University of the West of Scotland
Final Year Project
on
Gas Turbine Thermal Efficiency Analysis
ILJA ZIMAKOVS
B00346648
BEng (Hons) Mechanical Engineering
08/04/2022
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Contents
Table of Figures ....................................................................................................................................... 4
Tables ...................................................................................................................................................... 4
Chapter 1 - Introduction ......................................................................................................................... 5
Chapter 2 – Literature Review ................................................................................................................ 5
2.1. Gas Turbine Overview .................................................................................................................. 5
2.2. Categories of Gas Turbines .......................................................................................................... 6
2.3. Gas Turbine Components ............................................................................................................ 7
2.3.1. Compressors ......................................................................................................................... 7
2.3.2. Combustors ........................................................................................................................... 8
2.3.3. Turbines .............................................................................................................................. 13
2.3.4. Rotors .................................................................................................................................. 13
2.3.5. Blades .................................................................................................................................. 14
2.3.6. Gas Turbine Nozzles ............................................................................................................ 16
2.4. Gas Turbine Cycles ..................................................................................................................... 17
2.4.1. Simple Gas Turbine Cycle .................................................................................................... 17
2.4.2. Gas Turbine Cycle with Heat Regeneration ........................................................................ 19
2.4.3. Calculation of the Thermal Circuit of a Simple Gas Turbine ............................................... 23
2.5. Fuel............................................................................................................................................. 26
2.5.1. Natural Gas ......................................................................................................................... 26
Chapter 3 - Project Definition ............................................................................................................... 28
3.1. Aim ............................................................................................................................................. 28
3.2. Methodologies ........................................................................................................................... 29
Chapter 4 – Gas Turbine operation analysis with different fuels ......................................................... 29
4.1. Fuel variable parameters ........................................................................................................... 29
4.2. Base case with standard natural gas.......................................................................................... 30
4.2.1 Base case calculations .......................................................................................................... 31
4.3. Different scenarios ..................................................................................................................... 34
4.3.1. Natural gas with different methane concentration ............................................................ 34
4.3.2. Renewable fuels .................................................................................................................. 35
4.3.3. A mixture of standard natural gas and renewable fuel ...................................................... 36
4.4. Emission and cost....................................................................................................................... 37
Chapter 5 - Analysis of the base case and scenarios ............................................................................ 38
5.1. Air flow rate analysis .................................................................................................................. 38
5.2. Fuel consumption analysis ......................................................................................................... 39
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5.3. Gas Turbine power analysis ....................................................................................................... 40
5.4. Compressor power consumption analysis ................................................................................. 41
5.5. Useful work ratio analysis .......................................................................................................... 42
5.6. Electrical efficiency analysis ....................................................................................................... 43
5.7. Cost analysis ............................................................................................................................... 44
5.8. Emission analysis........................................................................................................................ 45
5.9. Summary .................................................................................................................................... 47
Chapter 6 – Conclusion ......................................................................................................................... 48
Chapter 7 – Further work...................................................................................................................... 49
References ............................................................................................................................................ 50
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Table of Figures
Figure 1 Gas turbine with constant pressure combustion...................................................................... 6
Figure 2 – Perfomance of different types of compressors ..................................................................... 8
Figure 3 – Zones in tupical combustor .................................................................................................... 9
Figure 4 - Ring combustion chamber inside and outside...................................................................... 11
Figure 5 - Schematic diagram of a tube-ring combustion chamber burner ........................................ 12
Figure 6 - Schematic diagram of a simple Gas Turbine ......................................................................... 17
Figure 7 - Simple Gas Turbine cycle ...................................................................................................... 17
Figure 8 - Plot of efficiency of a Simple Gas Turbine on Pressure-Temperature relationship.............. 19
Figure 9 - Schematic diagram of a simple Gas Turbine with Regenerator............................................ 20
Figure 10 - Simple Gas Turbine cycle with regeneration ...................................................................... 20
Figure 11 - Schematic diagram of a counterflow regenerator.............................................................. 20
Figure 12 - Efficiency of a Gas Turbine with regeneration.................................................................... 22
Figure 13 - Optimal pressure ratio of a Gas Turbine with heat recovery ............................................. 23
Figure 14 - Simply Gas Turbine diagram with main measuring points ................................................. 30
Figure 15 - Air flow rate comparison graph .......................................................................................... 39
Figure 16 - Fuel consumption comparison graph ................................................................................. 40
Figure 17 - Gas Turbine power comparison graph ............................................................................... 41
Figure 18 - Compressor power consumption comparison graph ......................................................... 42
Figure 19 - Useful work ratio comparison graph .................................................................................. 43
Figure 20 - Electrical efficiency comparison graph ............................................................................... 44
Figure 21 - Cost comparison graph ....................................................................................................... 45
Figure 22 - Carbon dioxide emission comparison graph....................................................................... 46
Figure 23 - Nitrous oxide emission comparison graph ......................................................................... 47
Tables
Table 1 - Gas turbine efficiency depending on gas temperature and degree of regeneration ............ 22
Table 2 - Specific isobaric heat capacity and enthalpy of dry air and combustion products ............... 31
Table 3 - Air flow rate comparison........................................................................................................ 38
Table 4 - Fuel consumption comparison ............................................................................................... 39
Table 5 - Gas Turbine power comparison ............................................................................................. 40
Table 6 - Compressor power consumption comparison ....................................................................... 41
Table 7 - Useful work ratio comparison ................................................................................................ 42
Table 8 - Electrical efficiency comparison............................................................................................. 43
Table 9 - Cost comparison..................................................................................................................... 44
Table 10 - Carbon dioxide emission comparison .................................................................................. 45
Table 11 - Nitrous oxide emission comparison ..................................................................................... 46
Table 12 - Gas Turbine key parameters summary ................................................................................ 47
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Chapter 1 - Introduction
The efficiency of a gas turbine in comparison with other heat engines is achieved only at high gas
temperatures and high efficiency of the turbine and compressor. The gas turbine began to be used
later than other heat engines. Only after progress was made in the technology of obtaining heatresistant materials and the necessary knowledge in the field of aerodynamics of turbomachines was
accumulated, the simple in its principle of operation gas turbine engine began to be used in industry.
The last 30 years has seen a large growth in Gas Turbine Technology. The growth is spearheaded by
the growth of materials technology, new coatings, and new cooling schemes. This, with the
conjunction of increase in compressor pressure ratio, has increased the gas turbine thermal
efficiency from about 15% to over 50%. Whereas the pressure ratio in 1955 was 10:1, in 2000 it was
40:1 and continue growing. Gas turbines are low stage compared to steam turbines. The utilization
of gas turbine exhaust gases, for steam generation or the heating of other heat transfer mediums, or
in the use of cooling or heating buildings or parts of cities, is not a new concept and is currently
being exploited to its full potential. Gas turbines are the most profitable in terms of cost per kW and
are therefore the main way of generating power worldwide. Gas turbines have high efficiency that
can be increased even further with an advanced gas turbine combined cycle power plant. High
reliability, availability, low cost of repair and maintenance make gas turbines the most efficient way
to generate power. This makes the gas turbine one of the most efficient prime movers on the
market today reaching efficiencies of 60% in Combined Cycle Turbine.
Taxation on carbon emissions is being tightened every year due to the global impact of CO2
emissions on the earth's climate. Therefore, all industries pay great attention to what carbon
footprint they leave. This is important not only for the ecology of the earth, but also for the financial
side of the enterprise. Gas Turbines have consistently managed to improve its efficiency for over 70
years, thereby lowering its carbon footprint per unit of work. Improvements occur in design,
materials, construction, and fuel - which will be covered in this work.
Chapter 2 – Literature Review
2.1. Gas Turbine Overview
A gas turbine is a heat engine consisting of three main elements:
1. Air compressor
2. Combustion chamber
3. Gas turbine
Gas turbine operation is shown in Figure 1 and the principle is following:
Air is extracted from the atmosphere by compressor “1”, then at increased pressure it is delivered to
the combustion chamber “2”, where simultaneously liquid fuel is delivered by the fuel pump “3” or
gaseous fuel from the gas compressor. In the combustion chamber air is divided into two flows: one
flow in the amount required for fuel combustion enters the flame tube “4” and the second flow
around the fire tube from the outside and is mixed with the combustion product to lower
temperature of the gas. The combustion process in the chamber takes place at an almost constant
pressure and called Gas turbine with constant pressure combustion. The cooled gas produced after
mixing enters the gas turbine “5”, where it expands, performs work, and is then discharged into the
atmosphere. The power generated by the gas turbine is partially consumed to drive the compressor,
and the rest is the useful power of the gas turbine plant.
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FIGURE 1 GAS TURBINE WITH CONSTANT PRESSURE COMBUSTION
The useful capacity of a gas turbine is 30-50% of its work. Useful power can be increased by
increasing the gas temperature upstream of the turbine “5”, so the gas expansion work in the
turbine increases. The other way is to reduce the temperature of the air drawn in by the compressor
“1”, this will reduce the work required to compress the air in the compressor. Both methods lead to
increase in a share of useful power. Useful power of gas turbine also depends on aerodynamic
characteristics of turbine and compressor flow parts: the less aerodynamic losses in the turbine and
compressor, the more share of gas turbine power becomes useful.
2.2. Categories of Gas Turbines
The gas turbine is a vane machine in whose stages the energy of compressed and heated gas is
converted into mechanical work on the shaft. A gas turbine is a bladed machine, in the steps of
which the energy of compressed and heated gas is converted into mechanical work on the shaft. The
main components of a gas turbine are the casing, combustion chamber, rotor, and stator. Gas
turbines are used in gas turbine engines, stationary gas turbines and combined cycle plants.
The simple-cycle gas turbine is classified into five broad groups:
1. Frame Type Heavy-Duty Gas Turbines.
2. Aircraft-Derivative Gas Turbines Aero-derivative.
3. Industrial Type-Gas Turbines.
4. Small Gas Turbines.
5. Micro-Turbines.
Frame Type Heavy-Duty Gas Turbines will be used as a main group for review and analysis. This is
because it is this group of gas turbines that are used to generate electricity worldwide. The frame
units are the large power generation units ranging from 3 MW to 480 MW in a simple cycle
configuration, with efficiencies ranging from 30-46%. The early heavy-duty gas turbine design was
largely an extension of steam turbine design. Restrictions of weight and space were not important
factors for these ground-based units, and so the design characteristics included heavy-wall casings
split on horizontal centerlines, sleeve bearings, large-diameter combustors, thick airfoil sections for
blades and stators, and large frontal areas. The average pressure ratio for the first gas turbine
models was around 5:1, now the new models can reach a pressure ratio of 35:1 and to this day the
pressure ratio continues to increase. Turbine inlet temperatures have been increased and run as
high as 1370°C on some of these units. Projected temperatures approach 1650°C and, if achieved,
would make the gas turbine even a more efficient unit. To achieve these high temperatures, steam
cooling is being used in the latest designs to achieve the goals of maintaining blade metal
temperatures below 700°C and prevent hot corrosion problems. The relatively low combustion
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temperature of combustion inhibits the formation of harmful nitrogen oxides nitrogen oxides. The
industrial heavy-duty gas turbines employ axial-flow compressors and turbines. The industrial
turbine consists of a 15-17 stage axial-flow compressor, with multiple can-annular combustors each
connected to the other by cross-over tubes. The advantages of the heavy-duty gas turbines are their
long life, high availability, and slightly higher overall efficiencies. The noise level from this type of
turbine is considerably less than for example an aircraft-type turbine. The heavy-duty gas turbine's
largest customers are the electrical utilities, and independent power producers
A power plant with a gas turbine can also be plan and built faster than other plants, in less than a
year. The two factors, which most affect high turbine efficiencies, are pressure ratios and
temperature. The higher the temperature, the higher the efficiency of the gas turbine. Proper
cooling must be provided to achieve blade metal temperatures between 540°C and 700°C below the
levels of the onset of hot corrosion. Advanced type of cooling systems with proper blade coatings
and materials are needed to ensure the high reliability of a turbine. The axial-flow compressor,
which produces the high-pressure gas in the turbine, has seen dramatic change as the gas turbine
pressure ratio has increased from 7:1 to 40:1. The increase in pressure ratio increases the gas
turbine thermal efficiency when accompanied with the increase in turbine firing temperature. The
increase in the pressure ratio increases the overall efficiency at a given temperature, however
increasing the pressure ratio beyond a certain value at any given firing temperature can actually
result in lowering the overall cycle efficiency. High availability and reliability are the most important
design parameters for a Gas Turbine. Plant availability is the percentage of time a power plant is
ready to generate electricity in any given period. Plant reliability is the percentage of time between
scheduled overhauls. The efficiency of a Gas Turbine depends significantly on the turbine efficiency
(η𝑡 ): a 1% change in (η𝑡 ) leads to a 2-3% change in the efficiency of a gas turbine. When designing a
gas turbine, ideal methods of gas dynamic calculation of spatial flow are applied, allowing to choose
optimal shapes and to minimize aerodynamic losses in the elements of flow part - nozzle and
working grids, inlet, and outlet nozzles. Reduction of losses with outlet velocity is achieved by
installation of a diffuser behind the last stage of the gas turbine, usually diffusers with axial outlet
and optimal opening angle are used. If a Gas Turbine is designed for basic or half-peak operation,
Gas Turbine without cooling of nozzles and blades can be constructed at temperature upstream the
turbine not higher than 750-850°С. Modern Gas Turbines as a rule are designed with a developed
system of air cooling of nozzles, blades, rotors, and stator elements.
In recent years, the gas turbine has been increasingly used in various industries. The reason for this
is the characteristic of the Gas Turbine engine: simple thermal and kinematic scheme, relative
simplicity of design, low weight per unit of power, high manoeuvrability, relatively simple
automation of operation. In addition, in recent years there have been significant advances both in
the aerodynamics of turbomachinery and in the development of heat-resistant steels and alloys.
2.3. Gas Turbine Components
2.3.1. Compressors
The task of the compressor is to pump the working fluid under pressure. Figure 2 shows three
categories of compressors: Positive displacement compressors; Centrifugal compressors; Axial-flow
compressors.
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FIGURE 2 – PERFOMANCE OF DIFFERENT TYPES OF COMPRESSORS
•
•
•
Centrifugal compressors are used for medium flow and pressure.
Axial-flow compressors are used for high flow and low pressure.
Positive displacement compressors are used for low flow and high pressure.
Centrifugal and axial-flow compressors are continuous flow compressors, these two types of
compressors are used in gas turbines for compressing the air. Positive displacement compressors
used for lubrication systems in the gas turbines.
Centrifugal compressors are used in small Gas Turbines, have greater tolerance to process
fluctuations and are more reliable than other types of compressors, slightly less efficient than axial
compressors, but are more stable.
An axial-flow compressor accelerates air flow and then dissipates it to increase pressure. The fluid is
accelerated by a series of rotating blades, called the rotor, and dissipated by a series of stationary
blades, called the stator. Diffusion in the stator converts the speed increase obtained in the rotor
into a pressure increase. One rotor and one stator make up the compressor stage. A large Gas
Turbine compressor consists of several stages. One additional row of fixed blades (inlet guide vanes)
is often used at the compressor inlet to ensure that the air enters the first stage rotors at the correct
angle. In addition to the stators, an additional diffuser at the compressor outlet further disperses the
fluid and regulates its speed as it enters the combustion chambers. In an axial compressor, air passes
from one stage to the next, with the pressure at each stage increasing slightly. The axial-flow
compressors producing low-pressure increases on the order of 1.1:1-1.4:1, very high efficiencies can
be obtained. The use of multiple stages permits overall pressure increases up to 40:1. The rule of
thumb for a multistage gas turbine compressor will be that the energy increase per stage will be
constant, and not pressure increase per stage. Increasing the low pressure at each stage also
simplifies the calculations when designing a compressor, the air is assumed to be incompressible as
it passes through an individual stage. Centrifugal compressors range in size from pressure ratios of
1.3:1 per stage to as high as 13:1 on experimental models. This means that the compressor pressure
ratio must be between 3-7:1 per stage. This is considered a high-pressure centrifugal compressor.
With a pressure rise greater than 5:1, the flows entering the diffuser from the rotor have a
supersonic mach number (M > 1:0). This requires a special diffuser design.
2.3.2. Combustors
The main task of a gas turbine combustor is to raise the temperature of the high-pressure gas. The
gas turbine uses 90% of the air for cooling and only 10% of the air enters the gas turbine combustor
for the combustion process. The air from the compressor must be diffused to reduce its velocity
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before it enters the combustor. Air comes out of the compressor at around 120-180m/s, but to avoid
flame downstream the diffuser reduces the velocity in the combustor that must be maintained
below 15.2m/s. New combustors are also circulating steam for cooling purposes.
The combustor is a direct-fired air heater in which fuel is burned almost stoichiometrically with onethird or less of the compressor discharge air. Combustion products are then mixed with the
remaining air to arrive at a suitable turbine inlet temperature.
