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October 30, 2006

AskPablo: OTEC and Engine Efficiency

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This week I am looking into the theoretical maximum efficiency of a heat engine. Then I will focus on a technology that harnesses ocean water to generate electricity.

The ideal engine runs on the Carnot cycle. According to our friends at Wikipedia "it is the most efficient cycle possible for converting a given amount of thermal energy into work." In a Carnot cycle there is a heat source (flame, sunlight) and a cooling source (water, cold air). The definition of Carnot efficiency is 1 - Temp.Cold /Temp.Hot, where temperature is in Kelvin.

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Let's look at an example: Let's say that the University of Hawaii wants to take advantage of the temperature difference between water on the surface of the ocean and deep ocean water. To figure out the maximum efficiency that they could achieve they find the temperatures at the surface, 80F ( 299.6K), and the temperature at the ocean floor, 50F (283K), and plug them into the formula (1 - 283K/299.6K = 0.06, or 6%). 6% is pretty low, but is not bad (Solar PV is only around 15%). 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 283K/299.6K bit. This gives us a more realistic 2.8%. It is just our luck that someone has tried this sort of thing out in real life. And as is frequently the case, the actual efficiency is lower than the theoretical. The Ocean Thermal Energy Conversion (OTEC) plant Keahole Point in Hawaii is only about 1-3% efficient. Even at such poor efficiency one study estimates the cost to be around $0.07 per kWh. Ocean water is, after all, a free and renewable resource.

The same equations can be used for other power plants, such as a coal-fired power-plant. Assume that the cooling water from the river is at 25C (298K) and that the burning coal can make steam at 550C (823K). The Carnot theoretical maximum efficiency would be around 63.8%, the unreversible maximum efficiency would be 39.8%, while the actual efficiency of a coal-fired power plant is around 35%. Nuclear Power Plants are around 30% efficient.

Please note that I have a new URL, www.AskPablo.org. If you are currently linking to AskPablo on www.TriplePundit.com, please change it. My column will continue to be a part of www.TriplePundit.com, but we want to get past www.AskPablo.com on Google (it's a horse betting site, don't ask why).

Pablo Päster, MBA
Sustainability Engineer
www.AskPablo.org
pablo(dot)paster(at)gmail(dot)com

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Comments

Nice work pablito... can you throw a little more english into this one? Like... how does this apply to planes trains and automobiles?

» Nick at October 30, 2006 2:03 PM

Nick, The truth is that it does not apply directly to transportation engines since we are talking about electricity generations here. But similar methods can be used to determine the maximum engine efficiency of a vehicle. Our vehicle engines are around 30% efficient. Based on the theoretical maximum efficiency we can't go much higher. The majority of vehicle efficiency improvements are not through engine efficiency improvements. What we can do is to prevent the combustion of fuel when it is not needed (when stopped, going down hill), prevent the loss of energy (aerodynamics, tires, transmission, braking), and teach people to drive more efficiently (by not driving and taking public transit). I think I should save all this fun for another time though...

» Pablo at October 30, 2006 2:11 PM

Sorry got cut off... what I meant to ask it - what exactly are you measureing here? In the coal plant example are you telling me the amount of the coal's potential energy that is getting wasted as heat? How so? The coal has potential energy, it gets burned, it heats water, the water gets really really hot and blasts through a turbine which turns producing electricity. Then the steam get's shot out a smokestack of some kind. So... what are you measureing at the other ened? The coolant water that gets used to chill the spinning turbine? What if you put the coal plant in the arctic with an endless supply of 32 degree water - does this make the burning of coal more efficient in the arctic? How?

» Nick Aster at October 30, 2006 2:13 PM

Ah, I see... What we are measuring is the efficiency of turning coal (or any other fuel), which has a certain chemical potential energy, into work (turning a turbine), which generates electricity. So, when a power plant is 35% efficient, 65% of the energy in the fuel become waste (heat, noise, light) and is of no use to us.

A power plant in the arctic would be more efficient (you can try this out yourself with the Carnot equation) but the efficiency gained would be lost in transmission to a population center.

» Pablo at October 30, 2006 2:19 PM

Fascinating... so are there no other measurements of inefficiency in the context of mechanics other than heat production?

» Nick Aster at October 30, 2006 3:33 PM

Anything that does not contribute to the intended output is waste/inefficiency. You can have heat from combustion, heat from friction, heat from radiation but you can also have sound from friction, sound from a rapid release of energy (explosion, collision), etc. According to the 1st law of thermodynamics nothing can be created or destroyed. Fuel becomes heat, light, sound, and carbon emissions. Nothing is lost, even though we cannot harness certain "non-product outputs."

» Pablo at October 30, 2006 4:12 PM

So, when a power plant is 35% efficient, 65% of the energy in the fuel become waste (heat, noise, light) and is of no use to us.


The 65% you mention is of no use from a electrical generation point of view, but can of course be used to heat housing or other facilities, or can be used for other purposes.
To see how that works see: http://uschpa.admgt.com/CHPbasics.htm



In Scandinavia, modern Combined Heat and Power plants can reach as high as 90-95% in their energy use during the winter time. Nearly nothing goes to waste. In hotter climates one can use the waste heat for other purposes, for example to improve the efficiency of a seawater desalination plant.


Best regards


Thomas, Editor at OTEC News, http://www.otecnews.org/

» Thomas Bjelkeman-Pettersson at October 31, 2006 1:06 PM

Thomas, Thank you for bringing this up. Finding uses for what would otherwise be waste is a key part of sustainability. Cogeneration, the generation of electricity and hot water (for heating or domestic use), is a very smart way to maximize the efficiency of fuel use.

It seems that you are an authority on OTEC plants. Would you like to share any news or technology updates with us? I am sure that my column left out a few things. Thanks!

» Pablo at October 31, 2006 1:50 PM

Thank you Pablo for bringing up the "efficiency" question. I once worked for a VP of Engineering that insisted solar was far less efficient than Diesel...he designed machines, and didn't pay for fuel.

The NELHA example provides a similar situation in connection with OTEC efficiency.

NELHA was and is a subscale pilot plant which established that the minimum practical size of an OTEC plant for power production would be 30 MegaWatts. It is interesting that the US Navy, today, is building an OTEC plant at Diego Garcia. The proposed OTEC facility will be designed to provide 7 MW of electrical power and 1.25 million gallons of potable water per day for the island. No threat to the petro-establishment by the Navy! http://resourcescommittee.house.gov/archives/109/testimony/2006/waynearny.pdf

On the other hand, NOAA never looked at anything but electrical energy production efficiency. The plant is the second largest exporter in Hawaii, now. Exporting what? Bottled "Deep Ocean" water!

Exploiting the varied outputs of an OTEC plant might be very profitable in combination. Distilled water, Oxygen, Nitrogen, Hydrogen, or Ammonia, Methanol. Using cogeneration equipment presently available. At the very least, it could solve potable water problems in small island nations as no other technology can.

Please see www.caribotec.com for a few examples.

» Rick Gandenberger at November 28, 2006 7:33 PM

Hello, a question about "arctic OTEC": I saw somewhere the idea to utilize the temperature gradient between arctic under-ice seawhater (+1c) and the air above the ice (-40c). Would that be at all feasible for an OTEC-plant? olle

» olle holm at May 14, 2007 11:57 AM

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