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MAE 133A: Engineering Thermodynamics Final Project
Ocean Thermal
Energy Conversion MAE 133A: Engineering Thermodynamics Final Project
TA: Ladan Amouzegar
By: Sonny Pham, Andrew Schurr, Amanda Fujii, Justin Tran, and
Christopher Underhill 3/23/2012
ii
Abstract:
Ocean Thermal Energy Conversion (OTEC) utilizes the natural thermal gradients in the
ocean to drive a power cycle (typically a Rankine Cycle) for energy generation. These thermal
gradients are attributed to how the ocean constantly absorbs radiant energy from the sun, while
ocean waters deep down remain very cold. At ideal OTEC locations, the temperature difference
can get up to about 20oC. The advantage of using OTEC is that it uses a nearly endless supply of
fuel to drive its cycle, and ocean thermal energy is free. It also avoids the burning of fossil fuels
or other means which produce waste harmful to the environment. The main drawbacks are that it
takes an immense amount of money to build an OTEC plant, and the inherent inefficiency of the
cycle (around 7% theoretically). To improve the efficiency of OTEC, a heating tub which
encourages the ocean to absorb more energy from the sun than it normally does was proposed.
In the end, however, it was determined that OTEC is not a viable means to produce
energy today. Extremely large mass flow rates of seawater would be required to result in a
reasonably large net power output, and this would take a toll on the ocean environment.
Additionally, accounting for the power required to pump the seawater into the heat exchangers,
the thermal efficiency of the cycle wound up being 1.74% with ammonia, 1.93% for Refrigerant
22, and 2.54% for Refrigerant 134A. If the plant is only producing energy with this efficiency,
especially considering the large capital costs in constructing an OTEC plant, it would take a very
large amount of time the costs to break even.
iii
Contents Abstract: ........................................................................................................................................................ ii
1 List of Figures ...................................................................................................................................... iv
2 List of Tables ....................................................................................................................................... iv
3 Introduction ........................................................................................................................................... 1
3.1 Background ................................................................................................................................... 1
3.2 History........................................................................................................................................... 2
3.3 Benefits .......................................................................................................................................... 3
3.4 Limitations .................................................................................................................................... 3
3.5 Economic Feasibility .................................................................................................................... 5
3.6 Markets ......................................................................................................................................... 6
3.7 Location ........................................................................................................................................ 7
3.8 Current Systems ............................................................................................................................ 7
3.9 Land-based and Near-shore.......................................................................................................... 8
3.10 Deep Water ................................................................................................................................... 8
3.11 Shelf-Mounted Facility .................................................................................................................. 8
3.12 Floating Facility ........................................................................................................................... 9
4 Theory/Governing Equation ................................................................................................................. 9
5 Thermodynamic Analysis of a Simple OTEC System ........................................................................ 11
5.1 System Description and Assumptions ......................................................................................... 11
5.2 Setting the States ......................................................................................................................... 12
5.3 Determination of System Specifications ...................................................................................... 14
5.4 Discussion ................................................................................................................................... 16
6 Exergy Analysis .................................................................................................................................. 18
6.1 Background ................................................................................................................................. 18
6.2 Exergy Equations ........................................................................................................................ 19
6.2.1 Boiler ................................................................................................................................... 19
6.2.2 Turbine ................................................................................................................................ 20
6.2.3 Condenser ........................................................................................................................... 21
6.2.4 Pump ................................................................................................................................... 21
6.2.5 Exergy Accounting .............................................................................................................. 21
6.3 Problems With Exergy Analysis .................................................................................................. 22
iv
6.3.1 Calculations with T0 = 296K .............................................................................................. 23
6.3.2 Calculations with T0 = 288K .............................................................................................. 24
6.3.3 Calculations with T0 = 277K .............................................................................................. 24
7 Design Improvement Concept: ........................................................................................................... 25
7.1 Thermodynamic Analysis of Improved Design Concept ............................................................. 27
7.2 Design Problems ......................................................................................................................... 31
8 Microbial Fouling of Heat Exchanger Tubes ...................................................................................... 32
8.1 Theory and Sample Calculation .................................................................................................. 33
8.2 Results and Analysis ................................................................................................................... 35
9 Structural Analysis: Cold Water Pipe ................................................................................................. 38
9.1 Equations, Theory, and Assumptions .......................................................................................... 39
9.2 Results ......................................................................................................................................... 41
9.3 Analysis ....................................................................................................................................... 42
10 Conclusions ..................................................................................................................................... 44
11 References ....................................................................................................................................... 45
1 List of Figures Figure 1: T-s Diagram of a Typical Rankine Cycle6
................................................................................... 10
Figure 2: Simple OTEC System Cycle7 ...................................................................................................... 11
Figure 3: Normal Heat Absorption from Sun and Thermocline ................................................................. 25
Figure 4: Proposed Design Concept............................................................................................................ 27
Figure 5: T-S Diagram of Cycle ................................................................................................................. 28
Figure 6: Plot of Tub temperature versus Tub Size (Length Parameter) .................................................... 31
Figure 7: Generic Single Stream Heat Exchanger ...................................................................................... 33
Figure 8: Microbial fouling Thermal Resistance vs. Time for Free fouling1 .............................................. 35
Figure 9: Microbial fouling Thermal Resistance vs. Time, Spongeball treatment2 .................................... 37
Figure 10: Results of Chlorine Treatment on Fouling Thermal Resistance1 .............................................. 38
Figure 11: Effects on Principal Stress on Outer Diameter .......................................................................... 42
2 List of Tables Table 1: Achievements in OTEC Technology11
........................................................................................... 2
Table 2: Costs to Build a 1MW and 100MW plant ...................................................................................... 5
Table 3: Expected Output of Byproducts ...................................................................................................... 6
Table 4: Costs of Possible Working Fluids per Metric Ton .......................................................................... 6
v
Table 5: Cost of Electricity2 .......................................................................................................................... 6
Table 6: Summary of the Set States ............................................................................................................ 14
Table 7: System Specifications for 100MW Net Output ............................................................................ 16
Table 8: Summary of Working Fluid Enthalpies at Each State .................................................................. 17
Table 9: Comparison of System Specs for 100MW Net Output ................................................................. 17
Table 10: Comparison of System Specs for 1MW Net Output ................................................................... 18
Table 11: Summary of Exergy Accounting Equations ............................................................................... 22
Table 12: Exergy Analysis Results with T0 = 277K ................................................................................... 24
1
3 Introduction
3.1 Background
Energy is an essential resource for the evolution of mankind. As of 2000, the world
population was 6 billion, and that number continues to grow daily. With an increasing
population, energy consumption has correspondingly increased. As energy consumption
increases, and as current sources of energy become depleted, the search for new sources of
energy has become vitally important. Legislative pressure to push greener alternative energy
methods has identified OTEC as a potential source to investigate.
The goal of Ocean Thermal Energy Conversion (OTEC) is to use the ocean’s thermal
gradient to run heat engines and provide power in the form of electricity. Oceans cover
approximately 70% of the Earth’s surface, and they are constantly absorbing energy from the
sun. This means that oceans are essentially a huge energy reservoir waiting to be tapped in some
manner. Every day, the ocean absorbs energy from solar radiation equivalent to the quantity
produced by 250 billion barrels of oil. Every year that amounts to 4000 times the energy humans
consume annually7. OTEC was first proposed in the late 1800s, but never made a huge jump in
development and implementation because of the large scaling needed to produce a useful amount
of work. In 1970, Japan created an OTEC plant that generated a useful amount of work at
120kW, which gave it the highest power output of any OTEC plant at the time. Today, continual
development is being made on this concept in the United States and India. The focus here will be
on closed cycle systems.
