Pumping Power Dependence of OTEC Systems

L. ARESTI1,2, T. ONOUFRIOU1,2, C. MICHAILIDES3, P. CHRISTODOULIDES1

1Faculty of Engineering,

Cyprus University of Technology,

Limassol,

CYPRUS

2EMERGE CoE,

Limassol,

CYPRUS

3Department of Civil Engineering,

International Hellenic University,

Serres University Campus,

GREECE

Abstract: - Ocean Thermal Energy Conversion (OTEC) systems use seawater pipes to harness the natural

temperature difference between the surface water and the deep seawater mainly for electricity generation; they

also have the potential tof generate by-products. The temperature of seawater fluctuates according to the

geographical location but also depends on factors such as ocean depth and proximity to the coastline. This

paper examines several scenarios for the pumping power affected by various factors related to the cold-water

pipe and the warm-water pipe. A parametric analysis is performed on factors such as the size of the cold-water

pipe, the mass flow rate, and the distance from shore. The results could potentially be used to identify the

positioning of an OTEC systems, in terms of onshore or offshore placement.

Key-Words: - Ocean Thermal Energy Conversion, Cold Water Pipe, OTEC offshore, OTEC onshore, pumping

power, seawater.

Received: May 26, 2024. Revised: September 9, 2024. Accepted: November 12, 2024. Published: December 31, 2024.

1 Introduction

Ocean Thermal Energy Conversion (OTEC)

systems take advantage of the natural temperature

difference (ΔT) of the cold deep seawater and the

surface sea water to run a thermodynamic cycle and

generate power in terms of electricity and/ or by-

products such as fresh water.

This temperature difference however is

location-dependent (i.e., see distance from the

Equator), with ΔTs of 20°C (with 25°C surface

seawater and 5°C deep seawater) or higher being

recommended (which would lead to a Carnot

efficiency of 6.7%). As OTEC systems aim at the

highest possible ΔT, for a sufficiently high system

efficiency, it is suggested that they be ideally placed

in the tropical regions (or regions within ±20° from

the Equator, including the Caribbean) where such

high ΔTs are recorded.

Another important feature of OTEC systems is

itheir actual positioning in relation to the shore. For

example, the OTEC system can be positioned either

onshore or offshore as presented in Figure 1. Onshore

systems are built on land, based on land availability

and approximability, whereas offshore systems can be

positioned on fixed or floating sea platforms.

Fig. 1: OTEC positioning, from left to right: onshore

(land-based) systems, offshore fixed platform,

offshore floating and semi-submersible platform,

offshore spare platform, offshore FPSO (Floating

Production Storage and Offloading), [1]

This selection and availability play a crucial role

in the length of the required piping for both the cold-

water pipe (CWP) and the warm-water pipe (WWP).

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L. Aresti, T. Onoufriou, C. Michailides, P. Christodoulides

E-ISSN: 2224-3461

Volume 19, 2024

The pumping power required on the other hand

for the OTEC pipes, namely for CWP and WWP, is of

importance for the net output of the system, as these

values could be in the range of 20-30% of the net

generated OTEC system power, [2].

Onshore OTEC systems, are situated on land,

and therefore eliminate the need for a lashing

system for stability. Furthermore, the system’s

maintenance may be conducted with greater ease

and, as a result, at a reduced expense compared to

offshore systems. Additionally, the system is

fortified against severe weather conditions, as it may

be designed to endure storms. The generated power

can be efficiently disseminated in all scenarios,

including situations where desalinated water can

also be produced and transferred to the pre-existing

network, [3]. Conversely, the coastline land

possesses a significant high value, which can offset

the decreased expenses associated with installation

and upkeep. Another disadvantage is that

transporting seawater onto land increases the cost,

as it necessitates the installation of long-distance

pipes, with the pipes exposed to tides and storms,

[4]. Offshore systems, in contrast, effectively

address certain drawbacks associated with onshore

systems by being situated in closer proximity to the

necessary sea depth for cold seawater. However,

these systems are susceptible to the marine

environment. Offshore systems can be placed on a

platform at a maximum seawater depth of

approximately 100m, [5]. Alternatively, when

floating structures are used, they can be positioned

at the appropriate sea bed depth of over 1km, which

allows them to avoid the impact of breaking waves

and the associated nonlinear stresses. To ensure a

steady position, offshore systems are constructed as

either fixed platforms or floating ones that utilize

mooring lines for station keeping, [6].

Table 1 summarises the main benefits and

drawbacks between onshore and offshore systems.

As for every system, there are several other

factors that can characterize the performance of the

system; a review of the aspects related to the energy,

environment, and economy can be found in [1].

The current paper examines the factors affecting

the pumping power for the OTEC pipes, through a

small parametric analysis. The main equations

related to the pumping power are described in

Section 2 and the initial findings are presented in

Section 3. Note that the methodology is verified

with similar cases in the literature, due to the lack of

experimental data available.