Three features of combustor are shown in Figure 3: 1)Recirculation zone; 2)Burning zone; 3)Dilution
zone. Also, in Figure 2 the air entering a combustor is divided so that the flow is distributed between
three major regions: 1) Primary zone; 2) Dilution zone; 3) Annular space between the liner and
casing.
FIGURE 3 – ZONES IN TUPICAL COMBUSTOR
The combustion in a combustor takes place in the Primary Zone. Combustion of natural gas is a
chemical reaction that occurs between carbon or hydrogen and oxygen. Heat is given off as the
reaction takes place. The products of combustion are carbon dioxide and water. The reaction is
Stoichiometric, which means that the proportions of the reactants are such that there are exactly
enough oxidizer molecules to bring about a complete reaction to stable molecular forms in the
products. The air enters the combustor in a reverse flow. Most of the large frame type units have
reverse-flow. The function of the recirculation zone is to vaporise, partially burn and prepare the fuel
for rapid combustion in the remainder of the combustion zone. Ideally, at the end of the burning
zone, all fuel should be burnt so that the function of the dilution zone is solely to mix the hot
gas with the dilution air. Dilution air is supplied so abruptly that if combustion is not completed at
the end of the combustion zone, cooling occurs which prevents completion. However, in some
chambers there is evidence that, if the combustion zone is operated with over-enrichment, some
combustion does occur in the dilution zone. The theoretical or reference velocity is the air flow at
the combustion chamber inlet through an area equal to the maximum cross-section of the
combustion chamber body. The flow velocity is 7.6m/s in a combustion chamber with reverse flow.
Combustor inlet temperature depends on engine pressure ratio, load, and engine type, and whether
or not the turbine is regenerative or nonregenerative especially at the low-pressure ratios. The new
industrial turbine pressure ratios are between 17:1 and 35:1, which means that the combustor inlet
temperatures range from 450°C to 650°C. The air from the compressor outlet enters the annular
space and from it diverges to the combustion chambers, then the air passes through the annular
space between the chamber body and the flame tube. Having passed in the gap between the body
and the flame tube and having cooled it down, the air flows to the burner modules, to which the fuel
is fed. Combustion takes place in a short section of the flame tube, where the temperature is about
1450°C. The relatively low combustion temperature restrains the formation of harmful nitrogen
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oxides. The inside of the flame tube is covered with heat-resistant ceramic tiles that protect it from
the effects of high temperature. The flame tube itself is made of Inconel, a nickel-based alloy with
high chromium content. In its lower part there are special windows through which the secondary air
is fed. Its mixing with combustion products and thorough mixing in the transition elements provide
the gas temperature of 1100°C before the nozzle apparatus of the first stage of the gas turbine. The
temperature behind the nozzles of the first stage at standard conditions at the compressor inlet is
1050°C.
Combustion chamber efficiency is measured by efficiency, pressure drop in the combustion chamber
and the uniformity of the outlet temperature profile. Combustion efficiency is a measure of
combustion completeness. Combustion efficiency has a direct impact on fuel consumption because
the calorific value of any unburned fuel is not used to raise the inlet temperature to the turbine.
Normal combustion temperatures range from 1870°C to 1930°C. At this temperature, the volume of
nitric oxide in the combustion gas is about 0.01%. If the combustion temperature is lowered, the
amount of nitric oxide is substantially reduced.
Regardless of the design, combustion chambers are subject to a number of stringent technical
requirements. First and foremost, the combustion chamber must ensure the high environmental
performance of the gas turbine. Emissions of highly toxic nitrogen oxides, which make up 90-95 % of
all harmful emissions, in the gas turbine load range from 100% to 50% when natural gas is
combusted must not exceed 50 mg/m3, and when liquid fuel is combusted - 100 mg/m3 (at 15%
oxygen concentration). Reduction of nitrogen oxides concentration is achieved by decreasing the
maximum flare temperature and by reducing the residence time of the combusted fuel in the
maximum temperature zones.
The simplest and most proven way to suppress nitrogen oxides is to inject water or steam into the
combustion zone, these are called wet chambers. By injecting moisture, the amount of which is
approximately equal to the amount of fuel injected, approximately 1-2% of the air flow, the
concentration of nitrogen oxides is reduced by a factor of 3-4. However, in this case the heat of
vapour is carried away with the flue gases and the efficiency of the gas turbine is reduced. An
acceptable nitrogen oxides content at natural gas combustion can be obtained only by feeding into
the combustion zone a pre-prepared poor homogenous mixture of fuel gas and air with an excess air
ratio of 1.9-2.2, such chambers are called dry. In this case, in the flare volume there are no zones
with small excess air and with high combustion temperature. Experiments have shown that
conversion from diffusion combustion to premixed combustion reduces the nitrogen oxides content
by 4-5 times. However, the combustion of homogeneous lean mixtures, especially when the load
and consequently the fuel consumption are reduced, raises two problems:
1. Ensuring stable combustion chamber operation without inadmissible pulsations and without
flame failure flare or its spillage into the mixing zone.
2. Ensuring good combustion efficiency without the formation of carbon monoxide.
To solve these problems, measures must be taken to enrich the fuel-air mixture, which complicates
the design of the combustion chamber and the combustion devices and requires the use of
automatic control systems. Further, in accordance with the trend of increasing initial gas
temperature, the overall excess air ratio decreases to 2.5-2.8, and the preparation of poor mixtures
requires a large amount of air supply to the combustion zone. Because of this, less and less air is left
to cool the combustion chamber elements.
Combustion chambers are subjected to the highest temperatures and highly aggressive flowing
media. Despite the design measures used, various malfunctions and defects occur in its components.
The combustion chamber must be highly repairable. The combustion chambers of all modern gas
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turbines are designed to follow all the above principles. Three types of chambers are used: remote,
annular, and tubular-ring chambers.
2.3.2.1. Remote Combustion Chamber
Constructed and installed separately from the gas turbine unit. Their main disadvantage is that they
are separate from the compressor and turbine, resulting in large overall dimensions of the gas
turbine, separate transportation of these elements, complication of installation and assembly of the
gas turbine, increase in overall dimensions of the turbine hall and complication of equipment layout
in it. At the early stage of development of stationary gas turbine engineering, such design of the
chamber was forced, as it had large overall dimensions due to use of diffusion principle of
combustion in a long flare. Another important disadvantage of remote chambers is the difficulty to
provide circumferential temperature uniformity of gases entering the turbine's first stage nozzle
apparatus. A significant circumferential unevenness results in uneven heating of the nozzle
segments, temperature warpage and temperature stresses that lead to cracks in the segments. The
development of combustion of poor homogeneous mixtures with a short flame led first to a
reduction in the overall dimensions of the bypass chambers, and then to their complete
abandonment in the new designs. The combustion chambers of recent generations of gas turbines
are either annular or tubular-ring combustion chambers.
2.3.2.2. Annular Combustion Chamber
Figure 4 shows a modern annular combustion chamber with adjacent elements. The combustion
chamber is built between the compressor and the gas turbine, and its interior is a rotating body
formed by an inner and outer shell, in which low-emission burners are placed equidistantly one from
the other. At the chamber outlet, an annular slot is created, from which the fuel combustion
products, having almost the same temperature around the circumference, enter the nozzle of the
first turbine stage.
The axis of the annulus is tilted with respect to the gas turbine axis, which reduces the axial
dimension and eliminates direct exposure of the flare radiation to the blades of the nozzle
apparatus. The inner and outer shells are moulded and clad internally with ceramic-coated heatresistant steel tiles. The tiles are mounted on the shells with gaps and expand freely. Cooling air
flows in the gaps between the tiles, creating a cooling film
FIGURE 4 - RING COMBUSTION CHAMBER INSIDE AND OUTSIDE
2.3.2.3. Tubular Ring Combustion Chamber
Figure 5 shows a tubular ring combustion chamber. The gas turbine casing, the annular collar and
the inner circumference of the chamber casing form an annular space into which the tubular
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combustion devices are placed. Each of the combustion devices consists of a housing, the flange of
which secures it to the annular collar, a multi-flame burner and a flame tube. Combustion of the fuel
gas takes place inside each flame tube and the resulting combustion gases flow into transfer spigots
which convert the circular cross-section of the flame tube into an annular cross-section with an arc
length corresponding to one combustion unit. The transition spigots are placed in the chamber
housing in advance, and then the chambers themselves are installed so that the mutual thermal
expansions of these elements are allowed to occur freely. If the flame tubes, burners or individual
combustion devices need to be inspected, it is sufficient to loosen the flange connection and remove
the device from the chamber. This is a great advantage of tube-ring-type combustion chambers. The
flame tubes have a special thermal barrier coating on the inside which must not only provide high
resistance to high temperature corrosion, but also reduce the metal temperature of the flame tube
and the temperature gradients in it. Air supply for cooling of the transition pipe and flame tube is
carried out by a counter-current scheme. The transition pipe is double-walled using jet cooling.
Figure 5 shows the burner unit placed at the inlet of the flame tube. The central burner and a
number of burners (4-6 pcs) located around the central burner, under the control of the automation,
provide all the modes of operation. Inside the flame tube, an annular protrusion is made, which
gives it a Venturi nozzle shape. As a result the internal space of the flame tube is divided into three
zones: an annular zone 1, in which fuel is fed by burners, a zone 2 in which fuel combustion occurs at
modes close to nominal, and a zone 3 where combustion products are mixed with air to obtain the
required initial temperature before the gas turbine. The combustion system works as follows.
Ignition of the chamber burners, acceleration of the gas turbine rotor to synchronous speed,
switching on the mains and taking the load up to 20% is provided by feeding fuel to zone 1 burners
only. Then the central burner is additionally ignited, in which up to 30% of the total fuel
consumption is fed. The burning takes place in zones 1 and 2, thus increasing the load up to 40%.
Then the burners are put out and all fuel is fed only to the central burner, burning occurs only in
zone 2, after that the fuel part is transferred to fuel burners, but no burning occurs in zone 1, and it
serves for forming of a depleted homogeneous mixture of fuel gas and air, which is fed to zone 2.
Thus, the main mode of operation is mainly combustion of a homogeneous mixture, which contains
up to 83% of the fuel burned. The remaining 13% of fuel is fed to the central burner, which plays the
role of a stand-by burner. A toroidal recirculation vortex is formed behind the Venturi nozzle throat,
providing combustion stability.
FIGURE 5 - SCHEMATIC DIAGRAM OF A TUBE-RING COMBUSTION CHAMBER BURNER
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Flame tubes and transition spigots are manufactured using nickel-based alloys with a high chromium
and cobalt content of approximately 20% each or cobalt-based alloys with approximately the same
chromium and nickel content. From the inside, a two-layer 0.4-0.65mm thick thermal barrier coating
is applied to the walls of the flame tubes using air plasma spraying, reducing the wall temperature of
these elements by 60-130°C.
2.3.3. Turbines
Two type of turbines are used in gas turbine: 1)Axial-flow type; 2)Radial-inflow type. The axial-flow
type turbine is used almost in all applications, about 95%. These two turbines can be divided father
into impulse or reaction type units. Pulse turbines take the full enthalpy drop through the nozzles,
while the reaction turbine takes a partial drop through the nozzles and impeller blades.
2.3.3.1. Radial-Inflow Turbine
The radial-inflow turbine also called inward-flow radial turbine and been used for many years. This
turbine is used for lower loads and over a smaller operational range compare to axial turbine. Radialinflow turbine is very similar to centrifugal compressor, but with reversed flow and opposite
rotation. A lot has been learned about radial turbines in recent years, so many new applications
been found over the past 20 years. Radial turbines are used in turbochargers and in some types of
expanders, also in type of applications, where axial-flow turbines are not suited.
2.3.3.2. Axial-Flow Turbine
The axial-flow turbine, same as counterpart the axial-flow compressor, has flow that enter and
leaves in the axial direction. Axial turbines are in high demand due to its low frontal area, which
makes them suitable for the aircraft industry. However, the axial machine is much longer than the
radial, making it unsuitable for some applications. There is two types of axial turbines: 1)Impulse
type; 2)Reaction type. In a pulse turbine, the entire enthalpy drops in the nozzle, so it has a very high
speed at the rotor. The reaction turbine divides the enthalpy drop in the nozzle and rotor.
Powerful axial turbines consist of several stages. The first stages are usually impulse (zero reaction),
and the later stages have about 50% reaction. The impulse stages produce about twice as much
output as comparable 50% reaction stages, while the efficiency of a impulse stage is less than a 50%
reaction stage.
Improvements of the metallurgy of the blades in the turbines allow high temperatures in the turbine
section. The development of directionally solidified blades as well as new single crystal blades with
new coatings and new cooling schemes are responsible for raising the firing temperature. The highpressure ratio in the compressor also makes the cooling air in the first stages of the turbine very hot.
The temperature of the air leaving the gas turbine compressor can reach 650°C. Thus, the present
cooling schemes need revisiting, and the cooling passages are in many cases also coated. Cooling
schemes are limited in the amount of air they can use before there is a negating effort in overall
thermal efficiency due to an increase in the amount of air used in cooling. The rule of thumb in this
area is that if you need more than 8% of the air for cooling you are losing the advantage from the
increase in the firing temperature. The possibility of using steam as a cooling agent for the first and
second stages of turbines is being studied. Steam cooling is possible in new combined cycle power
plants. Steam as a cooling as well as part of the cycle power will be used in the new gas turbines in a
combined cycle mode. The additional power generated using steam is the cheapest MW/$ available.
Injection of about 5% steam by weight of air gives about 12% more power. The injected steam
pressure must be at least 4 bar higher than the compressor discharge pressure. The steam injection
method must be very careful to avoid compressor surge.
2.3.4. Rotors
Rotors of powerful power gas turbines in the vast majority are assembled from separate disks and
end parts. The disks have compressor and gas turbine working blades, and the end parts have
bearing journals and thrust bearing disk.
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The use of prefabricated rotors for a gas turbine provides the following advantages:
• The connection of the individual compressor and gas turbine discs to each other, to the end
pieces and to the spacer parts is made at large diameters. Therefore, the assembled rotor
acquires high bending stiffness, which together with low mass ensures high critical
frequencies. As a rule, assembled gas turbine rotors are either rigid or pass only one critical
speed at start-up. This simplifies the operation of the gas turbine.
• The main components of a gas turbine, such as the compressor and turbine, and even their
parts, operate under different conditions of temperature and degree of aggressiveness of
the environment, therefore they require different materials. The prefabricated design allows
to choose them in the optimal way.
• In the prefabricated disc rotor, it is relatively easy to provide air cooling of the components,
including the discs and blades of the gas turbine. For this purpose, cooling air at the required
pressure and temperature is extracted from the intermediate stages of the compressor and
routed through the central openings in the discs to cool the respective gas turbine stages.
This eliminates the need for cooling air intake and supply pipes, which simplifies repair and
operation.
• The relatively small overall dimensions and weight of the individual discs and other elements
of the prefabricated rotor enable the required metal properties to be obtained during
fabrication, the quality of fabrication can be well controlled, inspected and defectoscopy
under operating conditions can be easily performed.
• The comparatively small thicknesses of the discs and other rotor elements, as well as the
cooling air supply into the chambers between the discs, ensure that they are not subject to
high thermal stresses during steady-state and transient conditions, thus ensuring high
manoeuvrability of the gas turbine.
2.3.4.1. Rotor Materials
Due to special design of gas turbine blade shanks and developed cooling system, their disks operate
at significantly lower temperatures than nozzle and work blades. The large disc diameters,
considerable thickness, central holes for cooling air inlet and non-uniform radial temperature
distribution under steady and non-steady state operation conditions result in very high stresses and
therefore, the need to ensure their strength. At the same time there is a requirement for high
resistance to the appearance of defects (cracks) and their growth to an unacceptable size. To meet
these requirements, high-alloy steels and nickel-based alloys are used. The steels used comprise
approximately 12% chromium, 2.5% nickel, 1.7% molybdenum. The nickel alloys used contain 1619% chromium and a number of other elements like molybdenum, titanium which provide the
necessary strength.
2.3.5. Blades
The blade consists of a profiled portion and an elongated shank with a multi-supported herringbone
shank and an intermediate element. The intermediate element provides high thermal resistance,
preventing the tail joint from being heated by the heat of the hot gases washing over the profiled
portion of the vanes. The additional installation of seals on both sides cuts off the heat flux from the
working disc on which the vanes are mounted and reduces their temperature with a small radial
gradient. This ensures the long-term durability of the impeller disc despite the high level of
centrifugal forces and low thermal stresses. In addition, there is damping between the adjacent
surfaces of the intermediate elements of adjacent blades
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The blades are manufactured by precision investment casting under vacuum in a sophisticated
process. This creates a system of ducts inside the blade through which cooling air from a compressor
flow. The air is forced through radial holes in the disc rim to the face of each blade shank and carries
out convective cooling while passing through the channels. For its intensification the inner surface of
channels is covered by so-called vortex matrix system of ribs, ledges, pins and other turbulators,
which turbulence the flow inside the channels. The perforations in the blade walls are multiple
holes, sometimes over 600 small diameter 0.5-0.6 mm. Thus, in the blade design considered,
convective film cooling is realised. It is used in one or two first stages of a gas turbine, where gas
temperatures are high. In subsequent stages only convective air cooling through internal ducts is
used, with the heated air discharged through the discharge lip and holes in the profile face. The
working blades of the last stage, operating at relatively low temperatures, are not cooled, as the
materials used do not allow this.
