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Hydrodynamic modeling and feasibility study of harnessing tidal power at the Bay of Fundy
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Hydrodynamic modeling and feasibility study of harnessing tidal power at the Bay of Fundy
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Content
HYDRODYNAMIC MODELING AND FEASIBILITY STUDY OF
HARNESSING TIDAL POWER AT
THE BAY OF FUNDY
by
Jen Chang
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(CIVIL ENGINEERING)
May 2008
Copyright 2008 Jen Chang
ii
Acknowledgements
The writer would like to express his deepest gratitude to his academic advisor, Dr.
J.J. Lee, for his patient guidance, understanding and full support. The writer is also
grateful for the instruction form Drs. G. V. Chilingar, J. E. Moore, L. C. Wellford,
and H. L. Wong of the guidance committee.
Thanks are also due to Dr. C. P. Lai for his counsel on developing numerical
model, and to Professor M. Eskijian for the help on offshore structure cost estimation.
iii
Table of Contents
Acknowledgement ii
List of Tables v
List of Figures vi
Chapter 1: Introduction 1
Chapter 2: Issues Related to Energy Development 3
2.1 Sustainable Development 3
2.2 Oil Price 5
2.3 Crude Oil and Natural Gas Demand and Discovery 12
2.4 Environmental Considerations 18
2.5 Renewable Energy 23
Chapter 3: Tide and Tidal Energy at Bay of Fundy 27
3.1 Tide 27
3.2 The Bay of Fundy 33
3.3 Tidal Power Development at Bay of Fundy 35
3.4 Types of Tidal Energy Development 43
3.4.1 Barrage Type of Tidal Power Plant 43
3.4.1.1 Single Effect Operation 44
3.4.1.2 Double Effect Operation 46
3.4.1.3 Single Basin or Multi-basin 47
3.4.2 Tidal Current Turbine 50
3.4.3 Energy Storage 52
Chapter 4: Numerical Modeling 54
4.1 Related Studies 54
4.2 Theoretical Framework 55
4.3 Numerical Model Development 59
4.3.1 Related Studies 59
4.3.2 Galerkin’s Approach 61
4.3.3 Temporal approximation 63
4.4 Hydrodynamic Simulation at Bay of Fundy 71
4.4.1 Field Observation Data 71
4.4.2 Numerical Simulation Generate 80
4.4.3 Simulation Result 84
4.4.3.1 Simulation Result (for calibration) 84
4.4.3.2 Simulation Result (for verification) 87
4.4.3.3 Simulation Result (tidal chart) 91
iv
Chapter 5: Tidal Power Calculation 120
5.1 Barrage Type of Tidal Power Plant 120
5.2 Tidal Current Turbine 131
Chapter 6: Economic Feasibility 134
6.1 Barrage Type of Tidal Power Plant 135
6.2 Tidal Current Turbine 140
Chapter 7: Conclusion and Future Work 144
References 147
v
List of Tables
Table 1: Environmental cost for energy sources 20
Table 2: Major tidal components 30
Table 3: Tidal stations of MEDS in the Gulf of St. Lawrence 74
Table 4: Tidal range amplification factor 91
Table 5: Potential energy output from site A6, A8, and B9 130
Table 6: Summary of characteristics of Single-effect Tidal
Power Schemes 136
Table 7: Summary of at-site costs of Single-effect Tidal
Power Schemes 138
Table 8: Electric billing from Nova Scotia Power Inc. 139
Table 9: Power output for different rates of turbines 141
Table 10: Financial analysis for current turbine 142
vi
List of Figures
Figure 1: Annual spot price for crude oil product 7
Figure 2: Ratio of spot price of crude oil products to the price
in year 1987 7
Figure 3: Crude oil spot price 10
Figure 4: Historical crude oil price as measure by constant dollar
in year 1973 10
Figure 5: Predict oil price (EIA 2007) 12
Figure 6: Crude oil discovery and demand 14
Figure 7: Years left for crude oil 17
Figure 8: Years left for natural gas 17
Figure 9: The Bay of Fundy 33
Figure 10: Annapolis Tidal Generating Station 41
Figure 11: Single Effect Operation 45
Figure 12: Double Effect Operation 47
Figure 13: Single Basin 48
Figure 14: Double Basin 48
Figure 15: Tidal current turbine 51
Figure 16: Water depth of Bay of Fundy 72
Figure 17: Reference points in the Bay of Fundy 77
Figure 18: Tidal records at the mouth of the Bay of Fundy
between 12/14 and 12/20/2006 78
Figure 19: Tidal records between 12/14 and 12/20/2006 79
Figure 20: Tidal records between 2/23 and 3/1/2006 80
vii
Figure 21: Property zones 81
Figure 22: Grid layouts for numerical simulation 82
Figure 23: Simulation result between 12/14 and 12/20/2006 85
Figure 24: Simulation result between 2/23 and 3/1/2006 88
Figure 25: Tidal range in Outer Wood Island
between 1/1/2006 and 6/30/2007 92
Figure 26: Tidal record and simulation result
between 12/21/2006 and 1/10/2007 94
Figure 27: Water elevation contour 102
Figure 28: Current velocity 107
Figure 29: Maximum and minimum tidal range 113
Figure 30: Average tidal ranges in an hour 114
Figure 31: Average kinetic energy density (V
3
) 115
Figure 32: Average kinetic energy density (V
3
)
– when current velocity is higher than 1 m/sec 117
Figure 33: Single Effect Operation for a M2 Tide 122
Figure 34: Sites for Barrage Type of Tidal Power Plant 123
Figure 35: Tidal response at site A6, A8, and B9 124
Figure 36: Current velocity profile at Minas Channel 132
viii
Abstract
Due to rising fuel costs and environmental concerns, energy generation from
alternative power source has become one of the most important issues in energy
policy. Tidal power is one of the alternative energy sources. The tidal range at the
Bay of Fundy is the largest in the world (approximately 16 meters). It represents a
prime location for harnessing tidal power using the daily rising and ebbing tide.
In this study, a two dimensional finite element model has been developed and
applied to simulate the tidal responses, including water level and flow velocity, in the
Bay of Fundy region. The simulation results are used to choose the suitable location
for energy development and to predict possible energy generated from different types
of generation methods.
Fluid motion is assumed to be governed by the shallow water equation since the
wave length associated with tide is much longer than the water depth in the Bay of
Fundy. By using a real time series of water elevation at the entrance of the bay, the
computer model finds tidal response for each node in the study area, which is then
verified by the observation record from several tidal gauge stations inside the bay.
This study shows that the at-site cost of the energy for barrage type tidal power
plants is around $0.065 to $0.097 per kWh at the recommended Shepody Bay,
Cumberland Basin, and Cobequid Bay. The cost of energy for the current turbine
type tidal power plants is $0.13 /kWh to $0.24/kWh at the area with highest current
velocity. Compared with the recent bill of the local power company, the at-site unit
cost of energy from the barrage type of tidal power plant is feasible, but the
ix
environmental concerns of channel blocking by barrage present a formidable
constraint. For the current turbine type of tidal power plant, even the most suitable
sites are not financially feasible under current technology, but this type of power
generation may become feasible as oil prices continue to increase and more efficient
turbines become available.
1
Chapter 1: Introduction
Energy is one of the major factors influencing the development of modern
society. The world underwent an industrial revolution when James Watts built the
world’s first steam engine in 1765, and with the help of this powerful machine,
people were able to grow more food and produce more goods than ever before.
Thanks to this continuous progress in technology we were even able to conquer the
sky and eventually space. Until now, human life has depended on one type of
machine or another, but these machines will be useless without fuel or energy to
supply them. Thus, modern society is critically dependent on the existence of an
energy supply and the technology to use it efficiently.
The natural resources we rely on, however, will one day be exhausted. The
dominant source of energy, crude oil, is estimated to run out within the near future.
Compared the amount of proved reserves with annual consumption rate of recent
years, crude oil will be exhausted within 40 to 50 years, and the natural gas will last
for about 60 years. In order to maintain our modern standard of living and continued
societal development, human beings must find other sustainable energy sources to
meet the energy demands of the future.
Not only are alternative energy sources critical to the continued societal growth,
but our current energy practices have negatively affected the environment, as well.
Although the “greenhouse effect” is a natural phenomenon that helps keep the
temperatures on Earth at tolerable levels, due to the general use of fossil fuels, the
2
amount of greenhouse gases have increased and enhanced the greenhouse effect.
Some believe that this enhancement has caused the average temperature of the Earth
to increase, and has altered regional climates. The use of fossil fuels has also more
directly impacted society through increased levels of urban air and water pollution.
Renewable energy sources offer an opportunity to save the quickly depleting
fossil fuel resources, restore better air quality and ease global climate change. This
study is devoted to exploring the use of tidal energy and compares several renewable
energy technologies available. It will estimate the physical feasibility of tidal power
using a two dimensional numerical model applied to the highest tidal range in the
world, the Bay of Fundy, in Nova Scotia, Canada. The financial feasibility will also
be presented along with suggested technologies that make this renewable energy
more economically efficient. By synthesizing the information available on the
physics and economics related to tidal energy and the recent maturity of the related
technologies, the developmental prospects will be offered for a renewable tidal
energy supply.
3
Chapter 2: Issues Related to Energy Development
A comprehensive approach of energy development has to consider the social,
economic and environmental impacts. One part can no longer be compromised by
another. In recent decades, issues about sustainable development and environmental
protection have been emphasized in developed and developing countries. With the
current trend of rising oil prices, more and more renewable energy techniques are
being explored and utilized.
2.1 Sustainable Development
The concept of sustainable development is to meet the needs of the present
without compromising the ability of future generations to meet their own needs.
Sustainable development guarantees the existence of human society. For decades,
the environment has suffered due to some false pretense that the environmental
sustainability can only be achieved at an economic expense. From the loss of
rainforests to over-fishing, the negative effects on the environment are being felt.
This way of development is a burden on the planet and cannot be sustained. When
the population of the world continues to increase, the available resources and
environmental systems such as water, land and air cannot go on forever.
Other than that, human society still has problems to solve to supply basic living
needs. According to Department of Economic and Social Development of the
4
United Nations, at least one billion people live under the poverty level, without safe
drinking water or sanitation. About two billion people have no access to modern
energy services. If no action is taken, more species will become extinct and land will
turn to desert. Further, exhaustion of our resources, environmental damage due to
population growth, and social unbalance will all impact society more as time goes on.
We need to face the problems and take action immediately.
Even though the entire of human society has a common future, the request for
sustainable development is different from nation to nation even district to district.
Conflicts in values usually occur in countries under rapid industrial development
where conditions are in transition. The particular conditions relate to the country’s
history, geography, culture, economy, society and legal system, and the people must
work towards not only their own regional goals but common goals as well.
Countries may work on their own democracy and economy by making suitable
laws and using advance technology while still pursuing the global goal. In 1992, the
Rio Earth Summit articulated this goal as “Think Globally, Act Locally” to initiate
local action (Norway’s Special Report to Earth Summit+5, United Nations). This
report is the follow-up report to the UN General Assembly Special Session, five
years after UNCED (the United Nations Conference on Environment and
Development, also known as the Earth Summit) in Rio de Janeiro, Brazil. It indicated
that local sustainability can be built under the globally accepted value of
development, and the local development would be obtained while maintaining
5
sustainable practices. Finally, by integrating all the effort from the local level, global
sustainability can be achieved.
Among all the resources, Division for Sustainable Development, United Nations
believes that energy is central to achieving sustainable development goals. In order
to supply energy for sustainable development, we need to find ways to reconcile this
necessity and demand with its impact on the natural resource base. One of the
suggestions to achieve this goal from Division for Sustainable Development is to
combine and develop advanced, cleaner, more efficient and cost-effective energy
technologies.
2.2 Oil Price
Coal-fired energy systems were introduced in the nineteenth century and became
popular in most large cities in North America and Europe. The expansion of this
technology continued until World War II, when thermal power plants became the
major energy source. After the War, the rapid development of the petroleum
industry and cheap oil, gas and electricity in North America have played an
important part in ordinary life.
The sudden rise of oil prices in the 1970s motivated the development of alternate
energy systems. Many heating plants were modified to burn a variety of fuels such as
oil, natural gas and garbage, as well as a variety of biomass fuels including
6
woodchips, wood waste and straw. Rising oil prices also increased investments in
producing power by other natural resources like wind, solar and tidal energy.
However, when oil prices dropped from the peak in early 1980s, the techniques
became less economically attractive compared with thermal power plants.
Figure 1 shows the spot price of several oil products (Energy Information
Administration, Department of Energy, USA). It lists two types of crude oil and
heating oil, compared with conventional gasoline and diesel prices. West Texas
Intermediate, WTI, is a crude stream produced in Texas and southern Oklahoma.
Europe Brent is produced in North Sea region. Both WTI’s and Brent’s prices serve
as a reference or "marker" for pricing a number of other crude streams. The heating
oil prices from New York Harbor or Gulf Coast indicates either spot or futures
contracts for delivery in any port city in that category and also represents a reference
price. Because of the cost of refinery process, spot prices for heating oil do not show
a direct response to changing crude oil prices; they correlate in a long run. Figure 2
is modified by using the spot price of that year divided by the price in 1987. It
proves that most of the crude oil refining products’ prices can be represented by the
crude oil prices.
7
Annual Spot Price
0
50
100
150
200
250
1985 1990 1995 2000 2005 2010
Year
Europe Brent Spot Price FOB (Dollars per Barrel)
Cushing, OK WTI Spot Price FOB (Dollars per Barrel)
New York Harbor No. 2 Heating Oil Spot Price FOB (Cents per Gallon)
U.S. Gulf Coast No. 2 Heating Oil Spot Price FOB (Cents per Gallon)
New York Harbor Conventional Gasoline Regular Spot Price FOB (Cents per Gallon)
Los Angeles, CA No 2 Diesel Spot Price FOB (Cents per Gallon)
Figure 1: Annual spot price for crude oil products
Ratio Spot Price to Year 1987
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
1985 1990 1995 2000 2005 2010
Year
Europe Brent WTI New York Harbor No. 2 Heating Oil
U.S. Gulf Coast No. 2 Heating Oil NY Harbor Conventional Gasoline LA, CA No 2 Diesel
Figure 2: Ratio of spot price of crude oil products to the price at year 1987
8
In energy feasibility studies, the cost of energy should not only include the recent
costs but also the future costs and that depends on future crude oil prices, since fossil
fuels are the major energy source. Several studies attempt to estimate future crude
oil prices since the 1970 oil crisis. Hubbert (1962) uses an empirical approach based
on a bell-shaped curve to model crude oil production in the Unite States. This model
predicted a peak of oil extraction in the US and then decline in production. After
that, several researchers have used this ideal to predict the evolution of oil
production and demand. MacAvoy (1982) and Horn (2004) use the relationship of
supply, demand, and reserve amount in the world market as the basic factors to
predict future crude oil prices. They use historical data to estimate the future
discovery of oil reserves and oil consumption and find the elasticity of demand and
supply by varying assumptions. Kaufmann (2005) defines the heating oil prices by
crude oil price. They all predict that the energy demand will grow consistently, and
the crude oil prices might be as high as $49/barrel by year 2020. Burdette (2005)
presents a short term estimation by Energy Information Administration, US, for
crude oil prices. He believed that prices would not go higher than $55/barrel by
2007. The predicted prices in these reports appear to be underestimates when we
take a look at current crude oil prices, as indicated in Figure 3; however, this number
does not account for the recent spike in oil prices and it might be much larger if these
researchers’ models incorporated recent data. It also indicates that the price
prediction model does not fully work with important and vital commodities such as
oil, for there are too many factors to be considered.
9
In Figures 3 and 4, data from year 1985 and earlier come from the New York
State Energy Research and Development Authority, in the form of annual oil prices.
Data after 1985 comes from the Energy Information Administration, Department of
Energy, USA, in the format of weekly average prices. The red line indicates the
average of the fifty two weekly average prices in that year, where the vertical bar
shows the maximum and minimum of the weekly average prices in that year. For
example, in 2006, the highest weekly price is almost 80 dollar and lowest weekly
price is a little lower than 60 dollar from Figure 3. In Figure 4, we adjust the spot
prices for each data to the constant dollar in 1973 by using inflation factors (Bureau
of Labor Statistics, U.S. Department of Labor), and then we can evaluate the price
for each year. In Figure 3 and 4, we can see the recent trend is going higher and
more expensive since year 2002. We can also find the recent highest oil price is
actually more expensive than the highest point in the past (year 1981). That tells us
the crude oil price will maintain at this high level or get even higher.
10
Historical Crude Oil Spot Price
0
20
40
60
80
100
120
1973 1977 1981 1985 1989 1993 1997 2001 2005
Year
$/Barrel
Figure 3: Crude oil spot price
Source: New York State Energy Research and Development Authority
Energy Information Administration, Department of Energy, USA
Historical Crude Oil Price (Constant dollar in 1973)
0
5
10
15
20
25
1973 1977 1981 1985 1989 1993 1997 2001 2005
Year
$/Barrel
Figure 4: Historical crude oil price as measure by constant dollar in 1973
11
In order to make a more realistic prediction, the EIA predicts future oil prices in
a maximum/average-reference/minimum way in a recent report (International Energy
Outlook 2007). Their prediction prices come from one model with three different
sets of factors, one set for an average economic situation, one for a very high oil
price case and one for a very low oil price case. In this way, its prediction model
shows a range of predicted prices. Its result is shown in Figure 5, and the oil price
for each barrel is based on the 2005 constant dollar. We can see that the reference
case maintains a stable oil price or gets an even lower price in the report’s estimation.
