Page 160 - Fundamentals of Ocean Renewable Energy Generating Electricity From The Sea

Other Forms of Ocean Energy Chapter | 6 149

6.3.3 OTEC Thermodynamics
To better understand how ocean thermal energy is quantified, let us have a quick
review of some basic thermodynamic concepts. The amount of heat energy
◦
required to raise the temperature of a unit mass of water by 1 C is called specific
heat c h . The specific heat of water is 4184 J/kg, 1000 calories/kg, or simply
1 calorie/g (i.e. the definition of a calorie). For instance, if we wanted to increase
3
the temperature of a stream flow that has a flow rate of 10 m /s (or 10,000 kg/s)
by 2.5 C, the amount of power required (in Joules per second or megawatts)
◦
would be
3
3
◦
◦
P = (10 m /s)(1000 kg/m )(2.5 C)(4184 J/kg C)
6
= 104.6 × 10 J/s = 104.6 MW (6.1)
which is a very large amount of power (e.g. equivalent to about 100 tidal
turbines, each with a capacity of 1 MW!). An ocean thermal energy converter
tries to reverse this process. In other words, extracting energy from water by
cooling it down or converting heat to work. Unfortunately, the reverse process
is much more difficult, and not as efficient. The second law of thermodynamics
specifically deals with this concept, and the Carnot heat engine (proposed in
1824) was one of the first attempts to study this process. According to Carnot,
the maximum efficiency of this process is given by
T w − T c
η = (6.2)
T w
where T w and T c are the absolute temperatures of warm and cold water (in
Kelvin = Celsius + 273.15), respectively. Consequently, for ocean thermal
◦
energy, the upper bound of efficiency is quite low. For instance, if T w = 25 C
and T c = 5 C, the maximum efficiency will be
◦
20
η = ≈ 7% (6.3)
25 + 273.15
Nevertheless, the amount of energy is very high, and even a low efficiency
power plant can convert a significant amount of energy. Referring to Fig. 6.4,
assume that the warm water, with a temperature of T w , is pumped to the
out
evaporator and returns with a lower temperature T w after losing some energy.
The amount of heat energy that water loses per unit time (P h ) is given by
dm
d out
P h = mc h (T w − T w ) = c h ΔT w → P h = ρc h Q w ΔT w (6.4)
dt dt
where ρ is the density of water and Q w is the volumetric flow rate of warm
water (remember that mass flow rate, dm , is equal to volumetric flow rate times
dt
density). A power plant which works based on ocean thermal energy exploits
part of this energy. If we denote the efficiency of the power plant by η,the
generated power (in the steady-state case) can be estimated as follows
P OT = ηρc h Q w ΔT w (6.5)