2. 2
Introduction
With the growing interest in renewable energies around the world Ocean
Thermal Energy Conversion (OTEC) appears to have great potential as a tool for
harnessing a naturally replenishing recourse. Many are well aware that countries
dependence on finite recourses such as oil and coal is a major issue that must be
addressed. OTEC uses the naturally replenishing energy from the sun that is stored
in the ocean to operate a heat engine, which generates electric power. Specific
information on OTEC systems can be found from the book Renewable Energy From
the Ocean: A Guide to OTEC by Avery and Wu and is summarized in the rest of this
introduction. [1] The ocean stores the majority of energy from sunlight in a 35 to
100m region in the sea. In tropical oceans the temperature in this regions is
approximately 28° C. Winds at the surface and waves keep the temperature nearly
uniform throughout this region. Furthermore, the temperature of this region is
maintained nearly constant throughout the entire year. As depth increases
temperature increases until 800 to 1000m below the surface. Here the temperature
of the water reaches 4.4° C. After this region the temperature only decreases a few
degrees until one reaches the ocean bottom. This approximation is based on an
average ocean depth of 3650m. The ocean thus essentially is a very large area with
warm water at the surface and cold water at the lower depths. The temperature
difference is 20 to 25°C in tropical regions where depth exceeds 1000m. The
difference in temperature is maintained with slight variations throughout the year
similar to the surface temperature. OTEC systems can either be closed-systems or
open-systems. Closed OTEC systems are rather intriguing because they can be
modeled after many previously developed power generation systems. Ammonia is
an appropriate working fluid in a closed OTEC system because of its low boiling
point and easy availability. Warm water is drawn into the system from near the
surface, and warms an evaporator with ammonia inside of it. The ammonia boils,
and the vapor expands across a turbine, which produces power to operate an
electric generator. The vapor passes through a condenser that is cooled by the cold
water from the depths of the ocean. The ammonia is pumped back to the evaporator
3. 3
thus completing the OTEC closes cycle. A figure describing a standard OTEC closed
cycle is included below:
Power is infinitely created as long as the OTEC structure is operating properly. The
OTEC closed cycle can be modeled as a conventional Rankine Cycle, which is used in
steam engine designs.
OTEC systems are very attractive because of their potential to produce
limitless energy. Other renewable energy technologies such as wind and solar do
not produce power continuously. Cloud cover limits the productivity of solar panels,
while absence of wind limits wind turbines. A brief history of OTEC technology
summarized from Avery and Wu will now be provided. [1] By the 1800’s a sufficient
amount of knowledge on engines that could use working fluids other than steam had
been established. These engines were based on the Rankine Cycle. In 1881 Le Bon, a
French scientist published a paper where he introduced the concept of using
compressed gases for future power generation because of their ability to store
energy and transport it over a distance relatively easily. He mentioned that this
Figure 1 OTEC System Diagram [3]
4. 4
source of energy could come from natural recourses. This paper inspired Arsen
D’Arsonval to publish an article in the same year where he introduced the idea of
using liquefied gases that obtained energy from low-temperature heat sources in
nature to drive engines. He recognized the potential of tropical oceans as a great
power source because of temperature differences between the surface water and
the water located in the depths of the ocean. He is therefore known as the father of
OTEC. There were a few attempts at constructing large OTEC plants between the
1920’s and 1950’s by French engineers. They were largely plagues with feasibility
concerns from funding organizations, site location issues; sever storms, and Cold
Water Pipe (CWP) construction. The French did not gain interest in OTEC research
again until the 1970’s. In the 1960’s an American by the name of James H.
Anderson,Jr. proposed several ideas on OTEC systems in America. However, he
gained no support because nuclear energy and fossil fuels were assumed to be the
sources of energy for the future. The National Science Foundation supported
modern day OTEC research in response to an increase in fossil fuel prices in 1973,
thus two industry teams were able to design conceptual systems. In 1979 a
breakthrough in OTEC technology occurred when a team from Lockheed Martin
produced net power generation from a closes cycle OTEC at sea for the first time in
history. The system was called Mini-OTEC, was located off the coast of Hawaii, and
generated 15kW of net power. OTEC research was severely restricted in the 1980’s
in America because of limited funds from the Department of Energy. Today many
small companies support OTEC systems. These companies are working on research
and implementation of the technology. Lockheed Martin recently has begun its
research on OTEC technology again. In collaboration with smaller companies it is in
the process of developing an OTEC pilot plant.