The crystalline structure of the blade is called equiaxial, its weak point being the boundaries of the
crystal junctions. As a result, the long-term strength of such a metal, especially at elevated
temperatures, is insufficient. Further improvements in blade technology have resulted in singlecrystal blades, which are grown as a single crystal and are therefore even more durable. In modern
gas turbines, the blades of the first stage and sometimes the second stage are monocrystalline, and
the blades of the other stages are manufactured in a less complex process.
In addition to the traditional centrifugal and aerodynamic forces on turbomachinery blades, their
surfaces are susceptible to corrosion. Intense high-temperature corrosion results from the presence
of alkali metals such as sodium and potassium in the combustion products, which react with sulphur
to form molten sulphates that deposit on the surface and cause corrosion. These substances are
introduced into the combustion products either from the fuel or from the air drawn from the
compressor. High temperature corrosion occurs particularly fast in the presence of vanadium and
lead, which can be present in liquid fuels. High-temperature corrosion occurs at metal temperatures
of 815-930°C and was a major factor limiting blade life until the use of thermal protection coatings.
•
•
Low-temperature corrosion occurs at 590-760 °C at a significant partial vapour pressure of
sulphur oxide arising from the interaction of sodium sulphate with the surface of some
metals, in particular nickel and cobalt alloys.
High-temperature oxidation is also a type of corrosion resulting from high excess air in the
combustion products.
The radical remedy for all of these corrosion types is cermet thermal coatings, which extend the life
of parts by 10-20 times. The most advanced coating technology is the plasma deposition of two
protective layers onto the blade surface in a vacuum, the first of which (inner) provides high
adhesion between the outer coating and the base metal. Coatings are also applied to the inner
surfaces of cooling air passages, bindings and perforation hole surfaces that provide film cooling,
gas-circulation methods are used to apply it.
2.3.5.1 Turbine and Compressor Blades Material
For rotor blades of a turbines operating in an aggressive environment, high temperatures and
stresses from rotation and uneven heating - nickel alloys are used with high chromium content of
14-18%, cobalt 8-18%, molybdenum 1.5-5%, titanium 3-5% and some other elements
Compressor blades operate under lighter conditions than turbine blades. The first compressor stage
and the last turbine stage have almost identical mass flow rates, but the volume flow rates differ by
a factor of 3 in absolute temperature ratio. Therefore, the swept area of the first compressor stage is
smaller than the swept area of the last turbine stage. Consequently, the tensile stresses from
centrifugal forces in the compressor are also smaller. The air temperature in the compressor is
considerably lower than in the turbine. All this makes it possible to design compressor blades with
simple dovetail shanks. Despite the considerably lower stresses in compressor blades and guide
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vanes, the corrosive nature of the medium entering the compressor must be considered. Therefore,
they are manufactured by forging and machining from stainless steels containing 12% chromium.
The environment is particularly aggressive in the first stages of the compressor under conditions of
high humidity in the ambient air, from which moisture condenses on the shrouding surface and
creates the conditions for the formation of aggressive electrolytes. These electrolytes provoke the
formation of ulcers, accelerating the occurrence of corrosion fatigue cracks. Ulcer corrosion
intensifies at downtimes when the air temperature is below the dew point temperature, especially
when deposits are present in the flow section. Therefore, special coatings are used for the first five
to eight stages. They also protect compressor blades from possible drip erosion in the first stages.
2.3.6. Gas Turbine Nozzles
Nozzle apparatuses are made either as individual nozzle blades or as segments of two or three
nozzle blades. The profile parts of the nozzle apparatuses are cast as one piece with bandage shelves
with grips, by means of which they are installed in the upper and lower halves of the cages or
housings. The grips on the inner bandage shelf connect the nozzle apparatus to the half rings
carrying the diaphragm seal.
The operating conditions of the nozzles are lighter than those of the blades, as they are not subject
to centrifugal forces from rotation. However, the high temperature of the gases washing over them
requires cooling. Therefore, all nozzle apparatuses of powerful gas turbines are equipped with air
cooling. Convective-foam cooling is usually used for the first stages, for the rest - internal convective
cooling. Air for cooling nozzles of the first stage is taken behind the last compressor stage, for other
stages - from supply chambers to which it comes from the compressor stages with the
corresponding pressure. The complicated cooling system of the first stage nozzle blades is
determined by two requirements: to obtain a relatively low average temperature of the blade metal
and simultaneously a relatively uniform temperature field, which does not cause unacceptable
temperature stresses under steady-state and transient conditions and the appearance of thermal
fatigue cracks. Exactly therefore the perforations are carried out in areas where the heat transfer
coefficients from the gases to the metal are the highest.
2.3.6.1. Gas Turbine Nozzles Material
The working and inner surfaces of blades and flange flanges are provided with thermal protection
coatings that provide sufficient resistance to high-temperature corrosion and high-temperature
oxidation. Gas turbine nozzle materials must have good resistance to high-temperature corrosion
and oxidation, thermal fatigue and good foundry properties. These materials are cobalt and nickel
alloys. Cobalt alloys are alloyed with 10% nickel, 20-25% chrome and 7-8% tungsten. Nickel alloys are
alloyed with chromium and cobalt at around 20% each, with additions of tungsten, molybdenum and
titanium at 1-2%. For final stage nozzles, steels alloyed with nickel, chromium and cobalt at around
20% each are used.
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2.4. Gas Turbine Cycles
2.4.1. Simple Gas Turbine Cycle
The main elements of a simple cycle are Compressor,
Combustion Chamber and Turbine shown in Figure 6. To
simplify the cycle analysis, assume that the physical properties
of the air flowing through the compressor and the gases
passing through the turbine remain unchanged. Therefore, the
heat capacities of air and gas (𝑐𝑝𝑎 ) and (𝑐𝑝𝑔 ), as well as the
isentropic indices (𝑘𝑎 ) and (𝑘𝑔 ) will be assumed constant, the
error caused by the assumptions made is small and does not
affect the principle conclusions.
Figure 7 shows the cycle of a gas turbine in a T,s-diagram,
FIGURE 6 - SCHEMATIC DIAGRAM OF A SIMPLE
excluding pressure losses in the air and gas paths. Point (a)
GAS TURBINE
defines the initial parameters of the air before the compressor
(𝑝𝑎 ), 𝑇𝑎 ). Line (ab) corresponds to the process of air compression
in the compressor to the parameters (𝑝𝑏 , 𝑇𝑏 ), and line (ab′)
corresponds to isentropic compression to the same final pressure (𝑝𝑏 )
and temperature (𝑇𝑏 ). Let's conditionally mark the parameters at the
end of isentropic compression or expansion by the index "t". Line (bc)
corresponds to the isobaric heat input in the combustion chamber,
with the air temperature increasing from (𝑇𝑏 ) to (𝑇𝑐 ). There is a
pressure drop in the combustion chamber due to hydraulic losses, so
𝑝𝑐 < 𝑝𝑏 .
𝑝𝑐 = λ1 ∗ 𝑝𝑏
(1.0)
λ1 is a factor considering the pressure loss in the air duct between the
FIGURE 7 - SIMPLE GAS TURBINE
compressor and the combustion chamber and in the combustion
CYCLE
chamber itself, λ1 = 0.97 ... 0.98.
Line (cd) shows the expansion of the gas in the turbine up to pressure (Pd). Due to the pressure loss
in the gas path behind the turbine 𝑝𝑑 > 𝑝𝑎 .
𝑝𝑎 = λ2 ∗ 𝑝𝑑
(1.1)
λ2 is a coefficient considering pressure losses in the air intake (upstream of the compressor) and gas
outlet (downstream of the turbine) systems, λ2 =0.96...0.98.
Denoting λ = λ1 ∗ λ2 , we establish the relation between compressor and turbine pressure ratios.
𝑝
𝑝
𝜀 = 𝑝𝑏 (𝑤ℎ𝑖𝑐ℎ 𝑖𝑠 λ1 ); 𝛿 = 𝑝 𝑐 (𝑤ℎ𝑖𝑐ℎ 𝑖𝑠 λ2 )
𝑎
𝑑
𝛿 = λ𝜀
(1.2)
(1.3)
It is important to note conventionality of representation of the whole gas turbine cycle in a single
T,s-diagram, consisting in the fact that T,s-diagram is strictly built for one invariable substance, while
gas turbine cycle at different sections refers to different substances. On the (ab) section it
corresponds to air, on (cd) line - to combustion products, on (bc) line - heat supply because of fuel
combustion reaction. Line (da) is the conditional closure of the cycle. In fact, at point (d), combustion
products are released into the atmosphere, and at point (a) another substance, air, is taken from the
atmosphere by the compressor. The conventional representation of the cycle does not prevent the
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various processes from being correctly quantified by taking the heat capacity values inherent to the
substance in question for each part of the cycle.
The specific useful work of a gas turbine is the difference:
𝐻 = 𝐻𝑇 − 𝐻𝐶
(1.4)
Where (𝐻𝑇 ) is the expansion work of 1 kg of gas in the turbine and (𝐻𝐶 ) is work expended for
compression of 1 kg of air in the compressor.
𝐻𝑇 = 𝑐𝑝𝑔 (𝑇𝑐 − 𝑇𝑑 ); 𝐻𝐶 = 𝑐𝑝𝑎 (𝑇𝑏 − 𝑇𝑎 )
(1.5)
Where (𝑐𝑝𝑔 ) is the average heat capacity of gas in the temperature range (𝑇𝑐 – 𝑇𝑑 ) and (𝑐𝑝𝑎 ) is the
average heat capacity of air in the temperature range (𝑇𝑏 – 𝑇𝑎 ).
The dependencies of Equation (1.5) can be represented in terms of isentropic temperature
differences by using expressions for the isentropic efficiencies of compressor (η𝑐 ) and turbine (η𝑡 ).
“h” are the enthalpies of gas and air at the respective points).
𝑐
ℎ −ℎ
(𝑇 −𝑇 )
𝑇 −𝑇
η 𝑇 = ℎ 𝑐−ℎ 𝑑 = 𝑐 𝑝𝑔(𝑇 𝑐−𝑇 𝑑 ) ~ 𝑇 𝑐−𝑇 𝑑
𝑐
η𝑐 =
𝑑𝑡
ℎ𝑏𝑡 −ℎ𝑎
ℎ𝑏 −ℎ𝑎
𝑝𝑔
=
𝑐
𝑑𝑡
𝑐𝑝𝑎 (𝑇𝑏𝑡 −𝑇𝑎 )
𝑐𝑝𝑎 (𝑇𝑏 −𝑇𝑎 )
𝑐
~
(1.6)
𝑑𝑡
𝑇𝑏𝑡 −𝑇𝑎
𝑇𝑏 −𝑇𝑎
(1.7)
Using equations (1.6) and (1.7) as well as the isentropic equation:
𝑇𝑏𝑡
𝑇
= 𝜀 𝑚𝑎 ; 𝑇 𝑐 = 𝜀 𝑚𝑔
(1.8)
𝑇
𝑎
𝑑𝑡
𝑚𝑎 =
𝑘𝑎 −1
; 𝑚𝑔
𝑘𝑎
=
𝑘𝑔 −1
𝑘𝑔
(1.9)
Finding temperature (𝑇𝑑 ) and (𝑇𝑏 ):
𝑇𝑑 = 𝑇𝑐 [1 − (1 − 𝛿 −𝑚𝑔 )η 𝑇 ]
𝑇𝑏 = 𝑇𝑎 [1 +
𝜀 𝑚𝑎 −1
]
η𝑐
(1.10)
(1.11)
Given Equation (1.10) and (1.11), the dependence of Equation (1.5) takes the following form:
𝐻𝑇 = η 𝑇 ∗ 𝑐𝑝𝑔 ∗ 𝑇𝑐 (1 − 𝛿 −𝑚𝑔 )
(1.12)
1
η𝑐
𝐻𝐶 = ( ) 𝑐𝑝𝑎 ∗ 𝑇𝑎 (𝜀 𝑚𝑎 − 1)
(1.13)
It is assumed that the turbine and compressor efficiencies are known. The efficiency values
determine the degree of perfection of the flow parts of the turbine and compressor.
The specific heat input (𝑞1 ) is determined by from the difference of enthalpies at points (c) and (b).
1
𝑞1 = (η ) 𝑐𝑝 (𝑇𝑐 − 𝑇𝑏 ) (1.14)
𝑐𝑐
Where (𝑐𝑝 ) is the average heat capacity of the heat input process heat input into the combustion
chamber. Combustion chamber efficiency (η𝑐𝑐 ) takes into account incomplete combustion and heat
loss through the combustion chamber walls, usually (η𝑐𝑐 ) = 0.97 ... 0,99.
The first important characteristic of gas turbine cycle efficiency is defined by the expression:
𝐻 −𝐻
H
η = 𝑇𝑞 𝐶 = 𝑞
(1.15)
1
1
Which, when using Equation (1.10) - (1.14), takes the following form:
η=
𝑐̅𝑝𝑔 ∗𝜏∗η𝑇 (1−𝛿 −𝑚𝑔 )−𝑐̅𝑝𝑎 (𝜀 𝑚𝑎 −1)/η𝑐
𝜏−1−(𝜀 𝑚𝑎 −1)/η𝑐
η𝑐𝑐 (1.16)
Where, for brevity the designation: 𝐶̅ 𝑝𝑔 = 𝐶𝑝𝑔/𝐶𝑝; 𝐶̅ 𝑝𝑎 = 𝐶𝑝𝑎/𝐶𝑝; 𝜏 = 𝑇𝑐/𝑇𝑎. The efficiency (η)
depends only on the temperature ratio τ = Tc / Ta, but not their absolute values (if we ignore the
̅ ) and (𝐶𝑝𝑎
̅ ), which is acceptable).
effect of changes in (𝐶𝑝𝑔
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Figure 8 shows a graph of the dependence of Equation (1.16). The
calculations are performed without considering the losses in the
combustion chamber (η𝑐𝑐 =1) and in the air and gas paths (λ=1). In
addition, it is assumed that (η 𝑇 =0.87), (η𝑐 =0.84) and
(𝑚𝑔 =𝑚𝑎 =0.275). As (τ) increases, the maximum value of (η) and
the optimum pressure ratio (εη ) increase (ratio of pressures at
which the efficiency reaches its maximum value). The value of the
optimum pressure ratio can be found analytically from the
condition (∂η/∂ε=0). However, when designing a gas turbine,
there is always a need to plot the dependence (η=εη) at a given
temperature ratio in order to determine an economically feasible
pressure ratio (ε).
The second important characteristic of the cycle is the efficiency
factor, defined as the ratio of the gas turbine efficiency to the
turbine operation:
𝐻 −𝐻
𝐻
𝜑= 𝑇 𝐶=
(1.17)
𝐻𝑇
FIGURE 8 - PLOT OF EFFICIENCY OF A
SIMPLE GAS TURBINE ON PRESSURETEMPERATURE RELATIONSHIP
𝐻𝑇
It can be checked in:
𝜑 =1−
𝑐𝑝𝑎
𝑐𝑝𝑔
∗
1
𝜏∗η𝑇 ∗η𝑐
∗
𝜀 𝑚𝑎 −1
1−𝛿 −𝑚𝑔
(1.18)
For greater clarity, assume δ~ε and 𝑚𝑔 ~𝑚𝑎 ~m, then:
𝜑 =1−
𝜀𝑚
𝜏∗η𝑇 ∗η𝑐
(1.19)
According to Equation (1.19) the useful work factor increases with decreasing (ε) for given (τ), and
with increasing (τ), (η𝑡 ) and (η𝑐 ). If the useful work factor is small, it means that the useful work of
the cycle is small compared to the turbine's work and that most of the turbine's work is spent to
drive the compressor. In this case, a small change in turbine or compressor operation results in a
noticeable relative change in the useful work of the gas turbine, and hence in a change in its
efficiency (due to, for example, changes in η 𝑇 or η𝑐 ).
The third important characteristic of the cycle is the specific gas flow rate kg/kJ:
𝐺
𝑑 = 𝑁 (1.20)
Where (G) is the gas flow rate in kg/s and (N) is the useful power of the gas turbine in kW. The
specific work of a gas turbine (H=𝐻𝑇 -𝐻𝐶 ) is related to the specific flow rate (d) by a simple
relationship:
𝐻 = 𝑑−1
(1.21)
Equations (1.20) and (1.21) are used to determine the capacity of the gas turbine in kW:
𝐺
𝑁 = 𝑑 = 𝐺 ∗ 𝐻 (1.22)
Both (d) and (H) determine the capacity of 1 kg of gas. The higher the (H) and the lower the (d), the
lower the gas flow rate is needed to obtain a given capacity. Using the Equation for useful work (1.4)
and dependencies (1.12) and (1.13), it can be proven that the useful work reaches a maximum value
when the pressure ratio (ε𝐻 ) is less than the optimum ratio (εη ). When analysing gas turbine
schemes, in addition to efficiency, (ϕ) and (H) should also be considered as comparable
characteristics.