However, when we compare the recent variation of oil prices with EIA predictions,
the high price case will more accurately present the future oil price. If this high oil
price assumption becomes real, the price of crude oil will reach 90 dollar per barrel
in 2021 and 100 dollar in 2030.
12
EIA 2007 Oil Price Prediction
0
20
40
60
80
100
120
2005 2010 2015 2020 2025 2030 2035
Year
$/Barrel
Reference
Low Price
High Price
Figure 5: Predict oil price (EIA 2007)
2.3 Crude Oil and Natural Gas Demand and Discovery
Some researchers--Noreng and Tauris (2002), and Abosedra and Baghestani
(2004)--doubt the accuracy of the oil price prediction models using past and recent
reservation/consumption relationships. They believed that other human behavioral
factors, such as OPEC’s production constraint and other political issues, influence
the resulting demand and production of crude oil and consequently its price.
Furthermore, Bentley’s (2002) and Laherrere’s (2003) studies show that produced
crude oil has reached almost half of the earth’s reserves (due to recent mining
techniques and discoveries) as shown in Figure 6. In this figure, world oil demand
since 1970 and the other data after the year 2000 come from the Energy Information
13
Administration, Department of Energy, USA. The predicted oil demand (both
constrained and unconstrained) and new discovery, and natural gas demand and new
discovery before year 2000 come from Laherrere’s (2003). The unit for crude oil
and natural gas is in billion oil-equivalent barrels. The constrained and
unconstrained models for oil are simulation results which assume the crude oil
demand/consumption for a constrained or unconstrained market, when a constrained
market is for some reason under intentional controls by governments or
organizations.
14
Crude Oil and Natural Gas Discovery and Demand
(unit: Billion oil-equivalent barrels)
0
20
40
60
80
100
120
140
160
180
200
220
1900 1920 1940 1960 1980 2000 2020 2040
Year
Oil discovered Gas discovered Gas demand
Unconstrained model-oil Constrained model-oil Oil demand
Figure 6: Crude oil discovery and demand
Source: Laherrere (2003) and EIA, DOE
An unconstrained model, like those represented in section 2.2, uses the Hubbert
curve and the equation in which the production of oil is a function of the rate of new
oil well discovery; a "Hubbert peak" in the oil extraction rate will thus be followed
by a gradual decline of oil production. In reality, Laherrere (2000) says that when
the economy changes from good to bad, the poorer conditions will reduce oil
15
demand, and crude production will display neither a smooth peak nor an angular
high peak, but a bumpy plateau. He believes that an unconstrained model using the
simple Hubbert curve can be applied only when there is a large population of fields
(such that the sum of a large number of asymmetrical distributions becomes
symmetrical), and when exploration follows a natural pattern unimpeded by political
events or significant economic factors (for example: OPEC artificially cuts
production). Laherrere (2003), in his comments on the article by P. Holberg & R.
Hirsch, states that Hubbert assumes that oil needs to be found before being produced
and that the production pattern of a country is similar to the discovery pattern.
However, discoveries usually occur in cycles, and production is often constrained by
demand in most countries. Such examples can be shown in 1979 when world oil
production peaked because of the prediction of future high oil prices. In his
experience, the results from a constrained model are more realistic in predicting the
world production.
Even though Karbuz (2004) claims that it is very hard to work on oil statistics
because of the difficulty in defining correct conversion factors, we can see that the
recent trend of the rise in oil prices is going to continue. In order to secure the
energy supply, governments have to look for alternate energy sources. Bardi (2005)
presents on a model in the shape of an oil production curve. In his simulation, the
production curve of a non-renewable resource like crude oil will be affected by
factors such as a search strategy or improvement of technology. He concludes that
the after-peak downward slope might turn out to be steeper than the upward slope for
16
the worldwide crude oil production. That is, the reserved crude oil might run out
faster than previously estimated. Such situation would have a significant negative
impact on the economy.
How many years will the crude oil left if we keep the consumption rate of today?
If we divide the reserved crude oil by the consumption of that year we will have the
result shown in Figure 7. The same method gives us the result for natural gas shown
in Figure 8. Data for both figures come from EIA. In Figure 7, “Years Left for
Crude Oil” is jumping between 28 to 42 years since 1980; on the other hand, Figure
8 shows that we maintain the amount of natural gas for around sixty years usage
since the year 1995, with a slow reducing trend. There is decreasing trend for crude
oil before 1987 and between 1990 and 2002, but an increase from 30 to 41 years
during 1987 to 1990, and 36 to 42 years during 2002 - 2003. It is possible that new
discovery is motivated by the decreasing reservation/consumption rate or the
increasing crude oil market price. This increased new discovery can be shown in
Figure 6, where we can see an off-scale jump in new crude oil discovery at year 2003.
Oil shale is one of the examples. It was always slightly more expensive than crude
oil as an energy resource and it was overlooked until recent years. When the major
energy source price rises to a certain level, people work on developing new methods
or technology to harvest energy. When new technologies become feasible relative to
the major source, the new energy source will become one of the supports to human
society.
17
Years left for crude oil
20
25
30
35
40
45
1975 1980 1985 1990 1995 2000 2005 2010
years
Figure 7: Years left for crude oil
Years left for natural gas
30
40
50
60
70
1975 1980 1985 1990 1995 2000 2005 2010
year
years
Figure 8: Years left for natural gas
18
It is noted that the data in Figure 6 are not correlated with the data in Figure 7
between years 1980 and 2000. The difference is due to different data sources: the
data in Figure 6 come from Laherrer (April, 2003) and the data in Figures 7 and 8
come from the EIA. Laherrer (June, 2003) states that his research shows a decline in
the new discovery of crude oil in smooth five year average curve since 1963 and the
annual discovery becomes lower than the annual crude oil production since 1980.
He says his result agrees with the results published by J.H. Longwell from Exxon-
Mobil in 2002 and government agencies (EIA or other organizations) over-estimated
the annual discovery and proved reserves. If what he says is more reliable than
government agencies’ result, the curve in Figure 7 will be below 30 (years) and go
into a decline trend after 1980.
2.4 Environmental Considerations
The extensive use of fossil fuels has caused many problems. The burning of this
fuel produces smoke (aerosols) and odor, and increases the well-known greenhouse
gases. It is important to note that the greenhouse effect is a natural phenomenon.
According to Khilyuk and Chilingar (2004), Earth’s climate was determined by the
energy radiated from the Sun. This energy heats the surface of the Earth and
approximately 30 percent of solar radiation is reflected off at longer wavelengths.
The remaining energy is absorbed by the Earth’s surface and by the molecules of
“greenhouse gases” in the atmosphere which warm the planet. As a result,
19
greenhouse gases help regulate the temperature of the Earth’s surface and the lower
atmosphere to a level warm enough for natural life. If the concentration of the
greenhouse gases increases, more energy will be absorbed to heat the Earth, and
finally the climate may change. The process is called the “greenhouse effect.” Since
we have adopted the use of fossil fuels, the atmosphere has accumulated more
carbon dioxide and other anthropogenic gases. Many people believe that the
presence of these additional gases has increased the rate of heat absorption of the
atmosphere, and thus increased the temperature of the Earth’s surface. Khilyuk and
Chilingar do not agree that the temperature increase is solely caused by the human-
induced carbon dioxide. However, human activities do produce air pollution and
certain anthropogenic gases have even damaged the ozone layer at higher latitudes
and increased the intrusion of the radiation from the Sun. For example, according to
EIA, DOE, carbon dioxide emissions from the consumption and flaring of natural
gas are from 3.1 to 5.6 billion metric tons, and emissions from petroleum oil are
from 8.8 to 10.8 billion metric tons around the world every year (from 1980 to 2004).
The pollution caused by the consumption of oil or natural gas is a cost associated
with energy production.
20
Energy Source
Environmental
Cost
Basic
Cost
Total
Cost
cent/kWh cent/kWh cent/kWh
Traditional Coal (1.2% sulfur)
5.7 3.1 8.8
Coal (1.1% sulfur,AFBC)
2.8 3.1 5.9
Oil(2.2% sulfur)
6.7 3.9 10.6
Oil(1% sulfur)
3.8 3.9 7.7
Natural Gas 1.0
6.1 7.1
Nuclear
2.9 2.8 5.7
Renewable Waste Energy
4.0
3.6-7.2 7.6~11.2
Solar
0.4
6~8 6~8
Wind
0.1
5~7 5~7.1
Biomass
0.7
4.6-7 4.6-7.7
Hydro
0.2
3.6-7.2 3.6-7.4
Geothermal
5.7~7.5
AFBC = Atmospheric Fluidized Bed Combustion
Source: Bureau of Energy, MOEA, Taiwan(May, 1999)
Table 1: Environmental cost for energy sources
Table 1 shows an estimation of environmental cost per unit energy from different
sources. In this table, basic cost is the production cost without the concern of
environmental impact during the development of energy, including the cost for civic
work, mechanical and electrical equipment and installation, indirect expenses and
contingency, and maintenance. We can see that for traditional types of energy
development, environmental cost plays a significant part in the total cost, even
though it was usually not considered in a feasibility study ten years ago. On the
other hand, renewable energy--except waste energy--consumes minor environmental
21
costs. Although the generation of energy from waste causes some environmental
concern, it actually helps to process waste and benefits to the environment. In a
sense, renewable energy is competitive with traditional resources if environmental
impact is considered.
After the passing of the Kyoto Protocol, the countries which have ratified the
Protocol have agreed to reduce the world's carbon dioxide emissions below 1990
levels by the year 2012. The Protocol is an indication of the international effort to
minimize human influence on the environment. In fact, it is critical for public health,
and in helping to protect the natural environment while achieving sustainability.
Regardless of whether they signed the protocol or not, many countries make an effort
to follow the spirit of the treaty and declare sincere intention internationally, and to
promote green energy and the concept of sustainable development for their people,
and in turn to increase their competitiveness globally.
In addition to the Kyoto Protocol, countries are imposing restrictions on imported
products if the products damage the environment by their materials or by their
manufacturing processes. For example, European countries inspect the source of
their imported electronic products. Thus, even products excellently designed may be
barred from importation into Europe if they do not meet the required standards in the
European Union by 2010.
The international trend is toward promoting "zero waste." Instead of spending
money to process waste, some countries invest in reusing or recycling the waste, and
22
produce more job opportunities. For example, New Zealand and the EU have both
proposed the target of zero waste by 2020, so has the American State of Georgia.
Meanwhile, Australia's capital city, Canberra, intends to achieve that goal by 2010
(Zero Waste New Zealand Trust.) By contrast, Taiwan's goal is to achieve a waste
level of that is 60 percent of their 1988 level by the year 2010, and to reduce it to 70
percent of the level by 2020, according to Yu Shu-wei, director of the Center for
Environmental, Safety and Health Technology Development of the Industrial
Technology Research Institute of Taiwan. This goal can be achieved by modifying
the waste handling and recycling methods as well as the initial product design
standard. The Taiwanese government plans to use three environmental technology
parks and a budget of US$149 million for industries targeted at energy recycling and
environmental protection-related products. (Industrial Technology Research
Institute of Taiwan)
The World Commission on Environment and Development points it out that the
crises with the environment, economic development and energy are related. It
argues that "they are not separate crises: an environmental crisis, a development
crisis, an energy crisis. They are all one" (April, 1987). According to this statement,
we can solve the energy crises while working the environmental and developmental
problems, as well.
In order to save energy, to enhance air quality, and to ease global warming and
climate change, we should look towards using renewable or 'green' energy.
23
Governments set up plans to promote green industries by encouraging them to
adjust their structures and develop environmentally friendly, innovative, value-added
enterprises. Governments define new regulations, help the exchange and flow of
information, technological research and development. They also offer a sound
financial system for raising capital and recruiting talent to nurture start-up green
businesses. These efforts call for close cooperation between business and
governments, and with this joint effort, the development of green energy can be more
reliable in the near future.
2.5 Renewable Energy
The recent upward trend in the price of oil and natural gas has caused many
countries to reflect on the finite nature of fossil fuels and to take another look at
renewable sources. They are discovering that renewable energy technologies are
much better developed and reliable than those in the early 1970’s.
Several natural resources have been studied for hundreds of years. Other than
producing energy by burning fossil fuel or nuclear reaction, energy generated from
technologies and renewable resources such as the Sun, wind, hydropower, the
Earth’s natural heat and biomass. Because they provide energy that is renewable,
and produce less pollution, they are also called green energy.
24
Scientists have been developing techniques to harvest energy from natural
sources. For example, people build dams to accumulate water and transform the
hydropower to electric power, and the watermill has been used for centuries, to
irrigate farmland or grind barley. People also build windmills using wind energy,
and in the twentieth century, have adapted the design to incorporate electric power
generators. To make use of solar radiation, buildings are designed so that the passive
solar energy is used for lighting and heating. Some design features include large
south-facing windows, materials that absorb and slowly release the Sun's heat, and
solar heaters to heat either water or a heat-transfer fluid in collectors. Photovoltaic
solar cells, which were developed along with the space program and are made of
semi-conducting materials, directly convert sunlight into electricity. Similar to the
simplest cells used to power watches and calculators, the more complex systems can
light houses and even provide power to the electric grid.
Biomass technologies use renewable biomass resources to produce energy-
related products. The term "biomass" represents any organic matter available on a
renewable basis. For example, trees, agricultural food and feed crops, agricultural
crop wastes and residues, municipal wastes, and other waste materials can be used to
provide heat, chemicals or other energy products, including electricity, liquid, solid,
and gaseous fuels. Biomass technologies provide a way to use renewable energy in a
solid or liquid form for transportation purpose. The two most common bio-fuels are
ethanol and bio-diesel. Ethanol, an alcohol, is made by fermenting high-
carbohydrate biomass, like corn, and is mostly used as a fuel additive to cut down on
25
a vehicle's carbon monoxide and other smog-causing emissions. Bio-diesel is made
from vegetable oils, animal fats, algae, or even recycled cooking greases, and works
either as diesel additive to reduce vehicle emissions, or to fuel a vehicle by itself.
Biomass energy can be converted to electric power by direct-combustion
technology. According to U.S. Department of Energy, with ten giga-watts of
installed capacity and three percent of the primary energy production, bioenergy is
just second to hydropower in renewable U.S. primary energy production in the
United States.
Geothermal energy is the heat extracted from the Earth. It comes both from the
shallow ground, such as hot water or hot rock found within a few miles beneath the
Earth's surface, and from even deeper levels, the extremely high temperatures of the
molten rock called magma. Geothermal energy technologies use the heat of the
Earth for direct-use applications, geothermal heat pumps, and electrical power
production. For example, given a heat exchanger, a family can attach a heat pump
and transfer heat to the indoor air delivery system in the winter, and reverse the
process in the summer. Additionally, large underground reservoirs of hot water or
steam, which are heated by the magma underneath, can be captured for electrical
power production.
Zarnikau (2003) introduces several studies and also conducts a survey himself
about the consumer responses concerning the willingness to pay for electric utilities
generated by green resources. For an increase of $3 to $12 per month, many
26
residential energy consumers in the United States are willing to pay for minimal
environmental impact. More than 50% of consumers agree to pay at least $1 extra
toward their monthly electric bill for green energy. He also suggests that intensive
exposure to energy resource issues lead to an increased interest in paying modest
premiums to support utility investments in renewable energy and/or energy
efficiency.
In order to reduce greenhouse gas production and create a wider spectrum of
available energy resources, more government energy agencies must offer policies
suitable to promote renewable energy systems (Hass, 2004). Those policies may
come in the form of tax credits, guaranty selling tariffs, or reduced loan interest rates
on a variety of renewable energy systems. These policies will reduce the cost and
risk to whomever invests in the new energy system, as well as promote more project
possibility and encourage public acceptance and involvement.
This study will focus on the technology to harvest the energy from tides.
27
Chapter 3: Tide and Tidal Energy in Bay of Fundy
3.1 Tide
The Moon has been rotating around the Earth and the Earth has been rotating
around the Sun. As the Moon and the Earth rotate around the Sun, these celestial
bodies experience mutual attraction forces thus causing the Earth’s water to rise and
fall in a periodic manner. The tide is the composed of longest ocean waves and
usually rises and falls every half day or a day. The flooding period is when the tide
rises and water flows into the coastal basin, the reverse is the falling tide, it is also
called the ebb tide. Tidal flow is usually considered a coastal phenomenon because
it is noticeable by an observer in reference to the coast or other landmark. Thus, an
observer will describe a tide “flow in” during flood tide and “flow out” during ebb
tide. The change of water level due to tidal current occurs everywhere in the sea.
However, the change is most significant in the coastal zone due to the shallower
water depth in the coastal region.
The relationship between the cycles of the Moon and the tide has been known
since ancient times. High tides are highest and low tides are lowest when the Moon
is full or new, respectively. Additionally, the time of high tide and low tide is
usually related to the location of the Moon relative to the Earth. The Sun also has an
effect on the tide, even though it is not as dominant as the influence of the Moon.
After the publication of Issac Newton's “Principia” people knew more about the
relationship of tides and the Earth-Moon-Sun system. According to his theory, tides
28
on Earth are produced by the force of gravity from a massive astronomical body, like
the Sun or Moon, on large bodies of water. Depending on the location at the Earth’s
surface, the force moves the water to form a flood or ebb tide.
Brown, et al (1999) explains the concept of tide-producing force. The tide-
producing force at any point is a combination of gravitational force and centrifugal
force. Although the Sun’s mass is much larger than the Moon’s, the Moon is much
closer to the Earth, and the variation in the Moon's force across the Earth's diameter
is about two times larger than the variation in the Sun's force. Thus, the influence of
the Moon is considerably larger than that of the Sun. However, the pair of forces
aligns and combines to produce "spring" tides when the Moon is new or full, and
became unaligned to produce "neap" tides when the Moon is at first or third quarter.