As mentioned before there are numerous challenges when it comes to OTEC
technology. The CWP is one of the most difficult and complex design components of
the OTEC system. It has proven to be on of the most important design factors in an
OTEC system because of its numerous failures in the past when attempted to be
used in a large-scale system. The CWP must be large enough to supply the required
flow, have low drag, and be composed of a material that is durable in seawater and
5. 5
environmentally acceptable. Furthermore, the pipe must be able to withstand static
and dynamic loads caused by is own weight, relative motions caused by normal and
sever storm waves, and a collapsing load that is the result of water pump suction.
[1] In addition the CWP design entails the method in which it is attached to a
floating platform. The attachment must be able to withstand all of the same effect
that the pipe encounters.
In this preliminary analysis we shall explore the design of a CWP for a closed
OTEC system. We will first explore the efficiencies possible for a closed OTEC
system, and previously constructed or devised power generation plants. From this
point the temperature difference required can be determined, thus allowing the
length of the pipe to be selected. Structure of the CWP, flow rate within the CWP,
diameter of the CWP, wave motion influences on the CWP, and the pump required
for the CWP will all be considered after depth of the CWP is determined. We will
place our system off the coast of the Philippines where the average change in
temperature between the surface and 1000m of water depth is greater than 24°C as
seen in Figure 2. Data on temperature differences in different regions of the ocean
can be seen in the figure below:
Figure 2 Ocean Temperature Difference [1]
6. 6
Careful consideration of pipe design is crucial since it is one of the most difficult
components of the OTEC system. In the following sections we will discuss our
system in detail.
Background Analysis
In order to design our CWP we will use the parameters from a theoretically
developed 10MW power plant. The plant is part of an OTEC system and was
developed by D. Bharathan from the National Renewable Energy Laboratory. [7] The
system we will use contains a single stage turbine. Summary of data used in
Bharathan’s OTEC system can be found in the following tables:
Table 1 Summarized Parameters from D.Bharathan System [7]
7. 7
Table 2 Summarized Parameters from D.Bharathan System (Cont.) [7]
The main parameters we will utilize are seawater temperature difference and the
mass flow rate of the water. We will also utilize the power consumption used by the
warm water pump and ammonia pump. The theoretical maximum power output of
Bharathan’s system is 3.66238%(1.1). We find that the operating efficiency is
69.023%(1.2), and net power output is 2.528%(1.3). We will thus design a CWP that
utilizes a pump that consumes as much or less power as Bharathans system’s pump.
This way we will ensure that power generation stays at 10MW. The seawater
temperature difference in Bharathans system is 21.5°C as can be seen from Table 1.
By taking this data and using it for our system we can determine how deep our pipe
must travel into the depths of the ocean in order to obtain our desired seawater
temperature difference. The Philippines was chosen as a location because of its
large temperature difference in the seawater at 1000m. This will give us flexibility
when determining pipe length because the CWP can be shorter than 1000m. We
remember that after 1000m temperature of seawater decreases very slightly until
8. 8
reaching the ocean floor. [1] Thus there is no justification in designing a pipe that is
longer than 1000m. The additional length is not justifiable considering the amount
of temperature difference one can achieve. By using Figure 2, and the assumption
that at 1000m the temperature of the seawater is 4.4°C we can estimate surface
temperature off the coast of the Philippines to be 28.4°C. By assuming temperature
of the sweater increases linearly with depth we only have to reach a depth where
the seawater temperature is 6.9°C. Using interpolation from the data we have just
determined for temperature of the seawater at the surface and 1000m depth we can
calculate the required depth of our pipe to be 895.84m. We have now achieved the
length of our CWP. We will also take into consideration typhoons that plague the
Philippines by designing a pipe that can withstand severe storms later in our CWP
analysis.
Next we will determine the diameter of the pipe by using the mass flow rate
of the cold seawater from Bharathan’s system. The flow rate is 28,450 kg/s as seen
in Table 1. We will also assume a flow velocity of 2.5 m/s which is below the erosion
limit for concrete. The erosion limits for concrete that would be used in large
diameter pipes can be found from sewer pipe applications. This data can be found in
Paul Imm’s paper “Abrasion Resistance of Concrete Pipe.”[6] The selection of
concrete for our pipe material will be discussed later in the Detailed Analysis
section. The seawater density will be assumed to be 1023 kg/m3. [1] Seawater
density, pipe velocity, and the mass flow rate of the cold seawater can be utilized to
find a CWP diameter of 3.763m. (2.1) This completes the preliminary design of the
CWP. In the upcoming section we will explore the pipes structure, the relative
motion due to wave forces, and the required water pump.