2.4.2. Gas Turbine Cycle with Heat Regeneration
In a simple Gas Turbine, the gases leave the turbine with a high temperature (𝑇𝑑 ) and the heat 𝑞2 =
𝑐𝑝𝑔 (𝑇𝑑 − 𝑇𝑎 ) is lost uselessly. This circumstance is the main reason of low efficiency of simple Gas
Turbines. If at least a part of that heat (𝑞2 ) is used, it will cause a noticeable increase in efficiency.
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One way of utilising the waste gas heat is using heat exchangers “Regenerators” in which the waste
gases give up some of their heat to the air compressed in the compressor.
Figure 9 shows a schematic of a Gas Turbine with a
regenerator. The gases leaving the turbine (T) with
temperature (𝑇𝑑 ) that are directed to the regenerator (R),
where they give off part of the heat to the air supplied to the
regenerator from compressor (C) at temperature (𝑇𝑏 ). In the
regenerator, the air temperature rises to (𝑇𝑒 ), so that the
required amount of fuel consumed for heating the combustion
air in the combustion chamber is reduced and the Gas Turbine
efficiency increases compared to the efficiency of a simple Gas
Turbine without regeneration. The temperature of the gases in
the regenerator drops to the value (𝑇𝑓 ). At the temperature
(𝑇𝑓 ) the gases are discharged into the atmosphere.
FIGURE 9 - SCHEMATIC DIAGRAM OF A SIMPLE
GAS TURBINE WITH REGENERATOR
Process of Gas Turbine with regeneration in T, s-diagram is
shown in Figure 10. The line (be) corresponds to the air heating
and the line (df) to the cooling of the gases in the regenerator.
Counterflow heat exchanger regenerator shown in Figure 11. The
air in it flows through tubes fixed in the tube plates and the gas
moves between the tubes in the opposite direction. At the same
flow rates and heat capacities of gas and air in an ideal (without
heat loss) counterflow regenerator the air heating 𝑇𝑒 − 𝑇𝑏 is
equal to the gas temperature drop and the temperature head
between gas and air along the whole path is the same and equal
to the temperature head at air exit from the regenerator 𝑇𝑑 − 𝑇𝑒 .
The amount of heat delivered to the air is determined by increasing
the air temperature in the regenerator from (𝑇𝑏 ) to (𝑇𝑒 ).
𝑞𝑎 = 𝑐𝑝𝑎 (𝑇𝑒 − 𝑇𝑏 )
(2.01)
The maximum possible amount of heat depends on the drop in
temperature of the gases from (𝑇𝑑 ) to (𝑇𝑏 ).
𝑞𝑚𝑎𝑥 = 𝑐𝑝𝑔 (𝑇𝑑 − 𝑇𝑏 ) (2.02)
This is in an ideal counterflow regenerator, in a real regenerator
reducing the gas temperature to (𝑇𝑏 ) is impossible because it
would require an infinitely large regenerator surface. The
efficiency of a regenerator as a heat exchanger in Equation 2.03
is evaluated by the degree of regeneration (σ), defined as the
ratio of the amount of heat transferred to the air to the
maximum possible amount of amount of heat.
σ=𝑞
𝑞𝑎
𝑚𝑎𝑥
𝑐
(𝑇 −𝑇 )
FIGURE 10 - SIMPLE GAS TURBINE CYCLE
WITH REGENERATION
FIGURE 11 - SCHEMATIC DIAGRAM OF A
COUNTERFLOW REGENERATOR.
𝑇 −𝑇
= 𝑐 𝑝𝑎(𝑇𝑒 −𝑇𝑏 ) ≈ 𝑇𝑒 −𝑇𝑏 (2.03)
𝑝𝑔
𝑑
𝑏
𝑑
𝑏
The degree of regeneration depends on the surface area of the regenerator. Establish this
relationship for a counter-current regenerator as in Figure1234. Amount of heat delivered to the air
per unit time are shown in Equation 2.04.
Q = 𝑘𝑓(𝑇𝑑 − 𝑇𝑒 )
(2.04)
Where (k) is the heat transfer coefficient of the regenerator and (f) is the heat transfer surface area
of the regenerator. Also, Equation 2.05 can be used.
Q = 𝑐𝑝𝑎 (𝑇𝑒 − 𝑇𝑏 )
(2.05)
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Excluding Q from Equation 2.04 and 2.05 and using Equation 2.03, the transformed Equation 2.06 is
obtained.
𝑐
𝑓
σ
= 𝑝𝑎
(2.06)
𝐺
𝑘 1−σ
If in Equation 2.06 the consumption (G) is replaced by power (N) and useful work (H), it will be that
the surface area of the regenerator related to power is shown in Equation 2.07.
𝑐𝑝𝑎 σ
𝑓
= 𝑘𝐻
(2.07)
𝑁
1−σ
The resulting ratio shows that the specific surface area of the regenerator (f/N) depends on the
degree of regeneration and at (σ) tending to unity, the ratio (f/N) grows indefinitely. Consider that at
(σ=1) the temperature head between gas and air in the regenerator is zero (𝑇𝑒 = 𝑇𝑑 ). Equation 2.07
also shows that a reduction in the specific surface area of the regenerator can be achieved by
intensifying the heat transfer (increasing (k)) and increasing the useful work (H). An increase in (H)
for a given capacity corresponds to a drop in consumption (G) and hence in the amount of heat
transferred in the regenerator from the gas to the air.
Equations 1.17, 1.18 and 1.19, which define (ϕ) and (H) will remain the same in the presence of
regeneration. Equation 1.15 for efficiency (η) will change because less heat will now be supplied to
the combustion chamber.
𝑞1 = 𝑐𝑝 (𝑇𝑐 − 𝑇𝑒 )
(2.08)
The temperature (𝑇𝑒 ) can be determined using Equation 2.03, assuming a given degree of
regeneration σ.
𝑇𝑒 = 𝑇𝑏 + (𝑇𝑑 − 𝑇𝑏 )σ (2.09)
or
1
𝑇𝑒 = 𝑇𝑐 (𝜏 (1 +
𝜀 𝑚𝑎 −1
)+
η𝑘
1
σ (1 − (1 − 𝛿 −𝑚𝑔 )η 𝑇 − 𝜏 (1 +
𝜀 𝑚𝑎 −1
)))
η𝑘
(2.10)
The expression for efficiency can be obtained from Equation 1.15 and 1.12, 1.13, considering the last
dependencies for (𝑞1 ) and (𝑇𝑒 ).
η𝑐𝑐 =
𝑐̅𝑝𝑔 ∗η𝑇 (1−𝛿 −𝑚𝑔 )−𝑐̅𝑝𝑎 (𝜀 𝑚𝑎 −1)/τη𝑐
1
𝜏
𝜀𝑚𝑎 −1
1
𝜀𝑚𝑎 −1
)−σ(1−η𝑇 (1−𝛿 −𝑚𝑔 )− (1+
))
η𝑐
𝜏
η𝑐
1− (1+
(2.11)
In the absence of regeneration (σ=0), Equation 2.11 is the same as Equation 1.16. The dependence
of Equation 2.11 is plotted in Figure 12 for two values of (τ) and several values of (σ). The curves
(η=η(ε)) at (τ=const) converge to one point characterised by the fact that in this point (𝑇𝑑 = 𝑇𝑏 ). In
this case the effect of introducing a regenerator is zero, as gas and air at the entrance to the
regenerator have the same temperature and there is no heat exchange. A further increase in (ε)
leads to a negative regenerator effect, as the temperature of the air entering the regenerator
becomes higher than the gas outlet temperature from the turbine (𝑇𝑏 > 𝑇𝑑 ).
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Figure 12 shows a graph for the efficiency of a Gas
Turbine with regeneration at η 𝑇 = 0.87, η𝑐 = 0.84,
𝑚 = 0.275 and numbered variables No.1 - σ=0, No.2 σ=0.2, No.3 - σ=0.5, No.4 - σ=0,8, No.5 - σ=1 and 𝜏 = 4
for the solid line and 𝜏 = 3.2 for a dashed line.
Figure 12 shows that the introduction of regeneration
significantly increases the cycle efficiency. The
optimum pressure ratio (εη ) decreases as the degree
of regeneration increases. This is explained by the fact
that with increasing (ε) at fixed temperatures (𝑇𝑎 ) and
(𝑇𝑐 ) the available temperature difference (𝑇𝑑 − 𝑇𝑏 ) in
the regenerator decreases and consequently the
efficiency of heat regeneration also decreases. The
data from Table 16 as well as the data in Figure 1228
are obtained without taking into account the hydraulic
resistance of the regenerator, the actual efficiency
gain from the use of regeneration is much smaller. The
useful operation of a simple Gas Turbine without
regeneration reaches the maximum value when the
pressure ratio (εH ) is less than the optimum. The value
of (εH ) is independent of the degree of regeneration.
At the same time the optimum pressure ratio (εη )
decreases with increasing regeneration. Consequently,
as (σ) increases the values of (εη ) and (εH ) converge,
FIGURE 12 - EFFICIENCY OF A GAS TURBINE WITH
and with a considerable degree of regeneration εη <
REGENERATION
εH .
Example provided in Tablet 1 to demonstrate the increase in Gas Turbine efficiency when
introducing heat recovery at t c = 800°C, t a = 15°C, 𝜏 = 3.73; η 𝑇 = 0.87; η𝑐 = 0.84, m = 0.275; 𝛾 = 1.
TABLE 1 - GAS TURBINE EFFICIENCY DEPENDING ON GAS TEMPERATURE AND DEGREE OF REGENERATION
Figure 13 shows a graph of εη = 𝑓(σ) for 𝜏 = 4. In the same place the value εH = 7 is shown for
comparison. The graph of Figure 13 allows to conclude, that at normal regeneration degree
σ=0,6...0,8 in order to reduce sizes and mass of Gas Turbine it is advisable to take pressure ratio
higher than the optimum, because the maximum Gas Turbine operation is reached at εH > εη .
Useful work factor (𝜑) with the introduction of regeneration increases noticeably due to the
reduction of (εη ) as can bee seen in Figure 12.
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FIGURE 13 - OPTIMAL PRESSURE RATIO OF A GAS TURBINE WITH HEAT RECOVERY
2.4.3. Calculation of the Thermal Circuit of a Simple Gas Turbine
When defining Simple Gas Turbine characteristics: 𝐻𝑇 , 𝐻𝐶 , 𝜑, η, N, peculiarities of heat supply in
combustion chamber, influence of fuel type and excess air ratio on enthalpy of working gases
entering the gas turbine were not taken into account. Equation 3.01 shows the thermal balance of
the combustion chamber.
𝐺𝑇 ℎ𝑐 = 𝐺𝐶 ℎ𝑏 + 𝐵𝐾𝐹 η𝑐𝑐 + 𝐵ℎ𝑓𝑢𝑒𝑙
(3.01)
Where (𝐺𝑇 ) is consumption of gases leaving the combustion chamber, (ℎ𝑐 ) is the enthalpy of the
combustion products at the combustion chamber outlet, (𝐺𝐶 ) is the air consumption at the
combustion chamber inlet, (ℎ𝑏 ) is the enthalpy of air behind the compressor or at the combustion
chamber inlet, (B) is the fuel consumption supplied to the combustion chamber by the pump or gas
compressor, (𝐾𝐹 ) is the calorific value of the fuel, mean the amount of heat released upon complete
combustion of 1kg of fuel, (ℎ𝑓𝑢𝑒𝑙 ) is enthalpy of fuel. The left side of Equation 3.01 contains the total
amount of heat coming out of the combustion chamber, the right side of the equation contains the
sum of the amounts of heat brought into the combustion chamber by air and fuel, and the amount
of heat released by the combustion reaction of the fuel.
When calculating thermal processes in combustors, in particular in Gas Turbine combustion
chambers, it is assumed that (𝐾𝐹 ) is a constant for a given fuel, determined experimentally at a
standard initial temperature (usually 25 °С) of the fuel-oxidizer (air) mixture. Value of (𝐾𝐹 ) depends
on fuel composition, (𝐾𝐹 ) slightly differs for gaseous fuels of different deposits, however this
difference has little effect on basic Gas Turbine characteristics, except for fuel consumption (B). The
latter for Gas Turbine of the given capacity and parameters depending on (𝐾𝐹 ) is found under the
condition: 𝐵𝐾𝐹 ≈ constant.
A distinction is made between "Higher" (𝑄𝐻 ) and "Lower" (𝑄𝐿 ), whereby it can be 𝐾𝐹 = 𝑄𝐻 or 𝐾𝐹 =
𝑄𝐿 . The relationship between (𝑄𝐻 ) and (𝑄𝐿 ) is shown in Equation 3.02.
𝑄𝐿 = 𝑄𝐻 − 229𝐻
(3.02)
where (H) is the mass fraction of hydrogen in the fuel, in percentage, (𝑄𝐿 ) and (𝑄𝐻 ), kJ/kg. The
subtracted term in Equation 3.02 represents the heat of vaporisation of water vapour, which is
produced by the combustion of hydrogen in the fuel. The use of (𝑄𝐿 ) in the heat balance is justified
by the fact that combustion products are emitted into the atmosphere at temperatures at which the
water vapour remains completely in the gas phase. Therefore, the thermal effect of fuel combustion
is less than (𝑄𝐻 ) by the value of the heat of water vapour evaporation, from which Equation 3.02 is
derived. When using the heat balance in the form of Equation 3.01, 𝐾𝐹 = 𝑄𝐿 is assumed, and the
enthalpy of water vapour, which is included in (ℎ𝑐 ), is determined for the ideal gas state, mean
without considering the heat of evaporation. In this case the enthalpies of substances are counted
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from their values at standard temperature, (ℎ𝑐 ), (ℎ𝑏 ), (ℎ𝑓𝑢𝑒𝑙 ) are the enthalpy differences at the
respective temperatures and the enthalpy at the standard temperature at 𝑡0 = 25°C. The
calculation of the heat input by (𝑄𝐿 ) and without considering the heat of vapour formation in
enthalpy (ℎ𝑐 ) gives an overestimate of the efficiency of the Gas Turbine, since when 1 kg of fuel is
burned in the combustion chamber, the amount of heat released is close to the value (𝑄𝐻 ). Convert
the efficiency to (𝑄𝐻 ) using the Equation 3.03.
η(𝐻) = η𝑄𝐿 /𝑄𝐻
(3.03)
Where (η) is the efficiency of the Gas Turbine, determined according to the adopted methodology,
(η(𝐻) ) is the efficiency related to the upper calorific value, considering the loss of heat of vapour
formation of water vapour with the exhaust gases. There is a relationship between flow rates (𝐺𝑇 ),
(𝐺𝐶 ) and (B) as shown in Equation 3.04 and 3.05.
𝐺𝐶 = 𝛼𝐿0 𝐵
(3.04)
𝐺𝑇 = (1 + 𝛼𝐿0 )𝐵
(3.05)
Where (𝐿0 ) is the amount of air minimally required for complete combustion of 1 kg of fuel (kg/kg),
α is the excess air ratio, mean the ratio of the actual amount of air supplied to the combustion
chamber to burn 1 kg of fuel to the minimum required amount. (𝐿0 ) is a characteristic that depends
only on the fuel composition. There is little variation in (𝐿0 ) values for different gas fields. When
designing a Gas Turbine, it must be considered that it must be adapted for combustion of any
gaseous fuel and in some cases for combustion of light liquid fuels, it is reasonable to consider some
standard fuel, on the use of which the Gas Turbine should be designed. As such a fuel is taken as a
conditional fuel called a standard hydrocarbon. Standard hydrocarbon has the following mass
composition: Carbon (C) - 85 % and Hydrogen (H) - 15 %. The following characteristics are used for a
standard hydrocarbon: 𝑄𝐻 = 47,700kJ/kg; 𝑄𝐿 = 44,650kJ/kg; 𝐿0 = 14.671kg/kg.
The combustion products coming out of the combustion chamber can be considered as a mixture of
the so-called "clean" combustion products, resulting from combustion of fuel without excess air, and
supplementary air. Combustion of 1 kg of fuel results in 1 + 𝐿0 of clean combustion products
(kg/kg), and (𝛼 − 1)𝐿0 of supplementary air (kg/kg). The enthalpy of the mixture (ℎ𝑐 ) at
temperature (𝑇𝑐 ) is represented in Equation 3.06.