To describe the strength of the tide, the difference in water elevation between high
tide and low tide is called the tidal range. Another factor having a substantial
influence on tidal ranges is the elliptical shape of the Moon's orbit. Although the
Moon is only 9 to 14% closer at its close point to Earth (perigee) than at its far point
(apogee), the gravitational force is inversely proportional to the square of the
distance. Adding up the centrifugal force in this Earth-Moon system, we can show
that the tide-producing force at one point on Earth is proportional to D
-3
, where D is
the distance between the position at the Earth’s surface and the Moon, and the
Moon's tidal influence is 30 to 48% greater at perigee than at apogee. In some
locations, where there is a large tidal range, we can observe that the perigee-apogee
influence of the Moon is greater than the spring-neap influence. Although the
29
variation of the Moon's distance is not readily apparent to observers viewing the
Moon directly, at certain locations, the large increase in the vertical tidal range
makes it obvious when the Moon is near perigee.
The position of the astronomical bodies relative to the Earth is periodic, as is the
influence of these bodies. In most locations, the tide rises and falls twice per day,
and called the semi-diurnal tide. Dronkers (1964) indicates that in part of the Gulf of
Mexico, the Gulf of St. Lawrence, the Indonesian Archipel, and the Chinese Sea, the
tides are irregular and diurnal during part of each month. In order to predict a tide at
a specific location, a harmonic method is developed. The harmonic method is the
most common method of predicting tidal high, and gets acceptable results. It is
based on the concept that the tide is the summation of the partial tides, and each
partial tide has its own period which corresponds to the period, or some component,
of certain astronomical movements, like Sun to Earth, Moon to Earth, or all three
together. For a specific point along either the coast line or the middle of sea, each
partial tide has a particular amplitude and phase. The phase represents the fraction of
the partial tidal cycle that has been passed at a reference point in time. Depending on
the period of component tide producing the force, strength and lag of the cycle at the
certain location, we are able to define the period, amplitude and phase for the
specific partial tide. By adding a great number of partial tides, the user gets a wave
form which is closer to the observed tide at a particular location. The accuracy of the
wave form is increased when more partial tides can be included in the sum, if the
record is sufficiently long to analyze the factors of these partial tides.
30
In order to get better results on tide predictions for important locations, including
the harbors, the amplitude and phase must be determined for as many as possible
partial tides. This usually requires a long history of observed tidal records covering
about 400 harmonic constituents which have been identified. Such a long record is
difficult to obtain and analyze to retrieve all the harmonic constituents. Since some
of the astronomical motions have a larger effect on tidal flows, a relatively good
approximation can be achieved by adding only a few major tide components. The
following table shows the most important partial tide for most locations, including
four semi-diurnal, three diurnal and two longer-period components.
Tidal Component Symbol Period (hours)
Principal lunar M2 12.42
Principal solar S2 12.00
Larger lunar elliptic N2 12.66
Semi-diurnal:
Luni-solar K2 11.97
Luni-solar K1 23.93
Principal lunar O1 25.82
Diurnal:
Principal solar P1 24.07
Lunar fortnightly Mf 327.86(13.66 days) Longer Period
Lunar monthly Mm 661.30(27.5 days)
Table 2: Major tidal components
31
Water elevation ( η ) can be represented as the following equation, assumed it is a
sum of all the partial tides:
∑
− + ⋅ = ) arg
2
cos(
i
i
i
t
T
a φ
π
η (3.1)
where arg: tide argument
i
φ : phase angle
i
T : period of each tide component
i
a : amplitude of each tide component
Among all the tidal components, M2, S2 of semi-diurnal partial tides and K1 of
diurnal tides are the most significant, since the amplitudes of these three tide
components are usually greatest and dominate the observed tides. However, there
are other factors which affect the propagation of tidal waves, and any one of the tidal
components may be dominant.
In addition to astronomical factors, the tides on Earth are strongly influenced by
the sizes, boundaries, and bathymetry of the costal basins and inlets. Typical tidal
ranges are about one or two meters, though there are regions in the oceans where
various influences cooperate to produce virtually no tides at all, and other regions
where the tides are greatly amplified. There are several locations where large tidal
ranges are observed: the Sea of Okhotsk and Korea’s west coast on northwest of
Pacific Ocean, the northern coast of Australia, the Bristol Channel on the west coast
32
of England, the Ungava Bay in northern Quebec, Canada, and the Bay of Fundy
between New Brunswick and Nova Scotia. The tidal ranges in these regions are of
the order of ten meters.
The highest tides on Earth occur in the Minas Basin, located at the eastern
extremity of the Bay of Fundy, where the average tidal range is 12 meters and can
reach 16 meters when various high tide-promoting factors occur concurrently.
33
3.2 The Bay of Fundy
Figure 9: The Bay of Fundy
Source: http://www.all-science-fair-
projects.com/science_fair_projects_encyclopedia/Bay_of_Fundy
34
The Bay of Fundy is located northeast of the state of Maine, between New
Brunswick and Nova Scotia, Canada, and is made up of two sections in the upper
zone: Chignecto Bay and Cobequid Bay (see Figure 9). It covers 620 square
kilometers (239 square miles), including 168 square kilometers (65 square miles) in
Minas Basin, Nova Scotia and 50 square kilometers (19.5 square miles) in Shepody
Bay, New Brunswick. The region is mostly intertidal mudflat and salt marsh around
the head of the Bay of Fundy, where tides rise and fall over 12-15 meters (36-45 feet)
twice daily. Sediments range from coarse sand to fine silt and clay (Museum of
Natural History, Nova Scotia). Most of the salt marshes have been drained for
agriculture.
Minas Basin, the northeast arm of the Bay of Fundy, is famous for being the
highest tidal range in the world. Bishop introduces a view of the surrounding area.
Wolfville, located on the southern shore of Minas Basin, offers the most dramatic
views of the tidal rise and fall, including vast areas of sea bottom uncovered by the
falling tide. These extensive intertidal mudflats provide a rich source of food for
many shorebirds in these areas. However, since the seventeenth century, Acadian
settlers have moved in and built dykes to convert tidal flats into rich farmland and
many of the original flats now lie behind man-made dykes. A tidal bore forms as the
incoming tide flows upstream against the freshwater of the river, and tumbles
upstream in some of the rivers which flow into Minas Basin (e.g. the Meander River
near Windsor, east of Wolfville, and the Shubenacadie River and Salmon River near
Truro).
35
The most significant tides or current activities are found around Cape Split. It is
located on the southern side of the entrance to Minas Basin, and, at its maximum
flow, experiences turbulence of the waters surging over the submarine ridges below
for a considerable distance. This maximum tidal current exceed eight knots (4m/s),
and the flow rate thru the deep, five kilometer-wide channel on the north side of
Cape Split is about four cubic kilometers per hour. This kind of current repeats itself
about three hours later in the opposite direction. In total, almost 14 billion tons (14
cubic kilometers) of muddy sea water flows into and out of Minas Basin every six
hours.
The primary cause of the immense tides at the Bay of Fundy is a resonance of the
Bay of Fundy-Gulf of Maine system at the tidal period. The area is bounded to the
north by the edge of the continental shelf and gradually increases in depth.
Researchers believe that the system has a natural period of approximately 13 hours,
which is close to the 12.42 hour period of the dominant lunar tide (M2) of the
Atlantic Ocean.
3.3 Tidal Power Development in Bay of Fundy
Given the significant tidal range, the Bay of Fundy is considered one of the
premier locations for the development of tidal power. Other than the 16-meter tidal
36
range, the surrounding environment and the social economic development of the
region are also encouraging the use of this green energy:
• Favorable topography
By the curving coast line and narrow channels, a tidal power plant can be
built with a relatively shorter barrage, minimizing the cost of construction.
• Predicted energy shortages
The surrounding area is not heavily populated, but it is estimated that the
population will grow significantly in the near future and increase the energy
demand further and in turn require new energy supply resources.
• Most hydroelectric potential has been developed
There are several rivers in the surrounding area with steep channels, which
have been suitable in yielding cheap energy through hydroelectric power
plants. Most of the hydro resources, however, have been developed and can
not supply the extra energy needed in the future.
• Rising fuel cost
In order to supply extra energy for the expected growth, The Bay of Fundy
and the surrounding area would need more fire power plants and heating oil if
a new energy source were not developed.
The government of Canada and the provincial governments of New Brunswick
and Nova Scotia began a comprehensive investigation in August, 1966 to analyse the
feasibility of developing a large scale tidal power plant in the area of the Bay of
37
Fundy. The investigations were reported by the Atlantic Tidal Power Programming
Board (ATPPB), and concluded that, although technically feasible, the proposed tidal
power plants could not exploit energy at a competitive cost to energy from traditional
sources. But the Programming Board also suggested that further studies should be
required when one or more of the following situations occurred, making a tidal
power plant economically feasible:
(i) the interest rate of construction loan drops sufficiently;
(ii) there is a major breakthrough in construction costs or in the cost of
generating the necessary equipment;
(iii) pollution abatement requirements magnify the cost of using alternative
sources of power;
(iv) alternative sources or more economic power supply become exhausted.
In February, 1972, when the cost of energy supply increased, the governments of
Canada, New Brunswick and Nova Scotia established the Bay of Fundy Tidal Power
Review Board (FTPRB) to make a critical review of the findings of the ATPPB.
FTPRB also recommended procedures for an appropriate reassessment of economic
feasibility.
The Review Board completed its preliminary study in September, 1974 and
indicated that tidal power had become significantly more economically competitive
since the 1969 report (FTPRB 1974). The Board's major concerns were based on the
significant changes in the international price of fuel oil and the trends in power
38
system development. Other than the requirements for a financial feasibility, they
also noticed additional merits that might attract tidal power development, such as
reduced air/water pollution and better energy management by reduce fossil-fire
energy production. Reductions in fossil-fired energy production would reduce
atmospheric and water pollution and increased oil and gas reserves which could be
diverted to more critical uses. However, the report also mentioned that the
transmission facilities were needed to support a tidal power project and more
interchange of power within and between power systems of eastern Canada.
Upon the recommendations of the Review Board, the governments of Canada
along with New Brunswick and Nova Scotia agreed in December, 1975 that it was in
the public interest for further investigation on the tidal power energy resource in the
Atlantic region and authorized a series studies. These studies were divided into two
phases. Phase I consisted of a series of technical and economic assessments aimed at
determining the competitiveness of tidal power and Phase II would include more
in-depth technical, environmental, economic and financial assessments of those
projects selected from Phase I. However, Phase II was planned to proceed only if
Phase I studies returned a positive project prospects. Both Phase I and II studies
included assessments of environmental implications, resource availability and related
socio-economic level of the surrounding area.
The Phase I studies required parallel consideration of five major interdependent
tasks. The tasks included:
39
1. Tidal power plant design;
2. Tidal power generation;
3. Market and system analysis for supply and transmission;
4. Socio-economic aspect;
5. Environmental aspect.
Within Phase I, all five tasks went through parametric interact analysis. At first,
tidal power plant and generation process was designed and compared to prospective
tidal power sites and schemes. They then used preliminary aspects of system and
market analysis to calculate the "at-site" and "at-market" costs of tidal energy and
systems costs, compared with displaceable energy from alternative sources. By
presenting the potential energy production and cost comparison, the studies provided
a progressive screening of tidal sites, and limited the possible sites/design to a
manageable number of representative projects for further analysis. Finally, the
environmental impact and social-economic aspect were studied for the representative
projects.
The Phase II studies, which were conducted given the economic competitiveness
of tidal power, were suggested to provide further review, and to help optimize the
most favorable project. The studies produced two economically viable sites--the
Cumberland Basin and Cobequid Bay--with the potential of producing up to 6,000
megawatts of economic electricity, based on the assumptions made.
40
Eventually the process was held up in the “review” phase and no project was
ever constructed. Because the proposed project was using the barrage type of design
(to be discussed later) for the tidal plant, the large construction fee for the barrage
and the large amount of capital investment required was the major reason for
delaying the project. As it turns out, the development of barrages for the generation
of tidal power is considered potentially hazardous to the surrounding ecosystem. At
the landward edge of the barrage, water supplies, flooding, drainage and tidal estuary
water quality could be affected. Additionally the new tidal regime, with a higher
mean headpond level, could decrease the dyke stability. Reduced tidal mixing in
estuaries behind the barrage may also accelerate water quality deterioration. Gordon
and Dadswell (1984) presents a report on the tidal power developments study at the
Cobequid Bay site, which is supported by the province of Nova Scotia. It indicated
that the tidal power developments will drastically alter tidal oscillation patterns and,
since then, no proposals have been under active consideration. Shepherd, et al. (1995)
writes that the long-term changes in sediment quality and distribution, which were
due to the construction of a causeway across the Petitcodiac River in Moncton, may
have contributed to the change of invertebrate fauna in the intertidal mudflats in that
area. As a result of studies similar to this, the Canadian Wildlife Service and the
New Brunswick Department of Natural Resources & Energy prepared a Protection
Plan for the New Brunswick and Nova Scotia sections of the Bay of Fundy
Shorebird Hemispheric Reserve. These plans concentrate on protecting important
41
shorebird roosting and feeding sites and surrounding lands. The environmental
aspect and ecopolicy finally delayed the development of tidal power.
Figure 10: Annapolis Tidal Generating Station
(www.annapolisroyal.com)
Although the large-scale tidal power plant discussed above has not yet been
successful, the Annapolis Tidal Generating Station located in the southeast region of
the Bay, was completed in 1984 (see Figure 10). It is one of three tidal power plants
42
in the world, and the first and only modern tidal plant in North America. It uses a
twenty-megawatt straflo turbine, the largest in the world, to produce power for 4,000
homes, or roughly one percent of Nova Scotia’s electrical power capacity. It was a
pilot project sponsored by the provincial and federal governments designed to
explore the potential of harnessing energy from the sea.
The reason of the Annapolis Tidal Generating Station was environmentally
successful is because it made use of a pre-existing causeway to form a headpond, and
uses the water stored in the headpond to generate power. Margaret Murphy, of Nova
Scotia Power, reported the good, uninterrupted sustainable performance of this plant,
but she also indicated that Nova Scotia would never build a tidal project like the one
at Annapolis Royal because of the environmental concerns.
The concerns about tidal power development however, are all related to the
barrage type of tidal power generation. The characteristic problems of barrage-type
projects are the inevitable disconnected pathway and its environmental/ecosystem
impact. Other concepts to develop tidal power are being studied, such as using the
kinematical energy from tidal currents, as opposed to the potential energy used in
barrage-type projects.
43
3.4 Types of Tidal Energy Development
There are two major types of tidal power plant design: the barrage type, using a
dam to divide a basin to be a headpond in order to store water and harvest energy
from the potential energy from the water; and the turbine type, deriving energy from
kinematical force in a tidal current.
3.4.1 Barrage Type of Tidal Power Plant
The barrage type of tidal power plant, like the one at Annapolis, works like a
river hydro power plant, with some differences in the activating forces. For example,
in a river hydro power plant, the downward-acting terrestrial gravitation causes the
water to flow on the Earth's surface, whereas with barrage tidal power plants, the
upward-acting lunar gravitation causes oscillations in the estuaries. Additionally,
there are differences in the hydraulics, machinery design and construction between
these two types of development. The power and energy, however, can be developed
at any tidal site or river dam depending upon the usable head which varies
continuously, the area of the basin, the capacity of the sluiceways used to fill or
empty the basin, the capacity of the generating units, and the method of operation.
44
3.4.1.1 Single Effect Operation
With a single basin or headpond, the sluices are closed until sea level reaches a
certain head range above the basin. Flow is then permitted through the turbines,
generating power. This is the simple operating principle of the old tidal mills and is
known as "single-effect" operation since power is generated in only one direction
(see Figure 11). To maximize energy production from a single-effect operation,
energy is typically generated on the ebb-tide instead of flood tide, when water flows
out of the headpond, because higher head range can be achieved in the upper level of
the basin.
45
Figure 11: Single Effect Operation
The energy output of this simple scheme can also be improved by pumping water
at appropriate times. For example, the water level of the basin can be raised by
pumping so that the basin stores more water with higher head, and then the energy
output can be increased. If the turbines are also designed to act as pumps, the
pumping operation works at or near high tide, while the basin is being filled through
the sluices, and for a short time after they have been closed. This way, little energy
is needed to lift the water from sea level to headpond near high tide, but a larger
amount of energy can be generated by the extra water with the larger head. Similar,
46
the level of the basin can be lowered further by pumping water from basin to sea at
or near ebb-tide. This would create additional filling capacity which would be
advantageous if energy were being generated as the basin was being filled. It will be
more profitable if such pumping is done during hours when relatively low-cost
energy is available from the power system.
3.4.1.2 Double Effect Operation
Turbines can be designed to operate not only in the basin-to-sea direction, but
also in the sea-to-basin direction, in addition to operating as pumps in either
direction. Thus, energy can be produced from the flow in both directions: during the
emptying and filling operations (Figure 10). The tidal power development installed
in the La Rance, France, possesses these capabilities. This plant is a "single-basin"
development with "double-effect" generation and "double-effect" pumping. Such an
operation is illustrated in Figure 12 for comparison with the "single-effect" operation.
47
Figure 12: Double Effect Operation
3.4.1.3 Single Basin or Multi-basin
The barrage type of plant can use single basin or two basins. Civil works for the
single-basin scheme are less complex and a shorter barrage can be constructed thus
making the project less costly. However, the single-basin concept of development
cannot produce firm capacity as the period of generation is limited by the times of
the tides which vary from day to day. It is possible that such a system could be
generating power at the time of low demand and low price.