2
3.2 History
A French physicist named Jacques Arsene d’Arsonval first proposed OTEC in 1881 as a
method of converting the thermal energy of the ocean into power. In 1930, one of his students,
Georges Claude, built a small open-cycle system that produced 22kW of power and then another
in 1935. Both plants, however, were destroyed by the ocean environment.
J.H. Anderson developed a closed system OTEC plant in 1964, which lead the U.S. and
Japan to push for OTEC research during the 1973 energy crisis. After this point, more OTEC
plants were constructed. The following table provides a chronological summary of important
advances in OTEC technology:
Table 1: Achievements in OTEC Technology11
1881 Mr. J. D'Arsonval developed his idea of OTEC theory 1933 Mr. G. Claude generated a net 12 kW output OTEC near Cuba 1977 Saga University succeeded with 1 kW experimental plant 1979 “Mini-OTEC” used cold-water pipe to produce 15kW power (52kW gross) 1980 U.S. DOE built a test site for closed-cycle OTEC heat exchangers, OTEC-1.
Results showed that OTEC systems can operate from floating platforms with little effect on the marine environment. The same year 2 laws were enacted to promote OTEC development: Ocean Thermal Energy Conversion Act and Ocean Thermal Energy Conversion Research, Development, and Demonstration Act.
1981 Tokyo Electric Co., and its subsidiary undertook successful experiment of a 120 kW OTEC in the Republic of Nauru. Used cold-water pipe on the sea bed at 580m depth. Freon was the working fluid. Produced 31.5 kW of net power.
1984 DOE developed a vertical-spout evaporator that converts warm seawater to steam with efficiencies as high as 97%
1985 A 75 kW experimental OTEC plant was installed at Saga University. 1993 USA completed their 210kW open cycle OTEC demonstration facility off
coast of Kona, Hawaii. 2009-2013 Lockheed Martin's Alternative Energy Development team has partnered with
Makai Ocean Engineering to complete the final design phase of a 10-MW closed cycle OTEC pilot system which will become operational in Hawaii in the 2012-2013 time frame. This system is being designed to expand to 100-MW commercial systems in the near future
3
3.3 Benefits
OTEC plants have several benefits over conventional power plants. The main advantage
is that it is a renewable source and operates on a base load platform allowing it to run 24/7 which
is advantageous over other sources such as wind. There are also beneficial by-products of OTEC
systems. Some of these potential by-products are:11
1. Desalination of seawater to fresh water: A system, created by Saga University in Japan,
can distill 1% of seawater it absorbs into pure fresh water. In deep ocean waters, the
desalinated water can also be turned into mineral water.
2. Lithium extraction: Fuel cells and other batteries use lithium as a main proponent and
OTEC can extract chloride-lithium in seawater as a by-product. This adds greatly to the
feasibility of OTEC systems.
3. Hydrogen production: OTEC systems can also provide clean hydrogen production from
seawater.
4. Air conditioning possibilities: OTEC systems can also use produce cool air with the cold
water source. Using OTEC with air conditioning uses much less energy than having an
independent electrical system.
5. Aquaculture support: OTEC can provide pure water and nutrients which supports
aquaculture.
6. It is also a market outside the control of other nations and is of low-risk to develop
making it an ideal field to research for a new source of energy.
3.4 Limitations
Some main problems with implementing OTEC plants are cost and legal concerns since
there are so few facilities at the moment. For deepwater locations, there are issues over their
4
legal status in relation to the United Nations Convention on the Law of the Sea4 because they can
be categorized as an artificial island. In terms of cost, OTEC needs subsiding and capital
investment early on to develop. Due to the low number of existing plants, costs are high and ill-
estimated.
There are many technical engineering problems as well. First off, there is a need of large
quantities of warm and cold seawater to provide sufficient heat transfer to and from the working
fluid and as a result a decent portion of the power produced by the system will be used to power
the pumps in the system itself. The size of the plant itself, and therefore the costs, must be large
because of the low conversion percentage of 3-4% out of an ideal 8% due to irreversibilities12.
One of the main complexities is the design of the cold water pipe which has had most of
its studies through computational methods due to a lack of larger systems. So far, there has been
the design of a 2.5m diameter, 120m long, fiberglass reinforced plastic sandwich piping for
floating OTEC plants and a smaller 2.6m high-density polyethylene pipe for land-based plants10.
Other complexities are the structural and stability issues with holding the actual plant in place.
Possible options are delineated further below.
Environmental impacts are also a concern because OTEC plants can disturb ocean life
due to huge discharges of water6 12. These discharges are estimated to equal the flow of the
Colorado River for a 100MW plant. Flow of cold, nutrient-rich deep ocean waters could disturb
the sea surface temperatures which could affect the ocean’s food web. Organisms are also more
directly affected by OTEC plants because they can be killed by the plant’s operations. Organisms
can be drawn into the plant and get caught in the filters or be exposed to the working fluids or
other unnatural substances used in construction. These concerns with the huge amount of
seawater needed can be a significant concern. Huge plants can also disturb fishing habits and
5
population as the fish will be drawn to the OTEC plants and the rich nutrients it produces.
Fishing in these areas may grow and the fishes may be exposed to trace biocides released from
the plant. Overall, there could be any sort of outcome on the marine life.
In terms of health, the working fluid in an OTEC system can be hazardous. Ammonia is
one of the usual working fluids and can be toxic is released; ammonia can damage eyes, skin,
mucous membranes, and inhibit respiration.
3.5 Economic Feasibility
The key to the implementation of OTEC systems is economic feasibility even with the
on-going pressure to provide renewable energy. According to estimated costs in India for a 50-
100MW plant, the costs would be similar to that of a coal-fueled power plant. A 1-5MW plant
would be similar to a diesel power plant. The economic feasibility of OTEC, however, is further
supported by its by-products. Glancing at the charts below, OTEC is a very promising solution to
the energy problems. These numbers are the estimated unit cost of electricity estimated from an
OTEC plant proposed for India12.
Table 2: Costs to Build a 1MW and 100MW plant
Power Output Gross (MW) 1 100 Power Output Net (MW) 0.617 64.23 Heat Exchanger Cost (US Mil$) 1.70 152.58 Cost of Cold W. Pipe 0.69 4.65 Cost of Barge 0.69 9.30 Mooring Cost 2.09 5.81 Turbine + Inst Cost 1.16 69.76 Total Cost 6.42 242.10 Cost of Electricity ($/kWh) 0.189 0.068
6
Table 3: Expected Output of Byproducts
Gross Power Output (MW) 1 10 Net Power Output (MW) 0.7 7.5 Net Electricity (MWh/year) 4,900 52,500 Up-welled DOW (t/h) 4,700 43,000 Fresh Water (t/h) 1,100 10,000 Hydrogen (Nm^3/h) 2,000 22,000 Chloride Lithium (kg/day) 30 260 Mineral Water (bottle/day) 16,000 150,000 DOW = Deep Ocean Water
Table 4: Costs of Possible Working Fluids per Metric Ton
Working Fluid Price per Metric Ton Ammonia $310 R-22 $3250 R-134a* $29900 *calculated off price per kg
3.6 Markets
Within the next decade, OTEC may find considerable markets in small island names of
the South Pacific and Hawaii. Diesel-generated electricity on island nations is generally
expensive making OTEC a more economically feasible source of energy production. Possible
locations include: Molokai in Hawaii, Guam, American Samoa, Puerto Rico, and areas in the
Gulf of Mexico, Pacific, Atlantic, and Indian Oceans. In total, however, there are 98 nations with
access to an ocean thermal source according to the US Department of State7.
