Title: Design, Simulation and Optimisation

University of Hertfordshire

MSc Project Report

Title:

Design, Simulation and Optimisation Of a Combined Power to Power and Heating (CPPH) Cycle

Author:

Bashar Dan-asabe

Pathway Point:

MSc Mechanical Engineering

Year:

2008/2009

Hand-in Date:

25th September 2009

Department of Aerospace, Automotive & Design Engineering Faculty of Engineering and Information Sciences

Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle

Abstract

This project entails the design, simulation and optimisation of a combined power to power and heating (CPPH) cycle involving a 3-stage gas turbine topping cycle and a dual-pressure steam turbine bottoming cycle. Series of practical power plants such as the Rankine cycle, Joule cycle, combined heat and power (CHP) cycle, combined cycle gas turbines (CCGT) were reviewed after intensive studies to come up with a realistic model as the CPPH plant. Relevant theoretical equations were derived, analysed and simulated using Microsoft excel spread. The optimised form of the CPPH was achieved at the topping cycle stage pressure ratio of 4 – 6 and at an optimum plant energy utilisation factor of 87% thus producing a net power and useful heat output of 82MW and 36MW respectively.

1st Print on 25th September, 2009: 2 copies printed and submitted to the university. 2nd Reprint on 9th October, 2009: Additional (personal) 2 copies printed.

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Acknowledgements

I am very pleased and happy to have come to this stage in earning a master’s degree in mechanical engineering at the University of Hertfordshire, United Kingdom. I owe this to the Almighty Allah for his infinite mercy and guidance. I also extend my gratitude to my supervisor the program tutor of Automotive Engineering, Dr Sami Nasser for his role in giving me the appropriate advice, courage and his unrelenting time towards the successful completion of my project. My gratitude also goes to the petroleum technology development fund (PTDF) of the Federal Republic of Nigeria for their scholarship award sponsorship and care given to me throughout the duration of my program.

Dedication

I dedicate this project to my beloved mother, Hajiya Rabi’at Sani ‘Ubandoman Zazzau’ (Mrs Dan-asabe Dahiru Tanko) who died on 7th October, 2009 after she performed an early morning prayer at the age of 45. I will miss her as my only confidant whom I share, seek and accept advices. I have grown up to learn a lot from her some of which are patience, perseverance and brevity. Allah ya jikanta, ya gafarta mata, yasa Aljanna Makoma ne a gareta. Allah yasa mai cetoce a ranar lahira.

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Table of Contents Abstract.......................................................................................ii Acknowledgements.....................................................................iii Dedication...................................................................................iii Glossary......................................................................................vi Nomenclature.............................................................................viii

1.0

Introduction.......................................................................10 1.1 Background...............................................................................10 1.2 Aims and objectives...................................................................11

2.0

Methodology......................................................................12

3.0

Literature survey................................................................13 3.1 Classification of CPPH..............................................................13 3.2 Some Examples of Practical CC...............................................19 3.3 Description of the basic component of a CC.............................26 3.4 Fuel types used in a CC............................................................29

3.0 Theoretical Consideration and Background.......................32 4.1 Joule-Brayton Cycle...................................................................32 4.2 Rankine Cycle............................................................................37 4.3 Combined Cycle.........................................................................43

5.0 Schematic Model of the CPPH............................................48 5.1 Schematic Model of the CPPH cycle and its T – S Diagram......49 5.2 Basic Assumptions of the CPPH plant.......................................50

6.0 Program Generation using Excel.........................................51 6.1 The implant Steam Table............................................................52

7.0 Analysis and Calculations....................................................54 Bashar Dan-asabe

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7.1 Theoretical Equation of the 3-Stage GT without Regeneration.54 7.2 Theoretical Equation of the 3-Stage GT with Regeneration.......57 7.3 Input data, Formulation and Computation in Microsoft Excel Spreadsheet................................................................................60

8.0 Optimisation.........................................................................67 8.1 Comparison of the Practical 3-stage cycle with the Ideal 3- stage Cycle...........................................................................................67 8.2 Optimisation of the GT cycle.......................................................68 8.3 Optimisation of the ST cycle.......................................................72 8.4 Optimisation of the CPPH...........................................................84

9.0 Conclusion...........................................................................80 References...........................................................................81

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Glossary

AC

Air Compressor

AOG

Aluminium of Greece combined cycle plant

B

Boiler

C

Condenser

CC

Combined Cycle

CCGT

Combined Cycle Gas Turbines

CFBC

Circulating Fluidised Bed Combustion

CHAT

Cascaded -humid air turbine

CHP

Combined Heat and Power

CO

Carbon monoxide

Comp.

Compressor

CPPH

Combined Power to Power and Heating

DA

Deaerator

EC

Economiser

Ex.

Exhaust

FWH

Feed Water Heater

GT

Gas Turbine

HAT

Humid Air Turbine

HP

High Pressure

HRSG

Heat Recovery Steam Generator

HT

Helium Turbine

IC

Intercooler

IGCC

Integrated Coal Gasification Combined Cycle

IP

Intermediate Pressure

Isen.

Isentropic

LP

Low Pressure

MCF

Molten carbonate fuel cells

MP

Medium Pressure

MPB

Medium Pressure Boiler

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle ORSG

Once Through Heat Recovery Boiler

P

Pump

PFBC

Pressurised Fluid Bed Combustion

R

Recuperator

Reg.

Regenerator/Regeneration

SH

Super Heater

SOFC

Solid Oxide Fuel Cell

ST

Steam Turbine

STD

Standard Temperature and Pressure

STIG

Steam Injected Gas Turbine

Temp.

Temperature

Turb.

Turbine

WT

Water Treatment Unit

1st Exhaust temperature

Exhaust gas temperature after expansion in GT cycle

2nd Exhaust temperature

Final Exhaust gas temperature after passing through the HRSG

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Nomenclature

Specific heat capacity of air at compressor unit in kJ/kgK Specific heat capacity of air at combustion chamber/turbine unit in kJ/kgK Combined cycle energy utilisation factor in % Combined cycle plant energy utilisation factor in % Useful rejected heat from the air compressors in kJ/kg Useful rejected heat from the condenser unit in kJ/kg Total useful rejected heat in kJ/kg Potential energy given in KJ Low calorific value of combustion fuel energy given in kJ/kg Generalised mass flow rate in kg/s Air mass flow rate in kg/s Mass flow rate of calorifiers for district heating in kg/s Mass flow rate of combustion fuel in kg/s Mass of cooling water going into the condenser in kg/s Mercury mass flow rate in kg/s Gas turbine cycle efficiency in % Steam turbine inlet pressure in kJ Extraction pressure in kJ Condenser pressure in kJ Potential energy given in KJ Rejected heat from a real cycle unit in kJ/kg Rejected heat from an ideal cycle unit in kJ/kg Heat energy supplied to a plant in kJ/kg Heat energy exiting a topping cycle in combined plant in kJ/kg Air compressor pressure ratio

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle Turbine pressure ratio Entropy given in kJ/kgK Temperature in Kelvin (K) Inlet water cooling temperature in degrees ( ) Out let water cooling temperature in degrees ( ) Temperature of rejected heat from the condenser in K Final exhaust gas energy in kJ/kg Work done by air compressor in kJ/kg Work done by gas turbine in kJ/kg Net work done by gas turbine cycle in kJ/kg Work done by 1st pump after condensation in kJ/kg Work done by 2ndt pump after extraction in kJ/kg Net work done by steam turbine cycle in kJ/kg Work done by steam turbine in kJ/kg Work done by steam turbine in kJ/kg Dryness fraction of dry steam in the wet region Fraction of extracted steam Combined cycle efficiency in% Combined cycle plant efficiency in % Compressor isentropic efficiency in % Gas turbine cycle efficiency in % Gas turbine plant efficiency in % Efficiency of a real or irreversible cycle in % Turbine isentropic efficiency in %

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1.0

INTRODUCTION

1.1 Background The project basically centred on optimization of the plant efficiency in a combined power to power cycle with the heating output usually for district heating. The combined power to power plant with heating (CPPH) is a combined cycle power and heating producing plant that involves more than one thermodynamic cycle. Generally it is the combination of the steam Rankine cycle and the gas JouleBrayton cycle. CPPH is an energy conversion process which is independent on the form of output since power can be electricity or shaft horse power and thermal energy can either be heating or cooling. The disposition of power can either be used on site or sold to a regulated utility. The size can be as a few kilowatts to as large as hundred megawatts. CPPH economic viability and performance can be site specific, which can depend on both the features of the facilities energy utilization factor as well as utility rates and fuel costs. CPPH is also a form of cogeneration. It is in general capital intensive which requires the need for intensive preliminary studies. While the engineering evaluation cost for CPPH is important, the cost should be economically suited as the final expenditure leading to the selection of the most effective utility system. Combined cycles (CC) in the 1970’s have efficiencies of about 40% compared to recent ones that attain efficiencies of more than 58% (Goswam & Kreith, 2007). International Energy Agency (IEA) has supported the take-up of CHP and has awarded countries for their exemplary performance in using it; Denmark and Finland won the highest score cards followed by Germany, Japan, Korea, the Netherlands, UK, US, China and India (Hodgson, 2009). Combined cycle using renewable fuels such as wood waste and Bagasse has helped in achieving a 41.5% total power generation using sustainable energy means in Australia (Colley, 2008) In conventional practice of using only the Rankine or Joule-Brayton cycle, their individual respective efficiencies are generally low, usually less than 45% i.e. about 55% or more of the heat of combustion is wasted. Therefore the idea about the CC is to utilize the heat energy that would have been wasted to generate more power and heat to increase the overall efficiency of the plant. Good design CPPH will ensure optimized production of both electricity and useful heat thus improving the energy utilization. The heat should be provided at a sufficiently high temperature for space and hot water requirements for use by i.e. domestic, commercial and public buildings. Alternatively, the steam can be provided to meet the industries processes needs e.g. the paper industry where low thermal heat is required. Many countries have implemented the CC system. These countries include the United State, France, United Kingdom, Russia, South Africa and many Asian countries. However, the combined power to power plant with heating (CPPH) system otherwise known as the Rankine and Joule-Brayton cycle consists of four main groups of machinery components. These are:  Gas turbine set, consisting of an air compressor, gas turbine and regenerator with additional components such as combustion chamber, regenerative air heater, heat exchangers for inter-stage heating of gases and cooling of air.  Steam boiler or HRSG with auxiliary appliances. Bashar Dan-asabe

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle  Steam generator or superheater (components in the boiler or HRSG) in which heat energy supplied by hot gases is used to produce superheated steam.  Steam turbine set consisting of a steam turbine and generator together with regenerative water heaters. Improved efficiency is realized with optimal combination of these components. Basic study of thermodynamics leads to accurate assessment of cogenerated plants fuel and energy savings but matching the plant to the required heat and electrical power parameters could be quiet a tremendous task. In the analysis of the CPPH, some basic parameters are taken into consideration. These parameters i.e. pressure ratios, temperature ratios, combustion gases (fuel), mass of compressed air etc. These parameters play a very important role in maximizing the thermal and power potential of this cycle.

The fuel consumption for electrical power and heat energy in CPPH is less than that for the independent conventional power and heating producing plants. Difference in the amount of fuel savings in comparison with individual systems, constitute the main economic advantage of the cogeneration (CC) plant. In line with world vision 2020 in promoting sustainable efficient energy producing methods that reduces green house effects, this method offers a much reduced risk of green house gases such as carbon dioxide (CO2) and carbon monoxide (CO) that can have devastating effects on our climate conditions. Hence the usage of the CPPH saves fuel costs and gives significantly improved overall cycle efficiency. The overall efficiency can be up to 70 % and above.

1.2 Aims and Objectives The aim and objective of this work is to simulate, model and optimise the performance characteristic of a combined power to power and heating plant (CPPH). This should include the production of an optimum power and heating while operating at an optimised pressure ratio and GT inlet temperature. Regeneration is employed as this will help save fuel and cost hence reducing the green house effects that affects global warming. The objectives in satisfying these aims are to:     

Design a realistic combined cycle plant incorporating both power and heating outputs. Determine accurate thermodynamic equations of the combined cycle plant. Simulate the plant together with relevant sections of a steam table using Microsoft excel spreadsheet to produce instantaneous results outputs. Optimise these results by varying input parameters accordingly to produce graphical trends. Interpret these graphical trends objectively and constructively.

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2.0

METHODOLOGY

This was carried out with respect to the title of the project as follows: i.

Design: This was carried out after intensive review of various literatures on thermal power generation involving vapour power plants, gas power plants, combined cycle gas turbines (CCGT), combined cycle and heating (CHP) and their various thermodynamic energy and exergy analyses. A suitable combined cycle that provides both heat and power (CPPH) was designed to serve as the specimen plant.

ii. Programming: Intensive calculations of the plant were first carried out to obtain accurate thermodynamic results outputs. Analytical equations of the CPPH were then modelled and simulated in Microsoft excel spreadsheet using the various referencing functions as further explained in section 6.0. iii. Optimisation: This was performed beginning with the topping cycle, the bottoming cycle and subsequently their combined effects (CPPH) optimised accordingly. Series of graphical trends were analysed and interpreted constructively.

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3.0 LITERATURE SURVEY

Combined thermal and power cycles have been proposed since the beginning of the 20th century and the first plant was constructed in 1950. A significant number of these cycles have been installed by late 1970 which were estimated to be about 100 plants with a total of 150,000 MW output throughout the world.

3.1 Classification of CPPH The combined power and power with heating can be classified based: A. Combined power plant with power output priority. B. Combined heat and power plant with both heat and power outputs as priority. Generally, combined power plants can be further subdivided according to Bauxmann and Haywood (Horlock, 1992) classification into; 1. Closed plants using a single working fluid internally coupled known as Doubly Cyclic Plants. These are: a) Joule-Brayton cycle side-by-side with steam cycle: Typical of these cycles include Ideal super-regenerative steam cycle, Sonnenfield cycle and Field cycle. The ideal super-regenerative cycle is the impractical cycle used as the reference Carnot cycle for a combined power plants. It consists of the upper modified Joule-Brayton gas cycle and the lower regenerative ST cycle. It uses steam as the working fluid. it receives all it heat supplied at the maximum temperature and rejects heat at the minimum condenser temperature.