Table 1. Comparison between onshore and offshore

OTEC systems

Onshore OTEC Systems

Offshore OTEC Systems

Installation

No lashing system needed

to secure in place

Minimal pipe distance,

reducing construction and

material costs

The system can be

designed to withstand

strong weather conditions,

like storms

Constant sea movement

(waves, currents)

necessitates sophisticated,

costly design for pipes and

components

The generated electricity

can be distributed easily,

with the potential for

integration into existing

networks

Requires subsea cables or

additional infrastructure to

connect to land-based

distribution systems

Coastal land often has

a high value, potentially

increasing land acquisition

costs

Generally higher

installation costs due to

structural needs to

withstand sea movement

and anchoring requirements

Higher initial investment

due to the need for long

seawater transfer pipes that

are secure against tides and

storms

Anchoring a floating

platform in the deep sea is

complex and costly

Environmental Impact

Coastal impact is higher

due to land use and

possible effects on coastal

ecosystems

Lower impact on coastal

land but may disturb deep-

sea ecosystems

Maintenance Complexity

Easier and more accessible

on land, reducing overall

maintenance costs and

complexity

Maintenance is challenging

and expensive due to the

exposed environment

Energy Distribution

Easier integration into

existing grids and water

distribution networks

Requires subsea cables or

additional infrastructure to

connect to land-based

distribution systems

2 Methodology

The pumping power of the pipes is of high importance

to the overall efficiency of the system, and for either

the CWP or the WWP, it is estimated using the

following equation, [7], [8]:



󰇗 



(1)

where  is the pipe mass flowrate [kg s–1],  is the

gravitational acceleration [m s–2],  is the pump

efficiency, and  the total head difference of the

pipe [m], [9]. The main difference between the CWP

and the WWP lies in the estimation of the total head

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difference of the pipe, which is essentially the sum of

the pump head difference, the friction losses (of the

pipe), the friction loss of the heat exchangers, the

bending/ minor losses, and the density difference

losses. The total head difference is expressed as:

   

(2)

where  is the pump head difference, which is

the sum of the head loss due to friction (Equation 3),

and the minor losses of the pipes (Equation 5). The

head loss due to friction can be described by the

Darcy’s friction factor as shown in Equation (3),

and the fluid velocity of the pipe is described by

Equation (4). Both of the pipes (CWP and WWP),

being placed in the seawater, are subject to

biofouling, which in turn can have an effect on the

friction factor as well as the velocity profile in the

pipe [10]. In fact,

  









(3)

  







(4)

 





(5)

where  is the pipe’s length [m], is the inner

diameter of the pipe [m],  is the Darcy’s friction

factor [unitless],  is the cross-sectional area of the

pipe,  is the seawater density, and  is the sum

of all of the bending and minor loss coefficients. The

bending and minor losses are due to fittings, pipe

bends, valves, etc. These losses are theoretically

added to the pipe length, where the pipe is considered

as frictionless and straight.

The head difference due to the density differences

in the seawater (as density changes with depth), is

only applicable to the CWP (due to discharging at

shallower depths from the pumping depth), and it is

described by:

  

 

󰇛 󰇜

(6)

where  is the density of the cold seawater and 

is the density of the warm seawater [kg m–3]. Finally,

the head difference due to the heat exchanger mainly

depends on system capacity and hence the size.

Therefore, these values will vary depending on the

size of the heat exchangers, either the condenser or the

evaporator, and they can be neglected in the

estimations here, to avoid any miscalculations of the

system.

3 Initial Results and Discussion

The initial results regarding different head losses are

presented in Figure 2 and Figure 3. The fluid velocity

and the pipe length were varied, as shown in Figure

2(a) and Figure 2(b). Both variables are presented

against the head difference due to friction and

bending and minor losses. The ranges of the pipe are

based on the distance from shore and were assumed

to vary between 1km to 10km in length. On the

other hand, the CWP diameter values as well as

flowrate values are based on the literature, for either

computational or experimental set-ups.

In Figure 2(a) and Figure 2(b), it is observed

that with a reduction in velocity, the head

differences both due to friction and due to bending

& minor losses are increased. However, the

velocities are generally kept at high values in the

OTEC systems due to the high amount of heat

exchange required. In Figure 2(c) the length of the

pipe was varied, and the head difference due to

density is presented, for a fixed mass flow rate at 45

kg s–1 and an inner diameter of 1.9022 m.

Increasing the value of the inner diameter does

not have a significant effect on the head differences

(all  values observed are well below 1 m); note

that the contribution on the total head difference

change due to the inner diameter change is of the

order of 5% (not shown here). As expected,

increasing the pipe’s length has the highest impact

on , with the head difference due to density

rapidly increasing. Note that  due to density has a

contribution to the total head difference change of

the order of 95% (for high  values), although it is

only 25% for an inner diameter of 0.2m (with the

head difference due to friction at 67%). Also, the

smaller the  the smaller the  contribution.