48
Figure 13: Single Basin
Figure 14: Double Basin
49
The problem of discontinuous energy output from a single-basin scheme (Figure
13) can be overcome by the two-basin design. This development concept (Figure 14)
is possible when the coastal configuration is favorable to the creation of two basins.
The water level in the larger basin is held high and that in the other, low, with
generation always from the high to the low basin. The high basin is filled during high
tide through one set of gates, and the low basin emptied during low tide through
another set of gates. The major attraction of such a linked-basin arrangement is its
ability to generate continuous energy. A major drawback, however, is that the energy
production is less than that from a single-basin scheme using either of the basins
separately. Moreover, since the linked-basin scheme requires an interconnecting
waterway in which the power plant is located, as well as dyke and gate structures to
control the levels of each basin, it tends to be high in capital cost.
However, due to the fact that a barrage must block a large area of sea, the huge
environmental impact is inevitable. As with the Bay of Fundy project, this
environmental impact presents a substantial obstacle to the tidal power development.
When the idea of barrage type was put on hold, people started looking for another
form of tidal energy, that is, the energy from tidal current.
50
3.4.2 Tidal Current Turbine
Instead of harvesting energy from the potential energy lifted by a tidal range,
tidal turbines use the kinematical force of tidal current to rotate the turbine. Working
like a windmill under sea, the tidal turbines are turned by water movement and go
through a generator to make electricity. Compared to the air that acts on the
windmill, the density of seawater passing through a current turbine is about 800
times denser than the air. That is, a current turbine produces 800 times more energy
than a windmill with the same wind/current velocity, or, a current turbine requires
lower current velocity to produce the same amount of energy. Another benefit of
using tidal current, rather than wind, is the predictability factor, both in the time and
the velocity of the current at a certain location. A proper design of tidal turbine can
be made according to the data collected, and the performance can be more reliably
predicted.
51
Figure 15: Tidal current turbine
Source: http://www.marineturbines.com
Contrary to the construction of a barrage, a tidal current turbine does not require
the blocking of a waterway, and thus has less of an environmental impact and less
52
capital investment. Tidal turbines are already being tested in pilot projects off
England, Italy and on a small scale in the United States. One of the projects is
supported by Marine Current Turbines Ltd., in Bristol, England. Its tidal current
turbine (see Figure 15) occupies only a small section of seabed with an 11m diameter
rotor system. The rotors turn at a maximum speed of 15 rpm, and marine biologists
believe sea creatures can easily avoid the equipment. The company launched their
pilot offshore tidal energy turbine off the English coast in 2003 at a cost of almost
seven million US dollars, and the experimental turbine is capable of producing 300
kilowatts of electricity by the 2.7m/s (5.5 knot) current, enough to supply 200
households. According to its pilot project, the company suggests the requirements
for cost-effective power generation from tidal streams using their technology are a
mean spring peak velocity exceeding about 2.25 to 2.5m/s (4.5 to 5 knots) at a depth
of 20 to 30m. Based on the success of this project, the company plans to install a
one-megawatt commercial prototype in 2007 or 2008, which will start supplying
power to households.
3.4.3 Energy Storage
The output from both the barrage type of tidal power plant and the tidal current
turbine are constrained by the tide and may not produce power during the period of
highest demand. Thus, it is necessary to preserve the tidal output using an energy
storage device and meet the varying demand pattern. These energy storage devices
53
do not necessarily need to match the total output of the tidal power development, as
some of the energy can be used directly. Furthermore, when tidal power projects
become integrated into the large interconnected power system, continuity of supply
is assessed by the diversity of power sources feeding any given area. Once a tidal
power project is viewed simply as another system source, an appreciable portion of
the raw energy could be absorbed directly and displace thermal energy.
54
Chapter 4: Numerical Modeling
In order to find a better location with a larger tidal range or faster tidal current
and achieve the highest economic potential, this study uses numerical model to
simulate the response within the study area – Bay of Fundy.
4.1 Related Studies
Because of the significantly large tidal range in this region, several of numerical
studies have been conducted. Rao (1968) finds that the natural wave period of the
Bay of Fundy is close to the period of M2 tide. This explains the significant tidal
range in this region. Greenberg (1969) works on a finite difference model to study
the response of M2 tide in the Bay of Fundy. Lawton (1970) promotes the concept
of generating power by tide. His study shows that the tidal power generation is
feasible under some conditions. Greenberg, Shore and Shen (1997) develop a 3D
finite element model for Passamaquoddy Bay. Sankaranarayanan, and McCay (2003)
create a boundary-fitted coordinate hydrodynamic model for Saint John Harbour
region. Both of the recent papers study smaller regions with a more detail scale.
The studies show that the vertical circulation due to the tide is less significant than
the horizontal movement in this region, and a two dimensional model is sufficient to
be used here.
55
We can see that these studies were conducted base on wave with a single
wavelength. Because the tide can be considered as a summation of series of single-
wavelength tidal components, it is reasonable to study the tidal responses base on
one tidal component such as M2, the dominant tidal component. However, in order
to get a through study, a time series responses of this region is required.
4.2 Theoretical Framework
One of the major objections of the present study is to develop a mathematical
model using finite element methods (FEM) for solving shallow water equations in
order to simulate the current and water level in the Bay of Fundy. This study
chooses to use the finite element method because it is able to represent the
boundaries more efficiently than the conventional finite difference method. Finite
element method also presents variable resolution capabilities. Oceanographers,
especially in the tidal community use FE models to represent tidal interactions and
resonance which occur at different scales, from ocean basin to coastal inlets ( Connor
and Wang, 1974, Lynch and Gray, 1979, Walters and Cheng, 1979).
The physical processes of water movement can be expressed by a set of
equations derived from the conservation laws. The laws are the principles of
conservation of mass and conservation of momentum. Assuming a constant water
56
density, the set of equations governing the fluid flow in three dimensional space can
be expressed as (Crowe, et al, 2001):
1. Equation of continuity (conservation of mass)
0 =
∂
∂
+
∂
∂
+
∂
∂
z
w
y
v
x
u
(4.1)
2. Equation of motion (conservation of momentum)
bz
yz
xz zz
by
zy xy yy
bx
zx
yx
xx
F
z y x z
p
z
w
w
y
w
v
x
w
u
t
w
F
z y x y
p
z
u
w
y
v
v
x
v
u
t
v
F
z y x x
p
z
u
w
y
u
v
x
u
u
t
u
+
∂
∂
+
∂
∂
+
∂
∂
+
∂
∂
− =
∂
∂
+
∂
∂
+
∂
∂
+
∂
∂
+
∂
∂
+
∂
∂
+
∂
∂
+
∂
∂
− =
∂
∂
+
∂
∂
+
∂
∂
+
∂
∂
+
∂
∂
+
∂
∂
+
∂
∂
+
∂
∂
− =
∂
∂
+
∂
∂
+
∂
∂
+
∂
∂
τ
τ τ
ρ
τ τ τ
ρ
τ
τ
τ
ρ
) (
) (
) (
(4.2)
The independent variables are the three components of the spatial coordinate
system (x, y, z) and time t, and ρ is the water density. The dependent variables are:
u, v, w = velocity components in x, y, and z direction, and are
function of (x, y, z, t).
P(x, y, z, t) = pressure, the normal stress on a water element.
b
F (x, y, z, t) = body force exerts on a water element, in x, y, and z direction.
Although the water depth may vary in a gulf or bay, the wavelength of tide is
significantly larger than the water depth, thus allowing us to treat it as a shallow
57
water system. The physical processes are dominated by horizontal movement and
are relatively homogeneous in the vertical direction (z). Consequently, we can
average the variable in vertical direction and simplify the three dimensional system
to two dimensional.
This simplification also assumes the following condition:
1. The density of water is constant.
2. The pressure in the water is hydrostatic.
3. The shear stress by the vertical velocity is neglected.
4. Body force includes only gravity and Coriolis force.
5. The vertical distribution of velocity is constant.
In general, a property can be vertically averaged by the equation:
∫
=
H
dz t z y x m
H
t y x M
0
) , , , (
1
) , , ( (4.3)
where:
z = surface elevation in the vertical direction.
H = distance from bottom to the top.
m = dependent variable.
M = vertically-averaged dependent variable.
58
Applying this vertical average to our governing equations, the vertical dimension
will be simplified and the system becomes two-dimensional. The equations become
(Leendertse, 1970):
0 ) ( =
∂
∂
+
∂
∂
+
∂
∂
y
v
x
u
H
t
H
(4.4)
0 ) (
0 ) (
= − + +
∂
∂
+
∂
∂
+
∂
∂
+
∂
∂
= − + −
∂
∂
+
∂
∂
+
∂
∂
+
∂
∂
y
x
W v fu
y
g
y
v
x
u
v
t
v
W u fv
x
g
y
v
x
u
u
t
u
τ
ζ
τ
ζ
(4.5)
where all the dependent variables are vertically-averaged. f is the Coriolis
parameter,where:
f = 2 ωsin(latitude) (4.6)
and ω is the angular velocity vector for Earth’s rotation.
τ is the bottom stress and W is the shear stress at the water surface due to wind.
This set of equations is called “Shallow Water Equations” since they are working on
flow movement in a shallow water basin.
59
4.3 Numerical Model Development
The finite element method provides estimation of the entire study domain by the
sum of the response of each piece of the domain. If a functional requirement to the
shape function is given, the convergence of the solution can be achieved as the
subdomains are made infinitesimal. The size and the shape of the elements in a
finite element model are easily chosen and modified to fit the property of study
domain such as the water depth and complex domain boundary. In the Bay of Fundy,
water depth is from few meters in the coastal region at the north end of the bay to
several hundred meters at the mouth, and the coast line is very complex. A finite
element model is a suited choice to study the response of tidal waves in the Bay of
Fundy.
4.3.1 Related Studies
The shallow water equations are nonlinear, non-homogeneous, and hyperbolic,
with the three independent variables (x, y, and t) and three dependent variables
(water elevation, H, and velocity in x and y direction, u, v). Several studies have
been conducted using finite element methods to solve this set of equations. For
example, Grotkop (1973) uses Galerkin’s method with six nodes triangular element
to calculate the tidal oscillations in the North Sea. He used zero normal velocity at
each node as the boundary conditions on the solid boundary (coastal line), and no
60
specific velocity or elevation was assigned to the open boundary. Taylor and Davis
(1975) also apply Galerkin’s approach to formulate a finite element method model
for tidal propagation and dispersion study.
Connor and Wang (1974) replace the velocity variables in the governing
equations with unit transport variables and used an eddy viscosity coefficient for the
energy dissipation, helping to reduce the error in their numerical simulation. They
assumed the energy was reduced due to the internal friction force caused by turbulent
eddy. In this study, three approaches where compared for time integration, and it
was concluded that the Runge-Kutta method performed the best. Later on, they used
a time-stepping scheme which integrated surface elevation and velocity at different
time steps (Wang and Connor, 1975). They used triangular elements and Galerkin’s
approach. The tidal level or the normal flux across the boundary was used as
boundary conditions. It is found that the time-split scheme is stable even without the
eddy viscosity or Coriolis force. However, the size of the time step is limited by the
Courant condition.
Norton and King published an operation manual for their horizontal flow model,
RMA2 in 1978. This model used a vertically averaged continuity equation and the
modified two-dimensional Navier-Stokes equation. The model analyzes the pressure
by the hydraulic head, refers to as a datum, and presents shear stress induced by the
wind stress on the water surface and frictional stress on the bottom. The velocity
term is transformed into a flow transport rate per unit width. The program uses
61
either quadratic triangular elements (6 nodes) or quadratic quadrilateral elements (8
nodes), and the water level is calculated by the average of the corner points. The
dependent variables are expressed by a power series in time domain; they were used
it to obtain the time derivatives. The eddy viscosity serves as the damping force to
maintain the stability in the model and it is proportional to the size of the element.
In 1980, Walters and Cheng conducted several numerical experiments to test the
accuracy and sensitivity of the RM2 model with a smooth-curve-sided element.
They found that the boundary condition with a spatially constant water level across
an open boundary performed less accurately. They suggested setting up the water
level at only one point and assigning the direction of velocity on all other points
along the open boundary.
4.3.2 Galerkin’s Approach
Among the weighted residual methods, the Galerkin’s approach is most
commonly used. It generally offers better results and is easily implemented on a
computer.
When using this method, it is assumed that the dependent variable can be
calculated by a linear combination of shape functions:
Water surface elevation H :
62
∑
=
≅
N
j
j j
y x t H t y x H
1
) , ( ) ( ) , , ( φ (4.7)
and velocity vector:
∑
∑
=
=
≅
≅
N
j
j j
N
j
j j
y x t v t y x v
y x t u t y x u
1
1
) , ( ) ( ) , , (
) , ( ) ( ) , , (
φ
φ
(4.8)
Here
j
φ is the shape function defined by space domain. The shape function for
water elevation and velocity can be different from one another but in this study, the
same shape function is used for simplicity. By using Galerkin’s approach on
equation (4.5) and (4.6), and making the equations orthogonal to the shape function
j
φ , we get a set of nonlinear, ordinary differential equations in time domain:
0 ), , , ( ,
1
>= < + > <
∑
=
N
j
i c i j j
t y x F H
dt
d
φ φ φ i=1,2…N (4.9)
0 ), , , ( ,
0 ), , , ( ,
1
1
>= < + > <
>= < + > <
∑
∑
=
=
N
j
i mx i j j
N
j
i mx i j j
t y x F v
dt
d
t y x F u
dt
d
φ φ φ
φ φ φ
i=1,2…N (4.10)
and
) ( ) , , (
y
v
x
u
H t y x F
c
∂
∂
+
∂
∂
= (4.11)
63
y my
x mx
W v fu
y
g
y
v
x
u
v t y x F
W u fv
x
g
y
v
x
u
u t y x F
− + +
∂
∂
+
∂
∂
+
∂
∂
=
− + −
∂
∂
+
∂
∂
+
∂
∂
=
τ
ζ
τ
ζ
) ( ) , , (
) ( ) , , (
(4.12)
Where <> represent integration over entire spatial domain. ) , , ( t y x F
c
,
) , , ( t y x F
m
are force terms of the continuity equation and momentum equation.
4.3.3 Temporal approximation
From equations (4.9) and (4.10), we obtain a typical solution for a time
dependent ordinary differential equation. In order to obtain an approximation in the
time domain, finite Taylor series have been used. The finite Taylor series are Taylor
series in which the higher order terms are neglected.
Using the concept of finite Taylor series, the water level can be approximated in
the vertical averaged equations as follows:
n n n n n
t
H t
t
H t
t
H
t H H |
6
|
2
|
3
3 3
2
2 2
1
∂
∂ ∆
+
∂
∂ ∆
+
∂
∂
∆ + ≈
+
(4.13)
n n n n n
t
H t
t
H t
t
H
t H H |
6
|
2
|
3
3 3
2
2 2
1
∂
∂ ∆
−
∂
∂ ∆
+
∂
∂
∆ − ≈
−
(4.14)
where n represents time steps, and all other higher order terms are eliminated.
Subtract equation (4.14) by (4.13), we obtain:
64
n n n n
t
H t
t
H
t H H |
3
| 2
3
3 3
1 1
∂
∂ ∆
+
∂
∂
∆ + ≈
− +
(4.15)
If equation (4.15) is put into equation (4.7), we obtain:
>
∂
∂
<
∆
+ >
∂
∂
< ∆ + > >≈< <
− + i i i n i n
t
H t
t
H
t H H φ φ φ φ ,
3
, 2 , ,
3
3 3
1 1
(4.16)
Using the same approach for the velocity vector, we find
>
∂
∂
<
∆
+ >
∂
∂
< ∆ + > >≈< <
>
∂
∂
<
∆
+ >
∂
∂
< ∆ + > >≈< <
− +
− +
i i i n i n
i i i n i n
t
v t
t
v
t v v
t
u t
t
u
t u u
φ φ φ φ
φ φ φ φ
,
3
, 2 , ,
,
3
, 2 , ,
3
3 3
1 1
3
3 3
1 1
(4.17)
Equation (4.16) and (4.17) are the finite element forms of the continuity and
momentum equations by using Galerkin’s approach with centered-difference in time.