T

4 my 3

2

1

qr

qs

qs 5

T

5

4 x

(1- my)

2

6 my

7

(1- my)

my 3 my

1

qr

S Figure 3.2(a): Super-regenrative cycle

y 6

7

S Figure 3.2(b): Field cycle

The Field cycle is similar to the ideal super-regenerative but heat is supplied at a temperature close to the maximum temperature. It has a major setback of internal irreversibility of wet steam at the mixing process leading to difficulty (impracticability) in compression although its efficiency is very high close to that of the ideal super-regenerative cycle.

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle The Sonnenfeld cycle consists of a supercritical modified Rankine cycle with incorporated Joule-Brayton cycle. External heat is supplied at the boiler pressure and the reheaters. The Joule cycle shares a parallel external heating (supply) from the first reheater. Feed heating is done from the low pressure turbine at multiple points and from the rejected heat of the Joule cycle at boiler pressure. This has added advantage of useful heat with overall efficiency close to the ideal regenerative cycle as all the heat supplied is applied close to the maximum temperature of the cycle. b) The Split double steam cycles: This cycle has the advantage of reducing irreversibility problem by splitting the cycle into two where the temperature difference between the condensed water and superheated steam is greatly reduced. The total heat being supplied by the upper cycle as its temperature difference is being reduced with small irreversibility. Similar proposals of this cycle are the Mangan and Pettit where expanded heat from the higher pressure turbine mixes with steam form the LP evaporator after supplementary firing before finally expanding in the LP turbine. The Wardall and Doorly is another similar proposal where heat from the HP turbine mixes with the steam from the superheater or LP boiler at superheated region before it finally expands in the LP turbine.

T

qs

mt

qtb

mb

qr

S Figure 3.3: The Split Rankine cycle T-S diagram

c) Combination of Joule to Joule cycle known as the Sulzer half cycle plant. This consists of an upper closed and a lower open Joule cycles. Atmospheric air is compressed in the lower Joule, mixes with the upper closed cycle to a point 2 and then cools down to state 3. The mixture is heated briefly in the low temperature side of the heat exchanger after which the two streams split into the respective open and closed cycles. The open cycle is burnt with fuel to a higher temperature and the closed cycle one heated by the burning gas where both attained a final temperature 9. The closed cycle is expanded to a temperature 6 and the open cycle fully expanded to the atmospheric pressure with a resultant heat rejection at this temperature. The cycle is an example of a joint or parallel heating where the combined efficiency is less than that of the upper cycle but with an increased work output.

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle 2. Closed power cycles with two or three working fluids externally coupled known as Binary and Ternary Closed Cycle Plants. These includes; a) Rankine to Rankine cycles with topping or bottoming cycles: The topping cycles can be mercury or potassium to a steam lower cycle. The bottoming cycles can be ammonia or organic fluid cycles with corresponding steam upper cycle. The topping cycle working fluids should have; i.

Upper cycle temperature lower than its critical temperature to give high latent heat of evaporation. Not too high and not too low saturation temperature at top and bottom. A working fluid that is inert, non-toxic and cheap with steep liquid saturation to reduce the supplied heat close to the top maximum temperature.

ii. iii.

An illustration is given of a mercury and steam binary cycle in Figure 3.4. Mercury with critical pressure of 106MN/m2 has saturation temperature and pressure chosen at 550 C and 1.4 MN/m2. The efficiency of the cycle in practice will be reduced when joint heating is adopted with some of the heat supplied to the steam cycle. mm

qs

T Mercury cycle

qtb ms Water/steam cycle

qr

S Figure 3.4: Binary cycle T-S Diagram

b) The three cycles Rankine to Rankine to Rankine using mercury, steam and ammonia working fluids. Potassium, mercury and steam combinations are also proposed. c) Joule to Rankine cycles: An example is nuclear upper cycle using helium gas and steam lower cycle. The heat rejected by the upper cycle is partly regenerated to heat the compressed helium gas and the steam cycle and the remainder unused heat recycled back to the upper cycle.

Schematic example of this plant is shown in Figure 3.5(a) with the helium used as the working fluid for the gas turbine.

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle Reactor HTGR

HC

G

HT

FWH

Steam Generator

ST

G

Fuel

P

C

Heat rejected

Figure 3.5(a): Helium to steam binary combined cycle layout

The corresponding T – S diagram is shown below: 3 mg

T x 2

2'

4

y

4'

7

1 ms 10 9

8 8'

S Figure 3.5(b): Binary cyclic combined T-S diagram

Helium is compressed in the helium compressor which then enters the hightemperature gas nuclear reactor (HTGR) as the source of heat for the gas cycle where it is expanded. It then regenerates heat for the compressed helium gas and subsequently to the feed water heater that supplies heat to the steam turbine. The gas turbine is a closed cycle. The feed water enters the steam generator (usually fossil fuelled) in the steam cycle and leaves as superheated steam. It can be noted that these cycles are coupled only through the feed water heater and heat rejection is only in the steam condenser.

3. Open gas cycle and closed steam cycle using two working fluids. This is the most popular and includes;

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle a) Externally coupled cycle with heat supplied to the steam cycle by exhaust of gas turbine. This can be with supplementary with or without supplementary firing of the heat recovery steam generator (HRSG) or with a fully fired exhaust boiler. The exhaust heated unfired HRSG uses gas or liquid fuel together with coal firing. The coal firing involves using an integrated gas combined cycle (IGCC) where generated synthetic gas is supplied directly to the combustion chamber and circulating fluidised bed combustion system (CFBC) where coal is burnt in the fluidised bed. Due to exhaust gas heat loss, the overall efficiency of the cycle is close to the ideal Carnotised efficiency of Figure 4.2 (in section 4.3) 3

T

mg 4

4' 5

2

1 ms

8 7

6 6'

S Figure 3.6: Unfired HRSG Combined cycle T-S diagram

However, exhaust heated with supplementary firing is employed where the initial heat supplied to the turbine cannot be higher than what the turbine can withstand, hence the supplementary firing of the gas turbine exhaust gas to generate steam at a higher temperature for the steam turbine. In this combination the efficiency of the overall cycle is less than the combined cycle without supplementary heating.

3

T

mg 2

4

2'

5

4'

7

1 10

ms 8 8'

9

S Figure 3.7: Supplimentary fired HRSG Combined cycle T-S Diagram

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle Another method is the exhaust gas with full firing. Here the exhaust gas is supplied to a conventional boiler instead of HRGS. More feed heating is employed due to the presence of higher heat energy as a result of the full firing. Some of the feed water at higher temperature is passed through the boiler economiser to reduce the temperature of the stack to a temperature not less than 180 C. This cycle gives an added advantage of increased power output at the expense of the efficiency. b) The cycles internally coupled with a pressurised boiler: These are combined plant with joint heating and are adopted in two ways. The first type is the clean combustion plant invented by Seippel and Bereuter. It involves burning of the fluid with compressed air in a joint boiler generating the flue gases that is expanded by the gas turbine. The second is the pressurised fluidised bed combined plant. The boiler in this is replaced is replaced by pressurised fluidised bed combustion (PFBC) since it cannot burn coal. Compressed air delivered to the fluidised bed is burnt with coal and water slurry. Sulphur oxide is reduced by limestone or dolomite (solvents) and the sulphur removed as calcium sulphate in the form of ash. Other types of cycles are; i.

Kalina cycle: This comprises of the upper cycle supplying heat to the lower liquid and vapour mixture cycle. Mixture of water and ammonia is an example of the working fluid for the lower cycle where ammonia vaporises easily due to its lower boiling point. The benefit of this Kalina cycle is the greater absorption of low heat energy (at low temperature of 200 C or less) rejected by the upper gas cycle as the mixture in the lower cycle vaporises easily to be expanded by the sequential gas turbines. The condensation of the expanded mixture from the last turbine is quite difficult and requires a quite complex process as ammonia cannot be condensed at water cooling temperature. The condensation set up comprises of an evaporator, economiser, mixing chamber and the condenser where the ammonia is finally condensed to liquid mixture with water having the same concentration to be pumped again through the HRSG and the cycle continues.

ii.

Topping gasification with fluidised bed combustion plant. Two proposals have been identified here. The first is the PFBC topping cycle comprising of a gasifier and the PFBC both supplying clean-up hot gases to combustion chamber. The PFBC and exhaust gas from the gas turbine supplies the steam and extra heat energy respectively needed by the steam cycle. The second proposal is the CFBC and the topping plant. The major difference from the former is that the CFBC does not provide hot clean-up gases to the combustion chamber but supplies steam to the steam cycle and also continuously receive additional heat from the topping cycle exhaust gases. The benefit of these proposals is to provide inlet gas turbine temperature and minimise energy in the production of fuel gas with no oxygen production plant.

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle The efficiency of the above cycles is compromised at the expense of the parallel heating involved in these cycles. 4. Open gas and open steam cycle using two working fluids internally coupled also known as Doubly Open Circuit Plants. This involves heating of water by the exhaust of the steam turbine and the steam subsequently passed to the combustion chamber of a gas turbine plant. This is an example of a series heating of feed water heating by the exhaust gas and a parallel heating of the steam from the HRGS and air in the combustion chamber. In a whole, there is appreciable increase in the efficiency of the plant since the joint heating is done by the initial heat supplied in the combustion chamber. The cycle is also known as the Cheng cycle.

3.2 Some Examples of Practical CC Examples of practical combined power plants with electrical power as priority are; A. The Mercury/Steam Binary Vapour Plant in New Hampshire: This was a 40MW plant built by General Electric in 1949. The plant attained an efficiency of 36.4% as opposed by Emmet’s proposal of an ideal efficiency of approximately 55.5%. Figure 3.8 shows the sketch of the plant consisting of the mercury upper cycle and the steam lower cycle. The feed heating is done at 171 C where it is further heated by 39 C. The steam receives additional heat from the mercury condenser/boiler and then finally reheated in the combustion chamber before it is expanded by the steam turbine. Exhaust flue gas

Fuel and air B

mm G

MT

P

C/B

ms G

FH

ST

C

FP

Figure 3.8: Schiller Mercury/Steam binary vapour plant

B. The Unfired HRSG combined gas power plant at Kornenburg: This was a 125MW (nominal) output combined plant with the gas turbine providing about 62% of the total power output. The overall efficiency of the plant is 47% (based on the LCV) and 46% after deduction for station auxiliaries. The combined plant operates with air mass flow rate of 357kg/s, pressure ratio of 10

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle and turbine inlet temperature of 1000 C for the gas turbine. The exhaust gas at 491 C regenerates steam for the steam cycle. The exhaust gas finally leaves at a temperature of 95 C which is allowed for burning of natural gas with low sulphur content. The steam cycle has mass flow rate of 43.2 kg/s, condenser pressure of 0.163 bar and 28 C. C. The Supplementary fired combined gas Plant A at Korneuburg: This plant was installed in 1960 with an output power capacity of 75MW consisting of a two-stage gas turbine-compressor sets. Figure 3.9 shows the two-stage gas turbine producing about 67% of the overall power output. The gas turbine has turbine inlet temperature of 625 C, overall pressure ratio of about 20 and exhaust gas temperature of 310 C. Supplementary superheat boiler provides 18% of additional heat to the steam cycle. The steam cycle has inlet temperature of 440 C, inlet pressure of 14.2 bars and a condenser pressure and temperature of 0.02 bars and 18 C respectively after expansion in the steam turbine. The plant has an overall efficiency of 32% but with an increase of 43% power from the steam turbine. Fuel CC

AC2

G

GT2

IC

CC

Fuel

GT1

AC1

G

Fuel Atmospheric Air

P

SHB

Exhaust flue gas

From GT2 turbine

WHB

ST

0.02 bar

P FH/DA

G

P

C

Figure 3.9: Simplified diagram of Korneuburg GT/ST combined cycle with supplimentary firing

D. The Maximally fired combined Plant at Hemweg: This plant was built in Amsterdam, Netherlands. It has an overall power output of 600MW with the steam turbine producing 77.5% of the output. The gas turbine has an inlet temperature of 1070 C, pressure ratio of 14.6 and an exhaust temperature after expansion of 534 C. The exhaust gas supplies 15% of oxygen to the steam boiler before regenerating heat to the feed heaters and finally goes to the atmosphere. The steam turbine has inlet temperature of 540 C, inlet pressure of 186 bars and a

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle reheat temperature of 535 C at 46 bars. The overall efficiency of the cycle is 45.9%. Both cycles use natural gas as fuel firing with possible substitute for the steam turbine as light distillate oil. E. The IGCC Plant at Cool Water: The plant was built in California by General Electric Company. This is one of the most complex practical unfired HRSG plant built in the world. The heat supply is essentially a coal gasification process where a complex mixture of coal, water and oxygen is used to produce synthetic gas (syngas). The syngas which primarily consists of hydrogen and carbon oxide is passed through a particulate scrubber after which it is cooled to remove sulphur and is then supplied to the combustion chamber of the gas turbine. The exhaust from the gas turbine and the by-product of the gasifier comprising of 40% steam provides and regenerates superheated steam in the HRSG to the steam turbine. The plant has an overall net efficiency of 29.7% and an overall net power output of 91.9MW with the gas turbine producing about 55.5% of the total power. Slag Oxygen supply

Coal handling and preparation

Gas Production

Sulphur recovery

Gasification

Gas cooler

Sulphur removal

Steam turbine

Steam generation

Particle scrubble Gas turbine

gas

Combined Cycle Figure 3.10: Cool Water IGCC Plant (Plumley)