Table 5: Cost of Electricity2
Location Cost $/kWh California .1480 Hawaii .3631 Guam .2400 Germany .3066 Italy .3723 Philippines .3046 Australia .288
7
3.7 Location
To operate an OTEC plant requires a large enough temperature gradient, which is at least
20 degrees Celsius (36 degrees F), between the condenser and the heat exchanger. To assure
these aspects, tropical regions are the target locations for OTEC plants. These areas are between
latitude 20 deg N and 20 deg S and contains many island nations such as those listed above7.
Also, the deep water used cannot be greater than 1000 meters (3280) feet due to structural
reasons.
Other reasons to consider potential sites relate to socioeconomic factors including the
level of development of an island. Although having an OTEC plant would give island nations
some independence, they would still need the infrastructure and population to use and maintain
the plant.
3.8 Current Systems
Currently, there are no large active OTEC plants, but there are ones in development. In
India, there is a prototype that produces 1MW of power off the coast of Tirechendur5. The U.S.
Navy is also planning to place a small plant in the Indian Ocean.
Makai Ocean Engineering, based in Honolulu Hawaii, has a proposal for a 10MW OTEC
plant off the shoes of Guam. Lockheed Martin, in partnering with Makai, is also in the process of
building another 10MW OTEC plant in Hawaii that will be operational in 2013 as an
experimental prelude to a 100MW plant for future implementation5/10.
There are several options to consider in building an OTEC plant. There are two types of
locations and two types of facilities for current designs. The location types are Land-based/Near-
shore and Deep Water. The facility types for off-shore/deepwater are Shelf-Mounted and
Floating facilities7.
8
3.9 Land-based and Near-shore
These plants are more simplistic to maintain structurally because they do not require
extensive maintenance in a more difficult environment (the open-ocean). Being closer to land
also means they can be constructed with lower costs. Also, they can be built in safer places and
allow the plants to operate in the vicinity of other related industries without the need of long
power cables. Locations for these types of plants are areas of relatively flat sea floors and steep
offshore slopes. To reach a decent location for the condenser, however, will encapsulate a lot of
piping to reach depths low enough.
3.10 Deep Water
Deep water has two main advantages over land and shore-based plants. Deep water plants
avoid the turbulent surf zones which can produce high amounts of stress to piping. This stress
would call for more engineering solutions and higher costs to the overall plant. Open ocean
locations also allow for more defined areas of cold seawater and allows for shorter piping
directly into the cold seawater source for the condenser. On the other side, however, the plant’s
output would have to be carried long distances through extensive power cables that would be
difficult to maintain. These plants are also susceptible to storms and ocean conditions.
3.11 Shelf-Mounted Facility
Similar to an oil rig, this is an OTEC plant mounted to a continental shelf that is 100
meters below the sea. This allows the plant to avoid turbulent areas, but creates more difficulties
that need additional engineering and expenses to overcome such as the mounting system itself.
Open-ocean conditions cause stress on the piping as well which will be discussed. The power
produced would be difficult to transfer for usage again because there would be long power cables
9
that are difficult to maintain. Also, this type of facility needs a complex platform to maintain
stability.
3.12 Floating Facility
These facilities are essentially floating platforms with the OTEC plant on it. These plants
also have difficulties in dealing with stabilization and transferring power to land based
operations. Floating facilities are also vulnerable to storms leaving deep cables as another
difficulty. If the power cables are damaged during a storm then repairing them would be difficult
and expensive especially if they are submerged. Also, these cables must be designed to digress
from entanglement. An advantage or floating facilities, however, is that warm water can be
drawn directly into the platform for the heat exchanger.
4 Theory/Governing Equation
Ocean thermal energy conversion relies upon the ocean’s thermal gradient to run heat
engines and provide power in the form of electricity. As with any thermodynamic process,
conservation of energy is the main governing equation. The first law of thermodynamics is
stated in the following equation:
Equation 4.1
The concept of a heat engine is a basis of thermodynamics in which a system in contact with a
“hotter” body and a “cooler” body will produce a work output as heat from the hotter body
transfers to the colder body.6 OTEC is based upon this concept, and as such, the Rankine cycle
best describes the OTEC process. Most basically, the Rankine cycle consists of a heat
exchanger, turbine, condenser, and pump. The general processes are outlined as follows:
1-2: Isentropic expansion of the working fluid through the turbine from saturated vapor
12
energy effects of the system assumed to be negligible. The turbine efficiency and pump
efficiencies were taken to be 80% and 85%, respectively.
Knowing that current OTEC systems are found in tropical climates, seawater
temperatures at corresponding depths were found from seawater data collected off the coast of
Hawaii. At approximately 10 meters deep, the “warm” seawater had an average temperature of
24.92 oC. At approximately 900 meters deep, the “cold” seawater had an average temperature of
4.39 oC4. Based on these values, temperature estimates for the exit seawater were made.
Additionally, temperature estimates were made for the working fluid exiting the boiler and the
exit fluid entering the condenser based on the seawater temperatures.
5.2 Setting the States
After determining reasonable temperatures at various locations throughout the cycle,
ammonia was chosen as the initial working fluid, and the enthalpy and entropy values at each
point along the cycle were found. Sample calculations for setting the states using ammonia as
the working fluid can be seen below:
State 1 is found after the working fluid exits the boiler:
With , the corresponding values can be looked up in a chart.
State 2 is between the turbine and the condenser:
Equation 5.1
Equation 5.2
13
Equation 5.3
State 3 is after the condenser, and the working fluid at this state is a saturated liquid:
The corresponding values for a saturated liquid can also be looked up in a chart.
State 4 is located after the pump:
Equation 5.4
Equation 5.5
For the hot water stream through the boiler:
Using the compressed water tables:
For the cold water stream through the condenser:
14
Using the compressed water tables:
Once all the enthalpy and entropy values are found, system requirements and outputs can be
calculated. A summary of the calculated values for ammonia can be found in the table below:
Table 6: Summary of the Set States
HotWater
hin 104.67 sin 0.3660
hout 88.28 sout 0.3106
ColdWater
hin 27.57 sin 0.0669
hout 42.57 sout 0.1204
Ammonia
h1 1459.40 s1 5.0849
h2 1426.48 s2 5.1140
h3 226.75 s3 0.8769
h4 227.21 s4 0.8770
5.3 Determination of System Specifications
With the states being set, the initial goal was to determine what would be necessary to
achieve a net power output of 100MW. This would mean that the work output from the turbine
minus the work input required for the system would be equal to 100MW. The cycle diagram
above does not include pumps for pushing the seawater through the boiler and the condenser, but
in reality, a large amount of work would be required for these processes. It is estimated that the
15
work input required to pump the warm and cold seawater is approximately half the net output of
the system.10 Based on this, the work input for the cold water pump was estimated to be 27MW,
and the work input for the warm water pump was estimated to be 23MW for a total of 50MW.
