This week’s question comes from Olle Holm, the editor of The Baltic Eye. “A question about ‘arctic OTEC’: I saw somewhere the idea to utilize the temperature gradient between arctic under-ice seawater (+1¬∞C) and the air above the ice (-40¬∞C). Would that be at all feasible for an OTEC-plant?” This question came in response to a column on OTEC (Ocean Thermal Energy Conversion) that I wrote a few months ago (read it here).
Using the Carnot equation for thermal engine efficiency presented in my earlier column (1 – Tc/Th), where Tc is the colder temperature (in Kelvin) and Th is the warmer temperature (in Kelvin), we can determine the theoretical efficiency. So to calculate the efficiency of the proposed “Arctic OTEC” we first need to convert from ¬∞C to Kelvin (+273), so we get Tc = 233 K and Th = 274 K. When you plug this into the Carnot equation you get close to 15% efficiency (1 – 233 / 274). This sort of efficiency is close to that of solar photovoltaic but solar PV has a very powerful energy source, the sun. How much energy does the difference between subsurface and surface temperatures hold?
In my previous column I wrote “But, of course the Carnot cycle is the theoretical maximum, based on a reversible cycle, and the actual efficiency would be quite a bit lower. The formula for an unreversible cycle is very similar, just take the square root of the (Tc/Th) bit.” Using this equation we get a more realistic 8% efficiency (1 – sqrt(233 / 274)). But 8% of what? That’s what we need to find out next.
As temperatures cool, the molecules in a substance (solid, liquid, or gas) begin to slow. Slower molecules mean less energy so it is likely that the 41¬∞C temperature differential in this Arctic OTEC example will yield less than the 30¬∞F difference in the Hawaii example from my previous OTEC column. Another problem with the Arctic OTEC concept is that the water is very close to or below freezing and the system would likely freeze up very quickly. In fact I have heard that throwing a boiling cup of water into the air at -30¬∞C/-30¬∞F will turn it to steam instantly and it will snow down as ice crystals. The best way to overcome this problem is to transfer the Th and Tc from the air and water to a substance that won’t freeze, like an antifreeze that you might use in your car (Ethylene Glycol or Propylene Glycol).
Let’s assume a 65% concentration of Ethylene Glycol (diluted in water), which has a specific heat capacity of 2.943 kJ/(kg-K) at -40¬∞C and 3.019 kJ/(kg-K) at 4.4¬∞C. I think 4.4¬∞C is close enough to 1¬∞C for this example, so we will use those numbers. So, let’s find out how much energy is available (per kg)… At -40¬∞C the Ethylene Glycol has 2.943 kJ/kg-K, which amounts to 686 kJ [2.943 kJ/kg-K x (1 kg x 233 K)] and at 1¬∞C the Ethylene Glycol has about 3.0 kJ/kg-K, which comes out to 822 kJ [3.0 kJ/kg-K x (1 kg x 274 K)]. The difference between these two results is the amount of thermal energy that we can extract, so 822 kJ – 686 kJ = 136 kJ. At 8% efficiency the total extractable energy, per kg of Ethylene Glycol, is 10.88 kJ.
Let’s see what this is in terms of usable energy. If we assume a supply of 100 kg of Ethylene Glycol per minute we can expect 1088 kJ per minute, or 65,280 kJ per hour. This converts to 18.1 kWh per hour, or 434 kWh per day. This would be enough to power 15 average US households. Of course there would be further efficiency losses due to the required pumps and other electronics.
As another disclaimer… These calculations are strictly theoretical. There may be additional factors that come into play in such cold conditions that may complicate the OTEC process, or make it not function altogether. One such problem might be keeping the +1¬∞C side from freezing on the heat exchanger since it will be somewhere between +1¬∞C and -40¬∞C
Pablo P√§ster, MBA