In equation (4.16) and (4.17), first order time derivative term
t
v
t
u
t
H
∂
∂
∂
∂
∂
∂
, , can be
obtained by equation (4.5), (4.6). Higher order terms can be obtained by taking the
time derivative of them. The higher order terms of water level:
) ( ) ( ) ( ) (
] ) )( ( 4 ) ( 2 ) ( 2 [
2
2
2
2
2 2
2
2
2
2
2 2
2
2
y
W
x
W
H
y
v
x
u
H
x
v
y
u
fH
y x
gH
y x
u
v
y x
v
u
y
v
v
x
u
u
y
v
x
u
y
v
x
u
H
t
H
y
x
∂
∂
−
∂
∂
−
∂
∂
+
∂
∂
+
∂
∂
−
∂
∂
+
∂
∂
+
∂
∂
+
∂ ∂
∂
+
∂ ∂
∂
+
∂
∂
+
∂
∂
+
∂
∂
∂
∂
+
∂
∂
+
∂
∂
=
∂
∂
τ
ζ ζ
(4.18)
65
and
)
1
( )
1
(
2
2
2
2
3
3
t
H
H t
H
t
H
H t
H
t
H
∂
∂
∂
∂
+
∂
∂
∂
∂
=
∂
∂
(4.19)
where
) ( ) ( ) (
) ( ) ( ) (
) ( ) (
) )( ( 4
)
1
(
2
2
2
2 2 2 2 2
2
2
2
2
2
2
2
2
2
2
y
W
x
W
t t
v
y t
u
x t
v
x t
u
y
f
t y x
g
t
u
y x
v
y x
u
t
v
t
v
y x
u
y x
v
t
u
t
v
y
v
y
v
t
v
t
u
x
u
x
u
t
u
t
v
y t
u
x y
v
x
u
t
H
H t
y
x
∂
∂
+
∂
∂
∂
∂
−
∂
∂
∂
∂
+
∂
∂
∂
∂
+
∂
∂
∂
∂
−
∂
∂
∂
∂
+
∂
∂
∂
∂
+
∂
∂
+
∂
∂
∂ ∂
∂
+
∂ ∂
∂
∂
∂
+
∂
∂
∂ ∂
∂
+
∂ ∂
∂
∂
∂
+
∂
∂
∂
∂
+
∂
∂
∂
∂
+
∂
∂
∂
∂
+
∂
∂
∂
∂
+
∂
∂
∂
∂
+
∂
∂
∂
∂
∂
∂
+
∂
∂
=
∂
∂
∂
∂
τ
ζ
(4.20)
Using the same method we can calculate the higher order terms for velocity in x-
direction:
t
W
t
u
t
v
f
t x
g
t
v
y t
u
x
u
y
v
x
u
t
u
t
u
x
∂
∂
+
∂
∂
−
∂
∂
+
∂
∂
∂
∂
−
∂
∂
∂
∂
+
∂
∂
∂
∂
−
∂
∂
+
∂
∂
∂
∂
− =
∂
∂
τ
ζ
) ( ) (
2
2
(4.21)
) ( ) ( 2 ) (
2
2
2
2
2
2
3
3
t
v
y t
u
x
u
t
v
y t
u
x t
u
y
v
x
u
t
u
t
u
∂
∂
∂
∂
+
∂
∂
∂
∂
−
∂
∂
∂
∂
+
∂
∂
∂
∂
∂
∂
−
∂
∂
+
∂
∂
∂
∂
− =
∂
∂
66
2
2
2
2
2
2
2
2
t
W
t
u
t
v
f
t x
g
x
∂
∂
+
∂
∂
−
∂
∂
+
∂
∂
∂
∂
− τ
ζ
(4.22)
and in y- direction:
t
W
t
v
t
u
f
t y
g
t
v
y t
u
x
v
y
v
x
u
t
v
t
v
y
∂
∂
+
∂
∂
−
∂
∂
−
∂
∂
∂
∂
−
∂
∂
∂
∂
+
∂
∂
∂
∂
−
∂
∂
+
∂
∂
∂
∂
− =
∂
∂
τ
ζ
) ( ) (
2
2
(4.23)
) ( ) ( 2 ) (
2
2
2
2
2
2
3
3
t
v
y t
u
x
v
t
v
y t
u
x t
v
y
v
x
u
t
v
t
v
∂
∂
∂
∂
+
∂
∂
∂
∂
−
∂
∂
∂
∂
+
∂
∂
∂
∂
∂
∂
−
∂
∂
+
∂
∂
∂
∂
− =
∂
∂
2
2
2
2
2
2
2
2
t
W
t
v
t
u
f
t y
g
y
∂
∂
+
∂
∂
−
∂
∂
−
∂
∂
∂
∂
− τ
ζ
(4.24)
where
) ( ) ( ) ( ) (
) ( ) (
) )( ( 2 ) ( ) (
2
2
2
2
2
2
2 2
2
2
2
2
2 2
2
2
2
2
2
2
y
W
x
W
t t
v
y t
u
x t
u
y t
v
x
f
y x t
g
t
u
y x t
v
y
v
t
v
y x t
u
x
u
y
v
x
u
t
v
y t
u
x y x
u
y
v
t
v
y x
v
x
u
t
u
t
v
y t
u
x
y
x
∂
∂
+
∂
∂
∂
∂
+
∂
∂
∂
∂
+
∂
∂
∂
∂
−
∂
∂
∂
∂
−
∂
∂
∂
∂
+
∂
∂
+
∂
∂
∂
∂
−
∂
∂
∂ ∂
∂
+
∂
∂
∂
∂
−
∂
∂
∂ ∂
∂
+
∂
∂
∂
∂
−
∂
∂
+
∂
∂
∂
∂
∂
∂
+
∂
∂
∂
∂
−
∂ ∂
∂
+
∂
∂
∂
∂
−
∂ ∂
∂
+
∂
∂
∂
∂
− =
∂
∂
∂
∂
+
∂
∂
∂
∂
τ
ζ ζ
(4.25)
All the components in equation (4.18) to (4.25) can be obtained as follows:
67
x
W
x
u
x
v
f
x
g
y x
v
x
u
u
y
v
x
u
x
u
t
u
x
x
∂
∂
+
∂
∂
−
∂
∂
+
∂
∂
−
∂ ∂
∂
+
∂
∂
−
∂
∂
+
∂
∂
∂
∂
− =
∂
∂
∂
∂
τ
ζ
2
2 2
2
2
) ( ) (
(4.26)
2
2
2
2
2
2
3
3
2
3
3
3 2
2
2
2
2
2
2
) ( ) ( 2 ) (
x
W
x
u
x
v
f
x
g
y x
v
x
u
u
y x
v
x
u
x
u
y
v
x
u
x
u
t
u
x
x
∂
∂
+
∂
∂
−
∂
∂
+
∂
∂
−
∂ ∂
∂
+
∂
∂
−
∂ ∂
∂
+
∂
∂
∂
∂
−
∂
∂
+
∂
∂
∂
∂
− =
∂
∂
∂
∂
τ
ζ
(4.27)
y
W
y
v
y
u
f
y
g
y x
u
y
v
v
y
v
x
u
y
v
t
v
y
y
∂
∂
+
∂
∂
−
∂
∂
−
∂
∂
−
∂ ∂
∂
+
∂
∂
−
∂
∂
+
∂
∂
∂
∂
− =
∂
∂
∂
∂
τ
ζ
2
2 2
2
2
) ( ) (
(4.28)
2
2
2
2
2
2
3
3
2
3
3
3 2
2
2
2
2
2
2
) ( ) ( 2 ) (
y
W
y
v
y
u
f
y
g
y x
u
y
v
v
y x
u
y
v
y
v
y
v
x
u
y
v
t
v
y
y
∂
∂
+
∂
∂
−
∂
∂
−
∂
∂
−
∂ ∂
∂
+
∂
∂
−
∂ ∂
∂
+
∂
∂
∂
∂
−
∂
∂
+
∂
∂
∂
∂
− =
∂
∂
∂
∂
τ
ζ
(4.29)
68
y x
W
y x
u
y x
v
f
y x
g
y x
u
y x
v
u
x
u
y x
v
y
u
y
v
y x
u
x
u
y
v
x
u
y x
u
t
u
y x
x
∂ ∂
∂
+
∂ ∂
∂
−
∂ ∂
∂
+
∂ ∂
∂
−
∂ ∂
∂
+
∂ ∂
∂
−
∂
∂
+
∂ ∂
∂
∂
∂
−
∂
∂
+
∂ ∂
∂
∂
∂
−
∂
∂
+
∂
∂
∂ ∂
∂
− =
∂
∂
∂ ∂
∂
2 2 2
2
3
2
3
2
3
2
2 2
2
2 2 2
2
) ( ) ( ) ( ) (
τ
ζ
(4.30)
y x
W
y x
v
y x
u
f
y x
g
y x
u
y x
v
v
x
u
y x
v
y
v
y
v
y x
u
x
v
y
v
x
u
y x
v
t
v
y x
y
∂ ∂
∂
+
∂ ∂
∂
−
∂ ∂
∂
−
∂ ∂
∂
−
∂ ∂
∂
+
∂ ∂
∂
−
∂
∂
+
∂ ∂
∂
∂
∂
−
∂
∂
+
∂ ∂
∂
∂
∂
−
∂
∂
+
∂
∂
∂ ∂
∂
− =
∂
∂
∂ ∂
∂
2
2 2
2
3
2
3
2
3
2
2 2
2
2 2 2
2
) ( ) ( ) ( ) (
τ
ζ
(4.31)
For a forward difference approximation, we can generate the relationship of each
time step by substituting the Taylor series expansion into equation (4.5) and (4.6):
>
∂
∂
<
∆
+ >
∂
∂
< ∆ + > >≈< <
+ i i i n i n
t
H t
t
H
t H H φ φ φ φ ,
2
, , ,
2
2 2
1
(4.32)
>
∂
∂
<
∆
+ >
∂
∂
< ∆ + > >≈< <
+ i i i n i n
t
V t
t
V
t V V φ φ φ φ ,
2
, , ,
2
2 2
1
(4.33)
Equation (4.32) and (4.33) show a one step, explicit scheme for two time step.
69
Using the weighted residual method to calculate dependent variables, such as H
or V, in the time domain, we have:
∫
= + +
⋅
0 }) }{ { } }{ ]{ [ } }{ ]{ ([ dr F H K H m W
i
ψ ψ ψ i=1,2…N
(4.34)
∫
= + +
⋅
0 }) }{ { } }{ ]{ [ } }{ ]{ ([ dr F V K V m W
i
ψ ψ ψ (4.35)
where
∑
=
=
N
i
i i
t H t H
1
) ( ) ( ψ
∑
=
=
N
i
i i
t V t V
1
) ( ) ( ψ
i
H and
i
V = nodal value at time i.
i
ψ = shape function
i
W = weight function.
When using a linear time element between two nodal values at time step (n) and
(n+1), the shape function for each element can be gotten in the local coordinate
system:
ξ ψ
ξ ψ
=
− =
+1
1
n
n
and
t
t
n
n
∆ =
∆ − =
+
/ 1
/ 1
1
ψ
ψ
&
&
(4.36)
when t t ∆ = / ξ and 1 0 ≤ ≤ ξ
70
Put (4.26) into (4.24), we have:
) 1 ( } { } { } )){ 1 ]( [ / ] ([ } ){ ] [ / ] ([
1 1
θ θ θ θ − + − − − ∆ = + ∆
+ + n n n n
F F H K t M H K t M
(4.37)
with
∫ ∫
=
1
0
1
0
/ ξ ξ ξ θ d w d w
i i
Similar calculations can be made for velocity vector (V).
If we use a forward scheme and collect value at time step (n), then 0 = θ .
Equation (4.37) becomes:
t F H K H M H M
n n n n
∆ + − =
+
) } { } ]{ ([ } ]{ [ } ]{ [
1
(4.38)
and
t F v K v M v M
t F u K u M u M
n n n n
n n n n
∆ + − =
∆ + − =
+
+
) } { } ]{ ([ } ]{ [ } ]{ [
) } { } ]{ ([ } ]{ [ } ]{ [
1
1
(4.39)
This is the temporal frame that is used in this study.
71
4.4 Hydrodynamic Simulation at Bay of Fundy
The hydrodynamic model was applied for the Bay of Fundy to compute the tidal
response. The study area extends from the entrance of The Bay of Fundy to
Chignecto Bay and Cobequid Bay/Minas Basin (see Figure 9). This region has been
considered for possible basins for tidal power projects since 1930. The water depth
is shallow relative to the tide, thus making the vertically averaged shallow water
equations appropriate for the hydrodynamic model for this region. Furthermore, the
very irregular coastline or the system boundary necessitates the use of finite element
analysis.
4.4.1 Field Observation Data
The bathymetric data was collected from the navigation chart published by
Canadian Hydrographic Service, Minister of Fisheries and Oceans Canada, 1990.
The shore line and water depth were matched as closely as possible to prevent any
possible distortion. Figure 16 is a contour map showing the water depth in the Bay
of Fundy. The unit for X and Y coordinates is kilometers and the water depth is in
meters. From this figure, the water depth of the Bay of Fundy is deeper in the mouth
and center of the bay and gradually decreases when it approaches the north and the
coastal line. The cross section area of the Bay also decreases and then divides into
72
two major basins–Chignecto Bay in the northwest side and Minas Basin/Cobequid
Bay on the northeast side.
Figure 16: Water depth of Bay of Fundy
73
Tidal information was taken from The Bay of Fundy Tide Tables by Canadian
Hydrographic Service, and from the home page of Canadian Hydrographic Service
(CHS).
As Canada's national data center, the Marine Environmental Data Service
(MEDS) acquires and processes tide and water level database for CHS. MEDS
collects tidal data through several of tidal stations around the Gulf of St. Lawrence
and the costal zone of the Atlantic Ocean. Table 3 shows the locations of tidal
stations and data available during the past years. It shows that most tidal stations did
not operate continuously and caused several gaps in the observation data. However,
CHS’s web site provides predicted times and heights of high and low waters, and the
hourly water levels for over seven hundred stations in Canada. The predicted tidal
data are processed based on the data collected by MEDS and by the method
described in section 3.1. Thus, the predicted tidal data is influenced only by tides
and without any impact from meteorological conditions such as atmospheric pressure
changes, strong prolonged winds or variations of freshwater discharge. This is good
for the present research because the variable meteorological conditions will not be
sustained and would have to be removed to simulate a tidal response in the study
region.
74
Station Station Name LAT. LONG. Duration of Data
10 NORTH HEAD 44.76 66.75
1964/09/10~1964/10/09,
2006/06/22~2006/08/15
102 MACDONALD POINT 45.72 66.05 1970/06/21~1970/07/31
103 CAMBRIDGE NARROWS 45.83 65.95 1970/06/21~1970/07/27
105 GAGETOWN 45.77 66.13 Several periods between 1913 and 1970
108 Upper Gagetown 45.85 66.23 Several periods between 1965 and 1969
114 MAUGERVILLE 45.87 66.47 Several periods between 1965 and 1970
120 FREDERICTON 45.97 66.65 Several periods between 1913 and 1969
122 NEWCASTLE CREEK 46.07 66.00 Several periods between 1965 and 1969
124 JEMSEG 45.83 66.12 Several periods between 1966 and 1970
140 HERRING COVE 45.57 64.97 1960/08/24~1960/09/22
170 HOPEWELL CAPE 45.85 64.58 Several periods between 1898 and 1965
172 BELLIVEAU VILLAGE 45.93 64.62 1968/07/14 to 30
173 DOVER 45.98 64.68 1968/07/14 to 29
174 DIEPPE (IRVING WHARF) 46.10 64.77 1968/07/14 to 30
175 MONCTON 46.08 64.77 1898/08/04~18, 1920/09/01~16
176 MONCTON (CAUSEWAY) 46.07 64.82 1968/07/13 to 30
215 TWO RIVERS COVE 45.68 64.47 1919/06/27~1919/07/28
240 CAPE D'OR 45.30 64.78 Several periods between 1965 and 1980
242 SPENCERS ISLAND 45.33 64.70 Several periods between 1980 and 1983
247 DILIGENT R. 45.40 64.45 1965/08/01~1965/10/08
260 FIVE ISLANDS 45.38 64.13
1965/06/03~1965/08/09,
1965/09/16~1965/10/25
270 BURNTCOAT HEAD 45.30 63.80 Several periods between 1916 and 1975
280 WINDSOR 44.98 64.15 1975/07/31~1975/09/03
282 HANTSPORT 45.07 64.17 1969/09/19~1969/10/31
289 BLOMIDON 45.27 64.35 1965/06/04~1965/07/03
30 LETITE HARBOUR 45.05 66.87 Several periods between 1957 and 1972
312 ILE HAUTE 45.25 65.00 1976/04/26~1976/07/30
315 MARGARETSVILLE 45.05 65.07
1961/07/28~1961/08/12,
1965/06/22~1965/08/26
320 PARKERS COVE 44.80 65.53 Several periods between 1970 and 1992
324 Digby Ferry Wharf 44.66 65.76 Several periods in 2003 and 2004
325 DIGBY 44.63 65.75 Several periods between 1898 and 2006
327 ANNAPOLIS ROYAL 44.75 65.52 1987/05/21 to 26
Table 3 Tidal stations of MEDS in the Gulf of St. Lawrence
75
Station Station Name LAT. LONG. Duration of Data
330 CULLODEN 44.67 65.83
1963/06/20~1963/07/20,
1964/08/19~1964/10/17
333 GRAND EDDY 44.40 66.20 1966/06/18~1966/07/13
334 TROUT COVE 44.55 66.03 1965/05/16~1965/09/09
335 SANDY COVE 44.50 66.10 1966/04/22~1966/07/13
336 EAST SANDY COVE 44.48 66.08 1966/05/10~1966/07/18
337 TIVERTON 44.38 66.22 1966/01/01~1966/11/17
338 TIVERTON (BOARS HEAD) 44.40 66.22 1966/01/01~9, 1966/05/01~1966/10/30
339 WEST NARROWS 44.40 66.22 1966/04/26~1966/07/19
340 WESTPORT 44.27 66.35 1966/05/22~1966/07/21
345 LIGHTHOUSE COVE 44.25 66.40 2006/06/01~2006/09/07
40139 CHIGNECTO 45.48 64.98 1976/08/18~1976/11/10
40160 GRINDSTONE (INSHORE 3) 45.72 64.60 1976/04/29~1976/07/29
40217 CUMBERLAND BASIN 45.67 64.52 1976/11/01 ~ 07
40258 MINAS BASIN (INSHORE 4) 45.32 64.20 1976/04/28~1976/07/26
40262 ECONOMY (INSHORE 5) 45.32 63.90 1976/04/28~1976/07/27
40264 COBEQUID BAY STN. 6 45.37 63.73 1976/04/28~1976/07/27
42 BLACKS HARBOUR 45.05 66.80 1986/09/12~1986/10/29
46 WEST DIPPER HARBOUR 45.10 66.43 Several periods between 1965 and 1988
52 FIVE FATHOM HOLE 45.18 66.27 2001/05/08~2001/07/03
53 MUSQUASH HARBOUR 45.15 66.25
1988/05/21~1988/06/09,
2001/05/01~2001/06/28
55 LORNEVILLE 45.18 66.15 1988/05/19~1988/06/07
65 SAINT JOHN 45.25 66.06 Several periods between 1896 and 2007
75 INDIANTOWN 45.27 66.08 Several periods between 1907 and 1970
85 KENNEBECASIS BAY 45.40 66.00 Several periods between 1912 and 1969
89 WESTFIELD BEACH 45.35 66.22 Several periods between 1965 and 1969
96 OAK POINT 45.52 66.08 Several periods between 1966 and 1970
97 HATFIELD POINT 45.62 65.92 Several periods between 1965 and 1970
98 EVANDALE 45.60 66.03 Several periods between 1965 and 1969
99 BELLE ISLE BAY 45.65 65.87 1970/05/27~1970/06/12
Table 3: Tidal stations of MEDS in the Gulf of St. Lawrence, continued
76
A Google Earth map of the region being simulated is shown in Figure 17.