For this reason, the work output from the turbine was estimated to be 150MW in order to try to
achieve a net output around 100MW. Based on these conditions, system requirements can be
calculated. Sample calculations using ammonia as the working fluid are again shown below:
From an energy balance around the turbine, the mass flow rate of the working fluid can
be calculated:
If , then
From an energy balance around the boiler, the mass flow rate of warm seawater can be
calculated:
Equation 5.6
From an energy balance around the condenser, the mass flow rate of cold seawater can be
calculated:
Equation 5.7
From an energy balance around the pump, the work required by the pump can be calculated:
Equation 5.8
The heat input to the system is calculated as follows:
16
Equation 5.9
The net output of the system and the system efficiency are calculated as follows.
Equation 5.10
Equation 5.11
A summary of these calculated values can be found in the following table:
Table 7: System Specifications for 100MW Net Output
Ammonia
Net Work [MW] 97.9
Efficiency [%] 1.74
Mass Flow Rate Working Fluid [kg/s] 4,556.5
Mass Flow Rate Warm Sea Water [kg/s] 342,540
Mass Flow Rate Cold Sea Water [kg/s] 363,850
5.4 Discussion
In evaluating these numbers, many things stand out. For one, the mass flow rates of hot
and cold seawater are unrealistically large. The infrastructure required to support mass flow
rates on the order of hundreds of thousands of kilograms per second is nearly logistically
impossible. Additionally, the impact that mass flow rates of this magnitude would have on the
ocean ecosystem would likely be significant. The efficiency of the system is also extremely low.
In an attempt to see if a different working fluid would yield more reasonable mass flow rates and
a higher efficiency, using the same procedure as above, the states were reset using first R-22 and
then R-134A as the working fluid. A summary table of the enthalpies calculated at each state
throughout the cycle can be seen below:
17
Table 8: Summary of Working Fluid Enthalpies at Each State
Ammonia R22 R134A
h1 1459.4 h1 255.8 h1 258.36
h2 1426.48 h2 249.6 h2 250.72
h3 226.75 h3 52.97 h3 63.455
h4 227.21 h4 53.2 h4 63.6
Using these values, the system performance specifications and characteristics can be
calculated and compared with those of ammonia. The summary of these values can be seen in
the table below:
Table 9: Comparison of System Specs for 100MW Net Output
Ammonia R-22 R-134A
Net Work [MW] 97.9 94.4 97.1
Efficiency (%) 1.74 1.93 2.54
Mass Flow Rate Working Fluid [kg/s] 4,556.5 24,193.5 19,633.5 Mass Flow Rate Warm Sea Water [kg/s] 342,540 299,061 233,302
Mass Flow Rate Cold Sea Water [kg/s] 363,850 317,145 245,111
While the efficiencies with R-22 and R-134 were slightly better than ammonia, the
additional amount of working fluid required would result in greater cost and logistical issues.
Additionally, seeing that the mass flow rates of seawater that would be required to generate a net
output of 100MW remains unrealistically large regardless of the working fluid, the system was
scaled down in an attempt to give a 1MW net output. The summary of system specifications for
a net output of 1MW can be seen in the table below:
18
Table 10: Comparison of System Specs for 1MW Net Output
Ammonia R-22 R-134A
Net Work [MW] 0.98 0.94 0.97 Efficiency (%) 1.74 1.93 2.54
Mass Flow Rate Working Fluid [kg/s] 4,556.5 24,193.5 19,633.5 Mass Flow Rate Warm Sea Water [kg/s] 3,425 2,991 2,333 Mass Flow Rate Cold Sea Water [kg/s] 3,638 3,171 2,451
While the mass flow rates of the seawater are lower, the efficiencies remain the same, and the
amount of infrastructure that would be required relative to the amount of power that would be
produced is very low.
6 Exergy Analysis
6.1 Background
Exergy is the maximum theoretical value for the work that can be developed when two
systems come into equilibrium. For the OTEC plant, work could be extracted from the heat
source, the warm ocean water, if it were to come into equilibrium with a heat sink, also the
ocean. If the heat sink was in contact with another sink at a lower thermodynamic potential, more
work could be developed. If no other heat sinks were at a lower thermodynamic potential, exergy
would be the work developed when the heat source came into equilibrium with the heat sink.
This heat sink would be said to be at the dead state. In other words, when a system has reached
the dead state no more work can be developed.6, 13
19
6.2 Exergy Equations
Considering the Rankine cycle as the system, exergy is brought into the system through
the hot water stream, leaves the system as net power output and through the cold water stream,
and is destroyed in the boiler, turbine, condenser, and pump. The system is assumed to be at
steady-state and each component can be taken as a control volume for which an exergy rate
balance may be applied. The steady-state control volume exergy rate balance is given by
Equation 6.1
where is the boundary temperature at which heat transfer, , occurs, is the net power
output, is mass flow rate, subscript refers to inlet streams, subscript refer to outlet streams,
is exergy destroyed, and is the specific flow exergy given by
Equation 6.2
In this equation, all properties with subscript 0 refer to the property value at the dead state.
6.2.1 Boiler
Recall the boiler is assumed to have no net output work. Two streams flow through the
boiler, ammonia and hot water. The net exergy flowing into the boiler is through the hot water
stream and is given by
Equation 6.3
where potential and kinetic energy effects are negligible. Note that all quantities aside from T0
are solved for in the Section 5. Since exergy only comes into the overall system through the
boiler, a simple calculation check is to verify that exergy carried into the system is greater than
20
the net work output. Otherwise, the net work obtained by the cycle would be greater than the
maximum theoretical work available by the inputs to the cycle, which, by definition, is
impossible.
The net exergy carried out of the boiler is through the ammonia stream. Potential and
kinetic energy effects are negligible so the equation appears similarly to Equation 6.3.
Equation 6.4
Solving Equation 4.1 for the exergy destroyed in the boiler in terms of Equations 6.3 and
6.4 yields
Equation 6.5
Although heat is being added to the system, it is accounted for in the hot inlet and outlet streams,
rather than as .
6.2.2 Turbine
The turbine has one inlet and outlet stream of ammonia, is assumed to be adiabatic, and
yields , so an equation for the exergy destroyed in the turbine can be developed:
Equation 6.6
The work developed by the turbine is also considered to be an exergy loss, equal to , however
generally turbine work is combined with the work required by the pump, , to get the net work
developed, .