F. The STIG Plant at Ripon: The plant was built to produce both power and steam to a paper producing mill in California. Exhaust from the gas turbine is used to supply heat to the HRSG where three stages of steam generation are provided. The HP boiler operating at 5170 kN/m2 at 315 C produces 45,800 kg/hr of superheated steam. The STIG (steam injection gas plant) has an overall efficiency of 43% with a corresponding power output of 49.5MW. G. Aluminium of Greece (AOG) plant: A major combined heat and power (CHP) plant is the Aluminium of Greece (AOG) plant for the production of both alumina and aluminium located on the same site on the north of the Gulf of Corinth in Greece. The plant produces high and low pressure steam (HP and MP) for the alumina and aluminium production process while the electrical power may be used by the AOG in back-up mode and the remainder sold to the national grid. The simplified plant depicted is Figure 3.11. The plant is a 2 X 2 x 1 configuration CHP comprising of two groups of gas turbines (GTs) and heat recovery steam generator (HRSG) together with a single steam turbine. A back-

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle up dual fuel boiler (DFB) is also included to increase the reliability of the steam supply when the HRSG’s are out of operation. Natural gas (Fuel) Atmospheric Air

AC

GT

Chiller

Exhaust gas LP HP Steam Steam

HP Steam Header LP Steam Header

HRSG

HP Steam export

Natural gas (Fuel) Atmospheric Air Chiller

AC

G T

LP HP Steam Steam

Exhaust gas

LP Steam export

HRSG

HP DFB Steam

ST

G

Figure 3.11: Aluminium of Greece (AOG) CHP plant layout

The HP steam produced by the HRGS is partly channelled to the steam turbine and the remainder directly exported to the AOG for digestion alumina. The MP steam produced from the HRGS combines with the MP extracted steam from the steam turbine and then exported to the AOG where it is reduced to low pressure (LP) to be used in alumina plant evaporators and other low pressure steam users. Cooling water from the near sea is used to cool the condensed steam after expansion from the steam turbine with a temperature incremental limit of 8 C under normal circumstances. Condensate steam recovered from the AOG is sent to the flash tank deaerators to dissolve the air. Chillers are included in the CHP set-up to improve the overall plant efficiency by reducing the ambient temperature of 15 C to 8.5 C. The cogenerated plant produces an average of 321MW of electrical power, 237.23MW of thermal power and a corresponding overall efficiency of 71. 64%. Natural gas is used as the main fuel by the plant and light fuel oil (LFO) only is used by the DFB. Other examples of practical combined plants with heating priority (CHP) are: A. Back Pressure Steam Turbine at Zurich: The plant consists of two low pressure direct heat-supply boilers and three sets of back pressure CHP turbine. The LP boilers produce an output of 117MW which fluctuates to a minimum of 75% of its maximum load and is meant to supplement the winter peak loads. The back pressure turbines produces each a power of 45MW and a heat output of 348MW giving the overall plant the total heat output of 465MW. The heat to power ratio of the CHP alone is given as;

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Hot water supply for district heating

SC

District heating return

ST

LPB

LPB

ST

G

MPB

G

MPB

FWH

WT

C

P

SC

SC

SC

ST

G

MPB

FWH

FWH

P

P

P

P

FWT

FWT

FWT

FWT

P

Figure 3.12: Back pressure steam turbine plant at Aubrugg

Figure 3.12 shows the plant where recycled water at 40 C – 70 C is topped, treated, condensed in a condensate tank, fed to the deaerator’s tank and is pumped to the direct heat-supply boiler and the CHP feed water heaters respectively. The heat-supply only boiler supplies steam to the calorifiers which heats the district heat supply. The heated water in the CHP feed water preheaters are passed to the three medium-pressure boilers to generate steam and subsequently expanded by the back pressure turbines. The expanded LP steam is passed to the three calorifiers for district water heating from 70 C to 130 C at maximum load. B. Extraction Steam Turbine: This has been in use since the former Soviet Republic in 1972 as described by Oliker. The plant basically consists of four extraction steam turbines, a boiler, deaerators, condenser and a complex net work of feed heating and district heating. The steam turbines without district heating produce maximum load capacity of 300MW. With additional boiler heating, the plant produces 250MW of electrical power with 385MW of heat power. The Z factor is considerably low due to the complex network of feed heating and district heating thus is given as;

The steam enters the first high pressure turbine at a pressure of 24.1 MPa with a corresponding inlet and reheat temperatures of 560 C and 565 C respectively. The extracted steam and condensed water are feed to net work of LP feed heaters and finally pumped back via the boiler to the turbines. The district heating is supplied by the third IP turbine in two feed heaters, the last LP turbine Bashar Dan-asabe

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle via the condenser and the optional ‘peaking’ water heater for maximum load conditions. The heat to power ratio of the plant is 1.54 and district heat percentage throttle flow is at 70% – 80%. C. Gas turbine Plant at Beilen: The plant which operates both with unfired and supplementary fired HRSG was built in the Netherlands for producing dairy products. Figure 3.13 shows the plant which replaces the original separate electric power supplied by the national grid and the heat power supplied by two boilers. Fuel CC

AC

GT

G

Atmospheric Air at 20.5kg/s Gas for supplimentary firing

Extracted heat

Figure 3.13: HRSG fired CHP for Beilen Exhaust gas

The unfired plant (with a rated gas turbine of 3.65MW) produces 3.2MW of electric power for the plant and a corresponding heat load of 7.5MW at a saturated steam temperature of 191 C and 13 bar respectively. The supplementary fired HRSG with five burners produces heat load of 23MW at the same saturated steam temperature and pressure. The flue gas leaves at 138 C at maximum load conditions. The corresponding values of the heat to power ratio for both the unfired and supplementary fired HRSG are 2.34 and 7.19 respectively. D. The Gas turbine Plant at Saarbruken: This plant was built in 1974. It meets both electric power needs and district heat needs with either unfired or fired HRSG modes of operation. Figure 3.14 shows the plant where the exhaust from the gas turbine regenerates steam to the steam turbine leaving the atmosphere at 11 C. The district heating usually gains 5 C from the flue gas compartment and is then further heated by the bled steam in the heat exchanger.

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Water for district heating Fuel Bled steam

CC

AC

Atmospheric Air

GT

G

ST

P

ST

P Condenser cooling water

Optional fuel for additional heat HRSG

Exhaust gas Figure 3.14: Combined CHP at Saarbrucken

The gas cycle uses natural gas or light fuel and has a mass flow rate of 113.9kg/s, fuel energy supplied at 87.7MW, electrical output of 23.5MW and overall efficiency of 26.8%. The steam turbine parameters are given below; i.

With unfired HRSG- it produces mass flow rate of 13.1kg/s with heat to power ratio of 1.5 and 0.18 for with and without steam extraction respectively. It also gives a corresponding EUF of 80% and 44% for with and without steam extraction respectively. ii. With fired HRSG- it produces mass flow rate of 13.1kg/s with heat to power ratio of 1.4 and 0.53 for with and without steam extraction. It also gives a corresponding EUF of 73% and 54% for with and without steam extraction. E. The HRSG Diesel Engine Plant at Hereford: This was built to supply heat to two industries and electric power to the national grid. The dual diesel engine supplies electric power via a generator to the national grid. Its high temperature exhaust gas leaving at 436 C supplies energy to both the waste heat boiler and the economiser of the HRSG, thus finally leaving at 177 C to the atmosphere. The plant provides process heat at 96 C – 110 C, small district heating at 80 C and generates little return condensate with ‘topping’ raw water at 10 C. The plant has an of 0.75 with heat to power ratio of 0.895. This is as a result of low useful heat rejection as the power output in a diesel engine is higher. The dual diesel engine has a 20,400hp providing electrical and heating load of 14.96MW and 13.4MW respectively thus providing a maximum thermal efficiency of 39.6%. F. The proposed HRSG Gas Engine Plant for Open University in the UK: The plant is supposed to meet the electrical and heat demands of the Open University and hence requires a small prime mover. Therefore using gas turbine, back pressure steam turbine and diesel engine will be inefficient for the required need. Therefore a viable proposal was to use a turbo-charged (spark-ignition) ignition engine with the heat rejected from the engine and the exhaust gas used for space and district water heating. The plant is to supply electric power of

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle 700kW, useful heat of 620kW and an efficiency of 36%. The plant natural gas consumption rate of 3.26 m3/s is also proposed.

3.3 Description of the basic component of a CC

3.31 Air Compressors Most industrial applications use a pressure of about 8 bars. Some of the major air compressors used in industrial applications are categorised into two: i.

Positive displacement air compressors. This compresses air in successive volumes into an enclosed space by decreasing the volume. Examples of these are the rotary and reciprocating compressors. Multi-stage and high pressure capabilities are usually produced by reciprocating compressors. They are usually constant volume with variable pressure and are suitable for low flow capacity and high pressure. Discharge pressure can be as high as 700 bar or more.

ii.

Dynamic air compressors. This compresses air by the rotating impellers which exert kinetic energy into the air as it exits the impeller narrow passageway. Examples of these are the axial and centrifugal compressors. Centrifugal compressors are used with large flow capacity and low pressure ratio. The centrifugal compressors are used in mutil-stage GT with intercooler stages and can be used for pressures of up to 600 bars with zero tolerance on liquid in the gas entering the impeller. The axial compressors are used without the intercooler stages and usually have capacities from 7500KW and above. The axial compressors operate at lower pressures of up to 60 bars as compared with the centrifugal compressors (O’Neill, 1993).

3.32 Gas and Steam Turbines High power plants of 250 – 400MW capacity produce up to 58% efficiency due to break through in air craft jet engine technology. These CCGT have a maximum temperature of 1500˚C. The steam inlet temperature for the bottoming cycle can be as high as 550˚C with a condenser temperature at atmospheric temperature (Leo, Perez-Grande & Perez-del-Notario, 2003). Advanced gas turbines with high combustion temperature like the ‘G’ designs have about 60% efficiency. Examples of these are the humid-air and cascaded-humid air turbine (HAT and CHAT), intercooled reheat turbine cycle, steam injected steam injected gas turbine (STIG), Kalina cycle using ammonia/water steam cycle (OECD, 2005). Mitsubishi Heavy Industries Ltd (MHI) has developed G-Class GT in the range of 1500˚C. The classes of these turbines are:  

Class M701D 1150˚C GT Class M501F/M701F 1350˚C GT

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle 

Class M501G/M701G 1500˚C GT

The performance of these G-series is given below:

Parameters

M501G/M701G

M501F/M701F

Speed (rpm)

3600

3600

GT Output Power (MW)

254

185.4

GT thermal efficiency (% LHV)

38.7

37.0

Pressure ratio

20

16

Table 3.1: Performance of the G-series GT (Soares, 2007) However, there are two major types of power generating GT: i. ii.

Heavy duty industrial GT: This usually has a single-shaft output from 30MW up to 300MW electric power out. Aero-derivative GT: Their designs are imitated from the jet engine and are less in weight for a given power output than the industrial GT. It has variable compressor and turbine speed for part loading. It consists of two or three shaft with a variable speed compressor and has a limit of approximately 50MW output. In let GT temperature is very high with about 1350˚C.

Some of the characteristics of modern GT are: i. ii. iii. iv.

GT inlet temperature of 1100˚C – 1350˚C GT inlet pressure of 14 – 30 bar Exhaust gas temperature of 450˚C – 650˚C Exhaust gas mass flow rate of 50 – 550kg/s (Kehlhofer, 1999)

A new type of steam turbine with improved efficiency of up to 48.5% can operate at ultra-super critical pressure and temperature of 280 bar and 580˚C. However, with utilisation of the exhaust waste heat the efficiency can increase to 52% when used for district heating and can even reach 58.5% with a vacuum condensation turbine (Kolev, Schaber & KLolev, 2001). Basic and appropriate assumptions are necessary for the achievement of realistic plants operating conditions. Some of these assumptions that were applied in steam injected multi-stage gas turbine CC power plants (Sanjay, Singh & Prasad, 2007) with respect to the GT and ST cycles are: i.

GT cycle: Inlet air going into the compressor is taken at atmospheric temperature and pressure conditions of 25˚C and 1.01325 bars respectively. Pressure ratio is assumed as 20 with maximum GT inlet temperature at 1200˚C.

ii.

ST cycle: steam reheat approach point of 20 is used as is the temperature difference between the exhaust and reheat steam. Pressure drop in the combustion chamber is taken as 8%. Pressure drop across the HRSG, condenser and deaerator is neglected. Heat loss in the HRSG, condenser and deaerator are also neglected. The isentropic efficiencies for the ST and compressor are taken as 85% and corresponding GT taken as 90%.

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle 3.33 Heat Recovery Steam Generators (HRSG) or Waste Heat Recuperator (WHR) There are three types of HRSG. These are HRSG: i. ii. iii.

Without supplementary firing With supplementary firing Steam generation with maximum firing

Appropriate selection of HRSG also increases the efficiency taking in mind the overall cost of the plant. Typical HRSG components are water drums, economizers, super heaters, circulation systems, generating tubes and blow down systems. The operation of the HRSG begins with preheating in the economiser after which the water enters the drum and circulated in the evaporator where water and steam are separated. The saturated steam moves to the superheater where it gains maximum heat exchange with the exhaust gas leaving the GT. The steam generation in the HRSG can be multi-pressure level i.e. up to three pressure levels depending on the energy and exergy to be recovered. Another type of the HRSG is the once through heat recovery steam generators (OTSG) which has water cooled drums to prevent scaling and corrosion making it competitive with respect to initial cost and installation cost. The types of HRSG based on cost of installation, efficiency and power is depicted below as given below:

Types of Process

Cost increase

Power increase

1.0

Efficiency increase 1

Single Pressure HRSG Single Pressure OTSG Dual Pressure HRSG Triple Pressure HRSG Dual Pressure HRSG Triple Pressure HRSG

0.98

1

1

1.025

1.015

1.015

1.03

1.02

1.02

1.04

1.035

1.035

1.035

1.027

1.027

1

Table 3.2: Cost and Efficiency increase in CC Power plant Mehrwan (1979)

Modern CC power plants have inlet ST inlet pressure and temperature as high as 100 – 150 bar and 520 – 565˚C as a result of sequential stage combustion (Kehlhofer, 1999). Consequently, higher exhaust temperature means higher efficiency of the steam plant. As a result of this we need: i. More expensive alloys in the HRSG, steam pipings and the corresponding incurred associated cost. ii. Thicker walls in the HRSG to reduce thermal flexibility due to heat loss iii. Moderate live steam and reheat flow rate as high live steam and reheat steam flow rate reduces the efficiency of the HP turbine due to short bladding.

