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Why do some people say that biofuels are renewable energy source if producing biofuels requires nitrogen fertilizers that are produced from natural gas (and energy output of biofuels is less than that of burning natural gas directly)?

They also require phosphates which are scarce.

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They're called renewable because it's possible to do them in a renewable manner. Specifically, the energy in them comes from the sun, in a fairly short time span (i.e. years, rather than millennia or longer). So the original energy source is renewable, and the route from original source to usable power is short.

It is also possible to do them in a non-renewable manner.

Nitrogen fertilizers don't have to be produced from fossil fuels. They are currently, but they don't have to be. There are renewable alternatives.

Using biofuels doesn't remove any of the essential elements (phosphorus, potassium) etc from their respective cycles. They're still around in the biosphere. This is most easily visible if the route is from biomass to biogas to energy; in that case, the solid matter left over after the extraction of the biogas (carbon and hydrogen) has all the nutrients, and can feed the next generation of biomass.

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There are dozens of sources that say that ethanol from corn is not carbon neutral.

But then ethanol from sorghum is carbon neutral. And hydrogen from ethanol from sorghum might be carbon neutral.

Now sorghum can be grown in areas of 25" of annual rainfall without irrigation and doesn't need to be grown in corn-belt areas. And sorghum requires less fertilizer than corn. Of course sorghum produces a thick growth.

Grain-sorghum can be processed to ethanol using enzymes and the entire plant is used. Or sweet-sorghum syrup can be fermented to ethanol and the part of the plant not used is livestock feed.

Ethanol doesn't have to go into cars. Ethanol can be run in gas-turbines at 60% efficiency to produce electricity. Or ethanol can be reformed to hydrogen and run in stationary hydrogen fuel cells at 85% efficiency. (These efficiencies are based on using waste heat in an additional process.)

To have a good profit margin, sorghum can only be transported short distances. So the distance to an ethanol plant from the farmland should be 10 miles or less.

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