By observing Equation (1), the above reported

head differences, have a direct impact on the

required pumping power. Hence, the pumping

power of CWP versus the head difference due to

friction (see Equation 3) is plotted in Figure 3. By

varying the friction factor, the length of the pipe, the

velocity of the fluid, and the inner diameter of the

pipe, one can obtain linear relations for each

parameter; the corresponding slopes are shown in

Table 2.

Figure 3 and Table 2 demonstrate that

 exhibits the highest slope, and consequently

the highest change in head difference and in

pumping power. It should be noted here, that the

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sum is used for the total pumping power (Equation

2) and not the individual values projected in Figure

(a)

(b)

(c)

Fig. 2: Head difference due to: (a) friction (ΔH,f)

and minor/ bending losses (ΔH,b), at various fluid

velocities; (b) friction (ΔH,f) and minor/ bending

losses (ΔH,b), at various inner pipe diameters; (c)

density difference between deep seawater and

surface seawater, at various pipe lengths

Pumping power change due to friction factor

and due to inner pipe diameter exhibit a lower

impact as observed with lower projected slopes.

Note that, even the presence of biofouling, which

will in turn affect the friction factor and the pipe

diameter, will not contribute to rapid changes in

pumping power (not shown here). The fouling factor

can be represented as an extra pipe wall resistance

(thermal), which will theoretically overestimate the

heat exchanger’s performance; as fouling develops

over time, it will be reduced until the cleaning

threshold is achieved.

Fig. 3: Head difference due to friction with different

varying parameters, namely the length of the pipe,

the inner diameter of the pipe, the fluid velocity and

the friction factor.

Table 2. Projected slope for the Head difference due

to friction with different varying parameters

Head difference

Parameter

Slope

ΔH,f



20.553



14.698



6.854



5.394

The parameters of fluid velocity and pipe length

are also presented in Figure 3 against CWP pumping

power. The higher impact can be observed with the

change in the length of the pipe. However

noticeable impact is also observed in the fluid

velocity. Although the length can be adjusted due to

the location, the velocity of the fluid is directly

related to the heat exchange required for the

thermodynamic cycle and the net power produced.

Consequently, the latter’s effect can be

computed in relation to the overall system power,

where a system could be characterized by the

optimum point of the pumping power and the net

power, in terms of the electricity output of the

system; this however requires further details into the

selection of thermodynamic cycles, the circulation

fluid selection, as well as on the characteristics of

the generator, the pumps, and the heat exchangers.

Unfortunately, the lack of data from real case

studies or pilot projects is a major issue surrounding

OTEC systems, and, hence, theoretical or

computational research cannot yet be validated. In

future funded systems and with the inclusion of

EU’s open access science, it is expected that data

will become available either for validation purposes

0,5

1,5

0 0,2 0,4 0,6 0,8

u [m s-1]

ΔH [m]

ΔH,f ΔH,b

0 0,5 1 1,5 2 2,5

CWP [m]

ΔH [m]

ΔH,f ΔH,b

010 20 30

LCWP [km]

ΔH[m]

ΔH,d

100

200

300

400

500

010 20 30

WCWP,p [kW]

ΔH,f [m]

Lcwp CWPi u,cwp fd

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or to effectively assist engineers to design and

characterise such systems.

4 Conclusion

The current research aimed to investigate the

different parameters affecting pumping power for

offshore and onshore OTEC systems. The net power

of an OTEC system highly depends on the required

pumping power, as the OTEC systems are highly

location-dependent. The current study has reported

on different variables, highlighting the factors with

the higher impacts on the pumping power.

The obtained results have indicated that the

highest impact on pumping power is due to the

change in the length of the pipe. The noticeable

impact is also observed by the fluid velocity or mass

flow rate of the CWP. Minimum impact on the other

hand is observed by head difference due to bending

(or minor losses) as well on the head difference due

to the friction effect.

The results reported and discussed in Section 3

could be used to determine whether an OTEC

system would have a higher performance when

placed onshore or offshore.

A further parametric analysis, in addition to

head difference by factors such as the CWP length

and diameter, and the mass flow rate, can be

performed in relation to temperature difference

between deep seawater and inlet to the condenser.

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Volume 19, 2024

The authors equally contributed in the present

research, at all stages from the formulation of the

problem to the final findings and solution.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

The research presented in this paper has received

co-funding from the European Union

CETPatnership and the Research and Innovation

Foundation of Cyprus under Grant agreement

EP/CETP/0922/0055.

Conflict of Interest

The authors have no conflicts of interest to declare.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en

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