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle 3.34 Intercoolers and Reheaters Intercoolers are part of compressor auxiliaries comprising of inlet air filters, intercoolers, after coolers and air driers developed to prevent moisture and other contaminants in the compressed air. Reheating is employed either by rechanneling the expanded air back into the CC or by some additional heating. There are two main types of cooling in sequential combustion GT. They are air and steam cooling. The steam cooling is more preferred as it gives a better thermal performance with additional district heating benefit than air (Mohammad, Alghamdi & Najjar, 2004). Reheaters and intercoolers increase the specific work output of a combined cycle. Intercoolers are usually bulky and not suitable when water cooling is involved in arid regions of the world. In these regions air cooling is more suitable. However, water cooling is very popular and economical in the naval application where cooling water is readily available (Saravanamuttoo, Rogers, Cohen & Straznicky, 2009).

3.35 Pumps and Deaerators Centrifugal pumps are the commonly used ones to pump steam or condensate in power plants. The several types of pumps used in combined cycle power plants are: i.

ii. iii. iv. v.

vi.

vii.

High pressure (HP) feed water pumps: These pumps are usually large in size and pumps heated water between the dearerator and the economizer in the boiler. They are usually multi-stage centrifugal pumps and with a capacity of up to 1500KW. Intermediate/low pressure (IP-LP) circulating pumps: These pumps circulate water between the deaerator and LP evaporator in the boiler or HRSG. High pressure (HP) circulating pumps: These circulate fluid between the HP drum and HP evaporator in the boiler or HRSG. Cooling water pumps: These pumps the cooling water used for cooling in the condenser. Condenser pumps: These type pumps condensate from the condenser to the deaerator. They are low temperature designed pumps. Additional standby ones are kept on alert. Lubrication pumps: They are usually gear-type and positive displacement pumps. They provide lubrication as well as cooling to the turbines. Standby pumps are kept in parallel to compensate failure Fuel pumps: These pumps require high head with relatively low flow. The fuel must be injected into the CC at a pressure above that of the GT compressor discharge air (Boyce, 2002) The deaerator uses extracted steam to dissolve air from the feed water before it returns back to the boiler (Petchers, 2003).

3.4 Fuel types used in a CC The commonest types of fuel used in a CC are coal and natural gas. Dominance and relevance of coal as a means of firing dates back to the early history of the power plant cycle in the nineteen century. Coal fired plants are very expensive because of the high cost of coal. For example a 500MW steam turbine requires about 5,000 tonnes of coal per day (equivalent to 80 car loads per day). About 50%

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle of the electricity generation in the united state is provided by coal fired plants that spent 85% of their total generating cost on the coal fuel, hence the significant of the combined cycle to use the exhaust flue gas for steam generation (Woodruff 2004).

Advantages of the combined cycles with natural gas as fuel over the coal-fired are low capital cost and reduced emission. Natural gas has minimal or no sulphur contents and particulates. The maintenance cost increases with type of fuel used from natural gas to heavy fuel. This is depicted in Table below; Fuel Type

Expected Actual Maintenance Cost

Relative Maintenance Cost Factor

Natural Gas Distillate Oil (No. 2) Typical crude oil Residual oil (No. 6)

0.35 0.49 0.77 1.23

1.0 1.4 2.2 3.5

Table 3.3: Types of Fuels with Relative Maintenance Cost (Mehrwan, 1979) Today, natural gas fired combined cycle plants are the most commonly used firing fuel in CC and provides the highest efficiency. In the event of unavailability of natural gas, parallel combined cycle plants and integrated gasification combined cycles (IGCC) can be used. The parallel combined cycle uses natural gas to repower existing older coal-fired plants. The IGCC uses coal pet coke fuel giving the plant an increased complexity with less overall plant efficiency. Table shows comparisons between the natural gas fired plants and parallel IGCC plants.

Plants

Fuel

Efficiency (%)

Gas Turbine

Natural gas

30 - 38

Combined cycle plants Parralel cycle CC power plant IGCC

Natural gas Coal, Natural gas

55 - 60 45 - 55

Coal, Petcoke

45 - 50

Table 3.4: Fuels used in natural gas fired plants and parallel IGCC plants In present times, GT exhaust temperature could be as high as 500˚C to 600˚C with a corresponding steam turbine inlet pressure as high as 165 bar (Goswam & Kreith, 2007). Fuel cells are also used as they react with hydrogen, CO and light hydrocarbons and oxygen from air to produce electricity through a reaction like that of a battery or a cell. Sometimes the exhaust may be significantly hot to supply heat energy to a steam cycle or HRSG. Hybrids of natural gas with fossil fuels have been proved to produce a very high thermal energy of about 75% LHV (Rao, Samuelsen & Yi, 2005). The combination of these hybrids can be: i.

A high pressure solid oxide fuel cell (SOFC) with high pressure ratio intercooled GT.

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle ii. iii.

A high pressure SOFC with humid air turbine (HAT) cycle. An atmospheric pressure molten carbonate fuel cells (MCFC) integrated with high pressure ratio intercooled GT.

Therefore, corresponding design parameters can accommodate GT firing temperature of about 1700˚C, with high turbine and compressor isentropic efficiencies of 88% and 92%. The corresponding LP isentropic efficiencies are 90% and 94% respectively. The turbine material for this temperature is ceramics with thermal bearing coating.

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4.0 THEORETICAL CONSIDERATION AND BACKGROUND

This covers the analysis of the various cycles together with their various components. The CPPH consists of at least more than one cycle. The major cycle configurations are the Joule Brayton cycle and the Rankine cycle. The analyses are detailed below starting with the Joule-Brayton cycle: 2

Heat exchanger

CC 3

GT

AC

1 Heat exchanger Figure 4.1(a): Ideal Closed Cycle Joule-Brayton GT

AC

4

GT

Atmospheric Air

Exhaust gas

Figure 4.1(b): Open Cycle Joule-Brayton GT

From Figure 4.1 above, the first law of thermodynamics says that the net heat supplied into a control system is equal to the net work and the change in internal energy. This is depicted in the equation below: (4.1) This is synonymous to the steady flow energy equation (SFEE) equation: (4.2) Also neglecting the change in potential and kinetic energy as they are minimal and assuming a thermodynamic transformation from state 1 to 2, integrating thus we have: (4.3)

4.1 Joule-Brayton Cycle This cycle was developed around 1870 for usage in the piston engine. The JouleBrayton cycle can be an open cycle with either internal or external combustion or a closed cycle with external combustion. The cycle is simple, very light in comparison with 4-stroke and with a high power to weight ratio. The closed cycle is usually applied in power generation.

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T

P

3

3

2 qin

2

qin

4

1 qout

qout

4

1

S Figure 4.2(a): Ideal Gas Cycle T-S Diagram

V Figure 4.2(b): Ideal Gas Cycle P-V Diagram

The ideal cycle in Figure 4.2 consists of four reversible processes of compression, heat addition, heat expansion and heat rejection. This is based on the ideal assumptions that: i. ii. iii. iv.

The compressor and turbine processes are isentropic. The heat addition and rejection are done at constant pressures in the heat exchangers. The effects of kinetic and potential energies are negligible. The ideal gas working fluid (e.g air) with its specific heat capacities ( and ) and gamma (γ) to be all constants.

Heat supplied from state 2 to 3: (4.4)

i.e.

as work done is negligible from equation (3)

Also heat rejected from state 4 to 1 is given as: (4.5) Therefore net heat supplied But

Hence: (4.6) The thermal efficiency is therefore given as the ratio of net heat transferred to the actual heat supplied: (4.7) Assuming constant

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33


(4.8) But processes 1 – 2 and 3 – 4 are isentropic and

and

Implying

(4.9)

and

(4.10)

Substituting equation (10) into (8), we have (4.11) Equation (11) shows that the efficiency of a single stage GT is proportional to the pressure ratio. Plotting a graph of the efficiency against the pressure ratio with values of chosen in increasing order from 1 – 30 is shown below:

Pressure Ratio 1 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

η (Single Stage) 0.00 0.18 0.33 0.40 0.45 0.48 0.51 0.53 0.55 0.56 0.58 0.59 0.60 0.61 0.61 0.62

Table 4.1: Pressure ratio with computed efficiency The corresponding graphical plot is given on the next page:

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A Single-Stage GT cycle Without Regeneration atures

ηS 0.70 0.60

Efficiency

0.50 0.40 0.30 0.20 0.10 0.00 0

4

8

12

16

20

24

28

32

Pressure ratio, rp Figure 4.3: Plot of efficiency against pressure ratio The highest temperature which is the GT inlet temperature is limited by the capability the turbine blade can withstand. However, optimising the net work can be achieved by fixing the GT inlet temperature (with the air inlet temperature) and subsequently raising the pressure ratio gradually and noting the graphical trend till it reaches to the optimum maximum as depicted below:

T 3

Tmax

Wnet1 2

Wnet2

Wnet3 4

Tatm

1

S Figure 4.4: Maximisation of Net Work at fixed t

From Figure 4.4, the optimum work done is observed to be at

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle A modified form of the Joule-Brayton cycle is feasible and practical as achieving an ideal reversible cycle is almost impossible. The modified assumptions are: i. ii. iii.

The compressor and turbine are non-isentropic. A combustion chamber is employed in the heat addition instead of the ideal heat exchanger. Gases are rejected to the atmosphere after expansion in the gas turbine instead of the ideal (closed cycle) cooling heat exchanger.

This can be depicted in the Figure 4.5 below:

T

Pressure drop during heat addition 3 3'

2

2'

4

4'

Pressure drop during heat removal 1

S Figure 4.5 Modified Cycle T-S Diagram Therefore changes in the specific heat capacities in the compressor and turbine are eminent. These values may be given for air as: The non-isentropic modifications from the idealised equations are given below: Isotropic compression at the compressor or pump is given by (4.12) Isotropic expansion at the turbine is given by (4.13) The combustion chamber isentropic efficiency is also given by (4.14)

However, for multi-stage GT intercoolers, reheaters, regenerators or recuperates may be added for the ultimate goal of improving the overall cycle efficiency.

4.12 Inclusion of the intercoolers, reheaters and regenerators in the JouleBrayton cycle. Intercoolers and reheaters are normally incorporated in a multi-stage or sequential combustion GT where the efficiency of the cycle is improved. The intercooler cools Bashar Dan-asabe

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle the compressed air in-between the multi-stage compression to avoid compression with excessive thermal energy which the compressor would not withstand. In this case the extracted heat energy during the cooling could be utilised into some useful form of energy thereby improving the overall energy utilisation factor of the plant. The reheater also allows for expansion between multi-stage levels of the GT where the expansion is carried out gradually in stage when a high compression ratio is involved. The regenerator compensates the amount of heat energy supplied by utilising some of the exhaust heat energy to heat the compressed air leaving the compressor. The recuperator is similar to regenerator but is used when some of the exhaust heat energy is channel to supply thermal energy to either the HRSG or used to feed other external heat demands like the district heating needs. However, increase in the number of the stages with regeneration increases the tendency of the cycle approaching the idealised Carnot cycle as all the heat is supplied close to the maximum temperature and heat rejected also close to the minimum temperature.

4.2 Rankine Cycle The Rankine cycle is a vapour generating cycle power plant. Beginning with analysis of its idealised Carnot cycle; basically consisting of a steam turbine (ST), a condenser, a pump and a boiler. The ideal reversible Carnot cycle is shown below in Figure 4.6.

T

T

qs

qs Tmax

Tmin

2

3

6

5

Tmax

5

6

Tmin

5'

4 4'

1

4

1

3

2

qr

qr

S

S Figure 4.6(a): Ideal Carnot Cycle T-S Diagram

Figure 4.6(b): Modified Carnot Cycle T-S Diagram

The work output for the reversible cycle is given as (4.15) Comparing the reversible cycle with an irreversible one; as this is true for all practical power plant cycles. Figure 4.6(b) shows the ideal irreversible Carnot cycle. Neglecting pump work we have

(4.16)

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle The heat supplied is assumed to be all supplied at the maximum temperature as: (4.17) From equation (15) and (16), it can be seen that the work output in irreversible cycle is less than that in the reversible cycle. The difference is given by: (4.18) Hence the efficiency is given by (4.19) Therefore the efficiency is reduced with irreversibility effect.

The useful heat rejection in a reversible cycle is given by

(4.20) Therefore the useful heat rejection in ideal reversible Carnot cycle remains unchanged but this is increased in the irreversible cycle. The energy utilisation factor for a reversible cycle is given by: (4.21)

And for irreversible cycle is:

(4.22) Thus the

remains unchanged for both the reversible and irreversible cycles.

Extending this analysis to the practical Rankine cycle as shown in Figure 4.7 below:

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T

3

Tmax

2 Tmin

1

4 4'

S Figure 4.7: Rankine Cycle T-S Diagram with Irreversibilty Effect

(4.23) (4.24) (4.25) Thermal efficiency is reduced by the factor

but the

is unchanged (4.26)

The of a reversible Carnot cycle is unity. Theoretical power analyses of the Rankine cycle are given below assuming changes in and are negligible: i.

Stage 1 – 2΄, pump work But

as no heat supplied by the pump, therefore (4.27)

ii.

Stage 2΄ – 3, boiler and superheater heat supply But

as no work done by the boiler, therefore (4.28)

iii.