21
6.2.3 Condenser
The condenser is similar to the boiler in that it has both a stream of ammonia and a
stream of water, this time cold. Exergy is transferred out of the cycle through the cold water
stream and is calculated as follows:
Equation 6.7
Exergy destroyed in the condenser is can be calculated and as expected, the equation resembles
Equation 6.5:
Equation 6.8
6.2.4 Pump
The pump is similar to the turbine with one inlet and one outlet stream of ammonia. It is
also assumed to be adiabatic, however it requires work, , rather than produces work as the
turbine does. The equation for exergy destruction in the pump is similar to Equation 6.6 as
anticipated:
Equation 6.9
6.2.5 Exergy Accounting
Exergy accounting is a way to evaluate and compare system inefficiency.6 All exergy
values are compared to the net exergy carried into the system, which yields:
22
Table 11: Summary of Exergy Accounting Equations
Net Exergy In Through Warm Water 100%
Exergy Destroyed:
Boiler
Turbine
Condenser
Pump
Net Exergy Out Through Cold Water
Net Work Output
6.3 Problems With Exergy Analysis Generally, when determining a value for T0 the environmental temperature is used. Since
most systems occur in air, as opposed to water in the case of OTEC, T0 is chosen as 25oC
(298K), the typical ambient air temperature. With OTEC, the Rankine cycle takes place in the
warmer regions of the ocean, where water is around 23oC (296K), so this temperature seems to
be a natural choice. D.H. Johnson’s The Exergy of the Ocean Thermal Resource and Analysis of
Second-Law Efficiencies of Idealized Ocean Thermal Energy Conversion Power Cycles makes a
case for:
Equation 6.10
This equation yields T0 = 15oC (288K). Johnson argues that when the sea water used in the
OTEC plant is dispelled at this temperature work is maximized, making this temperature the
dead state temperature.13 Still other papers involving exergy analysis for an OTEC system set T0
to be the deep water temperature.14, 15 Recall the description of exergy using heat sinks. The heat
source, warm ocean water, comes into equilibrium with a heat sink, initially taken to be the
23
surrounding ocean water, at around 23oC. Because the temperature of the ocean decreases with
depth, the heat sink selected initially is in contact with a heat sink at a lower thermodynamic
potential, the colder water below it. This is true until a heat sink is reached at the lowest
thermodynamic potential, which corresponds with the deep water temperature, around 4oC
(277K).
The exergy transferred to the ammonia from the hot water can also be looked at in terms
of into the system, where comes from the hot water. Therefore, the following is equal to
Equation 4.3:
Equation 6.11
where is the temperature at the boundary of the heat transfer, . This equation can be used to
evaluate the exergy results for the various T0 values state previously. The temperature at the
boundary of heat transfer is taken as 292K, the average temperature of the streams entering and
exiting the boiler.
6.3.1 Calculations with T0 = 296K
The net exergy carried into the system by the hot water must be positive, otherwise the
hot water would be carrying exergy out of the system. In Equation 4.11, is positive because
heat is going into the system, so must be less than unity for to be positive. However,
recalling and with the dead state temperature taken to be the temperature of the
surrounding sea water, , . Thus, is not suitable for this exergy
calculation.
24
6.3.2 Calculations with T0 = 288K
As suggested by Johnson, using calculated in Equation 4.10 gives
, so this value for T0 at least satisfies the requirement for . However, when
this value is applied to Equation 6.7 it yields a negative net exergy transferred into the system by
the cold stream, which is equivalent to the cold stream transferring exergy into the system.
Again, is also not suitable for this exergy calculation.
6.3.3 Calculations with T0 = 277K Taking T0 as the deep water temperature, 277K, satisfies . This value for the
dead state temperature proves to be suitable for the exergy calculations and the results from
using this dead state temperature value in Equations 6.3 through 6.9 and the exergy accounting
equations are tabulated below. This table demonstrates that the majority of exergy is developed
as work, which is desirable. If the efficiencies of individual components were looking to be
improved, Table 12 shows that the irreversibility in the boiler and condenser are greatest and
comparable so these components should be targeted, and that the irreversibility in the pump are
negligible, so the pump should be ignored..
Table 12: Exergy Analysis Results with T0 = 277K
Net exergy carried into system through hot water, 3,557 kW 100%
Net exergy carried out of boiler, 3,054 kW --
Exergy destroyed in boiler, 503 kW 14%
Exergy destroyed in turbine, 367 kW 10%
Net exergy carried out of system, 704 kW 20%
Exergy destroyed in condenser, 484 kW 14%
Exergy destroyed in pump, 20 kW <1%
Net work 1479 kW 42%
25
7 Design Improvement Concept:
When analyzing the current designs of OTEC systems, ways were searched for that
would improve the overall efficiency in order to maximize the net output. By taking a look at the
system in terms of exergy losses macroscopically, a potential method of increasing the overall
efficiency of the system was found.
OTEC, as previously
mentioned, utilizes the temperature
difference between shallow sea water
and deep sea water as reservoirs for
the heat source and heat sink. This
temperature difference is caused by
heating from the sun. Energy from the
sun's rays enter the ocean every day
and are slowly absorbed as the rays
go deeper. This slow absorption rate is a cause of exergy loss. Because water is clear, it allows
much infrared light to pass through, while only absorbing some at a time. Because OTEC utilizes
the relatively high temperature differential between shallow sea water and deep sea water, it
would benefit from increasing this temperature differential even more. The following system is a
preliminarily design which would preserve more of the sun's heat within the upper levels of the
sea by trapping it, thereby increasing the temperature differential for the OTEC system.
Figure 3: Normal Heat Absorption from Sun and Thermocline
26
The main design in this proposal is to create an insulated "heat tub" near the OTEC
system on the ocean's surface. This tub would be approximately 5m deep, have a highly
thermally conductive lining on the
interior, have approximately 10cm of
insulation, and be covered in a
protective, waterproof liner such as
fiberglass. The design is similar to that
of solar water heating design. Solar
water heaters use collectors on
rooftops to heat tanks of water by
convection. This system would do the
same, but the water would sit directly
on top of the collectors in the tub. The
goal is for the sun to heat the water in
the tub to a substantially higher
temperature than the standard sea
level water temperature. The working
fluid of the cycle would then pass through the tub (acting as a superheating heat exchanger) after
passing through an initial sea level water temperature boiler.
Inner Lining of Tub:
Ń 5052-Hンヲ Aﾉ┌ﾏｷﾐ┌ﾏが ヰくヰヲざЩっ-ヰくヰヰヲざ デｴｷIﾆﾐWゲゲ
Ń High Thermal Conductivity (138 W/m-K)
Ń Low Specific Heat Capacity (0.88J/g-Ԩ)
Ń Painted black for higher absorption/less reflection
and to protect against corrosion due to seawater.
Tub Core:
Ń Extruded Polystyrene Foam (Styrofoam), 0.1m
thickness
Ń R = 5 ft2-Ԭ-h/Btu-in = 60 ft-Ԭ-h/Btu = 373m-Ԩ/W
Outer Lining of Tub:
Ń Lining of Duratec primer
Ń Жざ FｷHWヴｪﾉ;ゲゲ W┝デWヴｷﾗヴ ｴ┌ﾉﾉ
Ń The Duratec primer allows for a bondable surface for
fiberglass, as well as sealing the foam from the resin
in fiberglass which could eat away the foam.
