Page 161 - Fundamentals of Ocean Renewable Energy Generating Electricity From The Sea

150 Fundamentals of Ocean Renewable Energy

Replacing the maximum efficiency from Eq. (6.2), this leads to

(T w − T c )ΔT w
P OT = ρc h Q w (6.6)
T w
For an idealized case in which the temperature can be reduced to that of cold
water (i.e. T w out = T c or ΔT w = T w − T c ), the maximum power is given by
(T w − T c ) 2
P OT = ρc h Q w (6.7)
T w
3
◦
For example, for T w = 25 C, T c = 5 C, and Q w = 1m /s, the power that is
◦
generated will be
2
(25 − 5)
P OT = (1000)(4184)(1) = 5.6 MW (6.8)
25 + 273.15
Moving towards a more realistic case, the efficiency of an OTEC power plant
depends on to the ratio of cold water flow rate to warm water flow rate (i.e.
Q w = rQ c ), which should be optimized for a project (e.g. see [16]). For instance,
3
r = 0.5 means that if the volumetric flow rate of warm water is 10 m /s, the
3
volumetric flow rate of cold water is 5 m /s. For a simplified case, it can be
shown that the warm water cools down by ΔT w =[3r/(1 + r)](T w − T c )/8
and the cold water warms by ΔT c =[3/(1 + r)](T w − T c )/8. Note that for this
simplified case, the heat lost by the warm water is gained by the cold water:
ρc h Q w ΔT w = ρc h Q c ΔT c . In other words, the extracted energy is neglected in
this simple heat and mass balance equation as the efficiency is small. Referring
to Eq. (6.6), and replacing ΔT w = 3r/(1 + r)ΔT/8, results in,
(T w − T c ) 2
P OT = 3rρc h Q w (6.9)
8(1 + r)T w

6.3.4 Commercial Progress
One might question how much electricity can realistically be generated from
a power plant that consists of turbines that are driven (for example) by vapour
produced from boiling ammonia. The real answer to this is a question of scale.
Although many test and research OTEC power plants have been developed
around the 30–120 kW scale (Fig. 6.5), it is possible, simply by using larger
diameter pipes and a larger volume of working fluid, to generate electricity at
around the 100 MW scale. However, part of the journey to such large-scale
OTEC power plants is to further develop and refine schemes at around the
1–20 MW scale, and there are many such schemes under development and
construction throughout the world (Fig. 6.5), for example, the 1 MW plant
in Tarawa Island (Pacific), and 20 MW plants in Qingdao (China) and La
Martinique (Carribean).