttle valve 1 (V1) 0.02 - - -

Absorber (ABS) 232.74 10.4 0.004 58.04

Evaporator (EV) 0.21 7.09 0.004 29.81

Throttle valve 2 (V2) 0.16 - - -

Condenser (CD2) 0.12 0.646 0 99.37

46

b. Energy Specific Results

With fixed parameters of system, we obtain 26.41 kW of net power output, 12.68

kW of evaporator cooling load and 12.41 kW of hot water load output. Based on the

analysis discussed in section Energy specific costing, total product power produced

in terms of electrical power comes out as 44.12 kW.

With the total system cost, based on exergy destruction cost rate and capital

investment cost rate, being $95.58/ℎ, The energy based cost (EBC) then becomes

$2.14/kWh.

4. Parametric Studies

A parametric study is performed to observe the effect of two individual

parameters including overall pressure ratio of Brayton cycle and turbine inlet

temperature (TIT) of ORC on the energy, exergy and economic performance of the

CCHP system.

Figure 6 shows the effect of overall pressure ratio on the generated power,

cooling and hot water production. Increase in pressure ratio increases the GT results

in reducing available energy to be passed to the next ORC and hence ORC mass flow

rate and in turn its power output decreases. This makes more energy available to the

generator of refrigeration cycle increasing the flow rates in cycle. This gives rise to

the greater cooling production and more hot water production that improves energy

efficiency. Exergy efficiency, ECOP are not affected much due to increase in exergy

47

related to generator heat load. Only 1.81% reduction is observed in exergy efficiency

when total pressure ratio increases from 7-11 bars.

Figure 6: EFFECT OF OVERALL PRESSURE RATIO OF BC ON ENERGY- EXERGY PERFORMANCE PARAMETERS

48

Figure 7 shows exergy destruction in generator increases with the increase in total

pressure ratio and the total exergy destruction cost rate increases by 25.02% when

pressure ratio rises from 7-11. This is mainly because of the increased exergy

Figure 7: EFFECT OF OVERALL PRESSURE RATIO OF BC ON EXERGY-ECONOMIC PERFORMANCE PARAMETERS

49

destruction cost rates in absorption cycle components. Also average cost per exergy

of product (net work + cooling + heating) decreases significantly due to increase in

the exergies related to hot water production and cooling.

Figure 8 shows the effect of turbine inlet temperature of the organic Rankine

cycle on power production, heating and cooling outputs also on the energy-exergy

efficiencies and corresponding refrigeration COP and ECOP. Increase in temperature

at the turbine inlet reduces the mass flow rate of the organic media and hence its

power output decreases. This gain outweighs the reduction in ORC net work output,

improving the energy efficiency of the system. Hot water production is also less as

the result of the lower absorber load. This reduces the exergy related to the water

heating and decrease in net work output reduces the balances the exergy related to

cooling hence ECOP and COP are almost maintained constant. Exergy efficiency of

the system reduces by 7.8% when TIT of ORC is increased from 325-355 C, this is

mainly due to exergy reduction of ORC power output and reduction of exergy related

to hot water production.

50

Figure 8: EFFECT OF TIT OF ORC ON ENERGY- EXERGY PERFORMANCE PARAMETERS

51

Figure 9 shows the effect of increasing TIT of ORC on the rates of exergy

destruction in the system and on to the average cost per exergy product. Exergy

destruction in CC is unaffected by any changes in ORC. Rate of exergy destroyed in

generator increases greatly because it directly increases fuel exergy in the generator.

Figure 9: EFFECT OF TIT OF ORC ON EXERGY-ECONOMIC PERFORMANCE PARAMETERS

52

This increment is about 61.9%. Steep rise is seen in the total exergy destruction cost

rate since exergy destruction rates in refrigeration cycle, mainly in absorber and

generator rises due to increase in their chemical exergies. Average cost per unit

exergy of products decreases owing to the increment in cooling exergy generation.

5. System Optimization Results

System optimization result in the form of a Pareto front as discussed in Chapter 4,

can be seen in Figure 10. Recall that in this study, objective (1) is energy efficiency

multiplied by a negative sign and objective (2) is the total cost to run the system.