Stage 3 – 4΄, turbine power output But

iv.

as no heat is supplied by the turbine and

, therefore (4.29)

Stage 4΄ – 1, condenser Assuming the heat rejected by the condenser is gained by the cooling water adiabatically

,

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle But no work is done by the condenser as only heat is transferred i.e. heat rejected, therefore (4.30) v.

Net power output is given by

(4.31) vi.

Cycle efficiency is given by

,

therefore,

(4.32)

vii.

Mass of cooling water is given by (4.33)

4.21 Modification of the Rankine cycle The aim is to improve the overall power and efficiency of the ST cycle. a. Inclusion of a reheater in the Rankine cycle This is done where the high pressure steam is expanded in a series of turbines to produce work output. The expanded gas after each stage is reheated to a higher temperature or back to the initial temperature of the HP turbine. Usually the first expansion is done in the HP turbine and then subsequently in the MP and LP turbines respectively depending on the number of turbines used. Figure 4.8 shows the T – S diagram of the reheat cycle.

T

3

2'

4

5

4'

2

1

5 5'

S Figure 4.8: Reheat Rankine Cycle T-S Diagram

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle The major changes in the thermodynamic equations of the cycle are the heat supplied and the work output. Heat supplied is therefore given by: (4.34)

(4.35) (4.36)

b. Inclusion of regenerative open feed heater in the Rankine cycle This involves the bleeding some of the steam in the GT at a much higher pressure than the condenser pressure where it mixes in an open chamber with feed water from the condenser. The resultant extracted steam and feed water mixture allowed at saturated water and at the pressure of the extracted steam is pumped by a second pump to the boiler depending on the number of extraction stages permitted. Figure 4.9 below shows the T – S diagram of the single regenerative open feed heater.

T

5

4

4'

2' 2 3

y

6 6'

(1-y)

1

7 7'

S Figure 4.9: Regenenerative Open Feed Rankine Cycle T-S Diagram

(4.37)

(4.38) (4.39)

(4.40) Therefore the cycle efficiency is given by

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c. Inclusion of regenerative closed feed heater in the Rankine cycle This involves the bleeding some of the steam from the GT which supplies heat to the pumped feed water line in a heat exchanger till it eventually condenses. The saturated water and steam is then pumped into the feed water pipe to the boiler depending on the number of extractions permitted. Figure 4.10 below shows the T – S diagram of a single regenerative closed feed heater.

T

4

2 2'

33' y

6 6'

5 (1-y) 1

7 7'

S Figure 4.10: Regenenerative Closed Feed Rankine Cycle T-S Diagram

(4.41)

(4.42) (4.43)


d. Inclusion of regeneration and reheating in the Rankine cycle This involves the inclusion of both reheating and regeneration together in the Rankine cycle. The main aim is to achieve a higher efficiency and save fuel. Figure 4.11 shows the T – S diagram of a single regenerative reheat Rankine cycle.

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T

5

4' 4 2' 2 3

6 y

7

6' 8 8'

(1-y) 1

9 9'

S Figure 4.11: Reheat Regenenerative Open Feed Rankine Cycle T-S Diagram (4.45)

(4.46) (4.47)


4.3 Combined Cycle The ideal combined cycle is one without heat losses, temperature drop and pressure drops. This is depicted in Figure 4.12:

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qs

Topping Cycle

Wt

qtb Bottoming Cycle

Wb

qr Figure 4.12: Scematic diagram of the Ideal combined cycle Exergy flux of the topping reversible cycle results in work done; (4.49) Heat supplied to the topping cycle results in work done:

Work done by bottoming cycle

, but The combined output

,

(4.50)

(4.51) Diving through by

, thus

(4.52)

Thus thermal efficiency of the ideal CC is greater than the upper cycle by as a result of inclusion of the lower cycle.

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle 4.32 Inclusion of Irreversibility The deviation of the practical CC from the ideal CC is as a result of irreversibility effect. This includes internal as well as external irreversibility. The internal irreversibility is as a result of isentropic expansion and compression, change in specific heat capacities and variable gamma ratio. The external factor can be as a result of temperature drop between the two cycles. This illustration is shown below: Et

Topping Cycle It

Wt

Etb Eb Bottoming Cycle Ib

Wb

Er Figure 4.13: Exergy analysis of the Topping and Botoming cycle with temperature drop

Exergy flux of the upper cycle (4.53) Exergy flux of the lower cycle (4.54) Combined work done

(4.55) Thus irreversibility effect as a result of the external and internal factors together with corresponding heat rejection actually reduces the work output of a CC.

4.33

Inclusion of heat loss between the two cycles

This is as a result of exhaust gas leaving at a higher temperature than the compressor suction temperature in practical plants. Figure 4.14 shows the equation of the CC with include exhaust heat loss.

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qt

Topping Cycle

qex

Wt

qtb qb Bottoming Cycle

Wb

qr Figure 4.14: Combined cyle with heat loss due to exhaust The upper and lower cycle efficiencies can be given by (4.56) Heat supplied to the lower cycle is (4.57)

(4.58) Where This cyclic equation can be modified for the open GT and closed ST combined cycle without HRSG firing as: (4.52) Where

4.4 Criterion of performance Some of the conventional criteria used in the thermodynamic analysis of Rankine cycle, Joule-Brayton cycle, CCGT,CHP and general combined cycles are given on the next page:

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle i.

Boiler efficiency. This is defined as:

ii. Combustion chamber efficiency. This is given as

iii. Turbine Isentropic efficiency. This is given as:

iv. Turbine Isentropic efficiency. This is given as:

v. Heat exchanger effectiveness or thermal ratio. This is given as:

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5.0 SCHEMATIC MODEL OF THE CPPH

The schematic diagram of the combined cycle power and heating (CPPH) is depicted in Figure 5.1. This consists of the topping multi-stage compression and expansion gas turbine and the corresponding bottoming single regenerative dualpressure reheat steam cycle. The GT cycle consists of the three- stage sequential air compressors, two intercoolers, a combustion chamber and the three-stage gas turbines. The process involves atmospheric air compressed sequentially in the air compressor in three stages with intermittent intercoolers to cool the compress air in each stage. The compressed air is then preheated by the exhaust of the GT where it then enters the combustion chamber. It is expanded in three-stages by the GTs with intermittent reheating to maximum temperature. Depending on the exhaust temperature, the exhaust gas is used to regenerates some of its heat to the gas cycle compressed air before moving to the HRSG where it finally exit to the atmosphere. The exhaust gas passing through the unfired HRSG regenerates thermal energy to produce super heated steam for expansion in the ST cycle. The high temperature steam of a maximum 600 C is expanded in the first HP steam turbine and then reheated back to its initial temperature in the HRSG. It is subsequently expanded in the second LP steam turbine where some steam is extracted for closed feed water heating. The fully expanded gas from the second ST is condensed to a condenser pressure where the rejected heat energy is extracted as useful heat energy. Some make up water is supplemented and the condensed saturated water is pumped to a pipe line where it meets with bled steam and finally rechanneled back to the boiler.

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5.1 Schematic Model of the CPPH cycle and its T – S Diagram Atmospheric 1 Air AC

AC 2

IC

5

9 10

7

6

GT

GT

8

3 4

IC

GT

AC

11

CC 7' Fuel

12

R 12' SH B SD

EC SH B

SD 16

EC

Exhaust gas

14

13

ST

ST 15

22

18

C

17 FWH

19 CP

WP

20

BFP 21

Schematic diagram of the 3-stage Combined Power to Power and Heating (CPPH) cycle with unfired HRSG

T

7 9 9' 11 11' 8 8' 10 10'

12

12'

15

14 7'

6

6'

4 4' 2' 2

20'

22' 16'

5

3

y

1

17'

21 (1-y) 19

18'

S Figure 5.2: Multi-Stage Gas and Steam Turbine Cycle T-S Diagram

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5.2 Basic Assumptions of the CPPH plant Some basic assumptions are carried to ensure practicability of the simulated plant with the real plant. These are: i.

The inlet air into the compressor is taken at standard atmospheric temperature and pressure i.e. STD at 25 C and 1.01325 bar respectively. ii. A maximum GT inlet temperature and overall pressure ratio of 1700 C and 21 are assumed respectively. iii. The stage pressure ratios are assumed to be equal i.e. stage pressure ratio of 7 means cumulative of 21 for the three stage compression and expansion GT cycle. iv. Specific heat capacities of air in the compressor and CC are taken as 1.006 and 1.15 kJ/kgK respectively. v. Gamma in the compressor and turbine are taken as 1.4 and 1.33 respectively. vi. Pressure drop of 0.08bar and 0.02 bar are assumed in the CC and the HRGS respectively. vii. The final exit gas exhaust temperature is assumed to be 200 C. viii. ST maximum inlet temperature and pressure are taken as 600 C and 100 bar respectively. ix. Temperature ratio between the HP and LP steam turbines is taken to be unity i.e. LP steam turbine reheated to the initial steam inlet temperature. x. Heat loss in the CC is taken as 5% i.e. combustion chamber efficiency of 95%. Heat loss in the HRGS and recuperator are each taken as 10% i.e. regenerator effectiveness of 90%. Heat loss in the condenser and pipings are taken to be 3% each respectively. xi. Pressure drop in the condenser and feed water heater are neglected. xii. Gas and steam turbine isentropic efficiency of 89% were assumed. Corresponding compressors and pumps isentropic efficiencies of 85% were used.

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6.0 PROGRAM GENERATION USING EXCEL

Microsoft Excel spread sheet was used in programming the CC calculations. This consists of data and implant steam table in one excel sheet and the corresponding analysis in another sheet. The simulation was carried out to enable an instantaneous output as the parameters are varied accordingly. The result’s output comprising the cycle efficiency, energy utilisation factor, net work and net heat supplied is also displayed on the data sheet for prompt comparison with the varied parameters. The programming of the GT calculation was quite straightforward as it requires imputing directly the isentropic expansion and compression in the analysis sheet equations with referencing values from the parameters in the data sheet. The ST cycle programming is quite painstaking as it requires changing entropy and enthalpy values from steam table as the any input parameter is varied. An excel referencing function of HLOOKUP was used to pick up the ST inlet temperature and pressure. Reference functions of IF and HLOOKUP commands where used instantaneously to readjust the enthalpy and entropy of the reheat pressure as it changes. The INDEX command was used to look up the reheat temperature and its corresponding enthalpy. The IF and HLOOK UP referencing commands were again used to pick the appropriate extraction pressure enthalpy as it changes. Finally, the IF statement was used to look up the condenser pressure enthalpies at the corresponding volume of the saturated liquid levels. If Statement: To

Hlook up Command:

If, Hlook up and Index Commands:

create coordinates in

To look up enthalpy and

To look up interpolation enthalpies,

a range of cells

entropy at 14

entropies and temperatures at 16

If, Hlook up and Index Commands:

Index Command: To

Match Command: To

To look up interpolation enthalpies,

look up reheat enthalpy

create coordinate for the

entropies and temperatures at 17

and entropy at 15

reheat at 15

If Statement: To

If Statement: To look up interpolation

look up enthalpy and

enthalpies, entropies and temperature

entropy at 21

for the condenser at 18 and 19

Figure 6.1: Flow Chart for the Excel Proramming

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle 6.1 The implant Steam Table The in-plant steam table is given below: Pressure 3 (Bar) 11 100

Enthalpy 200

250

6.186 2803 6.340 2799 6.452 2796 6.695 2829 6.753 2835 6.968 2851 7.312 2866 7.834 2876 2593 8.058 2584 8.149 2561 8.394 2514 8.974

6.289 2858 6.547 2904 6.711 2925 6.926 2944 6.980 2948 7.182 2958 7.517 2968 8.033 2975

80 60 40 30 20 15 10 9 6 3 1 0.15 0.10 0.05 0.01

3 7 8 4 7 8 175.4 0.001121 158.8 0.001098 133.5 0.001074 99.6 0.001044 53.9 0.0010140 45.8 0.0010102 32.9 0.0010052 7 0.0010002

6.180 2710 6.200 2731 6.210 2681 6.211 2607 6.623 2774.0 6.671 2757 6.910 2691 6.920 2516 214 0.7165 192 0.649 138 0.476 29 0.106

Temperature ( C) 350 400 450 3097 3241 6.213 6.419 3139 3272 6.364 6.555 3177 3301 6.541 6.719 3214 3330 6.769 6.935 6.541 6.744 6.921 7.082 2995 3117 3231 3343 6.768 6.957 7.126 7.283 3025 3138 3248 3357 6.919 7.102 7.268 7.423 3039 3148 3256 3364 7.124 7.301 7.464 7.617 3052 3158 3264 3370 7.176 7.352 7.515 7.667 3055 3161 3266 3372 7.373 7.547 7.707 7.858 3062 3166 3270 3376 7.702 7.874 8.032 8.182 3070 3173 3275 3380 8.215 8.386 8.543 8.693 3075 3177 3278 3382 300

5 6 6 5

500 3373 6.596 3398 6.723 3421 6.879 3445 7.089 7.233 3456 7.431 3467 7.569 3473 7.761 3478 7.811 3480 8.001 3483 8.324 3486 8.834 3488

743 670 561 417

The range of input parameter values are carefully chosen with respect to realistic and practical viability of the reviewed thermodynamic cycles. These ranges are given below; a. Air compressor and gas turbine pressure ratios respectively ; 2-8 and 1.9-7.9 b. Inlet gas turbine temperature; 1000-1700 C c. Exhaust gas temperature; 200 C

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600 3624 6.902 3641 7.019 3657 7.166 3674 7.368 7.507 3682 7.701 3690 7.838 3690 8.028 3698 8.077 3699 8.267 3701 8.588 3702 9.097 3703

Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle d. Steam turbine inlet pressure and temperature; 40-100 bars and 400-600 C respectively e. First steam turbine reheat pressure; 10-30 bar f. Second steam turbine extraction pressure; 1-9 bar g. Condenser pressure; 0.5-0.01 bar The analysis is subjected to varying input parameters such compressors/turbines pressure ratios, inlet GT temperature, exhaust gas temperature, steam turbine inlet pressure and condenser pressure.