Several reference locations have been indicated as key locations referred in tide
tables and CHS’s website. There are five tidal stations at the mouth of the Bay of
Fundy.
1. Wood Island is located at the west side of the mouth and close to Grand
Manan Island. The tide station Outer Wood Island is an offshore tidal station
located on the southeast side of Wood Island,
2. North Head is located north of Wood Island, and it is at the northeast coast of
Grand Manan Island,
3. Lighthouse Cove is on the east side of the mouth of the Bay,
4. Tiverton is also on the east side of the mouth of the Bay, north of Lighthouse
Cove,
5. Yarmouth is on the southwest coast of Nova Scotia which is located at west of
the line connecting Lighthouse Cove and Wood Island.
77
Figure 17: Reference points in the Bay of Fundy
Source: Google Earth
Figure 18 shows the tidal records between December 14 and December 20, 2006
at the mouth of the Bay of Fundy for five indicated stations. By comparing of the
data from five stations, we see that Lighthouse Cove and Tiverton have similar tidal
responses as the Outer Wood Island station. The present numerical model assumes
that the tidal elevations are the same for the locations between Wood Island and
78
Lighthouse Cove (the mouth of the bay), and uses the tidal elevation in this strip
zone to represent the incident tide.
12/14 - 12/20/2006
0.00
2.00
4.00
6.00
8.00
0 20 40 60 80 100 120 140 160 180
hours
m
Lighthouse Cove (Station #345) Tiverton, South Entrance (Station #337) Yarmouth (Station #365)
Outer Wood Island (Station #1) North Head (Station #10)
Figure 18: Tidal records at the mouth of the Bay of Fundy between 12/14 and 12/20/2006
Six reference tidal stations have been chosen for the calibration and verification
of the numerical model. Dipper Harbour and Saint John are the major cities and
harbor on the north/west bank of the bay. St. Martins is also located on the
north/west bank and before the entrance of Chignecto Bay. Scots Bay is located at
outside of Minas Channel and the entrance of Cobequid Bay/ Minas Basin, where
Isle Haute is in the middle of the Bay of Fundy. They measure the tide before it
transfers into the smaller bays. In the middle of the Cobequid bay, on the south bank,
79
Burntcoat Head monitors the tide at the end of the bay. This region is one of the
proposed tidal plant sites in 60’ and 70’.
Two sets of tidal elevation record are presented in Figure 19 and 20 to show the
change of tidal range at the reference points in the Bay of Fundy. These data have
also been used to calibrate and verify the numerical simulation model. Days with a
relatively uniform tide are chosen, from December 14 to December 20, 2006 (Figure
19). The second set of tidal records taken from February 23 and March 1, 2006 is
shown in Figure 20. It is seen from Figure 20 that the tidal ranges start small and
grow bigger with time.
12/14-12/20/2006
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
0 20 40 60 80 100 120 140 160 180
hours
m
Lighthouse Cove Dipper Harbour St. John St. Martins Scots Bay Burntcoat Head Isla Haute
Figure 19: Tidal records between 12/14 and 12/20/2006
From these records it is seen that the tidal range in Lighthouse Cove is about
three to four meters at the beginning of data and it gradually increases to eight to 11
80
meters at Burntcoat Head during December 14 to December 20, 2006. From Figure
20, it is seen that the tidal range in Lighthouse Cove is about three to six meters and
gradually increases to ten to 16 meters at Burntcoat Head during February 23 and
March 1, 2006.
2/23-3/1/2006
0
2
4
6
8
10
12
14
16
18
0 20 40 60 80 100 120 140 160 180
hours
m
Lighthouse Cove Dipper Harbour West Saint John Isle Haute St. Martins Scots Bay Burntcoat Head
Figure 20: Tidal records between 2/23 and 3/1/2006
4.4.2 Numerical Simulation
For the present study, linear triangular elements are used; this provides increased
geometrical flexibility. The sketch in Figure 21 shows the property zones. The
study region is divided into several property zones. The properties such as the
Manning coefficient or grid size for nodal points or elements in each zone are
specified using the available topographical information. A grid system with a total
of 8008 elements with 4363 nodal points is used to model the entire study area, this
81
is presented in Figure 22. The element size and time step are chosen to be small
enough to adequately describe any possible shorter period (higher frequency)
oscillation. Each triangle in the grid is also made as equilateral as possible for a
better approximation.
Figure 21: Property zones
82
Figure 22: Grid layouts for numerical simulation
The bottom stress term can be expressed as a function of bottom roughness,
velocity components, water depth and the Manning’s roughness (n) as follows (see
Lee et al, 1985):
2 2 3 / 1 2
v u H gn + =
−
τ (4.40)
83
where n is the Manning’s coefficient. The value for Manning’s coefficient has
been given in textbooks with a range of 0.025 and 0.05 (sec
3 / 1
m ) depending on the
bed form and material describing the sea bottom (Brater et al, 1996). In order to get
a better result, Manning coefficient was assigned for each of the nodes. For model
calibration, simulated runs are conducted by varying the value of n. The simulation
result is compared with the tidal data at some key tidal stations (reference points)
until the simulation result agree well as the measure data. In this study, several n
values have been tested with the largest value of n=0.055 at some regions to maintain
the stability of the program.
Along the mouth of the Bay, the water level is assigned for each node along the
open boundary line. The water level information is given every 10 or 15 minutes
and then interpolated using cubit spine distribution at each time step. In this way, the
water level information can be given as real water level and the program simulates a
real-time response.
A fixed boundary is set up along the coastline and a zero normal flow condition
is applied at the coastal line.
84
4.4.3 Simulation Result
Results from the simulation are shown in Figures 23 and 24. The water level was
recorded at selected nodes, which refer to the reference stations where the tidal data
is provided. Since the reference level (water level = 0) of the tidal data from tidal
gauge stations refers to lower low water level, the simulation result from the
numerical model is shifted to compare with the record from the tidal gauge stations.
The unit used for the water level is in meters; the tidal ranges selected here can be
easily converted to an amplification factor for each tidal gauge station relative to the
tidal height at the entrance wave of the Bay.
4.4.3.1 Simulation Result between 12/14 and 12/20/2006 (for calibration)
The numerical simulation result was used to calibrate the model by comparing
with the tide data for the period December 14 and December 20, 2006 at the
reference points. Through trial and error, the Manning’s coefficient in each node has
been modified and the final result is as shown. One node close to the entrance of the
Bay is monitored and compared to tidal station at Lighthouse Cove to verify the
accuracy of input data along the open boundary (the tidal elevation along the
entrance of Bay of Fundy.)
85
0
1
2
3
4
5
6
0 20 40 60 80 100 120 140 160 180
model Lighthouse Cove (Station #345)
Figure 23- a: Simulation Result at the entrance of bay between 12/14 and
12/20/2006
0
1
2
3
4
5
6
7
8
0 20 40 60 80 100 120 140 160 180
model Dipper Harbour West (Station #46)
Figure 23- b: Simulation Result at the Dipper Harbour between 12/14 and
12/20/2006
0
1
2
3
4
5
6
7
8
0 20 40 60 80 100 120 140 160 180
model Saint John (Station #65)
Figure 23- c: Simulation Result at St. John between 12/14 and 12/20/2006
0
2
4
6
8
10
12
0 20 40 60 80 100 120 140 160 180
model Isle Haute (Station #312)
Figure 23- d: Simulation Result at Isle Haute between 12/14 and 12/20/2006
86
0
1
2
3
4
5
6
7
8
9
10
0 20 40 60 80 100 120 140 160 180
model St. Martins (Station #129
Figure 23- e Simulation Result at St. Martins between 12/14 and 12/20/2006
0
2
4
6
8
10
12
0 20 40 60 80 100 120 140 160 180
model Scots Bay (Station #300
Figure 23- f: Simulation Result at Scots Bay between 12/14 and 12/20/2006
0
2
4
6
8
10
12
14
16
0 20 40 60 80 100 120 140 160 180
model Burntcoat Head (Station #270
Figure 23- g: Simulation Result at Burntcoat Head between 12/14 and
12/20/2006
Comparing with the simulation results with the measured tide data it is seen that
the computer simulation result is very close to the tidal station’s record at most of the
87
reference points. Most error occurs at Burntcoat Head. It should be noted that the
error is due to Burntcoat Head’s location deep inside the Cobequid Bay and is
connected to The Bay of Fundy by a narrow entrance – Minas Channel. With such
complicated coastline, narrowing and shallowing influences, it is expected that more
deviation could occure between the simulation results and measured data. However,
the error of the result at Burntcoat Head is less than fifteen percent, which is
acceptable since the results at all other reference points are very close.
4.4.3.2 Simulation Result between 2/23 and 3/1/2006 (for verification)
After the model has been calibrated, another set of data is used to verify the
numerical model to see if the model is capable of extending its simulation. The set
of data which is chosen to verify the model possess a different pattern from the one
which is chosen to calibrate the model. Since the data set used for calibration is
pretty much uniform with similar tidal range in each cycle, tidal data between
February 23 and March 1, 2006 has been chosen since it has more variances in the
tidal range within the specified time period. The model results and the measured tide
for the period of February 23 to March 1, 2006 are shown in Figures 24 for seven
tidal stations.
88
0
1
2
3
4
5
6
7
0 20 40 60 80 100 120 140 160 180
model Lighthouse Cove
Figure 24- a Simulation Result at entrance of the bay between 2/23 and 3/1/2006
0
2
4
6
8
10
0 20 40 60 80 100 120 140 160 180
model Dipper Harbour West
Figure 24- b Simulation Result at Dipper Harbour between 2/23 and 3/1/2006
0
2
4
6
8
10
0 20 40 60 80 100 120 140 160 180
model Saint John
Figure 24- c Simulation Result at St. John between 2/23 and 3/1/2006
89
0
2
4
6
8
10
12
14
0 20 40 60 80 100 120 140 160 180
model Isle Haute
Figure 24- d Simulation Result at Isle Haute between 2/23 and 3/1/2006
0
2
4
6
8
10
12
0 20 40 60 80 100 120 140 160 180
model St. Martins
Figure 24- e Simulation Result at St. Martins between 2/23 and 3/1/2006
0
2
4
6
8
10
12
14
0 20 40 60 80 100 120 140 160 180
model Scots Bay
Figure 24- f Simulation Result at Scots Bay between 2/23 and 3/1/2006
90
0
2
4
6
8
10
12
14
16
18
0 20 40 60 80 100 120 140 160 180
model Burntcoat Head
Figure 24- g Simulation Result at Burntcoat Head between 2/23 and 3/1/2006
The response of the tide at all reference points became stable within 10 hours
after the simulation started. From Figures 24 the simulation response at each
reference point from the hydrodynamic model compared very well with the data
from tide gauge stations. The maximum deviations occurred at Burntcoat Head;
however, the error was reduced after 60 hours. The result suggests that the current
model is capable of handling different patterns of incident tides and it can be used to
estimate the response to the incident tide during a long period of simulation.
Therefore, it is reasonable to use the model result to predict the responses for other
locations. The model results on the tidal range and current velocity pattern for the
entire region are therefore used.
From the result of simulation between February 23 and March 1, 2006, we can
calculate the tidal range amplification factor. This is shown in Table 4 for six key
stations referred in Figure 17. The tidal range amplification factors are a ratio of the
local tidal range to the tidal range at the entrance of the Bay.
91
Tidal Range
Amplification Factor
Location
Observed Computer Simulation
Dipper Harbour
1.08 – 1.29 1.08 – 1.29
Saint John
1.21 – 1.38 1.21 – 1.38
Isle Haute
1.71 – 1.76 1.71 – 1.80
St. Martins
1.53 – 1.79 1.53 – 1.79
Scots Bay
2.00 – 2.17 2.00 – 2.14
Burntcoat Head
2.47 – 2.66 2.50 – 2.76
Table 4: Tidal range amplification factor
From Figure 24 and Table 4, it is seen that the simulated result agrees well with
the measured result and that the tidal range increases as the distance from the bay
entrance is increased.
4.4.3.3 Simulation Result (tidal chart)
Figure 25 shows the tidal ranges at the Outer Wood Island station between
January 1, 2006 and June 30, 2007. Because high tide and low tide happen more
than once everyday, the tidal range which represented the difference of water
elevation between high tide and low tide happens more than once everyday. From
the statistics analysis, it shows the tidal range at the Outer Wood Island station is
within the range of 2.3 and 5.5 meters, with an average of 3.95 meters and standard
deviation equals to 0.71 meters. If we pick up the period of December 12, 2006 to
92
January 10, 2007, the tidal range in this period is also within the range of 2.3 and 5.5
meters, with an average of 3.94 meters and standard deviation equals to 0.55 meters.
The agreement in statistics supports that the water elevation during the period of
December 12, 2006 to January 10, 2007 is a common representative of the much
longer period of January 1, 2006 and June 30, 2007, and it is suitable to use the result
from the shorter period to represent the longer period.
Tidal range in Outer Wood Island
0
1
2
3
4
5
6
2005/12/14 2006/1/13 2006/2/12 2006/3/14 2006/4/13 2006/5/13 2006/6/12
Date
m
Figure 25- a Tidal range in Outer Wood Island between 1/1/2006 and 7/1/2006
93
Tidal range in Outer Wood Island
0
1
2
3
4
5
6
2006/7/2 2006/8/1 2006/8/31 2006/9/30 2006/10/30 2006/11/29 2006/12/29
Date
m
Figure 25- b Tidal range in Outer Wood Island between 7/2/2006 and 1/17/2007
Tidal range in Outer Wood Island
0
1
2
3
4
5
6
2007/1/18 2007/2/17 2007/3/19 2007/4/18 2007/5/18 2007/6/17 2007/7/17
Date
m
Figure 25- c Tidal range in Outer Wood Island between 1/18/2007 and 6/30/2007
The selected period of December 12, 2006 to January 10, 2007 is used to be the
example to present the results of numerical simulation. Figure 26 shows the
comparison of the simulation results and the tidal records from the reference stations.
Since the comparison for the period of December 12, to December 18, 2006 has been
94
shown in previous section, Figure 26 shows the rest of the time. The data in Figure
26-a are used as the input data for incident wave at the entrance of the Bay of Fundy.
As mentioned in the previous section, the simulation results are shifted to lower low
water level as the reference level as tidal records do. We can see that the simulation
results agree well with the tide record for each tidal station. This provides
confidence in using the simulated results for the entire study region.