ℎ𝑐 =
1+𝐿0
ℎ
1+𝛼𝐿0 𝑐.𝑝
+
(𝛼−1)𝐿0
ℎ
1+𝛼𝐿0 𝑎
(3.06)
Where (ℎ𝑝.𝑐 ) and (ℎ𝑎 ) are the enthalpies of the pure combustion products and air at temperature
(𝑇𝑐 ).
Using a table with the thermodynamic properties of the fuel it is possible to find the enthalpy of the
combustion products at the combustion chamber outlet, but the excess air ratio (𝛼) must be
determined. To determine it, the heat balance Equation 3.01 can be used. By substituting the righthand sides of Equation 3.04, 3.05 and 3.06 in 3.01 and reducing all terms by the common factor (B),
solve the equation with respect to (𝛼) and obtain Equation 3.07.
𝛼=
𝐾𝐹 η𝑐𝑐 +𝐿0 ℎ𝑎 +ℎ𝐹 −(1+𝐿0 )ℎ𝑝.𝑐
𝐿0 (ℎ𝑎 −ℎ𝑏 )
(3.07)
When calculating the thermal design of a simple Gas Turbine, without considering the cooling of the
gas turbine parts, the initial values given or estimated are:
-
Electrical power (𝑁𝑒 ), kW;
Gas temperature upstream the gas turbine (𝑇𝑐 ), K;
Temperature of air at compressor inlet (𝑇𝑎 ), K;
Compressor pressure ratio 𝜀 = 𝑝𝑏 /𝑝𝑎 ;
Pressure loss coefficient λ = 𝛿/𝜀;
Fuel heat utilization factor in combustion chamber (η𝑐𝑐 );
Mechanical efficiency of the turbine (η𝑚 );
Efficiency of electric generator (η𝑒.𝑔 );
Fuel characteristics: (K 𝐹 ), kJ/kg; (L0 ), kg/kg; (h𝑓𝑢𝑒𝑙 ), kJ/kg;
Turbine isoentropic efficiency (η 𝑇 ) ;
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-
Isoentropic efficiency of the compressor (η𝐶 );
Characteristics of clean combustion products and air;
Leakage factor (α𝑦 ).
The calculation of the Gas Turbine heat scheme is carried out as follows:
1) Determine the parameters of the air compression process in the compressor (𝑐𝑝𝑎 ) and (𝑚𝑎 ).
On the first approximation take 𝑚𝑎 = 𝑅𝑎 /𝑐𝑝𝑎 ≈ 0.28 . According to the Equation 1.10 and
1.11 find temperature (𝑇𝑏 ) of air at the end of compression process in the compressor using
Characteristics of clean combustion products and air, determine enthalpy ℎ𝑏 = ℎ𝑎′ (𝑡𝑏 ) −
ℎ𝑎′ (25), and by (𝑇𝑎 ) the initial enthalpy of air at compressor inlet ℎ𝑎 = ℎ𝑎′ (𝑡𝑎 ) − ℎ𝑎′ (25). It
should not be confused that (ℎ𝑎 ) will be negative if 𝑇𝑎 < 25 °С. Find the average heat
capacity of the air when it is compressed in the compressor, using Equation 3.08.
ℎ −ℎ
𝑐𝑝𝑎 = 𝑡𝑏 −𝑡 𝑎
(3.08)
𝑏
𝑎
Then refine the value of (𝑚𝑎 ) as in Equation 3.09.
𝑅
0.287
𝑚𝑎 = 𝑐 𝑎 = 𝑐
(3.09)
𝑝𝑎
𝑝𝑎
Also, the values of temperature (𝑇𝑏 ) at the end of the compression process in the
compressor according to Equation 1.11 and (ℎ𝑏 ) according to characteristics of clean
combustion products and air.
2) The coefficient (𝛼) is calculated using the Equation 3.07, having previously determined from
characteristics of clean combustion products and air table all necessary enthalpies by the
known parameters (𝑇𝑐 ) and (𝑇𝑏 ).
3) The enthalpy of the gas upstream of the turbine is found according to Equation 3.06.
4) Determine the parameters of the gas expansion process in the turbine, to pre-specifying the
value of (𝑚𝑔 ), for example 𝑚𝑔 ≈ 0.25, calculate the gas temperature (𝑇𝑑 ) behind the
turbine by the first Equation 1.10, then find the gas enthalpy (ℎ𝑑 ) behind the turbine, using
characteristics of clean combustion products and air table and Equation 3.06, where
enthalpies (ℎ𝑐.𝑝 ) and (ℎ𝑎 ) are determined for temperature (𝑇𝑑 ). Average heat capacity of gas
in the expansion process is calculated by Equation 3.10.
ℎ −ℎ
𝑐𝑝𝑔 = 𝑡𝑐 −𝑡 𝑑
(3.10)
𝑐
𝑑
The corrected value of (𝑚𝑔 ) is found as 𝑚𝑔 = 𝑅𝑔 /𝑐𝑝𝑔 . Gas constant, kJ/kg, of combustion
products in Equation 3.11.
8.314
𝑅𝑔 = 𝜇
(3.11)
𝑔
Where the molecular weight of the combustion products is shown in Equation 3.12.
𝜇𝑔 = 𝜇𝑎 𝑟𝑎 + 𝜇𝑐.𝑝 (1 − 𝑟𝑎 )
(3.12)
Where (𝜇𝑎 ), (𝜇𝑝.𝑐 ) are the molecular masses of air and the pure combustion products. The
volume fraction of air in the combustion products is shown in Equation 3.13 and Equation
3.14.
𝑟𝑎 =
𝑞=
𝑞(𝛼−1)
1+𝑞(𝛼−1)
𝜇𝑝.𝑐 𝐿0
𝜇𝑎 1+𝐿0
(3.13)
(3.14)
Knowing (𝑚𝑔 ), find the corrected value of (𝑇𝑑 ) by the Equation 1.10, enthalpy (ℎ𝑑 ) behind
the gas turbine by Equation 3.06, where enthalpies (ℎ𝑝.𝑐 ) and (ℎ𝑎 ) are determined by the
corrected temperature (𝑇𝑑 ), using a table for characteristics of clean combustion products
and air.
5) Expansion work of 1 kg of gas in the turbine as shown in Equation 3.15.
𝐻𝑇 = ℎ𝑐 − ℎ𝑑 (3.15)
6) Work required to compress 1 kg of air in a compressor as shown in Equation 3.16.
𝐻𝐶 = ℎ𝑏 − ℎ𝑎 (3.16)
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7) Gas turbine capacity from Equation 3.17, showing gas flow through the turbine.
𝐺𝑇 = 𝑁𝑒 /𝐻𝑒 (3.17)
Where
𝑁𝑒 = 𝑁𝐸 /η𝐸.𝑔 (3.18)
𝐻𝑒 = 𝐻𝑇 η𝑀 − 𝑏𝐻𝐶 (3.19)
𝑏 = 𝛼𝐿0 (1 + 𝛼𝑦 )/(1 + 𝛼𝐿0 )
(3.20)
Here (𝛼𝑦 ) is the coefficient characterising the additional leakage air flow through the
compressor and turbine seals, usually 𝛼𝑦 =0.005-0.02.
8) Air consumption supplied by the compressor shown in Equation 3.21.
𝐺𝐶′ = 𝐺𝑐 (1 + 𝛼𝑦 ) = 𝑏𝐺𝑇
(3.21)
9) Fuel consumption in Equation 3.22.
𝐵 = 𝐺𝑇 /(1 + 𝛼𝐿0 )
(3.22)
10) The power developed by the Gas Turbine in Equation 3.23.
𝑁𝑇 = 𝐺𝑇 𝐻𝑇
(3.23)
11) Power consumed by the compressor in Equation 3.24.
𝑁𝐶 = 𝐺𝐶′ 𝐻𝐶
(3.24)
12) Useful work coefficient in Equation 3.25.
𝑁
𝑏𝐻
𝜑 = 𝑁𝑒 = 1 − 𝐻 𝐶
(3.25)
𝑇
𝑇
13) Gas turbine efficiency (electrical efficiency) in Equation 3.26.
η𝐸 =
G𝑇 H𝑒 η𝐸.𝑔
𝐵K𝐹
(3.26)
2.5. Fuel
In power plant natural gas is the fuel of choice wherever it is available because of its price, clean
burning, ease and cost of installation, as well as safety and environmental friendliness compared to
installations using other fuels such as uranium or coal. Gas turbines operate on the principles of the
Brayton cycle, usually using natural gas as fuel, but also can run on different fuels for which they are
not designed. In order to reduce the carbon footprint, attempts have been made to modify the fuel
mix for Gas Turbines, using different blends and additives, e.g. diluting with biofuels. Such fuel
blends can degrade turbine performance, but in some cases the sacrifice in turbine power and
performance is compensated for by lower emissions of harmful gases.
2.5.1. Natural Gas
Type of fuel for a Gas Turbine depends on location and application. Natural gas is usually the choice
for most Gas Turbines. Natural gas is considered the least environmentally damaging fuel compared
to other fossil fuels and has the lowest maintenance costs. Natural gas is a mixture of at least 95%
methane and the rest is carbon dioxide. Natural gas is produced by the decay of biomass, such as
plants and living creatures, which has been buried over time. Because of the layers of material that
accumulate on top of the biomass, it pushes the biomass further down towards the earth's core,
where intense temperatures and pressure increase the rate of decomposition. As the biomass
decomposes, methane is released, which fills cavities and cracks in the ground. Natural gas is
extracted by drilling into the ground. Natural gas is seen as a transition fuel between old fossil fuels
such as coal and renewable fuels such as bioethanol. It is claimed to be the fossil fuel with the
cleanest combustion and currently accounts for one third of the total growth in energy demand.
2.5.2. Renewable Fuels
There are several renewable fuels available for different purposes, these fuels are called Biofuels these are fuels derived from biomass, the procedure for producing each of these fuels differs
depending on the form of biomass processed, but all biomasses must be processed to some degree
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in order to be used as fuel. Biofuels can be divided into 3 main groups according to the type of
biomass from which they are derived.
•
•
•
First-Generation Biofuels are biofuels made from foodstuffs such as oils, sugars and starches,
such as bioethanol from sugar cane and biodiesel from rapeseed.
Second-Generation Biofuel are biofuel made from non-food products such as grasses,
inedible parts of food crops and wood.
Third-Generation Biofuel are biofuel produced from algae that are cultivated for the purpose
of producing biomass. In addition to being able to produce bioethanol and biodiesel,
renewable fuels can also be produced in the form of gases such as biomethane and
biohydrogen.
Hydrogen is also being considered as a possible renewable fuel. In addition to producing hydrogen
from biomass, it can also be produced by water electrolysis. It can be considered renewable if a
renewable energy source is used for the hydrolysis, such as solar or wind power. Bioethanol is
predominantly used as a transport fuel, where it is blended with conventional fuels. It is also
increasingly being used to make a gasoline additive that increases the octane rating of fuel.
2.5.2.1. Bioethanol
Bioethanol is one of the oldest types of biofuels. However, due to the relatively high cost of
production and lower energy output per unit mass, it has given way to gasoline as the main fuel.
Now, with the growing interest in low emission fuels, there is a renewed interest in bioethanol.
Bioethanol is produced from plants, most of it from maize starch, by enzymatic hydrolysis and
subsequent fermentation.
As bioethanol is predominantly a first-generation biofuel, the method of production using maize as a
food source is generally considered unsustainable. Because the crops used are also foodstuffs, this
means that there are concerns about the impact of bioethanol production on food prices. On
average, bioethanol costs about 8 times more than natural gas. Also, the increase in first-generation
bioethanol production is also directly linked to deteriorating soil quality and water scarcity. In
addition, the heating power of such fuel is almost 20% less than diesel fuel, which means that more
fuel is required to achieve the same result.
2.5.2.2 Biogas and Biomethane
Biogas is a mixture of gases, which mainly consists of methane 60-70% and carbon dioxide 30-40%. It
is formed as a result of anaerobic digestion of biowaste and can be either first or second-generation.
Biogas can be further refined to increase its methane content, then it is called biomethane. The
methane content of biomethane is typically over 96%, so it can be treated like natural gas and used
as a direct replacement. The feedstock for biogas production is waste such as faeces and fat from
commercial kitchens or fish farms. Biowaste is first reduced in size and created in suspension to
make it easier to work with. Anaerobic digestion is carried out with the help of methanogenic
bacteria. At present, a small proportion of biogas is used in the fuel as an additive in the operation of
Gas Turbines that generate electricity in Europe, but natural gas still represents the main portion of
96%. The cost of biogas is, on average, about 3 times more expensive than natural gas.
Problems hindering the introduction of biogas into Gas Turbines relate primarily to the composition
of the gas. Biogas generally has a higher moisture content than natural gas due to the water present
in it. The presence of water can cause corrosion, so corrosion resistant materials must be selected.
The presence of water in the gas also increases the dew point of the system and hence the
combustion temperature. In each specific case, it may be necessary to increase the corrosion
resistance of turbines. Trace metals, which may be present due to the presence of metal particles in
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the biomass digestion process, can transfer to the molten metals and thereby reduce the service life
of the Gas Turbine. The burner should also be enlarged to ensure sufficient biogas combustion time.
2.5.2.3. Hydrogen
In past years, hydrogen was seen as the fuel of the future, and many initiatives were put forward to
channel public funds into various hydrogen projects, but various promising technologies did not pay
off. Currently, interest in hydrogen technology has revived and many countries are looking for ways
to introduce this type of fuel. Most of the hydrogen produced comes from syngas reforming. Syngas
is generated from the steam reforming of natural gas. Syngas consists of a mixture of carbon
monoxide and hydrogen. Renewable hydrogen can be produced in a variety of ways. The production
of hydrogen in this way can be integrated with the production of other fuels such as bioethanol. The
cost of hydrogen is, on average, about 8 times more expensive than natural gas. Different
technologies and catalysts used for the gasification process have different operating conditions and
processes. Hydrogen can also be a third-generation biofuel if algae is used to produce it. Gaseous
Hydrogen is produced from syngas, which is produced from algae. Algae can also be used to
photobiologically break down water molecules. The raw materials for this process are usually
hydrocarbons, and green algae or cyanobacteria are used as biological species. A new method for
the production of hydrogen fuel is the hydrolysis of water. Hydrogen fuel is currently being used to
power vehicles such as forklifts and passenger cars. The lack of widespread use of hydrogen fuel in
passenger vehicles can be explained by the lack of refuelling infrastructure.
When hydrogen is burned, due to the absence of hydrocarbons, no carbon dioxide is formed.
However, nitrogen oxide emissions are similar to those from fossil fuel combustion, and in some
cases may even exceed them due to the higher local flame temperature associated with hydrogen
combustion. The net calorific value of hydrogen is more than twice that of natural gas. To
successfully introduce hydrogen into gas turbines, major changes must be made to the combustion
chambers. Due to the high rate of combustion, a phenomenon known as "flash" can occur - when
the flame bursts back into the area where air and fuel are mixed. This usually results in complete
failure of the gas turbine. Flame flash is prevented by increasing the velocity of the gases at the
burner outlet, which increases the pressure drop.
Chapter 3 - Project Definition
3.1. Aim
The aim of this work is to analyse the Gas Turbine, which is widely used in manufacturing industry
and power plants. Investigate Gas Turbine operation and key parameters. The analysis will include
the use of different fuels such as natural gas, bioethanol, and biogas as well as their mixtures. The
analysis and conclusions are demonstrated by equation calculations and modelling using graphs and
tables. The analysis objectives are:
1. An overview of the development of the Gas Turbine in terms of structure, operating
processes, and ways to improve for power generation and efficiency. Overview of different
fuels - fossil fuels, renewable fuels, and their mixtures.
2. Determine the base case of the Gas Turbine and calculate the performance and waste
emissions. Based on these calculations, additionally perform different scenarios for different
and modified fuel. Determine Gas Turbine key parameters such as air flow rate, fuel
consumption, Gas Turbine power, power for compressor, work ratio, electrical efficiency,
emission, and cost.
3. Analysis of how different and modified fuels affect the main parameters of the Gas Turbine.
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4. Propose how to improve the efficiency of the Gas Turbine and how to reduce pollution
emissions by using bioethanol and biogas or by adding them to the fuel mix.
3.2. Methodologies
The methodology is based on analysing and compare base case and different scenarios on how they
affect the key parameters of the Gas Turbine with different fuels, methane concentrations and
mixtures. A Simple Gas Turbine cycle are using to calculate the key parameters of the gas turbine
and it is assumed that the pressure ratio, the outside temperature, the power generation, and the
temperature after combustion chamber are constant. The data will be transferred to graphs and
tables and the effect of the scenarios on key Gas Turbine parameters will be concluded, as well as
suggestion for efficiency and emissions improvements. The main methodology parts are:
1. Identify the Gas Turbine, its components and break down each component in detail. Identify
the key parameters, processes and analyse the working cycle of the Gas Turbine. Identify
main type of fuels.
2. Provide a base case using standard natural gas with 85% methane concentration as fuel. Use
a simple cycle to calculate the key parameters of the Gas Turbine. Assume that power
generation (100MW), the pressure ratio (16) inside Gas Turbine, temperature outside (15°𝐶)
and temperature after the combustion chamber (1200°𝐶) is constant.
