Motion Of The Ocean: Looking At Marine Energy

Editor’s Note: EarthTechling is proud to repost this article courtesy of Do The Math. Author credit goes to Tom Murphy.

With the exception of tidal energy, our focus thus far has been on land-based energy sources. Meanwhile, the ocean absorbs a prodigious fraction of the Sun’s incident energy, creating thermal gradients, currents, and waves whipped up by winds. Let’s put some scales on the energetics of these sources and see if we may turn to them for help. We’ve got our three boxes ready: abundant, potent, and niche (puny). Time to do some sorting!

Thermal Gradients

Wherever there is a thermal gradient, our eyes light up because we can create a heat flowacross the gradient and capture some fraction of the energy flow to do useful work. This is called a heat engine, the efficiency of which is capped by the theoretical maximum (Th − Tc)/Th, where “h” and “c” subscripts refer to absolute temperatures of the hot and cold reservoirs, respectively. In the ocean, we are rather limited in how much gradient is available. The surface does not tend to exceed 30°C (303 K), while the depths cannot get much cooler than 0°C (273 K; pressure and salinity allow it to go a few degrees negative). The maximum thermodynamic efficiency therefore tops out at 10%, and in practice we might get half of this in a real application. The general scheme of producing energy from thermal gradients in the ocean is called ocean thermal energy conversion (OTEC).


How much energy is available? First of all, water is tremendously efficient at storing thermal energy, packing 4184 Joules per liter per degree (definition of the kilocalorie). Therefore, extracting the heat from a cubic meter of water at 30°C—leaving it at 0°C—represents 125 MJ of energy. Turned into electricity at 5% efficiency, we would need to process 160 cubic meters per second to generate a standard power plant’s output of 1 GW. Remember that we’re using the most extreme temperature difference for our figures. Given that the elevated surface temperatures will only be found in the top 100 m of water (above the thermocline), we must chew through 1.6 m² of ocean area per second to make our gigawatt. In a day, we convert a square patch 370 m on a side.

But this doesn’t get at how much can be sustainably recharged. The thermal energy derives, after all, from solar input. In the tropics, we might expect a patch of ocean to receive 250 W/m² of sunlight on average. It takes a square area 9 km on a side to annually recharge the 1 GW draw (at 5% extraction efficiency: the other 95% is dumped into the depths as waste heat at close to 0°C). This figure ignores thermal exchange with the air, which will tend to be in the range of 5–20 W/m² per °C difference between air and water. Also, radiative losses will reach 150 W/m² in clear skies. Approximating these effects to produce a net 100 W/m² retained as heat, we need our annual square to be about 14 km on a side.

The 200 km² patch we need to supply a 1 GW “plant” gets multiplied by 13,000 to hit our 13 TW global appetite. That’s an area comparable to the land area of the Indonesian islands: New Guinea, Borneo, Sumatra, etc. (wanted to pick something in warm water to stare at on map). Clearly we have the oceanic space. And as such, we throw OTEC into the “abundant” box. It’s basically a form of solar power at 5% efficiency available over a large fraction of the globe. So no real surprise that it should be abundant.

I did not factor in evaporative cooling, which can be rather significant. But it would have a hard time knocking the total resource out of the abundant box. In rough numbers, half of the total solar energy budget reaches the ground, and something like 70% of this is absorbed by oceans, for 35% of the total. Meanwhile, evaporation claims 23% of the solar budget, effectively taking a 2/3 bite out of the thermal energy deposited. So we need something like the area of Australia in the ocean. Like I say—still abundant.

Comparing the daily volume/area draw to the recharge area, we compute an interesting timescale: 4 years. In other words, if we isolated a patch of ocean 14 km on a side that could generate 1 GW of OTEC power, it would take 4 years to process the entire volume (above 100 m depth). This is reassuringly longer than the one year recharge time, allowing for seasonal variation and adequate mixing.

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