27
7.1 Thermodynamic Analysis of Improved Design Concept
Assuming that the same cold water temperature (T = 8oC) and standard warm water
temperature (T = 25oC) as previously used will be utilized, several adjustments to the cycle will
be made by adding in the proposed design. Using the same expected efficiency of 0.8 for the
turbine and entropy of 5.2033 kJ/kg-K at a pressure of 0.61529 MPa for saturated vapor at T =
10oC, a temperature and pressure for the turbine inlet were needed to be found for a temperature
and pressure higher than the previously used T and P in the basic cycle. Using the formula for
turbine efficiency with relation to the starting and ending enthalpies along with the knowledge
Figure 3: Proposed Design Concept Figure 4: Proposed Design Concept
28
State 4s T = (irrelevant) p = 0.9843 MPa s = 0.8769 kJ/kg-K h = 227.34 kJ/kg (compressed liquid) State 4 T = (irrelevant) p = 0.9843 MPa s = 0.8769 kJ/kg-K h = 227.445 kJ/kg (compressed liquid) (turbine efficiency = 0.8) (pump efficiency = 0.85) Wout, turbine = 49.0 kJ/kg Win, NH3 pump = 0.69495 kJ/kg Win, water pumps = 10.97 kJ/kg Wnet = 37.34 kJ/kg Qin = 1273.34 kJ/kg さ = 2.93
State 2: T = 10oC p = 0.61529 MPa s = 5.2033 kJ/kg-K h = 1451.78 kJ/kg (saturated vapor) State 3: T = 10 oC p = 0.61529 MPa s = 0.8769 kJ/kg-K h = 226.75 kJ/kg v = 1.6008*10^(-3) m^3/kg
State 1: T = 37.11oC p = 0.9843 MPa s = 5.1600 kJ/kg-K h = 1500.78 kJ/kg (superheated vapor) State 2s: T = 10 oC p = 0.61529 MPa s = 5.1600 kJ/kg-K h = 1439.53 kJ/kg x = 0.99
that the entropy at the inlet to the turbine is equal to the entropy at state 2s, interpolation was
used to discover that a state at T = 37.11oC and P = 0.9843 MPa would be satisfactory for the
cycle. A complete thermodynamic analysis along with a T-S Diagram of the improved cycle are
shown in the following figure and table:
Figure 5: T-S Diagram of Cycle
29
The resulting effect of the superheating tub on the cycle is an increase in thermal
efficiency from 1.74% to 2.93%. While the thermal efficiency is still very small, this is a
relatively huge increase. For a 1MW plant, this would increase the net output to 1.7MW.
However, it still must be shown whether this will be cost effective, and it also must be analyzed
whether or not a heat tub could reasonably achieve a temperature increase to 37C.
Equation 7.1
Equation 7.2
Equation 7.3
Equation 7.4
Equation 7.5
Notes: 1) From analysis of solar water heating systems, collectors are able to harness
approximately 0.68 of the sun's heat. This represents the efficiency of the collector. 2)
Evaporation rates are dependent upon a vast number of factors, including water temperature,
air temperature, humidity, and wind. The rate term used above is an estimate which corresponds
well with evaporation data taken from seawater near the expected temperatures in an
environment of average humidity. 3) SA stands for surface area of exposed water in the tub. It is
taken to be l2, where l is the length of a side of the tub, and will be the independent variable in
the analysis. For practical purposes, the tub is designed to be square. The wall thickness is 0.1m.
The total wall area is l2+4dl, where d is the depth of the tub, which was arbitrarily chosen to be
5m. The deeper the tub, the better the system can handle temperature fluctuations between day
and night. is taken to be 25C, the expected temperature of sea level seawater. is the initial
30
temperature of ammonia when it enters the tub, which will be 20C. P is the (high) working fluid
pressure (0.9843 MPa). will be the dependent variable, and is desired to be 37C. 4) The last
remaining variable is . This represents the average enthalpy of water in the tub, or .
Using seawater steam table data, the equation h = 79.835 + 3.99525(Ttub-20) was developed.
This equation if very accurate for temperatures ranging from 20C to 40C. This was necessary in
order to be able to accurately plot the tub temperature against size. 5) Heat out through tub wall
rates were calculated using the R value of the Styrofoam insulation multiplied by the wall
thickness (0.1m) and the temperature difference between the tub water and ocean water.
Forming the energy balance around the tub,
Equation 7.6
Equation 7.7
Using Matlab and the preceding energy balance, the following plot was produced. Note that
because of several assumptions, it is only accurate for values of T=20C to T=40C (the graph
seems to indicated that the temperature would continue to rise linearly with the side length of the
tub, but this is not true as evaporation rates and other heat losses would start to significantly
increase above T=40C).
31
In order to produce an average tub temperature of 37C for a 1.7MW plant, a 112m x 112m tub is
predicted to be necessary. Based on prices of all the materials required, material shipping costs,
construction and assembly costs, it is estimated that such a tub would require approximately
$1.6mil to produce. This estimated additional cost would produce an additional 0.72 MW. The
original system produced 0.98MW at a capital cost of around $2.35mil. Thus, while the original
system would produce approximately 0.42MW/$mil(capital), this system would produce an
additional 0.45MW/mil(capital). This shows only a small increase in cost effectiveness.
7.2 Design Problems
As previously mentioned, a 1.7MW plant would require a 112m x 112m (12544m2) tub.
A 1.7MW power plant is fairly small, and such a tub would be a huge structure to go along with
such a small plant. For a 100MW plant, a 737,882 m2 (859m x 859m) would be required. Such a
large tub is simply not feasible for most OTEC locations. For deep water systems, such a tub
would not be able to withstand storms and the waves that come with them, unless more structural
Figure 6: Plot of Tub temperature versus Tub Size (Length Parameter)
32
supports were added, or the tub made flexible. Doing so, however, would require significantly
higher costs, and would render the system unfeasible in regard to cost. Other options include
near-shore and land based systems. However, land costs were not figured into the cost estimation
either. If placed in Hawaii, as planned, land costs would surely push the overall system cost into
an unfeasible state, unless somehow subsidized by the government and/or built on government
lands. A near-shore system seems to be the only feasible option, as the system would be safe
from storms and would avoid property costs.
8 Microbial Fouling of Heat Exchanger Tubes
One of the primary advantages of OTEC is its endless supply of a temperature difference
without any burning of fuel. This is, of course, the natural temperature gradient seen in ocean
layers. But using ocean water as a heat source and sink for this power cycle has its drawbacks as
well, especially from a heat transfer point of view. Since the seawater used in the heat
exchangers are unfiltered, they contain all of the bacteria and other micro-organisms living
naturally in the ocean. As seawater passes through the heat exchanger, some of these micro-
organisms can stick to the walls of the heat exchanger, forming a very thin layer between the
heat exchanger surface and the seawater. This accumulation of unintended material is called
fouling, and specifically for the case when bacteria and other living organisms accumulate is
called microbial fouling. What this thin layer does is increase the thermal resistance between the
seawater and the heat exchanger, making heat transfer more inefficient. As stated before, OTEC
plants are already inefficient as it is since it works within a small temperature difference. A
problem like microbial fouling can significantly impair an OTEC plant further if left unattended
and thus mitigate the economical worth of the plant. But fortunately methods for dealing with
33
microbial fouling have already been developed and this section aims to provide analysis on the
impact and solution to microbial fouling.
8.1 Theory and Sample Calculation
First, however, the effect microbial fouling has on heat exchanger efficiency will be
shown through a numerical example using typical system parameters found in an OTEC plants.
In an ideal Rankine cycle OTEC plant, the heat rejection through the condenser is an isobaric
and isothermal process as the two phase mixture at the outlet of the turbine condenses to
saturated liquid at the end of the condenser. Modeling the heat rejection in this process as a
single flow heat exchanger with a constant surface temperature, the effects of microbial fouling
on the efficiency of this heat exchanger can be analyzed. For this analysis, it is assumed that the
temperature at the surface and both the inlet and outlet temperatures for the seawater are fixed.