3. Explore how different scenarios with different fuels, with different methane concentrations
and different mixes, affect the key parameters of the Gas Turbine.
4. Compare and analyse the key parameters of the baseline Gas Turbine with all the different
fuel scenarios, their methane concentrations, and mixes. Build graphs and tables showing
results for air flow rate, fuel consumption, Gas Turbine power, power for compressor, work
ratio, electrical efficiency, emission, and cost for assumed power generation of 100MW.
Summarise the effect of fuels on efficiency and emissions. Suggest how to improve efficiency
and reduce emissions by using bioethanol and biogas or by adding them to standard natural
gas.
Chapter 4 – Gas Turbine operation analysis with different
fuels
4.1. Fuel variable parameters
The Gas Turbine should be adapted to burn any gaseous fuel, and in some cases to burn light liquid
fuels as well. The same fuel may have different parameters, depending on where it has been
extracted. Therefore, it is necessary to consider the so-called "Standard natural gas" where only its
concentration of methane (𝐶𝐻4) is considered, which is 85%. Standard natural gas will be used for
base case. Therefore, for different concentration, fuels, and mixtures only the change in methane
(𝐶𝐻4) concentration will be considered as main ingredient to identify parameters of the fuel. Gas
Turbine fuel has 2 variables, the value of which will depend on fuel type, concentration and mixture,
the main fuel parameter is (𝐿0 ) and (𝐾𝐹 ). (𝐿0 ) is the minimum amount of air required for the
complete combustion of 1 kg of gas and can be found using the molecular weight of methane (𝐶𝐻4).
(𝐾𝐹 ) is heat of combustion and can be calculated from the heat value of methane (𝐶𝐻4).
Air contains 21% oxygen, meaning that the ratio of oxygen in the air is 21:100 or 1:4.762, where "1"
is oxygen and "4.762" is the air, molecular weight of air 29𝑘𝑔/𝑘𝑚𝑜𝑙.
Methane requires oxygen to burn, so the chemical formula for the standard natural gas combustible
mixture is 𝐶𝐻4 + 2𝑂2 and their ratio is 1:2, where "1" is methane and "2" is oxygen, molecular
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weight of the methane is 16𝑘𝑔/𝑘𝑚𝑜𝑙. Following the chemical formula 𝐶𝐻4 + 2𝑂2 the ratio in the
combustible mixture is 1:2 and can be expressed as 1:2*4.762 which lead to 1:9.524. Now knowing
the ratio of methane to oxygen 𝐶𝐻4 + 2𝑂2 , it is possible to calculate the molecular weight ratio of
methane to air 𝐶𝐻4 + 𝐴𝑖𝑟, which is 1*16:9.524*29 that led to methane/air ratio of 1:17.26. This
means that it takes 17.26kg of air to burn 1kg of pure methane. If the standard natural gas has a
methane concentration of 85%, this means that (𝐿0 ) would be 14.671.
When calculating thermal processes in the combustion chambers of a Gas Turbine, it is assumed that
(𝐾𝐹 ) is a constant value for a given fuel, that is determined experimentally, it is assumed that its
lower heating value is equal to 44650𝑘𝐽/𝑘𝑔 for the standard natural gas.
4.2. Base case with standard natural gas
Simple Gast Turbine cycle are used for the calculations. Steps from the thermal circuit of a simple
Gas Turbine are used to calculate base case key parameters for a Gas Turbine, a diagram of a simple
Gas Turbine is shown in the Figure 14. The four main measuring area (a, b, c, d) are indicated by (T)
and (h), where (T) is temperature and (h) is enthalpy. To simplify the cycle analysis, it is assumed that
the physical properties of the air passing through the compressor and the gases passing through the
turbine remain unchanged. It is assumed that the temperature after the combustion chamber is
constant, and the same for the outside temperature and electrical power. The efficiency of the
different parts of the Gas Turbine is assumed with the largest margin of error that can be used. Table
2 is used to determine the enthalpy in specific areas for air and combustion product.
FIGURE 14 - SIMPLY GAS TURBINE DIAGRAM WITH MAIN MEASURING
POINTS
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TABLE 2 - SPECIFIC ISOBARIC HEAT CAPACITY AND ENTHALPY OF DRY AIR AND COMBUSTION PRODUCTS
4.2.1 Base case calculations
The base case uses standard natural gas as fuel, which has a methane concentration of 85%. To burn
1kg of pure methane it takes 17.26kg of air, If the standard natural gas has a methane concentration
of 85%, this means that (𝐿0 ) would be 0.85 ∗ 17.26 = 14.671𝑘𝑔. It is assumed that (𝐾𝐹 ) for
standard natural gas is 44650𝑘𝐽/𝑘𝑔.
Initial values:
𝐾𝐹 = 46500 𝑘𝐽/𝑘𝑔
𝐿0 = 14.671 𝑘𝑔
p
𝜀 = 𝑏 = 16
p𝑎
𝑇𝑎 = 15°𝐶 = 288𝐾
𝑇𝑐 = 1200°𝐶 = 1473𝐾
𝑁𝑒 = 100 𝑀𝑊
η𝑐 = 0.86
η𝑐𝑐 = 0.995
η 𝑇 = 0.88
η𝐸.𝑔 = 0.982
η𝑚 = 0.995
𝛼𝑦 = 0.005
Where (𝐾𝐹 ) is heat combustion; (𝐿0 ) is minimum amount of air required for the complete
combustion of 1 kg of fuel; (𝜀) is compressor pressure ratio; (𝑇𝑎 ) is temperature outside: (𝑇𝑐 ) is
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temperature after combustor; (𝑁𝑒 ) is electrical power; (η𝑐 ) is compressor efficiency; (η𝑐𝑐 ) is fuel heat
utilisation factor in the combustion chamber; (η 𝑇 ) is turbine efficiency; (η𝐸.𝑔 ) is efficiency of an
electric generator; (η𝑚 ) is mechanical efficiency of the turbine; (𝛼𝑦 ) is leakage rate.
The following steps are taken from Chapter 2.4.3. to calculate Gas Turbine key parameters for air
flow rate, fuel consumption, Gas Turbine power, power for compressor, work ratio, electrical
efficiency:
1. Determine the air compression process in a compressor. For now assuming that 𝑚𝑎 ≈ 0.28
𝑅
and 𝑅𝑎 ≈ 0.287, then 𝑐𝑝𝑎 = 𝑚𝑎 =
𝑎
0.287
0.28
= 1.025 𝑘𝐽/𝑘𝑔 from Equation 3.08
Calculating the temperature after the compressor using equation 1.11
𝑇𝑏 = 𝑇𝑎 [1 +
𝜀 𝑚𝑎 −1
]
η𝑐
= 288 [1 +
160.28 −1
]
0.86
= 680.98𝐾 𝑜𝑟 407.98°𝐶
Finding enthalpy for air using the Table 2, nearest to 407.98°𝐶 is 400°𝐶 and that mean
specific heat capacity is 1.0281𝑘𝐽/𝑘𝑔𝐾, value for 25°𝐶 is in the table
′
′
′
′
(𝑇𝑏 ) − ℎ𝑎𝑖𝑟
(25) = ℎ𝑎𝑖𝑟
(407.98) − ℎ𝑎𝑖𝑟
(25) = 419.44 − 25.08 = 394.36 𝑘𝐽/𝑘𝑔
ℎ𝑏 = ℎ𝑎𝑖𝑟
Finding enthalpy for air using the Table 2, nearest to 15°𝐶 is 0°𝐶 and that mean specific heat
capacity is 1.0028𝑘𝐽/𝑘𝑔𝐾, value for 25°𝐶 is in the table
′
′
′
′
(𝑡𝑎 ) − ℎ𝑎𝑖𝑟
(25) = ℎ𝑎𝑖𝑟
(15) − ℎ𝑎𝑖𝑟
(25) = 15.05 − 25.08 = −10.03 𝑘𝐽/𝑘𝑔
ℎ𝑎 = ℎ𝑎𝑖𝑟
Now calculate again the average heat capacity of the air during compression, but now with
accurate value
𝑐𝑝𝑎 =
ℎ𝑏 −ℎ𝑎
𝑡𝑏 −𝑡𝑎
Refine the
394.36−(−10.03)
= 1.029𝑘𝐽/𝑘𝑔𝐾
407.98−15
𝑅
0.287
value of 𝑚𝑎 = 𝑎 =
= 0.2789
𝑐𝑝𝑎
1.029
=
from Equation 3.09
Refining the temperature behind the compressor
𝑇𝑏 = 𝑇𝑎 [1 +
𝜀 𝑚𝑎 −1
]
η𝑐
= 288 [1 +
160.2789 −1
]
0.86
= 678.76𝐾 𝑜𝑟 405.76°𝐶
Refine the value of enthalpy for air using the Table 2, nearest to 405.76°𝐶 is 400°𝐶 and
that mean specific heat capacity is 1.0281𝑘𝐽/𝑘𝑔𝐾, value for 25°𝐶 is in the table
′
′
(405.36) − ℎ𝑎𝑖𝑟
(25) = 416.75 − 25.08 = 391.67 𝑘𝐽/𝑘𝑔
ℎ𝑏 = ℎ𝑎𝑖𝑟
2. Finding the air enthalpy at temperature 𝑇𝑐 , the heat value for the air at 1200°𝐶 and 25°𝐶 is
in Table 2
′
′
(𝑡𝑐 ) − ℎ𝑎𝑖𝑟
(25) = 1330.08 − 25.08 = 1305 𝑘𝐽/𝑘𝑔
ℎ𝑎𝑖𝑟 = ℎ𝑎𝑖𝑟
Finding the combustion product enthalpy at temperature 𝑇𝑐 , the heat value for the
combustion product at 1200°𝐶 and 25°𝐶 is in Table 2
′ (𝑡 )
′
ℎ𝑐.𝑝 = ℎ𝑐.𝑝
𝑐 − ℎ𝑐.𝑝 (25) = 1479.55 − 26.77 = 1452.78 𝑘𝐽/𝑘𝑔
Finding excess air ratio (𝛼), using Equation 3.07, assuming that ℎ𝐹 = 0
𝛼=
𝐾𝐹 η𝑐𝑐 +𝐿0 ℎ𝑎𝑖𝑟 +ℎ𝐹 −(1+𝐿0 )ℎ𝑐.𝑝
𝐿0 (ℎ𝑎𝑖𝑟 −ℎ𝑏 )
=
44650∗0.995+14.671∗1305−(1+14.671)∗1452.78
14.671(1305−391.67)
= 3.0453
3. Finding the enthalpy of the gas before the turbine, using formula 3.06
1+𝐿
ℎ𝑐 = 1+𝛼𝐿0 ℎ𝑐.𝑝 +
0
(𝛼−1)𝐿0
ℎ
1+𝛼𝐿0 𝑎𝑖𝑟
1+14.671
= 1+3.0453∗14.671 1452.78 +
(3.0453−1)14.671
1305
1+3.0453∗14.671
=
1355.7 𝑘𝐽/𝑘𝑔
4. Determine the gas expansion process in the turbine. Gas temperature after the turbine can
be found using δ = 𝜀λ = 16 ∗ 0.95 = 15.2, and assuming that 𝑚𝑔 ≈ 0.25
𝑇𝑑 = 𝑇𝑐 [1 − (1 − 𝛿 −𝑚𝑔 )η 𝑇 ] = 1473[1 − (1 − 15.2−0.25 )0.88] = 833.24𝐾 = 560.24°𝐶
Calculate the enthalpy of the air after the turbine using the Table 2, nearest to 560.24°𝐶 is
550°𝐶 and that mean specific heat capacity is 1.0438𝑘𝐽/𝑘𝑔𝐾, value for 25°𝐶 is in the table
′
′
(𝑇𝑑 ) − ℎ𝑎𝑖𝑟
(25) = 584.77 − 25.08 = 559.69 𝑘𝐽/𝑘𝑔
ℎ𝑎𝑖𝑟 (𝑇𝑑 ) = ℎ𝑎𝑖𝑟
Calculate the enthalpy of the combustion product after the turbine using the Table 2,
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nearest to 560.24°𝐶 is 550°𝐶 and that mean specific heat capacity is 1.1422𝑘𝐽/𝑘𝑔𝐾, value
for 25°𝐶 is in the table
′ (𝑇 )
′
ℎ𝑐.𝑝 (𝑇𝑑 ) = ℎ𝑐.𝑝
𝑑 − ℎ𝑐.𝑝 (25) = 639.9 − 26.77 = 613.13 𝑘𝐽/𝑘𝑔
Calculate (ℎ𝑑 ) using Equation 3.06
1+𝐿
ℎ𝑑 = 1+𝛼𝐿0 ℎ𝑐.𝑝 +
0
(𝛼−1)𝐿0
ℎ
1+𝛼𝐿0 𝑎𝑖𝑟
1+14.671
= 1+3.0453∗14.671 613.13 +
(3.0453−1)14.671
559.69
1+3.0453∗14.671
=
578.02 𝑘𝐽/𝑘𝑔
Determine the average heat capacity of the gas during expansion using Equation 3.10
𝑐𝑝𝑔 =
ℎ𝑐 −ℎ𝑑
𝑡𝑐 −𝑡𝑑
=
1355.7−578.02
1200−560.24
= 1.21558 𝑘𝐽/𝑘𝑔𝐾
Determine the air volume fraction in the combustion products using Equation 3.13 and 3.14
where 𝜇𝑐.𝑝 = 28.66 and 𝜇𝑎 = 28.97 from the Table 2
𝜇𝑝.𝑐 𝐿0
28.66 14.671
= 28.97 1+14.671 = 0.92617
𝜇𝑎 1+𝐿0
𝑞(𝛼−1)
0.92617(3.0453−1)
𝑟𝑎 = 1+𝑞(𝛼−1) = 1+0.92617(3.0453−1) = 0.6544
𝑞=
Determine molecular weight of combustion products using Equation 3.12
𝜇𝑔 = 𝜇𝑎 𝑟𝑎 + 𝜇𝑐.𝑝 (1 − 𝑟𝑎 ) = 28.97 ∗ 0.6544 + 28.66(1 − 0.6544) = 28.86
Determine gas constant of combustion products from Equation 3.11
𝑅𝑔 =
8.314
𝜇𝑔
8.314
= 28.86 = 0.288 𝑘𝐽/𝑘𝑔𝐾
Now refine the value of (𝑚𝑔 ), same as in Equation 3.09
𝑚𝑔 =
𝑅𝑔
𝑐𝑝𝑔
=
0.288
1.21558
= 0.2369
Refining the temperature the gas temperature behind the turbine (𝑇𝑑 )
𝑇𝑑 = 𝑇𝑐 [1 − (1 − 𝛿 −𝑚𝑔 )η 𝑇 ] = 1473[1 − (1 − 15.2−0.2369 )0.88) = 856.94𝐾 = 583.94°𝐶
This temperature is final and now determine the accurate value for (ℎ𝑎𝑖𝑟 ) and (ℎ𝑐.𝑝 ). The
enthalpy for air using the Table 2, nearest to 583.94°𝐶 is 600°𝐶 and that mean specific
heat capacity is 1.0493 𝑘𝐽/𝑘𝑔𝐾, value for 25°𝐶 is in the table
′
′
(583.94) − ℎ𝑎𝑖𝑟
(25) = 612.72 − 25.08 = 587.64 𝑘𝐽/𝑘𝑔
ℎ𝑎𝑖𝑟 (𝑇𝑑 ) = ℎ𝑎𝑖𝑟
The enthalpy for product combustion using the Table 2, nearest to 583.94°𝐶 is 600°𝐶
and that mean specific heat capacity is 1.1499 𝑘𝐽/𝑘𝑔𝐾, value for 25°𝐶 is in the table
′ (583.94)
′ (25)
ℎ𝑐.𝑝 (𝑇𝑑 ) = ℎ𝑐.𝑝
− ℎ𝑐.𝑝
= 668.64 − 26.77 = 644.7 𝑘𝐽/𝑘𝑔
Refined value for (ℎ𝑑 )
1+𝐿
ℎ𝑑 = 1+𝛼𝐿0 ℎ𝑐.𝑝 +
0
(𝛼−1)𝐿0
ℎ
1+𝛼𝐿0 𝑎𝑖𝑟
1+14.671
= 1+3.0453∗14.671 644.7 +
(3.0453−1)14.671
587.64
1+3.0453∗14.671
=
607.22 𝑘𝐽/𝑘𝑔
5. Determine the expansion work of 1 kg of gas in the turbine using Equation 3.15
𝐻𝑇 = ℎ𝑐 − ℎ𝑑 = 1355.7 − 607.22 = 748.47 𝑘𝐽/𝑘𝑔
6. Determine work required to compress 1 kg of air in the compressor using Equation 3.16
𝐻𝐶 = ℎ𝑏 − ℎ𝑎 = 391.67 + 10.03 = 401.7 𝑘𝐽/𝑘𝑔
7. Determine Gas Turbine operation on the unit shaft using Equation 3.20 and 3.19
𝑏=
𝛼𝐿0 (1+𝛼𝑦 )
1+𝛼𝐿0
=
3.0453∗14.671(1+0.005)
1+3.0453∗14.671
= 0.98299
𝑘𝐽
𝐻𝑒 = 𝐻𝑇 η𝑀 − 𝑏𝐻𝐶 = 748.47 ∗ 0.995 − 0.98299 ∗ 401.7 = 349.85 𝑘𝑔
8. Determine gas flow rate through the turbine using Equation 3.17
𝐺𝑇 = 𝐻
𝑁𝑒
𝑒 η𝐸.𝑔
100000
= 349.85∗0.982 = 291.06 𝑘𝑔/𝑠
9. Determine air flow rate supplied by the compressor using Equation 3.21
𝐺𝐶′ = 𝐺𝑐 (1 + 𝛼𝑦 ) = 𝑏𝐺𝑇 = 0.98299 ∗ 291.06 = 286.119 𝑘𝑔/𝑠
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10. Determine fuel consumption using Equation 3.22
𝐵=
𝐺𝑇
1+𝛼𝐿0
=
291.06
1+3.0453∗14.671
= 6.372 𝑘𝑔/𝑠
11. Determine Gas Turbine power using Equation 3.23
𝑁𝑇 = 𝐺𝑇 𝐻𝑇 = 291.06 ∗ 748.47 = 217856.5 𝑘𝑊 = 217.85𝑀𝑊
12. Determine power consumed by the compressor using Equation 3.24
𝑁𝐶 = 𝐺𝐶′ 𝐻𝐶 = 286.119 ∗ 401.7 = 114934.3 𝑘𝑊 = 114.93 𝑀𝑊
13. Determine useful work ratio using Equation 3.25
𝑁
𝜑 = 𝑁𝑒 = 1 −
𝑇
𝑏𝐻𝐶
𝐻𝑇
=1−
0.98299∗401.7
748.47
= 0.4724
14. Determine electrical efficiency of the Gas Turbine using Equation 3.26
η𝐸 =
G𝑇 H𝑒 η𝐸.𝑔
𝐵K𝐹
=
𝑁𝑒
𝐵K𝐹
=
100000
6.372∗44650
= 0.3514
4.3. Different scenarios
Different scenarios have been attempted to compare with the base case. Each scenario has the same
input data as in the base case, the difference only in the fuel type, its methane concentration and
mixtures differ. Variable readings for (𝐾𝐹 ) and (𝐿0 ).
