Thermo-Fluids Systems Design Midterm Project

OTEC Power Plant Cold Water Pipe Design

Frederick Avyasa Smith

December 4, 2014

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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

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thus completing the OTEC closes cycle. A figure describing a standard OTEC closed

cycle is included below:

Figure 1 OTEC System Diagram [3]

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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

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

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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

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

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can be seen in the figure below:

Figure 2 Ocean Temperature Difference [1]

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:

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Table 1 Summarized Parameters from D.Bharathan System [7]

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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

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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

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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

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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.

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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.

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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

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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.

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Calculated Analysis Evidence

(1.1) Theoretical Power Output of D. Bharathan 10MW OTEC System

Pmax ,theor=1−√ T c old w ater

T warmwater

[1]

T coldw ater=4.5 °C

T warmwater=26 °C

Pmax ,theor=3.663%

(1.2) Operating Efficiency of D. Bharathan 10MW OTEC System

ηoperating=Pnet

Pgross [1]

Pnet=11932KW

Pgros s=17287KW

ηoperating=69.023%

(1.3) Net Efficiency of D. Bharathan 10MW OTEC System

ηnet=(η¿¿ o perating)(Pmax, theor)¿ [1]

Pmax=3.663%

ηoperating=69.023%

ηnet=2.528%

(2.1) Diameter of Devised CWP

D=√ m

ρ( π4 )v inside p ipe [1]

m=28,450 kg/s

ρ=1023kg/m3

v inside pipe=2.5m /s

D=3.763m

(2.2) Thickness of Devised CWP

t=D [ ( poutside−p i nside)( 1−v22 E )]0.333

[1]

D=3.763m

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( poutside−pi nside)=30kPa v=0.23

E=11.7 x109n /m2

t=4.033cm

(3.1) Hydraulic Head to Overcome Pipe Drag in Devised CWP

hdrag=8 f m2 LD5 π2 ρ2g

[1]

D=3.763m

m=28,450 kg/s

ρ=1023kg/m3

L=895.84m f=0.0094

g=9.81m/ s2

hdrag=0.713m

(3.2) Total Hydraulic Head Required to Pump Seawater in Devised CWP

htotal=hdrag+hother

hother=3.0m

hdrag=0.713m

htotal=3.713

(3.2) Pumping Power in Devised CWP

Pcoldwater pump=¿ [1]

m=28,450 kg/s

h¿ tal=3.713

g=9.81m/ s2

Pcoldwater pump=1.036MW

(3.3) Power Required to Operate Pump in Devised CWP

Preq=Pcoldwater pump

ηcoldwater pump

Pcold water pump=1.036MW

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ηpump=72%

Preq=1.439MW

(4.1) Parasitic Power in Devised CWP

Pparasitic=Preqwarmwater pump+P req+P reqammonia feed pump

Preqwarmwater pump=2090KW

Preq=1439 .19KW

Preq ammonia feed pump=420KW

Pparasitic=3.949MW

(4.2) Net Power of Devised OTEC System

Pnet=Pgross−Pparasitic

Pgross=17287KW

Pparasitic=3949.19KW

Pnet=13.338MW

(4.3) Operating Efficiency of Devised OTEC System

ηoperating=Pnet

Pgross [1]

Pnet=13.338MW

Pgross=17287KW

ηoperating=77.152%

(4.4) Net Efficiency of Devised OTEC System

ηnet=(ηoperating)(Pmax,theor ) [1]

ηoperat ing=77 .152%

Pmax ,theor=3.663%

ηnet=2.826%

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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)

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