Steady state conditions and no heat generation within the fluid is also assumed. The only mode
of heat transfer will be convection to the moving seawater.
Figure 7: Generic Single Stream Heat Exchanger
The formula for the heat transfer through a heat exchanger with constant surface temperature is:
Equation 8.1
34
Where U is the overall heat transfer coefficient (a function of the flow conditions and any
fouling), As is the surface area of the tube, and is the log mean temperature difference,
defined as:
Equation 8.2
Typical values for the parameters so far are: = 55 oF, = 50oF, = 60 oF, and As =
226.19 m2 = 2434.688 ft2, which corresponds to a length of 72 meters and a diameter of 1 meter1.
The heat transfer takes place at a rate of 2540.98 Btu/s (which assumes a mass flowrate of 5.263
lb/s and a change in specific enthalpy from the inlet to outlet of the condenser to be 482.77
Btu/lb)1. When there is no fouling, the overall heat transfer coefficient, U, is simply the
convection heat transfer coefficient associated with the flow properties of the seawater:
Equation 8.3
The value of U will be affected by any microbial fouling resistance by adding to the total thermal
resistance between the heat exchanger and the seawater. A critical value for the thermal
resistance added by microbial fouling is 9*10-5 (m2 K/ W), which equals 1.84 (s ft2 oR/Btu) in
English units2. The new heat transfer coefficient is given by
Equation 8.4
Assuming the same conditions for the temperatures and area of the heat exchanger, the new heat
transfer with this heat transfer coefficient is:
Equation 8.5
This corresponds to a decrease of 21% of the original heat transfer without the fouling, a
significant drop in performance of the heat exchanger. This is especially significant considering
all other losses were ignored in this analysis. 21% is a pretty significant loss in an already
35
inefficient system like an OTEC plant and can be avoided if proper measures are taken to clean
out the microbial fouling.
8.2 Results and Analysis
So far three different methods have been developed to counteract the effects of microbial
fouling: Brushing, rubber sponge ball treatment, and chlorine treatment. Brushing away the
microbial fouling is by far the most effective and thorough way to get rid of any biofouling. As
this figure shows, when brushing is applied to the heat exchanger, the value for the thermal
resistance goes down nearly to 0:
Figure 8: Microbial fouling Thermal Resistance vs. Time for Free fouling1
Note that in this figure, Rf is the thermal resistance and is given in 105 oC-m2/W. The
critical value for Rf was 9, and whenever it reached this level the heat exchanger would be
brushed down. When the microbial fouling is allowed to grow unimpeded like in this case, it
took about 28 to 42 days for the thermal resistance to reach its critical value, as shown by Figure
(7). Even though periodic brushing was effective in getting completely rid of the microbial
fouling, it still has some drawbacks. Brushing by far takes the most amount of effort and
36
maintenance to keep up on a regular routine. The heat exchangers would have to be taken offline
in order to brush them thoroughly1. Whenever components in a power producing plant like this
have to go offline, it takes away from the overall power output of the system. In OTEC, where
the thermal efficiency is already low, constant cleaning of the heat exchanger would not be good
for its overall output. An alternative method that can deal with the microbial fouling without so
much maintenance would be a nice alternative.
The next method to deal with the microbial fouling is the rubber sponge ball treatment.
One sponge ball, whose radius is similar to the radius of the pipe, is released through the pipe
every five minutes for an hour1. Ideally, all the microbial fouling will catch on the spongy
surface of the ball and not grow on the side of the heat exchanger. Since it took over a month for
a significant amount of microbial fouling to occur unimpeded, daily treatment with the sponge
balls should clear out the microbial fouling before it got to critical levels. At first, the sponge
balls were effective at clearing out the microbial fouling in a new pipe. It took almost 75 days for
the thermal resistance to reach critical levels. Over time unfortunately, this method proved
ineffective in completely clearing out the microbial fouling. Brushing still had to take place
occasionally when the thermal resistance reached critical levels2. In fact, after the first brushing
the microbial fouling returned at a faster rate than when it was unimpeded. These trends are
shown in Figure (8). Although initially effective at keeping thermal resistance down, the sponge
ball treatment is not an effective long term solution for an OTEC plant which will operate for
many years. The following figure summarizes the results of the sponge ball treatment:
37
Figure 9: Microbial fouling Thermal Resistance vs. Time, Spongeball treatment2
Chemical treatment is also a solution to microbial fouling, specifically injecting regular
doses of chlorine into the heat exchanger with the water to kill off the bacteria before it forms.
This is the most effective way to deal with microbial fouling and the current industry standard.
As Figure (9) shows, over 1300 days of operation the thermal resistance never reached the
critical value that required brushing. The thermal resistance actually never exceeded a value of
3.32. This is a significant improvement over the other two solutions, because even though it took
a while for the microbial fouling to reach the critical value of 9, during the periods where the
thermal resistance was between 3.3 and 9, brushing and sponge ball treated heat exchangers
would be less efficient than the chlorine treated ones. Another advantage chlorine treatment has
over brushing is how much less work it takes to clean. Compared to simply injecting some
chlorine into a water stream, manually brushing out the heat exchanger tubes once a month is a
lot of work. The drawback to using chlorine treatment is that it only gives the impression of
cleaning out the microbial fouling. Over long periods of time, what the chlorine does is smooth
out the microbial fouling layer instead of eliminating it, steadily building up over time2. This
trend is supported in Figure (9) as the thermal resistance slowly climbs near the end of the tests.
38
Manual scrubbing would probably still be required occasionally to get rid of this smooth fouling
layer, but it would be required much less frequently than if the fouling were free to grow.
Figure 10: Results of Chlorine Treatment on Fouling Thermal Resistance1
Microbial fouling represents a unique challenge to OTEC plants since it gets water directly from
the ocean, where bacteria and other micro organisms grow. The accumulation of these organisms
present a significant threat to the overall efficiency of OTEC plants by reducing the amount of
heat transfer that can occur in heat exchangers that rely on the ocean water. The efficiency and
economic viability of OTEC plants are low to begin with and do not need further sources of loss
from something like microbial fouling. In any design of an OTEC plant, proper chlorine
treatment systems need to be built to periodically clean out the heat exchangers.
9 Structural Analysis: Cold Water Pipe
As mentioned before, one of the most difficult problems facing the implementation of
OTEC power plants is maintaining the structural integrity of deep cold water pipes that obtain
39
the ocean water necessary to run the condenser. Deep water forces caused by currents and
pressures cause stress on the cold water pipe which can be constructed as low as 1000 meters
below the surface10.
Previous studies and engineering have progressed to develop a 2.4m diameter pipe made
of fiberglass for a small system, but this analysis will be expanding this design for a 100MW
plant using previously gathered information needed to operate a plant of this magnitude3. A
100MW OTEC plant, in theory, will need a mass flow rate of 200 meters cubed per second with
a velocity of 2 meters per second to reduce losses within the pipes to 20%-30%10. This analysis
assumes the maximum depth of a thousand meters and iterates a design for the thickness of a
cold water pipe.
