Report on Thermodynamics of a Nuclear Power Plant

This report investigates and understands the application of thermodynamics in energy production process of nuclear power plants. It explores the advantages and disadvantages of these power plants relative to the other plants. Mathematical analysis of the thermodynamic processes involved in nuclear power plant is presented. The efficiency of the nuclear energy power plant is analytically determined and compared to the theoretically known efficiencies of the other power plants like oil, coal and natural gas. The report also discusses the demerits and merits of nuclear plant relative to coal-fired, oil and natural gas power plants.

REPORT ON THERMODYNAMICS OF A NUCLEAR POWER PLANT

ABSTRACT
This report is aimed at investigating and understanding the application of thermodynamics in
energy production process of nuclear power plants. It later explores on the advantages and
disadvantages of these power plants relative to the other plants.
Mathematical analysis of the thermodynamic processes involved in nuclear power plant is
presented. Here, the two laws of Thermodynamics are applied in determining various
temperatures and their corresponding entropies. The obtained state points are then plotted on a T-
S chart to bring out a clear picture of what thermodynamic cycles are. This plot eases
observation of phase change instants, compression and expansion stages. Consequently, the
overall process is easily comprehended. Further, the efficiency of the nuclear energy power plant
is analytically determined and the resulting value compared to the theoretically known
efficiencies of the other power plants like oil, coal and natural gas.
The second part of the report delves into the demerits and merits of nuclear plant relative to coal-
fired, oil and natural gas power plants. This discussion is constrained to specific factors such as
the lifecycle values for the power plants, carbon (IV) oxide emissions, de-commissioning and
pollution issues.
TABLE OF CONTENTS

TABLE OF CONTENTS............................................................................................................................3
INTRODUCTION...................................................................................................................................4
MAIN BODY..........................................................................................................................................5
RECOMMENDATION AND CONCLUSION.....................................................................................13
REFERENCES......................................................................................................................................15

INTRODUCTION
In the modern world, nearly all domestic activities and industrial processes are run by energy.
Electricity is the main source of energy used around the world for such. Electrical energy is
obtained from various sources such as coal. The frequent use of coal would however make it get
depleted. This therefore necessitates that other energy sources must be found to provide a
continued supply of unlimited power. Other alternative sources of energy that exists include:
hydropower, solar power, tidal power, nuclear power, geothermal power and biomass energy.
Production of nuclear energy is done via nuclear fusion and nuclear fission processes. Many
countries have currently adopted production of nuclear energy due to its associated advantages as
discussed.

MAIN BODY
PART A
The diagram below is the simplified version of the nuclear power plant flow diagram
There is no work done at the moisture separator hence no heat transfer as the system is in steady
state.
Determination of rate of work done in turbine of lower Pressure
Because of the steady state conditions of the low pressure turbine i.e. there is no heat transfer,
both the equation of continuity and energy equation hold.
The continuity equation here is,
´m4 = ´m5+ ´m8
And the energy equation is,
´m4 h4= ´m5 h5 + ´m8 h8+ ´W LP
Making ´m5 the subject of the formula from the continuity equation,
´m5= ´m4 − ´m8
58.212−2.772=55.44 kg /s
Making ´W LP the subject of the formula,
´W LP= ´´m4 h4 −m5 h5 − ´m8 h8

58.212 x 2673.9− ( 55.44 x 2279+2.772 x 2459 )
22489 kW
22489
103 =22.489 MW
High Pressure Turbine
Because of the steady state conditions of the high pressure turbine i.e. there is no heat transfer,
both the equation of continuity and energy equation hold.
The energy equation is,
´m2 h2= ´m3 h3+ ´m12 h12+ ´m17 h17 + ´W HP
Making ´W HP the subject of the formula,
´W HP= ´m2 h2− ´m3 h3− ´m12 h12− ´m17 h17
( 75.6 x 2765 )−¿
18394 kW
18394
103 =18.394 MW