12/21-12/27/2006
0.00
1.00
2.00
3.00
4.00
5.00
6.00
0 20 40 60 80 100 120 140 160 180
hr
m
Lighthouse Cove (Station #345)
Figure 26- a1:Tidal record at the entrance of bay between 12/21 and 12/27/2006
12/28/2006 - 1/3/2007
0
2
4
6
8
0 20 40 60 80 100 120 140 160 180
hr
m
Lighthouse Cove (Station #345)
Figure 26- a2: Tidal record at the entrance of bay between 12/28/2006 and
1/3/2007
95
1/4-1/10/2007
0
2
4
6
8
0 20 40 60 80 100 120 140 160 180
hr
m
Lighthouse Cove (Station #345)
Figure 26- a3: Tidal record at the entrance of bay between 1/4 and 1/10/2007
12/21-12/27/2006
0
2
4
6
8
10
0 25 50 75 100 125 150 175
hr
m
Simulation Dipper Harbour West (Station #46)
Figure 26- b1: Simulation Result at the Dipper Harbour between 12/21 and
12/27/2006
12/28/2006 - 1/3/2007
0
2
4
6
8
0 25 50 75 100 125 150 175
hr
m
Simulation Dipper Harbour West (Station #46)
Figure 26- b2: Simulation Result at the Dipper Harbour between 12/28/2006
and 1/3/2007
96
1/4-1/10/2007
0
2
4
6
8
0 25 50 75 100 125 150 175
hr
m
Simulation Dipper Harbour West (Station #46)
Figure 26- b3: Simulation Result at the Dipper Harbour between 1/4 and
1/10/2007
12/21-12/27/2006
0
2
4
6
8
10
0 25 50 75 100 125 150 175
hr
m
Simulation Saint John (Station #65)
Figure 26- c1: Simulation Result at St. John between 12/21 and 12/27/2006
12/28/2006 - 1/3/2007
0
2
4
6
8
10
0 25 50 75 100 125 150 175
hr
m
Simulation Saint John (Station #65)
Figure 26- c2: Simulation Result at St. John between 12/28/2006 and 1/3/2007
97
1/4-1/10/2007
0
2
4
6
8
10
0 255075 100 125 150 175
hr
m
Simulation Saint John (Station #65)
Figure 26- c3: Simulation Result at St. John between 1/4 and 1/10/2007
12/21-12/27/2006
0
2
4
6
8
10
12
0 25 50 75 100 125 150 175
hr
m
Simulation Isle Haute (Station #312)
Figure 26- d1: Simulation Result at Isle Haute between 12/21 and 12/27/2006
12/28/2006 - 1/3/2007
0
2
4
6
8
10
12
0 25 50 75 100 125 150 175
hr
m
Simulation Isle Haute (Station #312)
Figure 26- d2: Simulation Result at Isle Haute between 12/28/2006 and 1/3/2007
98
1/4-1/10/2007
0
2
4
6
8
10
12
0 25 50 75 100 125 150 175
hr
m
Simulation Isle Haute (Station #312)
Figure 26- d3: Simulation Result at Isle Haute between 1/4 and 1/10/2007
12/21-12/27/2006
0
2
4
6
8
10
12
0 25 50 75 100 125 150 175
hr
m
Simulation St. Martins (Station #129)
Figure 26- e1: Simulation Result at St. Martins between 12/21 and 12/27/2006
12/28/2006 - 1/3/2007
0
2
4
6
8
10
12
0 25 50 75 100 125 150 175
hr
m
Simulation St. Martins (Station #129)
Figure 26- e2: Simulation Result at St. Martins between 12/28/2006 and
1/3/2007
99
1/4-1/10/2007
0
2
4
6
8
10
12
0 25 50 75 100 125 150 175
hr
m
Simulation St. Martins (Station #129)
Figure 26- e3: Simulation Result at St. Martins between 1/4 and 1/10/2007
12/21-12/27/2006
0
2
4
6
8
10
12
14
0 25 50 75 100 125 150 175
hr
m
Simulation Scots Bay (Station #300)
Figure 26- f1: Simulation Result at Scots Bay between 12/21 and 12/27/2006
12/28/2006 - 1/3/2007
0
5
10
15
0 25 50 75 100 125 150 175
hr
m
Simulation Scots Bay (Station #300)
Figure 26- f2: Simulation Result at Scots Bay between 12/28/2006 and 1/3/2007
100
1/4-1/10/2007
0
5
10
15
0 255075 100 125 150 175
hr
m
Simulation Scots Bay (Station #300)
Figure 26- f3: Simulation Result at Scots Bay between 1/4 and 1/10/2007
12/21-12/27/2006
0
5
10
15
20
0 25 50 75 100 125 150 175
hr
m
Simulation Burntcoat Head (Station #270)
Figure 26- g1: Simulation Result at Burntcoat Head between 12/21 and
12/27/2006
12/28/2006 - 1/3/2007
0
5
10
15
20
0 25 50 75 100 125 150 175
hr
m
Simulation Burntcoat Head (Station #270)
Figure 26- g2: Simulation Result at Burntcoat Head between 12/28/2006 and
1/3/2007
101
1/4-1/10/2007
0
5
10
15
20
0 25 50 75 100 125 150 175
hr
m
Simulation Burntcoat Head (Station #270)
Figure 26- g3: Simulation Result at Burntcoat Head between 1/4 and 1/10/2007
The simulated results of the hourly tidal level are shown in Figure 27. These
represent the water level response at one hour interval between 1 am to 8 pm for
December 22, 2006. Since the major tidal period is around 12.5 hours, the twenty
hours response showing in Figure 27 covers the entire repeated cycle. The unit for X
and Y coordinate is kilometer. The water level at each point is represented by “h” in
meters and referred to mean sea level. It is seen from Figures 27 that the tide
gradually flows into and out of the bay, and the higher water levels are found in both
the north basins.
102
Figure 27-a: Water elevation, t=1 hour Figure 27-b: Water elevation, t= 2 hour
Figure 27-c: Water elevation, t = 3 hour Figure 27-d: Water elevation, t = 4 hour
103
Figure 27-e: Water elevation, t = 5 hour Figure 27-f: Water elevation, t = 6 hour
Figure 27-g: Water elevation t = 7 hour Figure 27-h: Water elevation t = 8 hour
104
Figure 27-i: Water elevation, t = 9 hour Figure 27-j: Water elevation, t = 10 hour
Figure 27-k: Water elevation, t = 11 hour Figure 27-l: Water elevation, t = 12 hour
105
Figure 27-m: Water elevation, t = 13 hour Figure 27-n: Water elevation, t = 14 hour
Figure 27-o: Water elevation, t = 15 hour Figure 27-p: Water elevation, t = 16 hour
106
Figure 27-q: Water elevation, t = 17 hour Figure 27-r: Water elevation, t = 18 hour
Figure 27-s: Water elevation, t = 19 hour Figure 27-t: Water elevation, t = 20 hour
The tidal current velocity for the model region is presented in Figure 28. The
time period covered is between 1 am to 8 pm for December 22
nd
, 2006. The scale of
one meter per second is shown as the legend at the upper right corner. It is seen from
107
the vector plots that the largest velocity vector is found at the mouth of the Bay of
Fundy, and at both the entrance of north basins, especially around the Minas Channel
-- the entrance to the Minas Basin and the Cobequid Bay. It is because that the water
body inside the basin needs to flow in and out of the basin to generate the spring or
ebb tide. The larger of the basin and the tidal range, and the narrower of the flow
channel, the larger tidal current will be generated.
Figure 28-a: Current velocity, t=1 hour Figure 28-b: Current velocity, t= 2 hour
108
Figure 28-c: Current velocity, t = 3 hour Figure 28-d: Current velocity, t = 4 hour
Figure 28-e: Current velocity, t = 5 hour Figure 28-f: Current velocity, t = 6 hour
109
Figure 28-g: Current velocity, t = 7 hour Figure 28-h: Current velocity, t = 8 hour
Figure 28-i: Current velocity, t = 9 hour Figure 28-j: Current velocity, t = 10 hour
110
Figure 28-k: Current velocity, t = 11 hour Figure 28-l: Current velocity, t = 12 hour
Figure 28-m: Current velocity, t = 13hour Figure 28-n: Current velocity, t = 14hour
111
Figure 28-o: Current velocity, t = 15hour Figure 28-p: Current velocity, t = 16hour
Figure 28-q: Current velocity, t = 17hour Figure 28-r: Current velocity, t = 18hour
112
Figure 28-s: Current velocity, t = 19hour Figure 28-t: Current velocity, t = 20hour
The maximum and minimum tidal ranges as well as the average tidal ranges for
the period of December 12, 2006 to January 10, 2007 are shown in Figures 29 and 30
can be made. In these figures, “Z” represents tidal range, and the unit is in meters.
Figure 29-a shows the maximum tidal range can be found at each location within this
period of time. It is about 6 meters at the entrance of the Bay of Fundy and gradually
increased to more than 14 meters to the north into the Cobequid Bay. Figure 29-b
shows the minimum tidal range in the simulation period. Cobequid Bay maintains
the highest minimum tidal range in the entire region at 12 meters. Since Cobequid
Bay has the highest tidal range in this region, it also maintains a larger minimum
tidal range. Thus, it is a favorable location for the generation of tidal power.
113
Figure 29-a: Maximum tidal range Figure 29-b: Minimum tidal range
The average tidal ranges in an hour can be found in Figure 30. For example,
within twelve hours, if there is a tidal pattern starting from spring tide, ebb tide and
end at spring tide, there will be two tidal range found. In this case, the average tidal
range in an hour can be calculated by add the tidal ranges and divided by twelve
hours. This value provides an indication of the average energy it can generate since
the energy output from a barrage type generation plant is proportional to the tidal
range. Another factor for the energy output is the size of the basin (or head pond in a
barrage type generation plant). For example, in going deep into Cobequid Bay, the
average hourly tidal range increase which is prefer to tidal power generation, but the
decreasing surface area of the basin offset the potential benefits.
114
Figure 30: Average tidal ranges in an hour
For the tidal current turbine type of tidal power plant, current velocity is the key
parameter for the choice of favorable location of installation. In this type of power
plant, the energy output is transferred from kinetic energy which is proportional to
the cubic power of the current velocity. Figure 31-a shows the average kinetic
energy density, which is calculated from the average of the cubic power of current
velocity in time (in hour), with a unit of m
3
/sec
3
/hour. A location with higher
115
average kinetic energy density is more suitable for the tidal current turbine type of
tidal power plant. In Figure 31-a, the suitable sites are concentrated in the entrance
of Minas Basin, that is, the Minas Channel. A more detail plot is seen in Figure 31-b.
Figure 31-a: Average kinetic energy density (V
3
)
116
Figure 31-b: Average kinetic energy density (V
3
)
117
Figure 32-a: Average kinetic energy density (V
3
)
– when current velocity is higher than 1 m/sec
118
Figure 32-b: Average kinetic energy density (V
3
)
– when current velocity is higher than 2 m/sec
A current turbine does not running all the time. Depend on the developing
technology and design, different turbines have their own characteristic curve for
performance which limit their operation pattern and operational current velocity.
Usually, the turbine will stop operating when the current velocity is too high or too
low. Since there is no prior reference for economically operated current turbine type
tidal power plant, this study assumes the turbine will start running when the current
119
velocity is higher than 1 m/sec (Figure 32-a) or higher than 2 m/sec (Figure 32-b).
However, there is not too much difference between these two figures. In the region
of Minas Channel, the velocity is higher than 1 or 2 meter per second most of the
time.
120
Chapter 5: Tidal Power Calculation
The energy output from both barrage type of tidal power plant and tidal current
turbine will be estimated according to the simulation result of tidal response and the
tidal current velocity. The possible energy output will be calculated for some
proposed sites and designs for the barrage type of tidal power plant; and the energy
derived from tidal current turbine will use the current turbine specified by Marine
Current Turbine, Ltd (shown in section 3.4.2).
5.1 Barrage Type of Tidal Power Plant
The potential energy output equation for the barrage type of tidal power plant is
similar to that used for regular hydro power plant, but the tidal range is used instead
of the hydraulic head. The energy output can be calculated by the following
equation:
T L L E E E H Q E
su t tr g t
∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ = γ (5.1)
Where:
E : energy generation in kilowatt-hours
γ : 10.1
3
/ m kN for sea water.
Q : turbine flow rate in cubic meter per second
121
H : net head on the turbine in meters
E
t
, E
g
, E
tr
: turbine, generator, and transformer efficiency
L
t
,L
su
: transmission and station loss factor
T : duration of operation in hours.
Since the tidal range is much less than the head of a regular hydropower plant,
the low concentration of energy and the need for a low head hydraulic turbine
present an economic draw back. Recent technology has improved the efficiency of
low head hydraulic turbine, but to compensate for the low energy concentration a
bigger pond is required. In equation (5.1), we noticed the multiple of Q*T represents
the amount of water that can be used during the power generation, and the amount of
water is proportional to the size of the headpond and the local tidal range. If the
variation of the headpond area due to the changing of water elevation is small, the
energy generated is proportional to the square of tidal range. Generally, Q is
controlled by the sluice gates of the power plant and is designed as large as possible
to make use of the tidal range but not too big to produce surge wave with impact to
the downstream area.
All the efficiency terms in equation (5.1) depend on the design of a plant,
including the choice of turbines, generators and design of transmission. Usually, the
total efficiency for hydro-electric generation will be between 40% ~ 80%. Recent
tidal power project in Sihwa Lake, South Korea plans to use ten "bulb-type" turbines
for 26 MW each. According to VA Tech Hydro, the sub-contractor and technology
122
provider (2005), the area of the headpond of the tidal power plant is 5.7 square
kilometers, with the tidal head difference of 5.82 meters and annual circulation of 60
billion tones of sea water. We can find the efficiency of this plant to be around 35%.
For the present study, it is assumed that 35%, 50% and 75% of the total efficiency is
reached and presented.
An example of single effect operation for a M2 tide is illustrated in Figure 33.
Figure 33: Single Effect Operation for a M2 Tide
This figure shows how to generate energy for a M2 tide in a single effect
operation, when generating power during an ebb tide. Sea level outside the barrage
moves normally up and down, and the water level inside the basin was controlled by
the sluices and power house. We can see that the head difference (between the water
level of headpond and sea level outside the barrage) is maintained within a range,
which will be corresponded to the design rate of the turbines to make the maximum
123
capacity rate of generation facility. The shaded area represents the energy-
generating stage and is dependent on the design rate for sluices and turbines. Extra
energy represented by the upper part of the shape area can be gotten by a pumping
storage system.
In 1977, three sites were recommended by The Bay of Fundy Tidal Power
Review Board for further study. They are shown in Figure 34:
Site A6 – Shepody Bay, at northwest part of Chignecto Bay.
Site A8 – Cumberland Basin, at northeast of Chignecto Bay.
Site B9 – Minas Basin.
Figure 34: Sites for Barrage Type of Tidal Power Plant
Resource: http://map.google.com
124
From the numerical simulation at the recommended sites, we found the water
elevation shown in Figure 35 for the period of December 12th, 2006 to January 10th,
2007. In Figure 35, the water elevation is for the mean sea water level, and the unit
is meter.
Site 6: 12/14 - 12/20/2006
-8
-6
-4
-2
0
2
4
6
0 20 40 60 80 100 120 140 160 180
Figure 35- a1: Tidal response at site A6: 12/14 - 12/20/2006
Site 6: 12/21-12/27/2006
-8
-6
-4
-2
0
2
4
6
8
0 25 50 75 100 125 150 175
Hour
Meter
Figure 35- a2: Tidal response at site A6: 12/21-12/27/2006
125
Site 6: 12/28/2006 - 1/3/2007
-8
-6
-4
-2
0
2
4
6
8
0 25 50 75 100 125 150 175
Hour
Meter
Figure 35- a3: Tidal response at site A6: 12/28/2006 - 1/3/2007
Site 6: 1/4-1/10/2007
-8
-6
-4
-2
0
2
4
6
8
0 25 50 75 100 125 150 175
Hour
Meter
Figure 35- a4: Tidal response at site A6: 1/4 - 1/10/2007
Site 8: 12/14 - 12/20/2006
-8
-6
-4
-2
0
2
4
6
0 20 40 60 80 100 120 140 160 180
Figure 35- b1: Tidal response at site A8: 12/14 - 12/20/2006
126
Site 8: 12/21-12/27/2006
-8
-6
-4
-2
0
2
4
6
8
0 25 50 75 100 125 150 175
Hour
Meter
Figure 35- b2: Tidal response at site A8: 12/21-12/27/2006
Site 8: 12/28/2006 - 1/3/2007
-8
-6
-4
-2
0
2
4
6
8
0 25 50 75 100 125 150 175
Hour
Meter
Figure 35- b3: Tidal response at site A8: 12/28/2006 - 1/3/2007
Site 8: 1/4-1/10/2007
-8
-6
-4
-2
0
2
4
6
8
0 25 50 75 100 125 150 175
Hour
Meter
Figure 35- b4: Tidal response at site A8: 1/4 - 1/10/2007
127
Site 9 (north side): 12/14 - 12/20/2006
-8
-6
-4
-2
0
2
4
6
8
0 25 50 75 100 125 150 175
Hour
Meter
Figure 35- c1: Tidal response at site B9 (north): 12/14 - 12/20/2006
Site 9 (south side): 12/14 - 12/20/2006
-8
-6
-4
-2
0
2
4
6
8
0 25 50 75 100 125 150 175
Hour
Meter
Figure 35- d1: Tidal response at site B9 (south): 12/14 - 12/20/2006
Site 9 (north): 12/21-12/27/2006
-10
-5
0
5
10
0 25 50 75 100 125 150 175
Hour
Meter
Figure 35- c2: Tidal response at site B9 (north): 12/21-12/27/2006
128
Site 9 (south): 12/21-12/27/2006
-10
-5
0
5
10
0 25 50 75 100 125 150 175
Hour
Meter
Figure 35- d2: Tidal response at site B9 (south): 12/21-12/27/2006
Site 9 (north): 12/28/2006 - 1/3/2007
-10
-5
0
5
10
0 25 50 75 100 125 150 175
Hour
Meter
Figure 35- c3: Tidal response at site B9 (north): 12/28/2006 - 1/3/2007
Site 9 (south): 12/28/2006 - 1/3/2007
-10
-5
0
5
10
0 25 50 75 100 125 150 175
Hour
Meter
Figure 35- d3: Tidal response at site B9 (south): 12/28/2006 - 1/3/2007
129
Site 9 (north): 1/4-1/10/2007
-10
-5
0
5
10
0 25 50 75 100 125 150 175
Hour
Meter
Figure 35- c4: Tidal response at site B9 (north): 1/4 - 1/10/2007
Site 9 (south): 1/4-1/10/2007
-10
-5
0
5
10
0 25 50 75 100 125 150 175
Hour
Meter
Figure 35- d4: Tidal response at site B9 (south): 1/4 - 1/10/2007
From the results presented in Figures 35, compared with Figure 25, the response
in site A6, A8 is about 2 times the tide range at the entrance of the bay, and about 2.5
times the tide level at site B9. The average tidal range, hourly average square tidal
range and the size of the basin for site A6, A8, and B9 are represented in Table 5.