9.1 Equations, Theory, and Assumptions
The inner diameter of the pipe is constrained by the required volumetric flow rate and flow
velocity. From this, the cross sectional area of the pipe and consequently the inner diameter of
the pipe are constrained. For a volumetric flow rate of 200 meters cubed per second and a
velocity of 2 meters per second:
The deep water pipe was modeled as a cylinder with finite thickness in cross flow of
seawater flowing at constant speed. Even though the velocity of the seawater on the outside of
the pipe changes with the ocean currents, this analysis assumes it to be a constant value of 1.78
meters per second2. This value was obtained from the average speed of currents in the Gulf
Stream. While the Gulf Stream is nowhere near Hawaii, it gives a good approximation for the
average speed of ocean currents. At 1000 m below the surface, there are mainly two forces acting
40
on the cylinder: hydrostatic pressure force and the drag force associated with the flow. The
hydrostatic pressure was found using:
Equation 9.1
Where is the density of seawater, g is the gravitational constant, and h is the depth of the pipe
in question. This analysis assumes the pressure on the inside of the pipe is negligible compared
to the hydrostatic pressure on the outside. Mechanical theory for axial members gives formulas
for the maximum stresses in the axial and azimuthal directions for structures under external
stress only:
Equation 9.2
Equation 9.3
Where a is the inner radius (fixed), b is the outer radius, and Pext is the external pressure caused
by the seawater. In this case, the maximum stress occurs on the outer radius. The drag force
associated with the ocean current in cross flow on the pipe is approximated using the drag
coefficient. To utilize the drag coefficient, the Reynold’s Number for this flow over the pipe
outer diameter had to be determined. Assuming an outer diameter of 13.5 meters, the Reynold’s
Number associated with this flow is:
Equation 9.4
For this high Reynold’s Number flow, the drag coefficient is approximately unity. Another
parameter required for finding the drag force is the effective area affected by the flow. For this
analysis, this area will be a rectangle with height equal to the total pipe depth and width equal to
the pipe diameter. The total drag force is then:
Equation 9.5
This force translates into a shearing stress on the pipe. This stress is:
41
Equation 9.6
The last assumption is that the axial stress is negligible compared to the other stresses analyzed
here. With all these stresses, now the principal stress can be found, which is the maximum stress
at a point inside the pipe. The formula for the principal stress is:
Equation 9.7
Where the principal stress is chosen as the maximum between the two. The principal stress was
compared with changing depth and with changing outer diameter to see their effects. Then based
on this analysis an optimal value for the outer diameter will be chosen.
9.2 Results
First the principal stress was plotted against changing pipe depth, from a depth of 900 m to 1100
m. Here are the results of the calculations:
Figure 10: Effects on Principal Stress on Changing Pipe Depth
42
The principal stress increases linearly with pipe depth. This analysis was done to show that pipe
segments in deeper water are under more stress than pipe segments near the surface. The
difference was not too great, but deeper pipes can be reinforced to withstand these stresses if
needed. Next the effect of outer diameter on the principal stresses was found:
Figure 11: Effects on Principal Stress on Outer Diameter
As this graph shows, increasing the pipe diameter significantly reduces the principal stress in the
pipe, especially in the region between 12 m and 13 m. It is reduced by about a factor of three in
this area.
9.3 Analysis
As Figure 2 shows, the most important factor for minimizing the principal stresses in deep water
pipes is the outer diameter. The diameter can be as big as possible to lower these stresses, and
lowering these stresses will increase the lifetime of these pipes since they do not have to carry so
much load. The drawback of making larger outer diameter pipes is the material cost in building
it. With the inner diameter fixed at 11.28 m, increasing the outer diameter from 12 m to 13.5 m
43
increases the pipe thickness from 0.72 m to 2.22 m, over tripling the amount of material required
to build these pipes. These pipes are not short either; this analysis assumed a pipe length of 1000
m. Tripling the material cost for this is a big deal when the capital cost for all the other
components are already so high.
Regardless, a diameter of about 13.5 m would be most optimal for the design of the cold water
pipes. This reduces the principal stress in the pipe from 160 MPa to about 50 MPa, significantly
reducing the stress in the pipe. Even though it might cost a lot initially to build these pipes, the
benefits to the reduced stress and thus lifetime make it more than worth it. If the pipes ever got
fatigued to a point close to failure, they would have to be replaced. Not only will this cost a lot of
money (the same as the capital cost for building them in the first place), the plant has to work
with reduced output since not all of its components would be running. The money lost from these
scenarios is much more than some more upfront cost, so over time having a thicker pipe will be
more cost beneficial to the plant. Also, compared to the cost of the other components at startup,
the cost of building the pipes is not nearly as much as the construction and installation of the
turbine or boiler. So a little more money there to ensure they work with minimal stress and
longer lifetime is very much worth it.
The typical chosen material for deep ocean pipes is high density polyethylene3, because
of its light weight and high corrosion resistance. Its yield strength, however, is only about 33
MPa, so the pipes are typically strengthened with steel embedded within the polyethylene pipes
to help it stand up to the deep sea pressures.
44
10 Conclusions Ocean Thermal Energy Conversion is not a viable option for power generations for
various reasons. It has been considered because of its ability to use a natural and free fuel source
while minimizing environmental impacts, but the drawbacks far outweigh the positives. With
thermal efficiencies of 1.74% with ammonia, 1.93% for Refrigerant 22, and 2.54% with
Refrigerant 134A, it is hard to recommend OTEC when better alternatives like fossil fuel and
nuclear plants still exist. Even with the improvement with the solar absorption tub, the thermal
efficiency only went up to 3.8%, which is still incredibly low. Taking into account the massive
capital costs and the cost of maintaining the plant underwater, OTEC just does not give enough
reasons to use it as a viable means to produce energy.
With a rapidly increasing population and the rise of new technology, the demand for
energy is higher than ever. Alternatives to fossil fuel need to be researched to meet these
demands, but OTEC is only one of those options. Many other viable options are available at the
time, like nuclear and geothermal energy production. The thermal gradients in the ocean just do
not provide enough difference in temperature to drive the power cycle needed for energy
production. Maybe someday in the future technology will be developed to better harvest Ocean
thermal energy as a resource, but today it is hard to recommend it with all of its flaws.
45
11 References 1Berger, Joyce, and Leslie Berger, eds. "Countermeasures to Microbiofouling in Simulated Ocean Thermal Energy Conversion Heat Exchangers with Surface and Deep Ocean Waters in Hawaii." AEM. AEM, 07 Mar 1996. Web. 22 Feb 2012. <http://aem.asm.org/content/51/6/1186.full.pdf>. 2"Electricity Price Differences between Countries | GREENDUMP." Greendump.net. Web. 21 Feb. 2012. <http://www.greendump.net/the-oil-drum/electricity-price-differences-between- countries> 3Hemmes, K. “OTEC Research & Initiatives.” Delft University of Technology. Web. 18 Feb. 2012. <http://www.otec.tudelft.nl/> 4"How Fast is the Gulf Stream?" National Ocean Service. National Oceanic and Atmospheric Administration, 17 Nov 2011. Web. 22 Feb 2012. < http://oceanservice.noaa.gov/facts/gulfstreamspeed.html> 5"Lockheed Martin · Ocean Thermal Energy Conversion." Lockheed Martin. Web. 15 Feb. 2012. <http://www.lockheedmartin.com/us/products/otec.html> 6Moran, Michael, and Howard Shapiro. Fundamentals of Engineering Thermodynamics.
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