Air-to-Fuels Energy and Cost Calculation

A gallon of gasoline has an energy equivalent to 32Kwh. For the purposes of this discussion 'gasoline' means n-heptane - C7H16. Diesel fuel has an energy equivalent to 40Kwh.

The amount of hydrogen needed to convert CO2 to a fuel is the sum of the hydrogens that attach themselves to carbon plus the hydrogens that attach themselves to oxygen. Therefore, making a molecule of methane requires 4H2 + CO2 -> CH4 + 2H2O. In this circumstance twice as much hydrogen is consumed in the total reaction as is left in the hydrocarbon fuel.

This would suggest that to make 32Kwh worth of methane requires at least 64Kwh of energy to hydrolyze water. Water hydrolysis is not 100% efficient, so it's possible that one might need 80Kwh in total.

If the product is n-heptane, then the ideal formula is 7CO2 + 22H2 -> C7H16 + 14H2O. 8 H2 molecules are reacted with the carbon to create n-heptane and 14 H2 molecules are reacted with the oxygens to create water. The ratio of hydrogens is therefore 4:7, so the 32Kwh used to create the n-heptane requires a corresponding 56Kwh to create the water. The total energy investment for one gallon of gasoline is no less than 88Kwh, and is probably closer to 100Kwh.

To produce one gallon of gasoline daily, a 20 kilowatt array producing 100Kwh over a five hour period would hydrolyze roughly 4 gallons of water. A reaction with 100% purity would produce a 2.5 gallons of water for every gallon of n-heptane. Most of the energy from this reaction would end up as steam rather than fuel.

A 20 kilowatt array at 20 cents per watt would cost $4000. At 20% efficiency, it would cover 100 square meters or roughly 1100 square feet. In theory, this is small enough to fit one one's house, if 'one's house' is a typical suburban ranch-style house of 1800 square feet.

If one uses a 7 year payback cycle, one gets 7*365.25 days times 1 gallon per day. Dividing the $4000 price of the solar panels alone by 2556 days, the cost per gallon works out to $1.56 per gallon. Given that the CO2 has to be extracted from the atmosphere, water has to be hydrolyzed, and one needs a well-built, efficient reactor, the actual costs could be several times higher. However, the implication of this is that the price of oil cannot rise very far before air to fuels becomes economically viable. Furthermore, this price boundary is sinking day by day.

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1 hour ago, Meredith Poor said:

A gallon of gasoline has an energy equivalent to 32Kwh. For the purposes of this discussion 'gasoline' means n-heptane - C7H16. Diesel fuel has an energy equivalent to 40Kwh.

The amount of hydrogen needed to convert CO2 to a fuel is the sum of the hydrogens that attach themselves to carbon plus the hydrogens that attach themselves to oxygen. Therefore, making a molecule of methane requires 4H2 + CO2 -> CH4 + 2H2O. In this circumstance twice as much hydrogen is consumed in the total reaction as is left in the hydrocarbon fuel.

This would suggest that to make 32Kwh worth of methane requires at least 64Kwh of energy to hydrolyze water. Water hydrolysis is not 100% efficient, so it's possible that one might need 80Kwh in total.

If the product is n-heptane, then the ideal formula is 7CO2 + 22H2 -> C7H16 + 14H2O. 8 H2 molecules are reacted with the carbon to create n-heptane and 14 H2 molecules are reacted with the oxygens to create water. The ratio of hydrogens is therefore 4:7, so the 32Kwh used to create the n-heptane requires a corresponding 56Kwh to create the water. The total energy investment for one gallon of gasoline is no less than 88Kwh, and is probably closer to 100Kwh.

To produce one gallon of gasoline daily, a 20 kilowatt array producing 100Kwh over a five hour period would hydrolyze roughly 4 gallons of water. A reaction with 100% purity would produce a 2.5 gallons of water for every gallon of n-heptane. Most of the energy from this reaction would end up as steam rather than fuel.

A 20 kilowatt array at 20 cents per watt would cost $4000. At 20% efficiency, it would cover 100 square meters or roughly 1100 square feet. In theory, this is small enough to fit one one's house, if 'one's house' is a typical suburban ranch-style house of 1800 square feet.

If one uses a 7 year payback cycle, one gets 7*365.25 days times 1 gallon per day. Dividing the $4000 price of the solar panels alone by 2556 days, the cost per gallon works out to $1.56 per gallon. Given that the CO2 has to be extracted from the atmosphere, water has to be hydrolyzed, and one needs a well-built, efficient reactor, the actual costs could be several times higher. However, the implication of this is that the price of oil cannot rise very far before air to fuels becomes economically viable. Furthermore, this price boundary is sinking day by day.

Why go through the trouble to make methane? when it is readily and easily available from more than 1 natural source.

Algae to fuels and other usable by-products such as vitamins, nutritional supplements, animal feed, bioplastics etc are more feasible in a very well planned out greenfield refinery or energy facility reusing water, heat from sources, co2 and as an add on retrofitting existing facilities.

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I agree there isn't much point in making methane. I used that formula to illustrate the simplest hydrocarbon synthesis reaction. The posting proceeds to explore the more complicated scenario with n-heptane (C7H16) as representative of the inputs needed for gasoline.

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6 hours ago, Meredith Poor said:

I agree there isn't much point in making methane. I used that formula to illustrate the simplest hydrocarbon synthesis reaction. The posting proceeds to explore the more complicated scenario with n-heptane (C7H16) as representative of the inputs needed for gasoline.

I thank you for your fascinating post.  

You have to wonder if home-brew gasoline could enter into the mainstream, were some energetic entrepreneurs ever able to figure out a "package" including the financing, to sell such home installations by the millions. 

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Things are moving on

https://www.sciencedaily.com/releases/2018/12/181212121845.htm

Interesting article on a new catalyst to produce hydrogen. As pointed out this can be part of a process with say algae that takes in hydrogen and CO2 and you end up with fuel or a chemical feedstock.

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Algae is more than a promising alternate-renewable fuel + multi use end product source. There are several companies who have been successful and beyond just the hype that is short lived. We have also been successful in identifying species/strains of algae that are best suited for biofuel production plus bioplastics and other products in fields that as agriculture and medicine. Tying the algae growth and harvesting of more than 1 cycle of algae with a stationary energy producing source has many benefits for both sides of the energy set up.

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2 hours ago, ceo_energemsier said:

Algae is more than a promising alternate-renewable fuel + multi use end product source. There are several companies who have been successful and beyond just the hype that is short lived. We have also been successful in identifying species/strains of algae that are best suited for biofuel production plus bioplastics and other products in fields that as agriculture and medicine. Tying the algae growth and harvesting of more than 1 cycle of algae with a stationary energy producing source has many benefits for both sides of the energy set up.

I think this approach is far underrated, it's amazing what you can get the likes of algae, yeast and such to create with a little bit of assistance.

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