Graphical Results

PART B

Determination of Enthalpy and Quality
There is no work done at the moisture separator hence no heat transfer as the system is in steady
state.
From the equation of continuity,
´m3= ´m4 + ´m9
Making ´m4 the subject of the formula,
´m4 = ´m3− ´m9
But ´m3=62.874 ∧ ´m9=4.662. Therefore,
´m4 = ´m3− ´m9=62.874−4.662=58.212 kg/ s
From the energy relation,
´m4 h4= ´m3 h3− ´m9 h9
Making h4 the subject of the formula,
h4= ´m3 h3 − ´m9 h9
´m4
But h3 =2517 ∧h9 =558.
Therefore,
h4= 62.874 x 2517−4.662 x 558
58.212
2673.9 kJ /kg
But h4 isalsogivenby , h4 =566.18+2160 x4 . Equating this to the previously obtained value, we
get:
h4=566.18+2160 x4 =2673.9

x4 =2673.9−566.18
2160 =0.9755
∴ Enthalpy , h4 =2673.9 kJ
kg ∧Quality , x4=0.9755
PART C
Ratio of total power output
Determination of rate of work done in turbine of lower Pressure
Because of the steady state conditions of the low pressure turbine i.e. there is no heat transfer,
both the equation of continuity and energy equation hold.
The continuity equation here is,
´m4 = ´m5+ ´m8
And the energy equation is,
´m4 h4= ´m5 h5 + ´m8 h8+ ´W LP
Making ´m5 the subject of the formula from the continuity equation,
´m5= ´m4 − ´m8
58.212−2.772=55.44 kg /s
Making ´W LP the subject of the formula,
´W LP= ´´m4 h4 −m5 h5 − ´m8 h8
58.212 x 2673.9− ( 55.44 x 2279+2.772 x 2459 )
22489 kW
22489
103 =22.489 MW

High Pressure Turbine
Because of the steady state conditions of the high pressure turbine i.e. there is no heat transfer,
both the equation of continuity and energy equation hold.
The energy equation is,
´m2 h2= ´m3 h3+ ´m12 h12+ ´m17 h17 + ´W HP
Making ´W HP the subject of the formula,
´W HP= ´m2 h2− ´m3 h3− ´m12 h12− ´m17 h17
( 75.6 x 2765 )−¿
18394 kW
18394
103 =18.394 MW
Total Power output
This equals to, ´W HP + ´W HP=22.489+13.394=40.883
Hence,
Ratio= 40.883
157 =0.260
This ratio, reflected as a percentage gives an efficiency of about 26%. This is a true
manifestation that the energy of the initial state is higher than the potential energy which
consequently affirms the second law of thermodynamics. If this efficiency were 100% and
above, then the second law of thermodynamics could have been contravened.
Theoretically, natural gas plant has its maximum efficiency at 52% while oil plant has it’s at
45%. Coal fired plant; however, is about 42% efficient. All these three plants, when compared to
the nuclear power plant, are more efficient with the natural gas being the most efficient.

PART D
Various electrical generation stations emit greenhouse gases to the environment which
consequently affect climate change. This dangerous phenomenon has thus sparked world’s
interest in determining the amount of emissions contributed by various electricity plants. Due to
increased demand of electricity, many electric plants must be constructed in special designs that
limit Greenhouse gases. A myriad of electrical generation methods exist; each faced with
demerits and merits with respect to environmental impact, operational cost etc. This essay
focuses its discussion on the advantages and disadvantages of nuclear power plant relative to
other plants like coal, oil and gas.
About twenty seven Gigatonnes of CO2e is emitted from various sources. Out of which the
electricity industry emits 10 Gigatonnes, a value approximately equal to 37% of the total
emissions. Varying quantities of CO2 is emitted at the construction, operation and
decommissioning stages of the power plants. Nuclear power plants emit most of the CO2
emissions during operation while coal fired power have majority of these emissions released
during operation. A lifecycle approach is the mechanism used to account for all the emissions in
all the project’s phases (decommissioning, operation and construction). A comparision of these
various methods of generation on a per gigawatt-hour basis is made after the lifecycle emissions
are normalized. The emitted quantity is proportional to the value of normalized lifecycle. Table
1.1 below provides lifecycle emission for various methods of generation of electricity (coal,
nuclear, gas and oil plants). To ensure relevance in comparision across generation of electricity,
the emissions are expressed as a function of electrical power produced i.e. kgCO2/kWh.
Table 1.1: Values of CO2e/GWh in tonnes
Tonnes CO2e/GWh
Generation Plant Low Value High Value Mean Value
Natural Gas 362 891 499
Oil Energy 547 935 733