Detailed Analysis
We will first explore static and dynamic loads on the CWP in order to
determine its structure. This analysis is heavily based on previous experiments and
research of CWPs summarized in Avery and Wu’s book, which has previously been
mentioned. [1] It is known that through these experiments and research we have
the technology to create a CWP from currently available recourses. Concrete will be
9. 9
our choice of material as it is used in countless applications, it is non-corrosive in
seawater, and is readily available. A concrete pipe was previously used for a 40MW
baseline OTEC plantship in which static and dynamic considerations were taken into
account. The concrete pipe was determined feasible for durability and its ability to
be manufactured.
Static Load considerations will consist of bending loads, longitudinal forces,
and collapse loads. There must be a pivot between the platform and CWP as
determined from the results of previous bending load analyses between the
platform and the CWP. This design parameter is linked to the fact that large bending
moments will possibly be caused by 100-year-storm values. Bending moments will
also vary with depth thus affecting the CWP even further. Having flexible joints
between the CWP can relieve the large moments. Previous engineers determined
that 15m sections of concrete pipe linked by flexible joints would be the best design
option when considering manufacturing, transport, instillation, and bending loads.
The sections were described in Avery and Wu’s book as, “…structures at the two
ends for the bayonet-type locking mechanism and bearing pads for the flexible
joint.’’(pg.276) It is reasonable to assume the structural design of our CWP to be
identical to that of the CWP described above. It is reasonable because this CWP
design is suitable for power plants up to 80MW net power generation. Because our
system only will be generating 10MW this is more than sufficient as a design choice.
Next the pipe weight must be selected. CWP weight must take into consideration
maximum load values of the pivot and the angle between the CWP and the platform.
The pipe weight will influence how much the CWP sways during severe storms. If
there is too large of an angle between the platform and CWP damage will occur. This
angle will be determined later when dynamic loads are discussed. It has previously
been determined that low density concrete of 1350 kg/m3 is sufficient for
suspended CWPs. Furthermore the CWP must have the longitudinal strength to bear
the tension caused by its own weight in the seawater. Additionally, it has previously
been determined that concrete suspended CWP’s must be post tensioned to 41MPa.
For the final consideration of static loads, collapsing loads, we will choose a smooth
concrete pipe. This will reduce the drag inside of the CWP therefore lowering the
10. 10
collapse load caused by suction. We will loosely model the thickness of our concrete
CWP after the values specified in table below:
Table 3 Wall Thickness in CWPs of Different Materials [1]
This table was considered from previous research that took into the consideration
the suction pressure cause within the smooth CWP. The suction pressure is caused
by flow drag with in the pipe, the density difference between the cold and warm
water, and accelerating the cold water outside the pipe to the flow velocity of the
water inside the pipe. In addition, the table was comprised using a pipe flow velocity
of 2.5 m/s. This matches the flow velocity of the CWP that we are exploring.
However, we will need to make a rather large assumption for the pressure
difference between the inside of the CWP and its surroundings. Table 3 has different
diameters, mass flow rates, and power generation specifications than our system.
We can assume that there will certainly not be a pressure difference of more than
30kPa based on the data in the table. The pressure difference of a 80MW system at
1000m is only 14.4kPa as seen in Table 3. Therefore it is reasonable to assume a
30kPa pressure difference for a preliminary determination of the thickness of our
CWP. Exact pressure difference values are beyond the scope of this analysis and
should later be precisely calculated in order to properly consider price values of
constructing the CWP. From this 30kPa pressure difference we achieve a pipe
thickness of 4.033cm(2.2). This thickness will certainly be able to withstand the
internal forces in the CWP caused by the pump.