4.3.1. Natural gas with different methane concentration
4.3.1.1. Scenario 1 – Natural gas with 75% methane concentration
For scenario 1, it is assumed that the concentration of methane in natural gas is 75%, which is 10%
less than the base case. This means that the reading for the fuel variable (𝐿0 ) will be 0.75 ∗ 17.26 =
12.945𝑘𝑔. And for (𝐾𝐹 ), if 85% is 44650𝑘𝐽/𝑘𝑔, then 1% is
44650
85
= 525.294𝑘𝐽/𝑘𝑔, so for 75% 𝐾𝐹 =
525.294 ∗ 75 = 39397𝑘𝐽/𝑘𝑔
By performing the same calculation steps as in Сhapter 4.2.1., the following results are obtained for
key Gas Turbine parameters:
Air flow rate – 284.1735 kg/s
Fuel consumption – 7.2068 kg/s
Gas Turbine power – 217070.8 kW = 217.07 MW
Power consumed by the compressor – 114152.5 kW = 114.15 MW
Useful work ratio – 0.4741
Electrical efficiency of the Gas Turbine – 0.3522
4.3.1.2. Scenario 2 – Natural gas with 65% methane concentration
For scenario 2, it is assumed that the concentration of methane in natural gas is 65%, which is 20%
less than the base case. This means that the reading for the fuel variable (𝐿0 ) will be 0.65 ∗ 17.26 =
11.219𝑘𝑔. And for (𝐾𝐹 ), if 85% is 44650𝑘𝐽/𝑘𝑔, then 1% is
44650
85
= 525.294𝑘𝐽/𝑘𝑔, so for 65% 𝐾𝐹 =
525.294 ∗ 65 = 34144𝑘𝐽/𝑘𝑔
By performing the same calculation steps as in Сhapter 4.2.1., the following results are obtained for
key Gas Turbine parameters:
Air flow rate – 281.64 kg/s
Fuel consumption – 8.29 kg/s
Gas Turbine power – 216048.3 kW = 216 MW
Power consumed by the compressor – 113135 kW = 113.1 MW
Useful work ratio – 0.4763
Electrical efficiency of the Gas Turbine – 0.35315
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4.3.1.3. Scenario 3 – Natural gas with 55% methane concentration
For scenario 3, it is assumed that the concentration of methane in natural gas is 55%, which is 30%
less than the base case. This means that the reading for the fuel variable (𝐿0 ) will be 0.55 ∗ 17.26 =
9.493𝑘𝑔. And for (𝐾𝐹 ), if 85% is 44650𝑘𝐽/𝑘𝑔, then 1% is
44650
85
= 525.294𝑘𝐽/𝑘𝑔, so for 55% 𝐾𝐹 =
525.294 ∗ 55 = 28891𝑘𝐽/𝑘𝑔
By performing the same calculation steps as in Сhapter 4.2.1., the following results are obtained for
key Gas Turbine parameters:
Air flow rate – 278.2 kg/s
Fuel consumption – 9.765 kg/s
Gas Turbine power – 214662.7 kW = 214.6 MW
Power consumed by the compressor – 111756.4 kW = 111.75 MW
Useful work ratio – 0.47938
Electrical efficiency of the Gas Turbine – 0.35444
4.3.2. Renewable fuels
4.3.2.1. Scenario 4 – Bioethanol
Following example from Chapter 4.1. to calculate (𝐿0 ) for Bioethanol. Bioethanol contain ethyl
alcohol 𝐶2 𝐻5 𝑂𝐻 and requires oxygen to burn, so the chemical formula for the bioethanol
combustible mixture is 𝐶2 𝐻5 𝑂𝐻 + 3𝑂2 and their ratio is 1:3, where "1" is bioethanol and "3" is
oxygen, molecular weight of the ethyl alcohol is 46𝑘𝑔/𝑘𝑚𝑜𝑙. Following the chemical formula
𝐶2 𝐻5 𝑂𝐻 + 3𝑂2 the ratio in the combustible mixture is 1:3 and can be expressed as 1:3*4.762 which
lead to 1:14.286. Now knowing the ratio of bioethanol to oxygen is 𝐶2 𝐻5 𝑂𝐻 + 3𝑂2 , it is possible to
calculate the molecular weight ratio of bioethanol to air 𝐶2 𝐻5 𝑂𝐻 + 𝐴𝑖𝑟, which is 1*46: 14.286*29
that led to bioethanol/air ratio of 1:9. This means that it takes 9kg of air to burn 1kg of pure
bioethanol.
When calculating thermal processes in the combustion chambers of a Gas Turbine, it is assumed that
(𝐾𝐹 ) is a constant value for a given fuel, that is determined experimentally, it is assumed that its
lower heating value is equal to 27430𝑘𝐽/𝑘𝑔 for the bioethanol.
By performing the same calculation steps as in Сhapter 4.2.1., the following results are obtained for
key Gas Turbine parameters:
Air flow rate – 277.04 kg/s
Fuel consumption – 10.272 kg/s
Gas Turbine power – 214191.9 kW = 214.2 MW
Power consumed by the compressor – 111287.9 kW = 111.3 MW
Useful work ratio – 0.48043
Electrical efficiency of the Gas Turbine – 0.3549
4.3.2.2. Scenario 5 - Biogas
Following example from Chapter 4.1. to calculate (𝐿0 ) for Biogas. Biogas, like natural gas, contains
methane 𝐶𝐻4, but also carbon dioxide 𝐶𝑂2 . This means that (𝐿0 ) will be the same as for natural gas.
On average, biogas production achieves methane concentrations of between 50% and 70%. For the
calculation the lowest number are taken and assumed that the concentration of methane in the
biogas is 50%. In that case 𝐿0 = 0.5 ∗ 17.26 = 8.63 𝑘𝑔.
(𝐾𝐹 ) is a constant value for a given fuel, that is determined experimentally, it is assumed that its
lower heating value is equal to 14494𝑘𝐽/𝑘𝑔 for the biogas.
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By performing the same calculation steps as in Сhapter 4.2.1., the following results are obtained for
key Gas Turbine parameters:
Air flow rate – 249.95 kg/s
Fuel consumption – 19.42 kg/s
Gas Turbine power – 204445.9 kW = 204.4 MW
Power consumed by the compressor – 101590.6 kW = 101.6 MW
Useful work ratio – 0.50309
Electrical efficiency of the Gas Turbine – 0.355249
4.3.3. A mixture of standard natural gas and renewable fuel
4.3.3.1. Scenario 6 - Mixture of standard natural gas and bioethanol at a ratio of 2:1
Scenario 6 assumes a mix with a 2:1 ratio, where the amount of standard natural gas would be twice
that of bioethanol. (𝐿0 ) for standard natural gas is 14.671𝑘𝑔 and (𝐿0 ) for bioethanol is 9kg, so for
the 2:1 ratio mixture 𝐿0 =
2∗14.671
1∗9
+
3
3
= 12.78𝑘𝑔. (𝐾𝐹 ) for standard natural gas is 44650𝑘𝐽/𝑘𝑔
and (𝐾𝐹 ) for bioethanol is 27430𝑘𝐽/𝑘𝑔, so for 2:1 ratio mixture 𝐾𝐹 =
2∗44650
1∗27430
+ 3
3
=
38910𝑘𝐽/𝑘𝑔.
By performing the same calculation steps as in Сhapter 4.2.1., the following results are obtained for
key Gas Turbine parameters:
Air flow rate – 283.97 kg/s
Fuel consumption – 7.29 kg/s
Gas Turbine power – 216989.2 kW = 216.99 MW
Power consumed by the compressor – 114071.3 kW = 114.07 MW
Useful work ratio – 0.4743
Electrical efficiency of the Gas Turbine – 0.352279
4.3.3.2. Scenario 7 - Mixture of standard natural gas and bioethanol at a ratio of 1:2
Scenario 7 assumes a mix with a 1:2 ratio, where the amount of standard natural gas would be half
that of bioethanol. (𝐿0 ) for standard natural gas is 14.671𝑘𝑔 and (𝐿0 ) for bioethanol is 9𝑘𝑔, so for
the 1:2 ratio mixture 𝐿0 =
1∗14.671
2∗9
+ 3
3
= 10.89𝑘𝑔. (𝐾𝐹 ) for standard natural gas is 44650𝑘𝐽/𝑘𝑔
and (𝐾𝐹 ) for bioethanol is 27430𝑘𝐽/𝑘𝑔, so for 1:2 ratio mixture 𝐾𝐹 =
1∗44650
2∗27430
+
3
3
=
33170𝑘𝐽/𝑘𝑔.
By performing the same calculation steps as in Сhapter 4.2.1., the following results are obtained for
key Gas Turbine parameters:
Air flow rate – 281.09 kg/s
Fuel consumption – 8.531 kg/s
Gas Turbine power – 215827.5 kW = 215.8 MW
Power consumed by the compressor – 112915.4 kW = 112.9 MW
Useful work ratio – 0.4768
Electrical efficiency of the Gas Turbine – 0.3514
4.3.3.3. Scenario 8 - Mixture of standard natural gas and biogas at a ratio of 2:1
Scenario 8 assumes a mix with a 2:1 ratio, where the amount of standard natural gas would be twice
that of biogas. Assuming it is the same biogas as in Scenario 5, with methane concentration 50%.
(𝐿0 ) for standard natural gas is 14.671𝑘𝑔 and (𝐿0 ) for biogas is 8.63𝑘𝑔, so for the 2:1 ratio mixture
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𝐿0 =
2∗14.671
1∗8.63
+
3
3
= 12.65𝑘𝑔. (𝐾𝐹 ) for standard natural gas is 44650𝑘𝐽/𝑘𝑔 and (𝐾𝐹 ) for biogas
is 14494𝑘𝐽/𝑘𝑔, so for 2:1 ratio mixture 𝐾𝐹 =
2∗44650
1∗14494
+
3
3
= 34598𝑘𝐽/𝑘𝑔.
By performing the same calculation steps as in Сhapter 4.2.1., the following results are obtained for
key Gas Turbine parameters:
Air flow rate – 280.619 kg/s
Fuel consumption – 8.199 kg/s
Gas Turbine power – 215636.1 kW = 215.6 MW
Power consumed by the compressor – 112724.9 kW = 112.7 MW
Useful work ratio – 0.4772
Electrical efficiency of the Gas Turbine – 0.351473
4.3.3.4. Scenario 9 - Mixture of standard natural gas and biogas at a ratio of 1:2
Scenario 9 assumes a mix with a 1:2 ratio, where the amount of standard natural gas would be twice
that of biogas. Assuming it is the same biogas as in Scenario 5, with methane concentration 50%.
(𝐿0 ) for standard natural gas is 14.671𝑘𝑔 and (𝐿0 ) for biogas is 8.63𝑘𝑔, so for the 1:2 ratio mixture
𝐿0 =
1∗14.671
2∗8.63
+ 3
3
= 10.64𝑘𝑔. (𝐾𝐹 ) for standard natural gas is 44650𝑘𝐽/𝑘𝑔 and (𝐾𝐹 ) for biogas
is 14494𝑘𝐽/𝑘𝑔, so for 1:2 ratio mixture 𝐾𝐹 =
1∗44650
2∗14494
+ 3
3
= 24546𝑘𝐽/𝑘𝑔.
By performing the same calculation steps as in Сhapter 4.2.1., the following results are obtained for
key Gas Turbine parameters:
Air flow rate – 270.68 kg/s
Fuel consumption – 11.496 kg/s
Gas Turbine power – 211625.2 kW = 211.6 MW
Power consumed by the compressor – 108734.1 kW = 108.7 MW
Useful work ratio – 0.48619
Electrical efficiency of the Gas Turbine – 0.35438
4.4. Emission and cost
The main emissions from fuel combustion are carbon dioxide and nitrous oxides. For standard
natural gas carbon dioxide emission are 2111.57 grams per kilogram of fuel and nitrous oxides
emission are 0.058 grams per kilogram of fuel. For bioethanol carbon dioxide emission are 1713.13
grams per kilogram of fuel and nitrous oxides emission are 0.002 grams per kilogram of fuel. For
biogas carbon dioxide emission are 3110.55 grams per kilogram of fuel and nitrous oxides emission
are 6.11 grams per kilogram of fuel.
The cheapest available fuel for a Gas Turbine is natural gas, and its cheapest price ranges around
$0.3 per kilogram. Bioethanol is about 8 times more expensive than natural gas, assuming the price
of natural gas is $0.3, then the price of bioethanol 0.3 ∗ 8 = $2.4 per kilogram. Biogas is about 3
times more expensive than natural gas, assuming the price of natural gas is $0.3, then the price of
bioethanol 0.3 ∗ 3 = $0.9 per kilogram.
Fuel consumption is one of the key parameters of the Gas Turbine and with it the cost of operation
and emissions for each scenario can be calculated. The calculations for the base case and the
scenario are as follows:
Base case: For standard natural gas to generate 100MW of electricity at a constant temperature of
1200°C after the combustion chamber, the operating costs are 6.372 ∗ 0.3 = 1.91$, carbon dioxide
emission are 6.372 ∗ 2111.57 = 13455𝑔 and nitrous oxides emission are 6.372 ∗ 0.058 = 0.369𝑔.
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Scenario 1: costs are 2.16$, carbon dioxide emission are 15217𝑔 and nitrous oxides emission are
0.417𝑔.
Scenario 2: costs are 2.48$, carbon dioxide emission are 17511𝑔 and nitrous oxides emission are
0.481𝑔.
Scenario 3: costs are 2.92$, carbon dioxide emission are 20620𝑔 and nitrous oxides emission are
0.566𝑔.
Scenario 4: costs are 24.65$, carbon dioxide emission are 17597𝑔 and nitrous oxides emission are
0.0205𝑔.
Scenario 5: costs are 17.47$, carbon dioxide emission are 60411𝑔 and nitrous oxides emission are
118.664𝑔.
Scenario 6: costs are 7.29$, carbon dioxide emission are 14435𝑔 and nitrous oxides emission are
0.286𝑔.
Scenario 7: costs are 14.5$, carbon dioxide emission are 15748𝑔 and nitrous oxides emission are
0.176𝑔.
Scenario 8: costs are 4.09$, carbon dioxide emission are 20043𝑔 and nitrous oxides emission are
17.016𝑔.
Scenario 9: costs are 8.04$, carbon dioxide emission are 31931𝑔 and nitrous oxides emission are
47.049𝑔.