Figure 10: PARETO FRONT OF THE MULTI-OBJECTIVE SYSTEM OPTIMIZATION

53

Since, in MATLAB, GA tries to minimize the objective function, and we needed

to maximize the energy efficiency, it had to be supplied as a negative objective

function. Thus, negation of minimizing would turn the objective function into

maximum. Therefore Objective (1) is – (Energy Efficiency).

Each point in the Pareto front represent an optimal solution to the problem.

Depending on the requirement, a trade-off between two objective function values

should be done to select the appropriate optimized operating parameters. A general

trend in Pareto front can be seen which suggests that achieving a greater energy

efficiency results in a higher cost rate for the system.

To discuss in-depth, the same Pareto front has been enlarged and re-structured in

Figure 11. The insets show X and Y as energy efficiency and corresponding total

cost in terms of rate for each selected (black squared) data set. The optimized points

“A” and “B” are selected for comparison. The optimized data set for point A has 54%

energy efficiency with the total plant cost rate of 19.38 $/hr whereas point B with

83.5% energy efficiency costs 96.16 $/hr. Shifting the operating point from A to B,

plant energy efficiency increases by 55% but the total plant cost rate increases hugely

by almost 400%. So, a clear trade-off is to be done between these two objectives and

then a particular operating point should be selected.

54

Figu

re 1

1: IN

DE

TA

IL P

AR

ET

O F

RO

NT

OF

TH

E S

YST

EM

WIT

H S

EL

EC

T P

OIN

TS

A A

ND

B

55

Table 10 enlists the optimized system variables for each operating points A and

B. The last column gives the values of variables considered for base case simulation.

Optimized values of variables are comparable. Increase in total cost rate from A to

B is mainly characterized by increment in total pressure ratio of BC and rise in

generator temperature.

Table 10: OPTIMIZED VARIABLES FOR DATA SET A AND B WITH VARIABLES USED IN BASE CASE

Optimized Variable Unit A B Base

Total pressure ratio of BC (𝐶𝐶𝑝𝑝) - 8.65 10.96 10

TIT of BC C 835.59 786.86 800

TIT of ORC C 321.00 354.27 350

Turbine inlet pressure of ORC Bar 27.5 27.1 25

ORC pinch temperature C 9.84 11.65 10

Generator temperature (𝑇𝑇𝑔𝑔) C 83.25 85.01 90

Evaporator temperature (𝑇𝑇𝑒𝑒) C 2.08 1.50 2.5

Effectiveness of HX (ref) % 77 71 80

56

Chapter 7 Conclusions

An energy, exergy and exergoeconomic analysis is conducted on a micro-CCHP

system. The cycle consists of Brayton cycle, organic Rankine cycle and absorption

refrigeration cycle. Exergy destruction through different components of the cycle are

evaluated and an economic analysis with an emphasis on calculating cost flow rates

related to exergy destruction and capital investment cost rates are performed. Authors

also conducted a parametric analyses to observe the effect of overall pressure ratio

of the Brayton cycle and turbine inlet temperature of ORC on the system’s overall

performance. Following conclusions can be made:

• With the selected design operating points, system energy efficiency and COP

of refrigeration were found to be 77% and 0.70 respectively. However, the

system suffers in terms of exergy efficiency and ECOP with just 33% and

0.31 in values respectively. Energy quality of the outcomes is small and

potential improvements should be considered.

• Components with high Exergy destruction rates such as generator and

absorber etc. must be assessed more closely for potential improvements.

• The total product energy based cost (EBC) is 2.14 $/kW-h

• Cost per unit exergy of useful products is 9.6 $/𝑀𝑀𝑀𝑀

57

• Total cost rate in terms of total exergy destruction cost rate and total initial

investment cost rates to operate the system was found as 95.58 $/hr.

• Exergoeconomic factor reduces with increase of component rate of exergy

destruction.

• Increase in total pressure ratio has minimal effect on exergy efficiency and

ECOP however, it does increase cooling, hot water production and energy

efficiency.

• Increase in total pressure ratio and TIT of ORC, both increase the average

cost of unit exergy product.

• Increment in optimized energy efficiency accompanies with greater

optimized total cost rate of the plant.

58

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