11. 11
Next Dynamic Loads on our CWP will be explored. As mentioned before the
information that will be presented is heavily based on previous research and
experiments summarized in Avery and Wu’s book. [1] The exploration of oscillatory
effects and hydrodynamic forces on a CWP is very complex and beyond the scope of
this analysis. However, we will explore some factors that are taken into
consideration when such an analysis would take place. As mentioned in previous
sections we must have a pivot that attaches the CWP to the base of the platform. For
a 40-MW system it was determined that the angular deflection of the pivot will be
18° in an equatorial site for a 100-year-storm values. Thus for a 10MW power
system it would be safe to assume an angular deflection that is similar to this value
because the Philippines are near the equator. The CWP vibrational characteristics
can be modeled after the characteristics of a stretched string. Forced vibrations and
displacements from platform motions also contribute to forces on the CWP.
Damping effects of the CWP are created by the friction of the seawater inside and
outside of the pipe. We know that our CWP can be modeled as a string of uniform
mass that has one fixed end, and another free end that is affected by a periodic force
caused by wave motion. When an object such as our CWP is exposed to periodic
forces at a certain frequency the CWP will begin to vibrate. The frequency at which
the CWP vibrates is described by as the resonant frequency. If the frequency is
doubled we reach an additional state called the first overtone. As frequency is
increased overtones will increase as well. However, by taking damping into
consideration as stated in Avery and Wu’s book, “…a limiting amplitude of vibration
is reached at resonance conditions.’’(pg.21) In a specific sea-state a small forcing
frequency range will have the most effect on our CWP. As also stated in Avery and
Wu’s Book, “…the CWP will vibrate in an overtone mode that closely matches the
exciting frequency.’’(pg.21) Previous at-sea experiments match theoretical data to
the extent that dynamic properties of CWPs can be determined with enough
accuracy to design and operate full scale CWPs. It has been deemed from previous
experiments and analysis that a concrete, sectional CWP such as ours is feasible for
an OTEC.
12. 12
Finally, a pump must be chosen in order to pump the cold seawater from the
depths of the ocean. We can use the parameters we have found throughout the
analysis to calculate the hydraulic head needed to overcome pipe drag to be
0.713m(3.1) We can calculate total hydraulic head needed by the CWP pump by
considering the pressure drop across the compressor, and minor losses. We will
assume all other losses will contribute 3.0m to the total head loss. The assumption is
made by using average pressure loss values in a CWP. [1] Thus our total hydraulic
head becomes 3.712m. Note that the values for head are per unit flow, thus they are
very small. We then calculate our pumping power requirement to be 1.036MW(3.2).
However, all pumps have inefficiencies and this must be taken into consideration.
Because pumps this large are not readily available we will utilize the pump
efficiency provided in Bharathan’s system which is 72%[7] With a pump efficiency
of 72% we find that our water pump will require 1.439MW(3.3) of power. Note that
a company will have to be constructed in order to construct such a massive custom
water pump. By applying our CWP parameters to Bharathan’s system we find a total
parasitic power value of 3.942MW(4.1). This value is less than the calculated values
first taken from Bharathan’s system. Thus our net power generation increases
because our parasitic consumption has decreased. We find a net generation power
of 13.338MW(4.2). Operating efficiency and net efficiency can then be determined
for our CWP also using Bharathan’s parameters. We find an operating efficiency of
77.155% (4.3) and a net efficiency of 2.826% (4.4). Thus we can draw the
conclusion that our preliminary analysis is sufficient to operate a 10MW power
generation OTEC system. By reaching higher values than the initial efficiencies of
the system it is shown that our CWP will not cause a decrease in power generation.
Conclusion
The intention of this preliminary analysis was to design a CWP that could be
utilized by a 10MW OTEC power plant. Consideration of the common problems that
plague CWPs were taken into consideration and discussed. The many years of work
from engineers was directly applied to this analysis. OTEC systems are not only an
interesting field of study because of challenging issues, but also a valuable field of
13. 13
study that can possibly impact mankind. Renewable energies are no longer simply
an interesting field of study, but will soon become a necessity as fossil fuels begin to
diminish. Therefore, OTEC system analyses can be concluded to be challenging,
stimulating, and a gateway into the future.