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7.0 ANALYSIS AND CALCULATIONS

The 3-stage GT is analysed theoretically and then compared with theoretical equation (4.11) of the single-stage GT.

7.1 Theoretical Equation of the 3-Stage GT without Regeneration Figure 7.1 below shows the 3-stage GT:

Atmospheric Air 1 AC

AC

AC 2

GT 8

3 4

5

6

7

GT

GT 9 10

CC Fuel

11 12

Exhaust gas

Figure 7.1: A 3-Stage GT cycle Without Regeneration

The corresponding T-S diagram is given below:

8

T

10 12 qin qin

7

9

11

13

qin

6

4

2 qout

5

1 qout qout

3

S Figure 7.2: Ideal 3-Stage Gas Cycle T-S Diagram

Assuming the 3-stage GT to be an ideal cycle with the following basic assumptions are: i. ii. iii.

The compression and expansion are isentropic. The specific heat capacity of the air remains unchanged. γ in the compressor and combustion chamber remains the same.

But processes 5 – 6 and 8 – 9 are isentropic and

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(7.1)

Implying

(7.2)

The heat supplied is given by (7.3) The net work done is given by (7.4) Therefore ideal cycle efficiency (with constant

is given by:

Rearranging we have:

Dividing through by

and substituting equations (7.1) and (7.2) we have

(7.5) From the equation, it can be seen that the 3-stage GT turbine depends on both the pressure ratio and the maximum firing temperature unlike the single-stage GT that depends only on the pressure ratio. Both these assumptions are true keeping the inlet temperature constant. A tabular results of the ideal 3-stage (equation 7.5) and single-stage (equation 4.11) GT were evaluated with increasing values of the pressure ratio from 1 – 30. The 3stage GT was evaluated at different firing temperatures as given:

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Pressure Ratio 1 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

η (Single-stage) 0.000 0.180 0.327 0.401 0.448 0.482 0.508 0.530 0.547 0.562 0.575 0.587 0.597 0.606 0.614 0.622

η at 1000 C 0.000 0.358 0.489 0.518 0.524 0.522 0.516 0.509 0.500 0.491 0.482 0.472 0.462 0.453 0.443 0.434

η at 1400 C 0.000 0.369 0.519 0.561 0.578 0.584 0.586 0.586 0.584 0.581 0.577 0.573 0.569 0.564 0.559 0.555

η at 1700 C 0.000 0.374 0.532 0.580 0.601 0.612 0.617 0.619 0.620 0.619 0.618 0.616 0.614 0.611 0.609 0.606

Table 7.1: Efficiencies of single and three-stage GT without regeneration The corresponding graphical result is plotted below:

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Comparison of a 3-Stage Ideal GT cycle with an Ideal SingleStage GT cycle η (Single-stage) η at 1400 C

0.700

η at 1000 C η at 1700 C

0.600

Efficiency

0.500 0.400 0.300 0.200 0.100 0.000 0

4

8

12

16

20

24

28

32

Pressure ratio, rp

Figure 7.3: Comparison of efficiencies of single and three-stage GT This shows that the 3-stage GT is very efficient at low pressure ratio and also increases with increasing maximum temperatures. At higher pressure ratios the efficiency of the 3-stage GT decreases considerably. The optimum efficiencies at the various temperatures for the 3-stage GT are tabulated below as extracted from table 7.1:

3-stage GT firing temperature ( C) 1000

Optimum pressure ratio 8

1400

12

1700

16

Table 7.2: Optimum efficiency at various temperatures This shows that 3-stage GT can be operated at even lower temperature ratio say from 4 – 8 at all the various GT inlet temperatures since the increase in efficiency above these pressure ratios is marginal. The single-stage GT can only be operated at higher pressure ratios as depicted from the Figure 7.3 above.

7.2 Theoretical Equation of the 3-Stage GT with Regeneration The 3-stage GT with regeneration gives the equivalent of the work ratio. Both the work ratio and the efficiency are expected to be at least high or up to an optimum level where they are equal. Figure 7.4 below shows the regenerated 3-stage GT:

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Exhaust gas

14 Atmospheric Air

13

1

6

AC

AC

AC 2

GT 7

3 4

9

10

8

5

GT

GT 11

12

CC Fuel Figure 7.4: A 3-Stage GT cycle With Regeneration

The corresponding T-S diagram is given below:

8

T 7

9

qin

10 12 qin

qin

6

4

2

3

1 qout

13

11

qreg

qout

5

qout

S Figure 7.5: Ideal 3-Stage Gas Cycle Regenerative T-S Diagram With the same theoretical assumption of Section 7.1, with heat supplied and work done given as: (7.6) (7.7) The cycle efficiency therefore cycle is given as:

Dividing the numerator by

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and the denominator by

, we have

58


But from equations (7.1) and (7.2), Therefore the cycle efficiency is (7.8) From the equation, it can be seen that the regenerated 3-stage GT turbine depends on the pressure ratio and temperature unlike the regenerated single-stage GT.

A tabular results of the regenerated 3-stage and single-stage GT were evaluated with increasing values of the pressure ratio from 1 – 30. The 3-stage GT was evaluated at different firing temperatures as shown below:

Pressure Ratio 1 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

η(Singlestage)

0.000 0.180 0.327 0.401 0.448 0.482 0.508 0.530 0.547 0.562 0.575 0.587 0.597 0.606 0.614 0.622

η at 1000 C 0.000 0.358 0.489 0.518 0.524 0.522 0.516 0.509 0.500 0.491 0.482 0.472 0.462 0.453 0.443 0.434

η at 1400 C 0.000 0.369 0.519 0.561 0.578 0.584 0.586 0.586 0.584 0.581 0.577 0.573 0.569 0.564 0.559 0.555

η at 1700 C 0.000 0.374 0.532 0.580 0.601 0.612 0.617 0.619 0.620 0.619 0.618 0.616 0.614 0.611 0.609 0.606

Reg. at 1000 C 0.764 0.713 0.650 0.607 0.573 0.545 0.521 0.499 0.480 0.462 0.445 0.430 0.416 0.402 0.389 0.377

Reg. at 1400 C 0.821 0.781 0.734 0.701 0.675 0.654 0.635 0.619 0.604 0.590 0.578 0.566 0.555 0.545 0.535 0.526

Reg. at 1700 C 0.848 0.815 0.774 0.746 0.725 0.706 0.691 0.677 0.664 0.653 0.642 0.632 0.623 0.614 0.606 0.598

Table 7.3: Efficiencies of single and three-stage GT with regeneration The corresponding graphical result is plotted below:

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Comparison of a 3-Stage Ideal GT cycle with an Ideal Single-Stage GT cycle With Regeneration at various Temperatures η (Single-stage) η at 1700 C Reg. at 1700 C

η at 1000 C Reg. at 1000 C

ηs at 1400 C Reg. at 1400 C

0.900 0.800 0.700

Efficiency

0.600 0.500 0.400 0.300 0.200 0.100 0.000 0

4

8

12

16

20

24

28

32

Pressure ratio, rp

Figure 7.6: Comparison of efficiencies of single and three-stage GT without regeneration

7.3

Input data, Formulation and Computation in Excel spreadsheet

The excel data section is tabulated below from excel spread sheet. The variable input data of the GT are given below; the shaded exhaust value cell is not an input value as it is instantaneously computed. Gas Turbine Cycle Data

Symbol

Unit

Values

1

Comp. Inlet Pressure

P1

KPa

101.325

2

Comp. Inlet Temperature Turb. Inlet Temperature & Percentage regeneration

T1

C

25

T7 ; Reg.

C; %

1700

54

T13

C; K

200

532.37

3 4

nd

st

2 & 1 Exhaust temperature

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5

Comp. & Turb. Pressure ratios

6

Comp. & Turb. Isen. Efficiencies Gamma in comp. & Comb. Chamber S.H.C. in comp. & Comb. Chamber

7 8 9

Pressure drop in CC CC & Regenerator 10 Effectiveness

6

5.9

85

89

1.4

1.33

KJ/kgK; KJ/kgK

1.006

1.15

KPa

8

2

%; %

95

90

Unit

Values

Bar

100

C

600

%; %

ΔP

;ε

The ST variable input data are given below: Rankine Cycle Data

Symbol

11

Boiler Outlet Pressure

12

Turbine Inlet Temperature

13

Pump &Turb. Isen. Efficiencies

%; %

85

14

Reheat Pressure Extracted Steam & Cond. Pressure

KPa

10

bar; bar

3

15

89

0.05

The instantaneous implant steam table computation results are given below: 16 17 18 19 20 21 22 23 24 25 26 27 28

Specific Volume at 19 & 21 Enthalpy & Entropy at 14; P14 , T14 Int. Enthalpy & Entropy at 16; Pre, S16L Int. Enthalpy & Entropy at 16; Pre, S16H Int. Temperatures at 16: Pre ,T16L, T16H Enthalpy & Entropy at 15; Pre, S15 Int. Enthalpy & Entropy at 17; Pext, S17 Int. Enthalpy & Entropy at 17; Pext, S17 Int. Temperatures at 17: Pext , T17L, T17H Enthalpy & Temperature at 21; Pext Int. Enthalpy & Entropy at 18: Pco, S18f Int. Enthalpy & Entropy at 19: Pco, S19g Enthalpy & Temperature at 19; Pco, S17

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V19; V20

m³/kg

0.0010052 0.001074

h14; S14

KJ/Kg; KJ/kgK

3624

6.902

h16L; S16L

KJ/Kg; KJ/kgK

2829

6.695

h16H; S16H

KJ/Kg; KJ/kgK

2944

6.926

200

250

T16L; T16H

C; C

h15f; S15f

KJ/Kg; KJ/kgK

3698

8.028

h17L; S17L

KJ/Kg; KJ/kgK

3172.5

7.874

h17H; S17H

KJ/Kg; KJ/kgK

3275

8.032

C; C

350

400

h21; T21

KJ/Kg; C

561

133.5

h18f; S18f

KJ/Kg; KJ/kgK

138

0.476

h19g; S19g

KJ/Kg; KJ/kgK

2561

8.394

h19g; T19

KJ/Kg; C

138

32.9

T17L; T17H

61

Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle The analyses and computation of the CC are given below: this is valid for only one simulation as depicted in the ST and GT data table above at 1700 C, pressure ratio of 6, percentage regeneration of 54% with other respective data inputs above. Formulations/Computations 1 Comp. Isen. & Real Outlet Temperature:

K; K

Results 497.22

532.37

2 Turb. Isen. & Real Outlet Temperature:

K; K

1270.17

1347.48

3 Enthalpy at 16:

kJ/Kg; kJ/kg

2932.05

3008.17

4 Enthalpy at 17:

kJ/Kg; KJ/kg

3272.41

3319.22

5 Steam Dryness Fraction at 18:

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Symbol

Unit

0.9538

62


6 Enthalpy at 18:

KJ/Kg; 2449.00 KJ/kg

2586.39

7 Enthalpy at 20:

KJ/Kg; 148.05 KJ/kg

149.82

8 Enthalpy at 22:

KJ/Kg; 571.42 KJ/kg

573.26

9 Temperature of Bled Steam at 16:

10 Temperature of Bled/Extracted Steam at 17:

11 Mass Fraction of Extracted Steam:

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C

244.81

283.88

C

398.74

420.87

0.1331

63


12 Heat Exchange with regenerator:

449.52

13 Mass of Steam per Kg of air leaving regenerator:

Kg/Kg of air

14 Pump Work 1 & 2:

KJ/Kg; 1.05 KJ/kg

15 Steam Turb. Work Output:

kJ

195.88

16 Steam Turb. Net Work in kJ:

kJ

194.66

17 Useful Heat delivered by AC & Cond.:

kJ; kJ

471.56

18 Exhaust Heat Gas in KJ:

kJ

176.05

0.1202

0.17

247.42

;

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle 19 Total Useful Heat Delivered in kJ:

kJ

718.98

20 Gas Turb. Heat Supplied i:

KJ

2589.22

21 Gas Turb. Heat Supplied in kJ & kW:

KJ

2725.50

;

; 22 Gas Turb. Comp. & Turb. Work:

707.33

23 Gas Turb. Net Work in kJ & kW:

KJ

1450.69

24 Gas Turb. Cycle Efficiency:

%

0.56

25 Total Plant Work Output in KJ:

kJ

1645.36

26 Total Useful Work in KJ:

kJ

2364.34

27 Total Plant Cycle & Engine Efficiency:

%; %

0.64

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2158.03

0.53

0.60

65

Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle 28 Plant Utilization factor:

0.98

%

0.87

Extracted result outputs from the above computations with percentage regeneration at 54% are given as: Summarised Result Outputs

With Regeneration

1

Total Cycle & Plant Eff. (%)

63.55

60.37

2

Gas Turb. Cycle & Plant Eff. (%)

56.03

53.23

3

CC Plant & Cycle Energy Utilisation Factor (%)

91.31

86.75

4

Net Power & Net Heat (KJ/Kg)

1645.36

718.98

5

Heat Supplied (KJ/Kg)

2589.22

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8.0 OPTIMISATION

The simulated 3-stage GT cycle is first compared with the ideal 3-stage GT cycle. Subsequently the GT cycle and ST cycle are optimised separately and then their combined overall effect optimised accordingly.

