10 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Ocean thermal energy conversion | 8/10 | https://en.wikipedia.org/wiki/Ocean_thermal_energy_conversion | reference | science, encyclopedia | 2026-05-05T07:35:54.854158+00:00 | kb-cron |
== Thermodynamics == A rigorous treatment of OTEC reveals that a 20 °C temperature difference will provide as much energy as a hydroelectric plant with 34 m head for the same volume of water flow. The low temperature difference means that water volumes must be very large to extract useful amounts of heat. A 100MW power plant would be expected to pump on the order of 12 million gallons (44,400 tonnes) per minute. For comparison, pumps must move a mass of water greater than the weight of the battleship Bismarck, which weighed 41,700 tonnes, every minute. This makes pumping a substantial parasitic drain on energy production in OTEC systems, with one Lockheed design consuming 19.55 MW in pumping costs for every 49.8 MW net electricity generated. For OTEC schemes using heat exchangers, to handle this volume of water the exchangers need to be enormous compared to those used in conventional thermal power generation plants, making them one of the most critical components due to their impact on overall efficiency. A 100 MW OTEC power plant would require 200 exchangers each larger than a 20-foot shipping container making them the single most expensive component.
=== Variation of ocean temperature with depth ===
The total insolation received by the oceans (covering 70% of the earth's surface, with clearness index of 0.5 and average energy retention of 15%) is: 5.45×1018 MJ/yr × 0.7 × 0.5 × 0.15 = 2.87×1017 MJ/yr We can use Beer–Lambert–Bouguer's law to quantify the solar energy absorption by water,
−
d
I
(
y
)
d
y
=
μ
I
{\displaystyle -{\frac {dI(y)}{dy}}=\mu I}
where, y is the depth of water, I is intensity and μ is the absorption coefficient. Solving the above differential equation,
I
(
y
)
=
I
0
exp
(
−
μ
y
)
{\displaystyle I(y)=I_{0}\exp(-\mu y)\,}
The absorption coefficient μ may range from 0.05 m−1 for very clear fresh water to 0.5 m−1 for very salty water. Since the intensity falls exponentially with depth y, heat absorption is concentrated at the top layers. Typically in the tropics, surface temperature values are in excess of 25 °C (77 °F), while at 1 kilometer (0.62 mi), the temperature is about 5–10 °C (41–50 °F). The warmer (and hence lighter) waters at the surface means there are no thermal convection currents. Due to the small temperature gradients, heat transfer by conduction is too low to equalize the temperatures. The ocean is thus both a practically infinite heat source and a practically infinite heat sink. This temperature difference varies with latitude and season, with the maximum in tropical, subtropical and equatorial waters. Hence the tropics are generally the best OTEC locations.
=== Open/Claude cycle === In this scheme, warm surface water at around 27 °C (81 °F) enters an evaporator at pressure slightly below the saturation pressures causing it to vaporize.
H
1
=
H
f
{\displaystyle H_{1}=H_{f}\,}
Where Hf is enthalpy of liquid water at the inlet temperature, T1.
This temporarily superheated water undergoes volume boiling as opposed to pool boiling in conventional boilers where the heating surface is in contact. Thus the water partially flashes to steam with two-phase equilibrium prevailing. Suppose that the pressure inside the evaporator is maintained at the saturation pressure, T2.
H
2
=
H
1
=
H
f
+
x
2
H
f
g
{\displaystyle H_{2}=H_{1}=H_{f}+x_{2}H_{fg}\,}
Here, x2 is the fraction of water by mass that vaporizes. The warm water mass flow rate per unit turbine mass flow rate is 1/x2. The low pressure in the evaporator is maintained by a vacuum pump that also removes the dissolved non-condensable gases from the evaporator. The evaporator now contains a mixture of water and steam of very low vapor quality (steam content). The steam is separated from the water as saturated vapor. The remaining water is saturated and is discharged to the ocean in the open cycle. The steam is a low pressure/high specific volume working fluid. It expands in a special low pressure turbine.
H
3
=
H
g
{\displaystyle H_{3}=H_{g}\,}
Here, Hg corresponds to T2. For an ideal isentropic (reversible adiabatic) turbine,
s
5
,
s
=
s
3
=
s
f
+
x
5
,
s
s
f
g
{\displaystyle s_{5,s}=s_{3}=s_{f}+x_{5,s}s_{fg}\,}
The above equation corresponds to the temperature at the exhaust of the turbine, T5. x5,s is the mass fraction of vapor at state 5. The enthalpy at T5 is,
H
5
,
s
=
H
f
+
x
5
,
s
H
f
g
{\displaystyle H_{5,s}=H_{f}+x_{5,s}H_{fg}\,}
This enthalpy is lower. The adiabatic reversible turbine work = H3-H5,s . Actual turbine work WT = (H3-H5,s) x polytropic efficiency
H
5
=
H
3
−
a
c
t
u
a
l
w
o
r
k
{\displaystyle H_{5}=H_{3}-\ \mathrm {actual} \ \mathrm {work} }
The condenser temperature and pressure are lower. Since the turbine exhaust is to be discharged back into the ocean, a direct contact condenser is used to mix the exhaust with cold water, which results in a near-saturated water. That water is now discharged back to the ocean. H6=Hf, at T5. T7 is the temperature of the exhaust mixed with cold sea water, as the vapor content now is negligible,
H
7
≈
H
f
a
t
T
7
{\displaystyle H_{7}\approx H_{f}\,\ at\ T_{7}\,}
The temperature differences between stages include that between warm surface water and working steam, that between exhaust steam and cooling water, and that between cooling water reaching the condenser and deep water. These represent external irreversibilities that reduce the overall temperature difference. The cold water flow rate per unit turbine mass flow rate,
m
c
=
H
5
−
H
6
H
6
−
H
7
˙
{\displaystyle {\dot {m_{c}={\frac {H_{5}-\ H_{6}}{H_{6}-\ H_{7}}}}}\,}
Turbine mass flow rate,
M
T
˙
=
t
u
r
b
i
n
e
w
o
r
k
r
e
q
u
i
r
e
d
W
T
{\displaystyle {\dot {M_{T}}}={\frac {\mathrm {turbine} \ \mathrm {work} \ \mathrm {required} }{W_{T}}}}