16. 16
(4.2) Net Power of Devised OTEC System
𝑷 𝒏𝒆𝒕 = 𝑷 𝒈𝒓𝒐𝒔𝒔 − 𝑷 𝒑𝒂𝒓𝒂𝒔𝒊𝒕𝒊𝒄
𝑃 𝑔𝑟𝑜𝑠𝑠 = 17287 𝐾𝑊
𝑃𝑝𝑎𝑟𝑎𝑠𝑖𝑡𝑖𝑐 = 3949.19 𝐾𝑊
𝑃 𝑛𝑒𝑡 = 13.338 𝑀𝑊
(4.3) Operating Efficiency of Devised OTEC System
𝜼 𝒐𝒑𝒆𝒓𝒂𝒕𝒊𝒏𝒈 =
𝑷 𝒏𝒆𝒕
𝑷 𝒈𝒓𝒐𝒔𝒔
[1]
𝑃𝑛𝑒𝑡 = 13.338 𝑀𝑊
𝑃𝑔𝑟𝑜𝑠𝑠 = 17287 𝐾𝑊
𝜂 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 = 77.152 %
(4.4) Net Efficiency of Devised OTEC System
𝜼 𝒏𝒆𝒕 = (𝜼 𝒐𝒑𝒆𝒓𝒂𝒕𝒊𝒏𝒈 )(𝑷 𝒎𝒂𝒙,𝒕𝒉𝒆𝒐𝒓) [1]
𝜂 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 = 77.152%
𝑃 𝑚𝑎𝑥,𝑡ℎ𝑒𝑜𝑟 = 3.663 %
𝜂 𝑛𝑒𝑡 = 2.826 %
17. 17
References
[1] Avery, William H., and Chih Wu. Renewable Energy from the Ocean: A Guide to
OTEC. New York, NY: Oxford Univ. Press, 1994.
[2] A. V. Da Rosa, Fundamentals of Renewable Energy Processes (Academic
Press/Elsevier, 2009)
[3] R. Bedard, P. T. Jacobson, M. Previsic, W. Musial, and R. Varley, “An Overview of
Ocean Renewable Energy Technologies,’’ Oceanography 23,22 (2010)
[4] O. M. Griffin, “Otec cold water pipe design for problems caused by vortex-excited
oscillations,’’ Ocean Engineering, 8(2), 129 (1981)
[5] R-H. Yeh, T-Z. Su, M-S. Yang, “Maximum output of an OTEC power plant,” Ocean
Engineering, 32(5-6),685 (2005)
[6] Imm, Paul. "Abrasion Resistance of Concrete Pipe." Ontario Concrete Pipe
Association. Accessed November 30, 2014. http://www.ocpa.com/Abrasion
Resistance.pdf.
[7] D. Bharathan, “Staging Rankine Cycles Using Ammonia for OTEC Power
Production.”(2011)
![2
Introduction
With the growing interest in renewable energies around the world Ocean
Thermal Energy Conversion (OTEC) appears to have great potential as a tool for
harnessing a naturally replenishing recourse. Many are well aware that countries
dependence on finite recourses such as oil and coal is a major issue that must be
addressed. OTEC uses the naturally replenishing energy from the sun that is stored
in the ocean to operate a heat engine, which generates electric power. Specific
information on OTEC systems can be found from the book Renewable Energy From
the Ocean: A Guide to OTEC by Avery and Wu and is summarized in the rest of this
introduction. [1] The ocean stores the majority of energy from sunlight in a 35 to
100m region in the sea. In tropical oceans the temperature in this regions is
approximately 28° C. Winds at the surface and waves keep the temperature nearly
uniform throughout this region. Furthermore, the temperature of this region is
maintained nearly constant throughout the entire year. As depth increases
temperature increases until 800 to 1000m below the surface. Here the temperature
of the water reaches 4.4° C. After this region the temperature only decreases a few
degrees until one reaches the ocean bottom. This approximation is based on an
average ocean depth of 3650m. The ocean thus essentially is a very large area with
warm water at the surface and cold water at the lower depths. The temperature
difference is 20 to 25°C in tropical regions where depth exceeds 1000m. The
difference in temperature is maintained with slight variations throughout the year
similar to the surface temperature. OTEC systems can either be closed-systems or
open-systems. Closed OTEC systems are rather intriguing because they can be
modeled after many previously developed power generation systems. Ammonia is
an appropriate working fluid in a closed OTEC system because of its low boiling
point and easy availability. Warm water is drawn into the system from near the
surface, and warms an evaporator with ammonia inside of it. The ammonia boils,
and the vapor expands across a turbine, which produces power to operate an
electric generator. The vapor passes through a condenser that is cooled by the cold
water from the depths of the ocean. The ammonia is pumped back to the evaporator](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)