Chapter 5 - Analysis of the base case and scenarios
5.1. Air flow rate analysis
Table 3 compares the base case and all scenarios for the Gas Turbine air flow rate, and the
percentage difference between the base case and each scenario. Figure 15 show in graph its visual
percentage difference.
TABLE 3 - AIR FLOW RATE COMPARISON
Fuel type
Standard natural gas
NG 75% methane
NG 65% methane
NG 55% methane
Bioethanol
Biogas
SNG + BE 2:1
SNG + BE 1:2
SNG + BG 2:1
SNG + BG 1:2
Gc (Air Flow rate kg/s)
Percentage difference
286.1196363
284.1734705
281.6405798
278.2085441
277.042384
249.9587457
283.9712838
281.0938599
280.6195592
270.6847758
0.000%
0.680%
1.565%
2.765%
3.173%
12.638%
0.751%
1.757%
1.922%
5.395%
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Air Flow Rate Difference
14.000%
12.000%
10.000%
8.000%
6.000%
4.000%
2.000%
0.000%
FIGURE 15 - AIR FLOW RATE COMPARISON GRAPH
5.2. Fuel consumption analysis
Table 4 compares the base case and all scenarios for the Gas Turbine fuel consumption, and the
percentage difference between the base case and each scenario. Figure 16 show in graph its visual
percentage difference.
TABLE 4 - FUEL CONSUMPTION COMPARISON
Fuel type
Standard natural gas
NG 75% methane
NG 65% methane
NG 55% methane
Bioethanol
Biogas
SNG + BE 2:1
SNG + BE 1:2
SNG + BG 2:1
SNG + BG 1:2
Fuel Consumption kg/s
Percentage difference
6.372157112
7.206878521
8.293254587
9.765290208
10.27220505
19.42135346
7.295438553
8.531620914
8.199359533
11.49608747
0.000%
13.100%
30.148%
53.249%
61.205%
204.785%
14.489%
33.889%
28.675%
80.411%
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Fuel Consumption Difference
250.000%
200.000%
150.000%
100.000%
50.000%
0.000%
FIGURE 16 - FUEL CONSUMPTION COMPARISON GRAPH
5.3. Gas Turbine power analysis
Table 5 compares the base case and all scenarios for the Gas Turbine power, and the percentage
difference between the base case and each scenario. Figure 17 show in graph its visual percentage
difference.
TABLE 5 - GAS TURBINE POWER COMPARISON
Fuel type
Standard natural gas
NG 75% methane
NG 65% methane
NG 55% methane
Bioethanol
Biogas
SNG + BE 2:1
SNG + BE 1:2
SNG + BG 2:1
SNG + BG 1:2
Gas Turbine Power kW
Percentage difference
217856.5345
217070.8311
216048.2561
214662.6794
214191.8789
204445.9567
216989.2046
215827.5351
215636.0511
211625.1943
0.000%
0.361%
0.830%
1.466%
1.682%
6.156%
0.398%
0.931%
1.019%
2.860%
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Gas Turbine Power Difference
7.000%
6.000%
5.000%
4.000%
3.000%
2.000%
1.000%
0.000%
FIGURE 17 - GAS TURBINE POWER COMPARISON GRAPH
5.4. Compressor power consumption analysis
Table 6 compares the base case and all scenarios for the Gas Turbine compressor power
consumption, and the percentage difference between the base case and each scenario. Figure 18
show in graph its visual percentage difference.
TABLE 6 - COMPRESSOR POWER CONSUMPTION COMPARISON
Fuel type
Standard natural gas
NG 75% methane
NG 65% methane
NG 55% methane
Bioethanol
Biogas
SNG + BE 2:1
SNG + BE 1:2
SNG + BG 2:1
SNG + BG 1:2
Power Consumed by the
Compressor kW
Percentage difference
114934.2579
114152.4831
113135.0209
111756.3722
111287.9257
101590.733
114071.2647
112915.4035
112724.8769
108734.0744
0.000%
0.680%
1.565%
2.765%
3.173%
11.610%
0.751%
1.757%
1.922%
5.395%
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Compressor Power Consumption Difference
14.000%
12.000%
10.000%
8.000%
6.000%
4.000%
2.000%
0.000%
FIGURE 18 - COMPRESSOR POWER CONSUMPTION COMPARISON GRAPH
5.5. Useful work ratio analysis
Table 7 compares the base case and all scenarios for the Gas Turbine useful work ratio, and the
percentage difference between the base case and each scenario. Figure 19 show in graph its visual
percentage difference.
TABLE 7 - USEFUL WORK RATIO COMPARISON
Fuel type
Standard natural gas
NG 75% methane
NG 65% methane
NG 55% methane
Bioethanol
Biogas
SNG + BE 2:1
SNG + BE 1:2
SNG + BG 2:1
SNG + BG 1:2
Useful Work Ration
Percentage difference
0.472431441
0.474123343
0.476343744
0.479386112
0.480428828
0.503092481
0.474299816
0.476825774
0.477244754
0.48619504
0.000%
0.358%
0.828%
1.472%
1.693%
6.490%
0.395%
0.930%
1.019%
2.913%
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Useful Work Ratio Difference
7.000%
6.000%
5.000%
4.000%
3.000%
2.000%
1.000%
0.000%
FIGURE 19 - USEFUL WORK RATIO COMPARISON GRAPH
5.6. Electrical efficiency analysis
Table 8 compares the base case and all scenarios for the Gas Turbine electrical efficiency, and the
percentage difference between the base case and each scenario. Figure 20 show in graph its visual
percentage difference.
TABLE 8 - ELECTRICAL EFFICIENCY COMPARISON
Fuel type
Standard natural gas
NG 75% methane
NG 65% methane
NG 55% methane
Bioethanol
Biogas
SNG + BE 2:1
SNG + BE 1:2
SNG + BG 2:1
SNG + BG 1:2
Electrical Efficiency
Percentage difference
0.351473075
0.352200239
0.353151134
0.354447789
0.354903688
0.355248498
0.352279495
0.35336455
0.35250808
0.354380005
0.000%
0.207%
0.477%
0.846%
0.976%
1.074%
0.229%
0.538%
0.294%
0.827%
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Electrical Efficiency Difference
1.200%
1.000%
0.800%
0.600%
0.400%
0.200%
0.000%
FIGURE 20 - ELECTRICAL EFFICIENCY COMPARISON GRAPH
5.7. Cost analysis
Table 9 compares the base case and all scenarios for the Gas Turbine operating cost, and the
percentage difference between the base case and each scenario. Figure 21 show in graph its visual
percentage difference.
TABLE 9 - COST COMPARISON
Fuel type
Standard natural gas
NG 75% methane
NG 65% methane
NG 55% methane
Bioethanol
Biogas
SNG + BE 2:1
SNG + BE 1:2
SNG + BG 2:1
SNG + BG 1:2
Cost $/kg
Percentage difference
1.911647134
2.162063556
2.487976376
2.929587062
24.65329211
17.47921811
7.295438553
14.50375555
4.099679766
8.047261231
0.000%
13.100%
30.148%
53.249%
1189.636%
814.354%
281.631%
658.705%
114.458%
320.960%
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Cost Difference
1400.000%
1200.000%
1000.000%
800.000%
600.000%
400.000%
200.000%
0.000%
FIGURE 21 - COST COMPARISON GRAPH
5.8. Emission analysis
Table 10 compares the base case and all scenarios for the Gas Turbine carbon dioxide emission, and
the percentage difference between the base case and each scenario. Figure 22 show in graph its
visual percentage difference.
TABLE 10 - CARBON DIOXIDE EMISSION COMPARISON
Fuel type
Standard natural gas
NG 75% methane
NG 65% methane
NG 55% methane
Bioethanol
Biogas
SNG + BE 2:1
SNG + BE 1:2
SNG + BG 2:1
SNG + BG 1:2
Carbon Dioxide Emission g/kg of
fuel
Percentage difference
13455.25579
15217.82848
17511.78759
20620.09384
17597.62263
60411.091
14435.89767
15748.88875
20043.85367
31931.0344
0.000%
13.100%
30.148%
53.249%
30.786%
348.978%
7.288%
17.046%
48.967%
137.313%
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Carbon Dioxide Emission Difference
400.000%
350.000%
300.000%
250.000%
200.000%
150.000%
100.000%
50.000%
0.000%
FIGURE 22 - CARBON DIOXIDE EMISSION COMPARISON GRAPH
Table 11 compares the base case and all scenarios for the Gas Turbine nitrous oxide emission, and
the percentage difference between the base case and each scenario. Figure 23 show in graph its
visual percentage difference.
TABLE 11 - NITROUS OXIDE EMISSION COMPARISON
Fuel type
Standard natural gas
NG 75% methane
NG 65% methane
NG 55% methane
Bioethanol
Biogas
SNG + BE 2:1
SNG + BE 1:2
SNG + BG 2:1
SNG + BG 1:2
Nitrous Oxide Emission g/kg of
fuel
Percentage difference
0.369585113
0.417998954
0.481008766
0.566386832
0.02054441
118.6644696
0.286953916
0.176320166
17.01640415
47.049654
0.000%
13.100%
30.148%
53.249%
-94.441%
32007.481%
-22.358%
-52.292%
4504.191%
12630.398%
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Nitroud Oxide Emission Difference
35000.000%
30000.000%
25000.000%
20000.000%
15000.000%
10000.000%
5000.000%
0.000%
-5000.000%
FIGURE 23 - NITROUS OXIDE EMISSION COMPARISON GRAPH
5.9. Summary
Table 12 present a general summary of all key parameters for the Gas Turbine for the base case and
all scenarios.
TABLE 12 - GAS TURBINE KEY PARAMETERS SUMMARY
There is a linear progression for the base case and scenarios 1-3, this is since it is the same fuel and
only the methane concentration in it changes, by 10% each time. Almost all the parameters
compared show that biogas varies the most. Biomethane is in most cases closest to natural gas with
a low methane concentration of 55%. The mixtures average out the different fuels and bring them
closer to the natural gas reading.
The percentage difference in air flow rate is greatest for biogas, at 12.64% shown in Figure 15. This is
because biogas has the lowest heating value, since temperature, pressure and generated energy are
constant, the Gas Turbine needs less air due to lower heat value in the fuel.
Fuel consumption is the critical key parameter for the Gas Turbine and depending on the fuel,
concentration or mix, fuel consumption varies by an average of 50% and biogas again varies the
most, where its fuel consumption is 204.79% shown in Figure 16. This is because biogas has the
lowest heating value, since temperature, pressure and generated energy are constant, the Gas
Turbine needs to compensate for the lack of heating value with more fuel, from which it will
compensate the missing heating value. It is worth noting that a lot of assumptions are made in the
calculations, and although this is difficult to achieve in real life conditions, it is possible when
maintaining a high temperature after the combustion chamber. One convention is that in real life,
biogas is only used for the Gas Turbine as an additive/mixture with another fuel, such as natural gas,
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to dilute it. This is because biogas has a low heating value and also contain other superfluous
elements.
Turbine power in percentages differs slightly, only 1-2% on average, but again biogas stands out and
shows 6.16% shown in Figure 17. This is largely due to the fact that the gas turbine, when using
biogas, which has a low heat value, needs more fuel. Therefore, the Gas Turbine needs less power,
which is consumed by the compressor to presses air. The difference in compressor power
consumption is 11.61% for biogas as shown in Figure 18, when other scenarios have an average
difference of 1-3%.
The work ratio is highest for biogas, at 6.49% as shown in Figure 19, when the other scenarios have
an average of 0.5-2%. As in the previous examples, this is also due to the fact that the compressor
takes less work to inject less air.
The electrical efficiency varies very little and varies on average from 0.2 to 1%, where the highest
difference is in biogas 1.07% as can be seen in Figure 20. This is because constant values are present
and the equation for electrical efficiency includes fuel consumption, this compensates for the
differences and makes them approximately the same.
Another critical key parameter for Gas Turbine is the cost of the operation. Here, bioethanol has the
biggest difference to the base case at 1189.64% shown in Figure 21. This is because bioethanol is 8
times more expensive than natural gas, and the Gas Turbine needs almost twice as much fuel to
produce the same amount of energy as with natural gas at the constant temperature after
combustion chamber. Biogas also shows a big difference of 814.35%, also because that the price is 3
times higher, and the fuel consumption is almost 4 times higher. Considering that the price of
natural gas is the same for fuels with different methane concentration, the price of operation
increases anyway if the methane concentration decreases, because with less methane the heat
value decreases and with it the fuel consumption increases, to compensate the lack of heat value to
keep the constant temperature after combustion chamber and produce constant power. For
mixtures, the price difference varies between approximately 100% and 300% and only for the
natural gas and bioethanol mixture with a ratio of 1:2 the price will rise by 658.71%.
The last critical parameter for the Gas Turbine is carbon dioxide emission. For natural gas, as the
concentration of methane decreases, the amount of carbon dioxide emission increases. This is
because as the methane concentration decreases, the Gas Turbine requires more fuel to maintain a
constant temperature and power output. As the methane concentration decreases from 85% to
55%, carbon dioxide emission increases by 53.25%. Bioethanol has about the same percentage
change as natural gas, but biogas differs by 348.98%, as shown in Figure 22. It must be considered
that this is a renewable fuel, so their emissions can be considered as 0. Additionally as emissions, but
not as critical is nitrous oxide emission, the percentage difference shows the same readings for
natural gas as in the case of carbon dioxide emission. Biogas shows that the percentage has
increased by 32007.48%, while bioethanol shows that the percentage has fallen by 94.44%
compared to standard natural gas. It is worth noting that this is a renewable fuel, so their emissions
readings can be considered as 0.
Chapter 6 – Conclusion
1. Scenario 1-3: Comparing the base case with scenarios 1 to 3, it is clear that a reduction in
methane concentration in natural gas would negatively affect the key parameters of the Gas
Turbine. In order to maintain a constant after combustion temperature and constant power
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output, the Gas Turbine has to consume more fuel. Due to increased fuel consumption, the
amount of emissions and the cost of operation increases. Increased fuel consumption
reduces the load on the compressor and the power required to run the compressor.
Therefore, readings for useful operation ration and energy efficiency increase.
2. Scenario 4-5: Comparing the base case with the renewable fuels in Scenario 4-5, bioethanol
is the best renewable fuel for the Gas Turbine. The performance of bioethanol is closest to
that of natural gas and using twice as much fuel will produce roughly the same result as in
the base case. Most striking is the cost of operating a Gas Turbine using bioethanol, due to
the increased fuel consumption and high price of the fuel itself.
3. Scenario 6-7: Comparing the base case with a 2:1 mixture of standard natural gas and
bioethanol, the higher concentration of natural gas at 66% keeps the price reasonably low,
while reducing carbon dioxide emissions with 33% bioethanol in the mix, and fuel
consumption is only slightly higher.
4. Scenario 8-9: Comparing the base case with a 2:1 mixture of standard natural gas and
biogas, the higher concentration of natural gas at 66% keeps the price reasonably low and
even with 33% concentration on natural gas the price is still not that high compare to
bioethanol, but fuel consumption with a mixture ratio of 1:2 is significantly higher.
For Scenario 1-3 the best fuel would be the natural gas with the highest methane concentration,
in this case it is the natural gas with 75% concentration from Scenario 1. Bioethanol is best fuel
for scenario 4-5, the biogas is not considered as a pure fuel because it has too low heat value
and should be in the mixture with other fuel, for example with natural gas. For scenario 6-7, a
mix of standard natural gas and bioethanol at a ratio of 2:1 is the best type of fuel. For the
Scenario 8-9, the best fuel is a 2:1 mix, given the fuel consumption.
Considering the critical key parameters as fuel consumption, carbon dioxide emissions and fuel
costs - the best fuel for a Gas Turbine is a mix of standard natural gas and biogas with a ratio of
2:1, where 66.6% is standard natural gas and 33.3% is biogas. This mix consumes 28.675% more
fuel than the basic version, and costs 114.458% more, which is the cheapest of all other variants
and the others fuels start at 300% or more. Carbon dioxide emissions are 48.967% higher, due to
higher fuel consumption, but don't forget that biogas emissions can be ignored and treated as 0.
Therefore, the real carbon dioxide figure for this mixture is much lower, and is lower than the
reading for standard natural gas.
Chapter 7 – Further work
The first recommendation for future work is to analyse the key parameters of the Gas Turbine when
changing constants, such as outside temperature, after combustion chamber temperature, pressure
ratio, power output. For example, with a lower constant temperature after combustion chamber,
the fuels with a low heat value may perform better.
The second recommendation for future work is to analyse the key parameters of the Gas Turbine
with other fuels. For example, with other mixtures, where the concentration between one fuel and
another is not 33% and 66%, but 10% and 90%. Or where the mix is not using 2 different fuels, but 3
different fuels.
The third recommendation for future work is a more in-depth fuel analysis. Given the chemical
composition of each fuel, the key parameters of the Gas Turbine may change (e.g. hydrogen, which
can be contained in renewable fuel).
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