130
Location A6 A8 B9
Simulation Average Tidal Range (m) 10.98 11.08 12.78
Hourly-Average Square Tidal Range(m
2
) 0.81 0.83 1.11
Basin Area (km
2
) 130 100 300
35% efficiency 3261 2570 10312
50% efficiency 4658 3672 14731
Annual Energy Output
(GWh)
75% efficiency 6987 5508 22097
Table 5: Potential Energy output from site A6, A8, and B9
In this table, the design characteristics used in Swales (1977) are reworked using
the data generated from the present model. Three different efficiency of the power
plant are assumed: 35%, 50% and 75% with 50% economic operation running time
for a single basin- single effect operation. The average tidal range is the average for
each cycle of tidal variation. The hourly average square tidal range is the summation
of the square of tidal ranges during a year, and then divided by the total hours. Since
we assume the area of the basin is not changing with the water elevation, the energy
output will be proportional to the square of the tidal range. The basin area is the area
at the high tide, which represents the maximal amount of water available for
operation when multiplied by hourly average square tidal range. From Table 5 it is
seen that the estimated annual energy output is around 3,300 to 7,000 GWh for site
A6, 2,600 to 5,500 GWh for site A8, and 10,000 to 22,000 GWh for site B9.
131
5.2 Tidal Current Turbine
A tidal current turbine operates like a windmill running underwater. The energy
generated from current can be calculated by the equation:
2 /
3
T AV Co E ρ ⋅ = (5.2)
where
E : energy generation in kilowatt-hours
Co : efficiency coefficient
ρ : the density of sea water, 1026 kg per cubic meter.
A : area of the cross section, blade sweep area.
V : current velocity, m/s.
T : operation duration, hours.
Several studies have been conducted to harvest energy from ocean current.
However, most of them are still in the developing or experimental stages. Among
various equipment providers, Marine Current Turbines Ltd (MCT) is a leader in this
field. As indicated previously, according to their pilot project, MCT believes their
turbine technology can be economically running if the current reaches a mean spring
peak velocity about 2.25 to 2.5m/s (4.5 to 5 knots) in the water depth of 20 to 30m.
As such, from Figures 28, 31, and 32, it seems that the Minas Channel can be a
possible site for harnessing the current energy, where the current velocity can reach
more than 8 m/s based on the present hydrodynamic model results.
132
Velocity Profile -x
12/21-12/27/2006
-10
-5
0
5
10
0 20 40 60 80 100 120 140 160 180
Hours
m/sec
Figure 36 – a: Current velocity profile in X direction at Minas Channel
Velocity Profile - y
12/21-12/27/2006
-3
-2
-1
0
1
2
0 20 40 60 80 100 120 140 160 180
Hours
m/sec
Figure 36 – b: Current velocity profile in Y direction at Minas Channel
133
Velocity Profile
12/21-12/27/2006
0.0
2.0
4.0
6.0
8.0
10.0
0 20 40 60 80 100 120 140 160 180
Hours
m/sec
Figure 36 – c: Absolute current velocity profile at Minas Channel
The pilot turbine model (SeaFlow) of Marine Current Turbines Ltd. has 11 m
diameter blade system which makes the swift area equal to 95 square meters. The
efficiency coefficient of this turbine is not released to public, but we can get a
reasonable estimation of 16% by the relationship between the power rate (300kW)
and operational current speed (2.7 m/sec). The efficiency coefficient is also very
close to 15% which was suggested by OEER (Offshore Energy Environmental
Research Association, 2005). From Figure 31, the energy density in Minas channel
is as high as 1196 (m
3
/ sec
3
per hour). From equation (5.2), using 16% as the
efficiency coefficient, the annual energy output will be 163.4GWh.
134
Chapter 6: Economic Feasibility
The purpose of economic feasibility study is to identify the power generation
projects which can operate at an acceptable benefit – cost ratio. It should provide a
measure of benefits to cost attributed by the projects as well as the impact to society
and environment. This study focuses on the cost of power generation by evaluating
the total power generated and the cost to build and to operate the power generating
facilities. From the computed at-site cost of energy, the economic feasibility of tidal
power generation will be analyzed. The issue of environmental impact as well as
impacts to the society due to these power generation ideas will not be addressed in
this study.
To estimate the engineering cost of a power generation project, three direct costs
must be considered:
• Equipment (turbine, generator, control system, and powerhouse)
• Construction Materials (loose rock, sand and gravel)
• Soft Costs (design, construction financing, permitting, etc.)
Other than direct costs, some indirect costs include:
• Indirect construction items
• Project management
• Owners expense
• Interest during the construction
135
A contingency allowance is also part of the engineering cost in case of
unforeseen events which could impact the overall costs such as accidents,
unexpected rise of material cost, etc.
It should be noted that the parameters and assumptions made is only for
economic analysis. The tidal power project similar to other type of engineering
projects is sensitive to interest rate and the cost of fuels, and cost of manufacturing of
the turbine/ generator may also modify the cost figures significantly.
6.1 Barrage Type of Tidal Power Plant
This study examines the schemes and designs of tidal power plants at the mouth
of Cumberland Basin (A8), Cobequid Bay (Site B9), and Shepody Bay (Site A6)
originally proposed by the Bay of Fundy Tidal Power Review Board in 1977. They
were the most promising and economic sites in the Bay of Fundy, according to the
studies at that time. The proposed design included the barrage design, the number of
sluices and generating units with rate capacity, provided by optimization analysis.
The design characteristics are shown in table 6. Even though the construction of the
tidal plant at any one of the sites was considered technically feasible, they were
never built.
136
Item Units Site B9 Site A6 Site A8
Total number of
generating units
106 53 37
Total number of sluices
60 30 24
Number of spare
generating units
6 3 2
Turbine diameter m
7.5 7.5 7.5
Generator rated capacity MW
38 31 31
Turbine rated head m
7.5 6.5 6.5
Total installed capacity MW
4028 1643 1147
Operating capacity MW
3800 1550 1085
Annual output million kWh
12653 4533 3423
Table 6: Summary of Characteristics of Single-effect Tidal Power Schemes
For the purpose of economic feasibility study, several assumptions are made.
They are adopted from the proposal (the Bay of Fundy Tidal Power Review Board,
1977) and modified to accompany the recent economic condition.
• Project operation life is 75 years. This is common to hydroelectric power
plants. The oldest commercial operational tidal power plant, La Rance of
France, has been operated since 1966 and it is still running.
• Interest rate is set as 5.5%. It is based on the average Contract Mortgage
Rate for the past 15 years.
• The cost of turbine (electrical equipment) is current price which referred
to VA Hydro, the sub-contractor and technical provider of Sihwa Lake
tidal power plant. It includes the equipments and installation cost on the
facility. It is approximated three quarter to one million dollars per one
mega-watts design rate.
137
• Maintenance & operation cost is 0.621% of capital cost.
• Annual cost is computed as amortization of capital cost (direct, indirect
and contingency cost) plus operation & maintenance cost.
The at-site cost of energy is computed as follows:
E
M CRF C
C
E
) (
0
+
= (6.1)
The Capital Recovery Factor (CRF) is obtained as:
1 ) 1 (
) 1 (
− +
+
=
n
n
i
i i
CRF (6.2)
where
E
C : At-site cost of energy. ($/kWh).
Co: Total capital investment. ($)
M : Annual operation & maintenance cost (%)
E : Annual energy produced. (kWh)
i : Interest rate
n : Operating period. (year)
The indirect and contingency costs are assumed as follows (adopt from the Bay
of Fundy Tidal Power Review Board, 1977, with its methodology):
• Indirect construction items: ten percent of total direct cost;
138
• Project management: ten percent of total direct cost;
• Owners expense: three percent of total direct cost;
• Interest during the construction: accumulated at interest rate
according to disbursement schedules;
• Contingency allowance: 12.5% of total direct and indirect cost.
Item Units Site B9 Site A6 Site A8
Direct Cost
Civil work million $
3527 2382 1330
Mechanical and electrical million $
3800 1550 1085
Total direct costs million $
7327 3932 2415
Indirect and contingency million $
5862 3145 1611
Total capital costs million $
13189 7077 4027
Amortization million $
739 396 226
Operation & maintenance cost million $
82 44 25
Annual cost million $
821 440 251
At-site cost of Energy $/kWh
0.0649 0.0971 0.0732
Table 7: Summary of At-site Costs of Single-effect Tidal Power Schemes
Table 7 represents the financial analysis for a single basin, single effect operation
tidal plants at three recommended sites. In this table, direct cost includes the cost of
civil work and the cost for mechanical and electrical equipments with installation.
For the cost of electrical equipments with installation, the higher end of estimation is
chosen (one million dollars per one mega-watts rate equipment). The total cost can
be paid through total of 75 years and the annual payment is shown in the item of
amortization. Since we assume that the operation and maintenance cost is 0.621% of
139
the total capital cost each year, the annual cost of operation and maintenance can be
added to the amortization of the total capital cost. The sum of these two costs is the
annual cost to build and operate a barrage type tidal power plant for 75 years of its
life. Compared with Table 6 for the annual energy output, the at-site cost of energy
can be found. This “at-site” cost does not consider any cost to connect to the power
grid of transportation or storage for the power being produced.
Energy Charge /kWh CA$ US$ Note
Private residence
0.1067 0.1087
Commercial adjustable by load factor
Small Commercial 0.1181 0.1204
< 24 MWh. Charge
CA$0.1039 after 200kWh
Commercial 0.0878 0.0895 CA$0.062 after 200kWh
Large Commercial 0.0598 0.0609 > 18 kW
Industrial adjustable by load factor
Small Industrial 0.0767 0.0782 CA$0.0585 after 200kWh
Medium Industrial 0.0546 0.0556
Large Industrial 0.0547 0.0557 > 1.8 MW
Extra Large Industrial 0.05655 0.0576 commit no less than 20 MW
Table 8: Electric billing from NOVA SCOTIA POWER INC.
Source: www.nspower.ca
CA$/US$ Exchange rate=1.01916
Table 8 shows the recent local electric company bill. The data is obtained from
Nova Scotia Power Inc., and the cost of energy estimation is the highest possible
(with the highest electrical equipments with installation charge) and it is compatible
to the recent energy market. We can see that the at-site energy cost is very
140
competitive for Site B9 which is less than seven cents per kWh, and is acceptable for
the other sites.
6.2 Tidal Current Turbine
As mentioned earlier, Marine Current Turbines Ltd (MCT) installed and tested
their first commercial-scale rotor system off Lynmouth, Devon, UK. This
experimental unit was installed in May 2003 and uses 300kW single 11m diameter
rotor and will only generally operate with the tide in one direction. This project costs
around 6 million US dollars. Assume a similar unit is installed at Minas Channel,
Bay of Fundy, we need to select a possible size of the turbine since the current
velocity is higher than the location of the recent pilot study of Marine Current
Turbines, Inc. Since the only change to be made is the rate of the current turbine, the
cost will be increased but not by much, and the increase of the cost will be
compensated by the decreasing of cost when a pilot model has been modified to a
commercial model.
A 300kW unit with 11m diameter rotor requires a minimum flow velocity of 2.3
m/s, if the efficiency is assumed 16%. For a M2 tide, there will 705 cycle of tide
annually and each cycle has two periods of the same magnitude of tidal current but
different direction. According to the present numerical model results, the average
tidal current at the best area for tidal current turbine is around 5.38 m/sec, and the
141
duration for the velocity higher than 5.38 m/sec is around seven hours each tidal
cycle. It is also noted that the duration for the current velocity which is less than
minimum requirement for turbine (0.75 m/sec) is around 10.4 hours. According to
equation 5.2, for the current velocity 5.8 m/sec with efficiency around 16%, the rate
of power output is around 1.2 MW. The similar assumption and calculation can be
made and the result is shown in Table 9.
Rate (MW) 1.2 2.1 2.7
Sweep area (m
2
) 95 95 95
Efficiency 16%16%16%
Energy per cycle (MWh) 9.53 15.10 17.85
Annual Energy (MWh) 6720.28 10647.19 12583.19
Table 9: Power output for different rates of turbines
In this table, rate 1.2 MW is good for the maximum current velocity around 5.5
m/sec, 2.1 MW for the velocity 6.5 m/sec, and 2.7 MW for 7 m/sec current. The
energy output for each type of turbine rate is generated from the minimum operation
velocity (0.75 m/sec) to the maximum working velocity with a uniform efficiency.
In reality, the efficiency will reach maximum when it is getting close to rate velocity
and decreases when the velocity decreases. The annual energy output is calculated
from 705 tidal cycles per year (since there is 705 tidal cycles each year for M2 tide).
From the design of the turbine/generator installed by MTC, the construction cost
is reported to be seven million US dollars. Assume the unit’s operating period is 20
years, and the operation & maintenance cost is another 1 million US dollars per year.
142
Compared with the annual total energy generated between 6.7 million kWh to 12.6
million kWh, we can calculate the at-site energy cost by equation 6.1 and the capital
recovery factor (CRF) by equation 6.2, and we assume that the interest rate is 5.5%
as indicated in previous analysis.
Rate (MW) 1.2 2.1 2.7
Capital Cost (million $) 7 7 7
Amortization (million $) 0.59 0.59 0.59
Maintenance &
operation(million $) 1 1 1
Annual cost (million $) 1.59 1.59 1.59
At-site Cost of Energy
($/kWh) 0.2359660.1489370.126022
where
CRF=
0.083679
i=
0.055
n=
20
Table 10: Financial analysis for current turbine
Table 10 indicates the at-site cost of the energy from current turbine type of
power plant. The at-site energy cost varies from $0.13 /kWh to $0.24/kWh. Such
estimate results are not very encouraging at this point even though it was based on
several conservative assumptions, when compared with the current electric billing in
Table 8. Further investigation is required to ascertain its efficiency, such as a more
accurate installation and operation & maintenance cost, the characteristic curve for
the turbine, the design operating period, and the development of more advanced
turbine/ generator.
143
Compared with the analysis for barrage-type of tidal power generation, current
turbine are more expensive. One of the possible reasons is the conservative
assumptions made in this study. The current turbine’s efficiency for the generation
is assumed 16%, which is much lower than wind turbines’ efficiencies, relatives to
the efficiency of 35% to 75% for barrage-type tidal power generation. Another
possible reason is the high cost estimation which is based on the pilot project of
MCT. The cost of construction of a current turbine should be reduced when it is in
mass production. Since it prevents the disadvantage of channel blocking by a
barrage, with a possible reducing cost and increasing efficiency, the current turbine
may be the future of tidal power generation.
144
Chapter 7: Conclusion and Future Work
Because of the rising cost of energy, environmental concern, and government
support, people are interested in alternative or green energy sources. In order to
research the potential of tidal energy, one source of alternative energy, this study
examines the area of the Bay of Fundy as an example. The Bay of Fundy has the
largest tidal range in the world (approximately 16 meters) with suitable surrounding
oceanographic and economic conditions to become a prime location for harnessing
tidal power using the daily rising and ebbing tide. It is a good location to examine if
the tidal power is feasible for additional energy sources.
In this study, a 2-D finite element model has been developed and applied to
simulate the tidal responses in the Bay of Fundy, including water level and water
particle velocities. The simulation result is used to choose the location for energy
development and to predict possible energy which can be developed using different
types of generation methods.
Fluid motion is assumed to be governed by the shallow water equation since the
wave length associated with tide is much longer than the water depth in the Bay of
Fundy. A three-node triangular element is used in this 2-D model. The simulated
area covers the entire Bay of Fundy from the mouth of the bay (the straight line
between Tiverton, Nova Scotia and Wood Island) to the north region including
Cobequid Bay and Chignecto Bay. By using a real time series of water elevation at
the entrance of the bay, the computer model finds tidal response at each node in the
145
study area, which is then verified by the observation record from several tidal gauge
stations inside the Bay.
A barrage type of tidal power plant uses the potential energy produced by the
tidal range, and real-time series of computer simulated water elevation at specific
locations are taken to calculate the potential energy generated; on the other hand, the
computer-simulated current velocity is used to compute the kinetic energy generated
by tidal current using a turbine type of power generation. The energy output
compared with the recent development cost defines the cost for unit energy. This
study shows that the at-site cost of energy for barrage type tidal power plants is
around $0.065 to $0.097 per kWh at the recommended Shepody Bay (project A6),
Cumberland Basin (project A8), and Cobequid Bay (project B9). The cost of energy
for the current turbine type tidal power plants is $0.13 /kWh to $0.24/kWh at the
Minas Channel, the area with the highest current velocity. Compared with a recent
bill from the local power company, the unit cost for the barrage type of power plant
is feasible but the cost for the current turbine is higher than the recent market price.
Based on the results generated in the present study, the barrage type of tidal
power plant is economically feasible but the environmental concern of channel
blocking by barrage will be a formidable constraint. The current turbine type of tidal
power plant, even at the most suitable sites, is not economically feasible under
current technology. It may become feasible as oil prices continue to increase and
more efficient turbines become available. Further studies are needed to improve the
146
characteristic curve for the turbine/generator efficiency to reduce the energy lost
during power generation for both the barrage type and tidal current turbine type
power plant.
147
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Abstract (if available)
Abstract
Due to rising fuel costs and environmental concerns, energy generation from alternative power source has become one of the most important issues in energy policy. Tidal power is one of the alternative energy sources. The tidal range at the Bay of Fundy is the largest in the world (approximately 16 meters). It represents a prime location for harnessing tidal power using the daily rising and ebbing tide.
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Asset Metadata
Creator
Chang, Jen
(author)
Core Title
Hydrodynamic modeling and feasibility study of harnessing tidal power at the Bay of Fundy
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Civil Engineering
Publication Date
03/12/2008
Defense Date
11/16/2007
Publisher
University of Southern California
(original),
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Tag
Bay of Fundy,numerical modeling,OAI-PMH Harvest,tidal energy
Place Name
bays: Fundy, Bay of
(geographic subject)
Language
English
Advisor
Lee, Jiin-Jen (
committee chair
), Chilingarian, George (
committee member
), Moore, James Elliott, II (
committee member
), Wellford, L. Carter (
committee member
), Wong, Hung Leung (
committee member
)
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