8.1 Comparison of the Practical 3-stage cycle with the Ideal 3-stage cycle of Sections 7.1 and 7.2 Comparison of the simulated 3-stage GC (without regeneration) with the ideal cycle of Section 7.1 shows a very strong similarity in terms of graphical trends between the two cycle. On the other hand, one of the deviations from the ideal is that practical simulated cycle cannot be operated at a pressure ratio of unity as a result of pressure drop across the GT cycle which means if the compressor pressure ratio is unity, that of the turbine will be a little less than one which is impracticable. It can also be observed that there is about 14% drop in efficiency as compared to the ideal cycle. This is traced to irreversibility effect of isentropic coefficients of compression, expansion, variable specific heat capacities, het and pressure losses across the GT cycle. The tabular and graphical illustrations of the cycle are given below: Pressure Ratio 2 4 8 12 16 20

η at

η at

η at

1000 C 0.231 0.344 0.367 0.350 0.330 0.300

1400 C 0.250 0.385 0.435 0.439 0.433 0.423

1700 C 0.258 0.402 0.464 0.477 0.477 0.473

Table 8.1: Values of efficiencies at the three different temperatures The 3-Stage Practical Simulated GT cycle at various Temperatures 0.600 η at 1000 C η at 1700 C

0.500

η at 1400 C

Efficiency

0.400 0.300 0.200 0.100 0.000 0

4

8

12

16

20

24

Pressure ratio, rp

Figure 8.1: Graphical trend of efficiency against pressure ratio

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However, with regeneration of the 3-stage GT cycle, similar comparison of the simulated 3-stage GT cycle with the regenerated ideal cycle of Section 7.2 shows also a strong similarity in terms of graphical trends between the two cycles. The results are depicted below in tabular and graphical trends respectively:

η3s at 1000 C 0.231 0.344 0.367 0.350 0.330 0.300

Pressure Ratio 2 4 8 12 16 20

η3 at 1400 CC 0.250 0.385 0.435 0.439 0.433 0.423

η3 at 1700 C 0.258 0.402 0.464 0.477 0.477 0.473

Reg. at

Reg. at

Reg. at

1000 C 0.567 0.514 0.430 0.371 0.324 0.286

1400 C 0.659 0.618 0.554 0.509 0.474 0.444

1700 C 0.703 0.669 0.619 0.576 0.546 0.521

Table 8.2: Efficiency with regeneration at the three different temperatures

The 3-Stage Practical Simulated GT cycle with Regeneration at various Temperatures η at 1000 C η at 1700 C Reg. at 1400 C

0.800

η at 1400 C Reg. at 1000 C Reg. at 1700 C

0.700 0.600

Efficiency

0.500 0.400 0.300 0.200 0.100 0.000 0

4

8

12

16

20

Pressure ratio, rp Figure 8.2: Plot of efficiency with regeneration at the three different temperatures

8.2 Optimisation of the GT cycle The optimisation was carried out with and without regeneration as:

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle 8.21 Optimisation of the GT cycle without regeneration This was carried out at three GT firing temperatures of 1000 C, 1400 C and 1700 C keeping in mind the maximum available exhaust temperature of about 600 C (about 900K) thermal energy is not exceeded. The maximum exhaust temperature for GT is between 500 C – 600 C. But 600 C limit was chosen to maximise the efficiency and useful thermal energy potential for the ST cycle. These were carried out as follows: a. GT Inlet temperature at 1000 C: The pressure ratio at firing temperature of 1000 C was varied accordingly and the respective efficiency and the exhaust temperature noted. It can be observed from the graph below that at pressure ratios from 4 – 8, the efficiency increases by about 4% but with less thermal energy potential for the ST cycle. The optimum efficiency can be realised at operating at with an efficiency of about 35% at the maximum exhaust temperature of 600 C (about 900K). Therefore it can be deduced that regeneration is of no significant operating at firing temperature of 1000 C for the GT since regeneration will further decrease the available thermal energy potential for the ST cycle. Regeneration may only be significant at this temperature when it is not a combined cycle. b. GT Inlet temperature at 1400 C: The pressure ratio at firing temperature of 1400 C was varied accordingly and the respective efficiency and the exhaust temperature noted. It can seen from the graph below that the maximisation of the efficiency can be realised at pressure ratio range of 6 – 8 which is very close to the optimum pressure ratio of 12. Operating at pressure ratio of 12 is not practicable since the cumulative for the 3-stage GT will now 36 which is significantly very high. But operating at pressure ratio range of 6 – 8 will mean operating with excessive exhaust temperature of about 837 C (1100K). This is significantly high as regeneration at this temperature will be of importance for the GT cycle. This was depicted in section 8.22 (a) to re-channel some of the high exhaust thermal potential back to GT till a feasible exhaust temperature of about 900K is realised. c. GT Inlet temperature at 1700 C: The pressure ratio at firing temperature of 1700 C was varied accordingly and the respective efficiency and the exhaust temperature noted. It can seen from the graph below that the maximisation of the efficiency can be realised at practical pressure ratio range of 6.5 – 8. The difference in efficiency between this range and the optimum pressure ratio of 14 is about 4% notwithstanding. Operating at pressure ratio of 14 is not practicable since the cumulative for the 3-stage GT will now 36 which is significantly very high. But operating at pressure ratio range of 6 – 8 will mean operating with excessive exhaust temperature of about 997 – 1057 C (1270 – 1330K). This is significantly very high as regeneration at this temperature will be of importance for the GT cycle. This was depicted in section 8.22 (b) to re-channel some of the high exhaust thermal potential back to GT till a feasible exhaust temperature of about 900K is realised.

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle Press. Ratio 2 4 8 12 16 20

Efficiency at 1000 C (%) 24 34 37 35 33 30

at 1400 C (%) 25 38 43 44 43 42

Efficiency at 1700 C (%) 26 40 46 48 48 47

Table 8.3: Efficiency at the three various temperatures Press. Ratio 2 4 8 12 16 20

Ex. Temp. at 1000 C (K) 1106.02 948.31 818.45 752.88 710.36 679.47

Ex. at 1400 C (K) 1453.79 1246.29 1075.62 989.45 933.57 892.98

Ex. Temp. at 1700 C (K) 1714.48 1469.77 1268.5 1166.87 1100.98 1053.11

Table 8.4: Exhaust temperature at the three various temperatures

Exhaust Heat Energy Available for the ST cycle Efficiency at 1700 C (%)

Efficiency at 1000 C (%)


Ex Temp. at 1700 C (K)



1800 1700

50

1600

Efficiency (%)

1500 40

1400 1300

30

1200

Exhaust Temp. ( C)

60

1100 20

1000 900

10

800 700

0

600 0

2

4

6

8

10

12

14

16

18

20

Pressure rario, rp

Figure 8.3: Efficiency and exhaust temp. at the three various temperatures

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle 8.22 Optimisation of the GT cycle with regeneration This is carried out at the two GT firing temperatures of 1400 C and 1700 C keeping in mind the maximum available exhaust temperature of about 600 C (about 900K) thermal energy is not exceeded. The maximum allowable exhaust temperature for GT is between 500 C – 600 C. But 600 C limit was chosen to maximise the efficiency and useful thermal energy potential for the ST cycle. These were carried out as follows a. GT Inlet temperature at 1400 C: The pressure ratio at firing temperature of 1400 C was varied accordingly and the respective efficiency and the exhaust temperature noted. It can seen from graph of Figure 8.4 that the maximisation of the efficiency can now be realised at pressure ratio of 6 which is very close to the optimum pressure ratio of now 10 as compared to 12 without regeneration. Operating at pressure ratio of 10 may not be feasible considering the overall pressure ratio to be 30 and the resulting design complexities and finances associated with it. This also shows that full regeneration of the exhaust gas energy in the GT cycle will only leave little available energy for the ST cycle. Therefore a percentage regeneration was employed and it was found out that the optimum for this GT inlet temperature of 1400 C is at 40% regeneration at a pressure ratio of 6 which also corresponds to the maximum available thermal energy of about 600 C for the ST cycle. b. GT Inlet temperature at 1700 C: The pressure ratio at firing temperature of 1400 C was varied accordingly and the respective efficiency and the exhaust temperature noted. It can seen from the graph below that the maximisation of the efficiency can now be realised at pressure ratio of 7.5 which is very close to the optimum pressure ratio of now 12 as compared to 14 without regeneration. Operating at this pressure ratio of 12 may not be feasible considering the overall pressure ratio to be 36 and the resulting design complexities and finances associated with it. This also shows that full regeneration of the exhaust gas energy in the GT cycle will only leave little available energy for the ST cycle. Therefore a percentage regeneration was employed and it was found out that the optimum for this GT inlet temperature of 1700 C is at 54% regeneration at a pressure ratio of 7.5 which also corresponds to the maximum available thermal energy of about 600 C for the ST cycle. The tabular results are given below: Press. Ratio 2 4 6 8 10 12

% of Exhaust Reg. 0 20 40 60 80 100

at 1400 C (%) 25 42 47 50 51 51

at 1700 C (%) 26 44 51 54 57 58

Table 8.5: Efficiency with regeneration at the three various temperatures Bashar Dan-asabe

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle Pressure Ratio 2 4 6 8 10 12

% of Exhaust Reg. 0 20 40 60 80 100

Ex. at 1400 C (K) 1453.79 1090.71 898.51 779.74 704.85 660.49

Ex. at 1700 C (K) 1714.48 1269.5 1021.44 856.89 741.68 660.49

Table 8.6: Exhaust gas with regeneration at the three various temperatures

Exhaust Heat Energy Available for the ST cycle Efficiency at 1400 C (%)




Reg. Exhaust (%) 0

20

40

60

80

100

70

1800 1700

60

1600

Efficiency (%)

1400 1300

40

1200 30

1100

Exhaust Temp. (K)

1500

50

1000 20

900 800

10

700 0

600 2

4

6

8

10

12

Pressure rario, rp

Figure 8.4: Exhaust gas energy temperature available for the ST cycle

8.3 Optimisation of the ST cycle The cycle was optimised at heat exchange energy of 490 KJ/Kg i.e. exhaust temperature of about 600 C from the GT. The various parameters considered are:

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle a. Inlet temperature and pressure: The inlet temperatures and pressures are increased and the result plotted against the ST net work. This shows an increase in the ST net work which invariably indicates an increase in efficiency. Increase in temperature at a higher pressure of 100 bars from 400 C – 600 C corresponds to net work energy of 187 kJ/kg – 206 kJ/kg. This indicates an increase in efficiency from 38.2% to 42%. This clearly shows that increase in either or both ST Inlet temperature and pressure increases the efficiency of the ST cycle. Therefore a ST inlet temperature and pressure of 600C and 100 bar is considered since a higher pressure cannot be justified considering the HRGS is unfired. The table of values and plots for the simulation are given below: Temperature Wnet at 40 (K) bar (kJ/kg) 400 177.43 450 181.54 500 185.62 600 193.41

Wnet at 60 bar (kJ/kg) 182.42 186.83 191.22 199.53

Wnet at 80 bar (kJ/kg) 185.34 189.84 194.52 203.13

Wnet at 100 bar(kJ/kg) 187.1 191.76 196.5 205.51

Table 8.7: Steam inlet temperature against the ST cycle net work

Effect of Steam Inlet Temperature on ST Net Work Wnet at 40 bar (kJ/kg) Wnet at 80 bar (kJ/kg) Linear (Wnet at 40 bar (kJ/kg))

Net Work (KJ/Kg)

210

Wnet at 60 bar (kJ/kg) Wnet at 100 bar (kJ/kg) Linear (Wnet at 60 bar (kJ/kg))

205

y = 0.0921x + 150.34 y = 0.089x + 149.81

200

y = 0.0855x + 148.34

195

y = 0.0798x + 145.59

190 185 180 175 170 350

400

450

500

550

600

Inlet Temperature (C)

Figure 8.5: Effect of steam inlet temperature against the ST cycle net work b. Reheat pressure and net work: The reheat pressure and inlet pressure are increased and the resultant ST net work plotted. This shows a decrease in ST net work with increasing ST inlet pressure even though the trend tends to stabilise at higher pressure. This implies the net work and corresponding efficiency are highest at the minimum reheat pressure. Therefore taking a reheat pressure of 10 bars at inlet pressure of 100 bars gives a net work of 206KJ/Kg.

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This maintains the ST cycle efficiency of 42% as seen in Figure 8.6. c. Extraction pressure and net work: the extraction pressure and the ST inlet pressure are increased and their corresponding results plotted with respect to the ST net work. The trend shows that the ST net work decreases at higher extraction pressure and lower ST inlet pressure but marginally increases and then decreases at a higher GT inlet pressures. This shows the net work stabilises at extraction pressure of about 3 bar and then gradually decreases at higher GT inlet pressures. Therefore a pressure of 3 bar is deemed the optimum extraction pressure. The table and graphical plots of 8.3(a) and (b) are:

Reheat Pressure (bar) 10 15 20 30

Wnet at 40 bar (kJ/kg) 193.41 191.48 189.86 186.05

Wnet at 60 bar (kJ/kg) 199.53 198.53 197.63 195.32

Wnet at 80 bar (kJ/kg) 203.13 202.73 202.3 200.76

Wnet at 100 bar (kJ/kg) 205.51 205.52 205.4 204.39

Table 8.8: Reheat pressure against the ST cycle net work

Extraction Pressure (bar) 1 3 6 9

Wnet at 40 bar (kJ/kg) 193.41 193.24 191.98 190.71

Wnet at 60 bar (kJ/kg) 199.53 199.6 198.58 197.47

Wnet at 80 bar (kJ/kg) 203.13 203.34 202.44 201.43

Wnet at 100 bar (kJ/kg) 205.51 205.81 204.99 204.45

Table 8.9: Extraction pressure against the ST cycle net work

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Effect of Extraction & Reheat Pressure on the ST Net Work Wnet at 40 bar (kJ/kg)

Wnet at 60 bar (kJ/kg)



210

Net Work (KJ/Kg)

205 200 195 190 185 180 0

3

6

9

12

15

18

21

24

27

30

Extraction/Reheat Pressure (Bar)

Figure 8.6: Effect of extraction/reheat pressure against the ST cycle net work d. Condenser pressure and net work: a condenser pressure range is considered and gradually increased at increasing ST inlet pressure and the resultant net work noted. The trend shows a significant decrease in the ST net work with increasing condenser pressure. A ST cycle efficiency of about 42% can be achieved but at a very low condenser pressure of 0.01 bar. Condensing at a pressure ratio of 0.01 bar is difficult. Therefore a condenser pressure of 0.05 bar with corresponding ST net work output of 190KJ/Kg and cycle efficiency of 39% that can be reasonably condensed without much sophistication is considered.