Coal Energy 756 1310 888
Nuclear Energy 2 130 29
Table 1.1 above is graphically represented in Figure 1.1 below.
Nuclear Coal Oil Gas
0
100
200
300
400
500
600
700
800
900
1000
CO2e/GWh Emissions in various Power
Plants
Tonnes CO2e/GWh
Fig 1.1: Variation of CO2e/GWh Emissions in various Power Plants
The absolute intensity of emission is observed to fluctuate despite of the consistency in the
relative magnitude of greenhouse emissions of the various power plants. This could be as a result
of the differences in the study scopes.
The data used is a function of the nature of facilities in the respective plants. So unique are the
rates of emission from power generation to the individual facility. The factors which affect the
rates of emission are specific to the sites and the regions. For instance, lifecycle emissions are
higher in cases where nuclear fuel is enriched by gaseous diffusion than in cases of enrichment
by centrifugation. This is because of the higher electrical load in nuclear fuel than in centrifuge.
The table shows that depending on the electrical supply, the emissions can even vary between
enrichment facilities.
Since some studies include treatment and management of waste in the definition of lifecycle
while others don’t, the data obtained during this study might not be consistent. It is evident that
the highest greenhouse emission intensities on a lifecycle basis occur in coal fired plants. Besides

oil and gas significantly having lower emissions, nuclear energy had the least of the four power
plants. A high degree of safety is achieved in Nuclear power plants. This is because of the plant’s
design to have numerous physical barriers which provides defence-in-approach. However, these
physical barriers make emissions at the construction stage of nuclear plants be higher in
comparision to the emissions during construction of coal, oil and natural gas power plants.
Nuclear energy emissions life cycle’s value still remain below that of the corresponding
emissions from other generation methods that are fossil fuel based despite the inclusion of
emissions from additional safety barriers. Reflected as a percentage of other sources of emission,
mathematical analysis shows that the intensity of emissions in nuclear plants is about 3% of coal-
fired power plants and 7% of natural gas plants. The lifecycle of greenhouse emissions of nuclear
power plants is however consistent with that of other renewable sources of energy.
The power plants cause various kinds of pollution including water, air and environmental
pollution. Burning of fuels during generation process may cause health problems to animals and
human beings. Long exposure to the low levels of radiation energy emitted in nuclear generation
process may affect the DNA of beings. This makes them somewhat dangerous.
The process of decommissioning a nuclear power plant is usually faced with a number of
challenges. The main challenge of this is the large costs involved i.e. the costs may be up to (10-
15) % of the initial cost of construction. Besides, difficulty to set up a long lasting feasible
disposal strategy for the high level waste is another problem that has to be dealt with. This
generally makes this process very cumbersome.
RECOMMENDATION AND CONCLUSION
In a nutshell, as presented in the discussion above, the following deductions hold:
Among all other electricity generation methods, greenhouse gas emissions of nuclear power
plants are among the lowest and are only comparable to other renewable energy sources like
biomass and wind.
Nuclear energy emissions lifecycle, when compared to that of natural gas, is lower by about
fifteen times.

Nuclear energy emissions lifecycle, when compared to that of coal energy, is lower by about
thirty times.
The results of lifecycle analysis are greatly influenced by the assumptions made. For example,
the life cycle for nuclear power plant varies based on whether gas centrifuge enrichment or
gaseous diffusion is included.
The mathematical computation carried out shows that the nuclear power plant under this
investigation is about 26% efficient. Therefore, nuclear energy plants are preferred to other
plants when very little emission is desired.

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