Monday, 7 December
Power Conversion Tutorial 1: Laws of Thermodynamics
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A geothermal power plant converts the geothermal heat to electricity.
The geothermal heat is transported to the surface by the geothermal fluid,
the brine. So a geothermal power plant takes the heat in the brine stream
and converts that to electricity. In other words, it is a heat engine.
Like other heat engines, for example, like those used in coal- and gas-fired
power plants, a geothermal power plant obeys the two laws of thermodynamics.
The first law of thermodynamics is nothing more than the principle of
energy conservation. Work and heat are different forms of energy and they
are convertible. The 1st Law states that to produce work one
must supply heat. There is no such thing as a free lunch and you do not
get something for nothing.
The second law says that, it is not only that you don't get something
for nothing, but you always get less than what you paid for. According
to the 2nd law of Thermodynamics, it is impossible to build
a heat engine that takes X units of heat from a source and produces X
units of electricity. The amount of electricity will always be substantially
less than the heat supplied to the heat engine. In fact, the only way
a heat engine may work is by extracting heat (Qh) from a hot
source, convert some of it to work (W), and dump the remainder (Qc).
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For this heat engine, the 1st Law is almost intuitive and says that W=Qh-Qc.
The Second Law goes one step further and sets the relationship between the three
terms, Qh, Qc, and W.
In 19th Century, Sadi Carnot demonstrated that the maximum power that can be
produced by a heat engine is related to the temperature, Th, at which
the heat is supplied, and the temperature Tc, at which it is rejected.
This maximum power is given by the following equation:
The temperatures Tc and Th are expressed in the absolute
temperature units, i.e. in degrees Kelvin.
The chart shows the maximum power conversion efficiency that a geothermal plant can enjoy as a function of Th on the x axis. The three curves correspond to the three different heat dump temperatures. Other things being the same, a geothermal resource at a higher temperature will always deliver a higher conversion efficiency. Similarly, a geothermal plant at a lower heat dump temperature Tc, e.g. a plant that can use sea water for its condensers, will also enjoy a higher efficiency, other things being the same.
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IMPORTANT: The actual geothermal plant efficiencies are much lower than what is shown on this chart. This is because the above equation calculates the maximum efficiency for a perfect heat engine. There is no such thing in the real world. The actual conversion efficiency depends on the type of the plant and the type of the power cycle. We will address these in another posting.
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