Condenser Pressure (bar) 0.01 0.05 0.1 0.15

Wnet at 40 bar (kJ/kg) 193.24 177.34 169.32 166.11

Wnet at 60 bar (kJ/kg) 199.6 184.11 176.29 173.16

Wnet at 80 bar (kJ/kg) 203.34 188.08 180.38 177.3

Wnet at 100 bar (kJ/kg) 205.81 190.71 183.09 180.4

Table 8.10: Condenser pressure against the ST cycle net work

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Effect of Condenser Pressure on the ST Net Work Wnet at 40 bar (kJ/kg) Wnet at 60 bar (kJ/kg) Wnet at 80 bar (kJ/kg)

210

Net Work (KJ/Kg)

200

190

180

170

160

150 0

0.05

0.1

0.15

Condenser Pressure (Bar)

Figure 8.7: Effect of condenser pressure against the ST cycle net work 8.4 Optimisation of the CPPH The CC is optimised at a bottoming cycle parameters of inlet pressure of 100 bars, inlet temperature of 600C, reheat pressure of 10 bars, extraction pressure of 3 bar and condenser pressure of 0.05 bar. The GT cycle optimisation at three various firing temperatures from section 8.2 were: i. ii. iii.

regeneration not required at 1000 C regeneration required at 40% at 1400 C GT inlet temperature regeneration required at 54% at 1700 C GT inlet temperature

These conditions implemented for the combined cycle as given below: a. CC efficiency: The optimised conditions of the topping and bottoming cycles are plotted with respect to increasing pressure ratio and the respective efficiency noted. The results shows that at the efficiency at the various firing temperature reach their optimum at a pressure ratio range of 4 – 6 as depicted in Figure 8.8 in the next page. The graph also shows that the firing temperature has significant effect on the efficiency of the CC cycle as the efficiency is highest with about 61% at a GT inlet temperature of 1700 C with 54% regeneration. At the pressure ratio of 6, the corresponding plant efficiencies at the various temperatures are given as 46%, 56% and 61% respectively. This means the corresponding cycle efficiency is actually 87%, 91% and 92% respectively.

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle It can also be appreciated that the efficiency of the CC cycle is considerably above that of the separate GT cycle. b. Energy utilisation factor ( ): The optimised conditions of the topping and bottoming cycles are plotted with respect to increasing pressure ratio and the respective energy utilisation factor noted. The results shows that at the increases with increasing pressure ratio and firing temperature as depicted in Figure 8.8 in the next page. The graph also shows that at a pressure ratio of 6, the corresponding for the plant efficiency at 1000 C, 1400 C and 1700 C are respectively 83%, 86% and 87% respectively. This means the corresponding cycle efficiency is actually 87%, 91% and 92% respectively. It can also be appreciated that the of the separate GT cycle. Press. Ratio 2 4 6 8 10 12

0 at 1000 C (%) 42.08 46.53 46.04 44.64 42.99 41.28

of the CC cycle is considerably above that

40 at 1400 C (%) 48.78 55.09 55.43 54.76 53.82 52.80

4 at 1700 C (%) 52.96 59.80 60.37 59.94 59.23 58.44

Table 8.11: CPPH Plant efficiency against pressure ratio

Press. Ratio 2 4 6 8 10 12

0 at 1000 C (%) 76.63 81.39 83.26 84.37 85.13 85.7

40 at 1400 C (%) 78.37 83.76 85.56 86.54 87.18 87.65

4 at 1700 C (%) 79.65 85.06 86.75 87.64 88.21 88.63

Table 8.12: Energy utilisation factor against pressure ratio

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Effect of Pressure ratio on the CPPH efficiency Efficiency at 1000 C (%) η at 54% Reg. & 1700 C Єu at 40% & Reg. 1400 C

η at 40% Reg. & 1400 C Єu at 0% Reg.&1000 C Єu at 54% & Reg. 1700 C

95

Efficiency (%)

85 75 65 55 45 35 0

2

4

6

8

10

12

Presure Ratio, rp

Figure 8.8: Plant and energy utilisation factor of the CPPH cycle

c. Net Work Output: The optimised conditions of the topping and bottoming cycles are plotted with respect to increasing pressure ratio and the respective net work done noted. The graph of Figure 8.9 shows the work done diverging at the different temperatures with increasing pressure ratios. At a pressure ratio of 6, the corresponding net work done are given as 650, 1320 and 1620kJ/kg of air. This shows that increasing the temperature significantly increases the net work output. The tabular and graphical plots are given below: Press. Ratio 2

0 at 1000 C (%) 627.52

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40 at 1400 C (%) 770.69

4 at 1700 C (%) 892.34

78

Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle 4 6 8 10 12

818.99 862.72 864.45 849.17 825.88

1165.05 1313.27 1384.06 1419.83 1436.77

1426.30 1645.36 1762.45 1832.13 1875.59

Table 8.13: Useful net heat at increasing pressure ratio

Effect of Pressure ratio on the CPPH Work Output 54% Reg. at 1700 C

1900

95000

1700

85000

1500

75000

1300

65000

1100

55000

900

45000

700

35000

500

Net Power Output (kW)

Net Work (KJ/Kg)

40% Reg. at 1400 C 0% Reg. at 1000 C

25000 0

2

4

6

8

10

12

Presure Ratio, rp

Figure 8.9: Net work and power at air mass flow rate of 50kg/s d. Net useful Heat: The optimised conditions of the topping and bottoming cycles are plotted with respect to increasing pressure ratio and the respective net useful heat noted. The graph shows the net useful heat at the various temperatures does not significantly changes. In other words, increase in GT inlet temperature has negligible effect on the amount of useful heat recovered from the cycle. However, the net useful heat increases with increasing pressure ratios. At a pressure ratio of 6, the corresponding net useful heat recovered are given as 700kJ/kg, 720kJ/kg and 720kJ/kg of air respectively for the various firing temperature. This shows that increasing the temperature significantly increases the net work output as seen below:

Press. Ratio

0 at 1000 C (%)

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40 at 1400 C (%)

4 at 1700 C (%)

79

Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle 2 4 6 8 10 12

515.21 613.59 697.38 769.18 832.25 888.76

467.35 606.08 713.96 803.31 880.36 948.57

449.61 602.60 718.98 814.52 896.50 968.83

Table 8.14: Useful net heat at increasing pressure ratio

Effect of Pressure ratio of the CPPH on the generated Useful Heat 40% at Reg. 1400 C

54% at Reg. 1700 C

50000

900

45000

800

40000

700

35000

600

30000

500

25000

400

20000

Net Useful Heat (KJ/Kg)

1000

0

2

4

6

8

10

Net Useful Heat Power (kW)

0% Reg. at 1000 C

12

Presure Ratio, rp

Figure 8.10: Useful Net heat and power at air mass flow rate of 50kg/s

9.0 CONCLUSION

The optimised form of the CPPH shows that thermal power plants i.e. Rankine cycles, Joule-Brayton cycles, CHP and CCGT can be suitably simulated, analysed and optimised using a simple Microsoft excel spread sheet. Using the relevant thermodynamic equations for a CPPH cycle, the individual topping cycle and bottoming cycles and their combined overall effect can be optimised accordingly. The main findings are detailed below with respect to the topping, bottoming and the overall CCHP as below:

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle i.

Gas turbine (GT) cycle: An ideal theoretical equation was derived which confirms the accuracy of the simulated practical plant. The cycle was optimised at various GT inlet temperatures of 1000 C, 1400 C and 1700 C respectively. This was achieved maintaining the maximum allowable exhaust temperature of 600 C as given below:   

At 1000 C gives 37% plant efficiency with no regeneration required. At 1400 C gives 45% plant efficiency with regeneration required at 40%. At 1700 C gives 55% plant efficiency with regeneration required at 54%.

ii. Steam turbine (ST) cycle: The optimisation was achieved at exhaust gas heat supplied energy of approximately 490 kJ/kg of air i.e. exhaust temperature of 600 C from the GT. The optimised parameters are given below:    

A maximum ST inlet temperature and pressure of 600 C and 100 bars A minimum reheat pressure 10 bar An intermediate extraction pressure of 3 bar A minimum condenser pressure of 0.01 bar. However a condenser pressure of 0.05 bar was used due to the difficulty associated with condensing at 0.01 bar.

The ST cycle produces an independent plant efficiency of 42%. iii. Combined cycle heat and power (CPPH) plant: the overall combined cycle optimisation was achieved:     

At a stage pressure ratio of between 4 – 6 (or an overall of 12 – 18) for all the various GT inlet temperature. At a plant efficiency of 47%, 56% and 61% for the GT inlet temperatures of 1000 C, 1400 C and 1700 C respectively. At a plant energy utilisation factor of 83%, 86% and 87% for the GT inlet temperatures of 1000 C, 1400 C and 1700 C respectively. At a net power output of 41MW, 65MW and 82MW using air mass flow rate of 50kg/s for the GT inlet temperatures of 1000 C, 1400 C and 1700 C respectively. At a net useful heat power output of 31MW, 36MW and 36MW using air mass flow rate of 50kg/s for the GT inlet temperatures of 1000 C, 1400 C and 1700 C respectively.

However, the achieved power output and useful heat power can be higher when the air mass flow rate is increased.

REFERENCES

1. Grote K. and Antonsson E. K., Springer Handbook of Mechanical Engineering, Springer Science and Business Media, New York, US, 2009. 2. Hodgson S., Support Policies for CHP and District Heating and Cooling, Cogeneration and On-Site Power Journal, 37 – 41, January – February 2009. 3. Saravanamuttoo H.I.H., Gordon Rogers, Henry Cohen and Paul Straznicky, Gas Turbine Theory 6th Edition, Pearson Education Limited, Essex, UK, 2009.

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4. Colley T., Australia’s Green House Target, Cogeneration and On-Site Power Journal, 19 – 27, November – December 2008. 5. Goswami D. Y. and Kreith F., Energy Conversion, CRC Press, New York, 2008. 6. Soares C., Gas Turbine: A handbook of air, land and sea applications, Elsevier Inc., London, UK, 2008. 7. Sanjay Y. and Singh O., Energy and exergy analysis of steam cooled reheat gas–steam combined cycle, Applied Thermal Engineering, 2779 – 2790, December 2007. 8. Smith P., Major Cogeneration Plant to Supply Steam for Alumina Plant in Greece, Cogeneration and On-Site Power Journal, 73 – 81, September – December 2007. 9. Srinnivas T., Gupta A. V. S. S. K. S. and Reddy B. V., Parametric simulation of steam injected gas turbine combined cycle, Proceedings of the Institution of Mechanical Engineers, 875, November 2007. 10. Farret F. A. and Simoes M. G., Integration of Alternative Sources of Energy, John Wiley & Sons, New Jersey, US, 2006. 11. OECD/IEA, Projected Cost of Generating Electricity, International Energy Agency, France, 159 – 160, 2005. 12. Woodruff E. B., Lammers H. B. and Lammers T. F. , Steam Plant Operation, McGraw-Hill Book Company, 2005. 13. Rao A. D., Samuelsen G. S. and Yi Y., Gas turbine based high-efficiency 'Vision 21' natural gas and coal central plants, Proceedings of the Institution of Mechanical Engineers, 127 – 128, November 2005. 14. Masters G. M., Renewable and Efficient Electric Power system, John Wiley & Sons, New Jersey, US, 2004. 15. Mohammad H., Alghamdi A. S. and Najjar Y.S., Heat transfer analysis for a multistage gas turbine using different blade-cooling schemes, Applied Thermal Engineering, 564 – 576, March 2004. 16. Ganesan V., Gas Turbines,Tata McGraw-Hill,New Delhi, India, 2003 17. Neil P., Combined heating, cooling and power handbook, The Fairmont Press, India, 2003. 18. Leo T. J., Perez-Grande I. and Perez-del-Notario P., Applied Thermal Engineering, 1915 – 1920, October 2003. 19. Meherwan P. B., Hand book for cogeneration and combined power plant, ASME, New York, 2002. 20. Kolev N., Schaber K. and Klolev D., Applied Thermal Engineering, 392 – 400, March 2001.

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Design, Simulation and Optimisation of a Combine Power to Power and Heating Cycle 21. Kehlhofer R. H., Nielson H., Warner J. and Bachmann R., Combined-cycle gas and Steam turbine power plants, PennWeell Publishing Company, Oklahama, US, 1999. 22. Heppenstall T., Advanced gas turbine cycles for power generation: a critical review, Applied Thermal Engineering, 838 – 840, September 1998. 23. Kharchenko N. K., Advanced Energy Systems, Taylor and Frances Publishing, US, 1998. 24. Marecki J., Combined Heat and Power generating systems, Peter Peregrininus Ltd., London, UK, 1998. 25. Mayhew Y., Hollingsworth, Engineering Thermodynamics Work and Heat Transfer, Addson Wesley Longman, UK, 1996. 26. O’Neill P. A., Centrifugal Compressors, Butterworth-Heinemann ltd, London, 1993. 27. Horlock, J. H., Combined Power Plants: including CCGT, Open University, Milton Keynes, UK, 1992. 28. Orlando J. A., Cogeneration Planner’s Handbook, The Fairmont Press, India, 1991. 29. Horlock, J. H., Cogeneration: Combined Heat and Power Thermodynamics and Economics, Open University, Milton Keynes, UK, 1987. 30. El-Wakil M. M., Powerplant Technology, McGraw-Hill Book Company, US, 1984. 31. Meherwan P. B., Hand Handbook for cogeneration and combined cycles power plants, ASME, New York, 1979. 32. Harry J. S. and Ronald H. Howell, Heat Pumps Systems, Wiley-Interscience Publication, US, 1976.

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Title: Design, Simulation and Optimisation

Title: Design, Simulation and Optimisation

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