Occasionally I am deluged with inquiries about a particular news story. That happened recently. As the inquiries mounted, I decided I had better address the story. After I saw one more gushing, uncritical report on CNN, I knew a reality check was in order.

Last month, German car manufacturer Audi announced it can economically produce carbon-neutral automotive fuel from ingredients found in the atmosphere. There is also an explanatory graphic that goes along with the story, and that’s where a few people might begin to ask some critical questions about this process:

Many people have already suspected that there has to be a catch. Of course there is. This process requires carbon dioxide to be captured from the air, and hydrogen to be produced from electrolysis.

It is true that the atmosphere -- nitrogen, oxygen, water vapor, carbon dioxide -- contains all of the ingredients necessary to make all sorts of unimaginable things. The raw ingredients are there for fertilizer, pharmaceuticals, plastics and certainly fuel. But the key ingredients, carbon dioxide and water, are the products of combustion. Burning diesel creates carbon dioxide and water. Converting them back into diesel takes a lot of energy.

Think of fuel as a rock at the top of a hill. It has a lot of potential energy. Roll the rock down the hill and that potential energy is released. This is similar to burning fuel to create carbon dioxide and water. Now, if you want to turn that carbon dioxide and water back into fuel, you have to carry the rock back up the hill. That takes energy. How much?

According to the laws of thermodynamics, it always takes more energy to carry that rock up the hill than you get from rolling it back down. In other words, the process is necessarily an energy sink. It is a dead certainty that more energy is required to produce this fuel than can be released by burning the fuel.

But is that a problem? It depends.

If you have a readily available and cheap energy source, it could make sense to produce fuel via a process that is an energy sink. Imagine for a moment that we have a process that uses nothing more than the sun’s energy to crack water into hydrogen, which we can then burn for fuel (and which converts the hydrogen back into water in the process). Yes, this would be an energy sink, but one using a nearly limitless source of energy. And if the value of the hydrogen is greater than the cost of the inputs, this may be a worthwhile process despite the fact that it is an energy sink.

This is essentially the claim being made by Audi. By invoking “ecological power generation," Audi is claiming that it can produce the fuel in a way that is cost-effective and carbon-neutral. So let’s look at the economics.

The company says it will sell to the public at a price point between 1 and 1.50 euros per liter, “dependent on the cost of renewable electricity.” Diesel in Europe is currently about 1.50 euros per liter, which works out to be $6.37 U.S. dollars per gallon at the current conversion rate.

At this point I am going to need to get a little bit technical, so I will partition this section for those who don’t care about technical things. If this is you, you can jump right over this section to the conclusions. Despite the fact that I can say with certainty that this is an energy sink, I don’t really know how much it will cost to produce the fuel. I suspect more than what Audi suggests, but let’s find out.

The economics of the process

In order to produce 1 ton of fuel, this process reportedly requires capture of 3.2 tons of carbon dioxide. That in turn requires 200 to 300 kilowatt-hours of electricity and 1,500 to 2,000 kilowatt-hours of thermal energy per ton of carbon dioxide. In my experience, the high end of these ranges is generally more representative of actual operations, while the lower end represents projections and best-case scenarios of much larger projects. But let’s use the midpoint of both for the analysis.

The average price of electricity for industrial users in the U.S. is currently 6.9 cents per kilowatt-hour. (It’s much higher for residential and commercial users.) In the European Union, prices are quite a bit higher than that. The most recent data showed an average price of 0.123 euros per kilowatt-hour in the E.U., which is 14 cents per kilowatt-hour at the current exchange rate. In Germany, where Audi is based, the cost of electricity is about 16 cents per kilowatt-hour.

If we use the lowest cost here -- the price for industrial users in the U.S. -- then the cost of the electricity to capture the carbon dioxide is 3.2 tons * 250 kilowatt-hours * $0.069 = $55.20 per ton of fuel produced. This is also $17.25 per ton of carbon dioxide captured, which is much lower than other numbers I have seen -- especially considering they are proposing extracting the carbon dioxide from air.

The cost of the thermal energy -- which is steam, as indicated by the inlet temperature of 105°C and an outlet temperature of 95°C -- is dependent upon the fuel cost. Presumably, this thermal energy is for shifting carbon dioxide into carbon monoxide via the water-gas shift reaction, which is required for the fuel synthesis reaction as described below. (Note: If this is how they are producing the carbon monoxide, it could significantly increase the hydrogen requirement that I calculated below.)

The average of the given range is 1,750 kilowatt-hours of thermal energy per ton of carbon dioxide. This is equivalent to 6 million British thermal units (MMBtu) -- almost exactly the energy content of a barrel of oil. Boilers are about 85 percent efficient at converting natural gas to steam, so the cost of the thermal energy at $4/million BTU natural gas would be around 3.2 * $4.00 * 6 / 0.85 = $90.35 per ton of fuel produced. Like electricity, natural gas costs in Europe would be significantly higher.

The other main ingredient in the process is hydrogen. They don’t indicate how much hydrogen is required, but they do indicate they are utilizing the Fischer-Tropsch reaction, which has the formula:

(2n+1) H2 + n CO → CnH (2n+2) + n H2O

Don’t worry, it’s not as complicated as it looks. The “n” represents the length of the carbon chain to be built. If we take a 12-carbon chain length as representative of diesel fuel (which is right in the range of diesel-length hydrocarbons) then the reaction becomes:

25 H2 + 12 CO → C12H26 + 12 H2O

Therefore, we can calculate the theoretical minimum of how much hydrogen this reaction is going to require per ton of fuel produced. If we convert all units of weight into units of molecular mass, we can solve the rest of the equation. C12H26 has a density of 0.7495 grams (g) per milliliter (mL) and a molecular weight of 170.3 grams (g) per mole. Thus, 1 (metric) ton of fuel would be equal to 1,000 kilograms (kg) * 1 liter/(0.7495 kg) = 1,334 liters, or 352 gallons.

A ton of fuel contains 1,000 kg * 1,000 g/kg * 1 mole/170.3 g = 5,872 moles of C12H26. We can cross-check our calculations by noting that this much C12H26 contains 70,464 moles of carbon (i.e., 5,872 * 12). In comparison, the 3.2 tons of carbon dioxide they stated is required per ton of fuel contains 72,727 moles of carbon, only 3 percent off based on our assumption of C12 as the fuel. So the calculation based on my assumption of C12H26 as representative of the fuel is internally consistent.

To produce a ton of fuel per the reaction above is going to require 5,872 moles C12H26 * 25 moles of H2 per mole of C12H26 = 147,000 moles of H2. Hydrogen is very light, with a molecular weight of 2 grams per mole, so this converts to 294,000 grams, or 294 kilograms of hydrogen. How much might that cost?

This is where Audi makes some assumptions that may not hold up well over time. They assume they will use wind andsolarpower to produce the hydrogen, and that this can be cheaply done. But the U.S. government has done a highly detailed hydrogen production cost analysis in which they estimate the costs of hydrogen production from wind and solar power across many locations in the U.S.

While the Department of Energy has a 2015 goal of producing hydrogen from renewable energy at a centralized site for $3.10/kg and for distributed hydrogen at $3.70/kg, they concluded that no sites could presently achieve this target. They calculated that base hydrogen costs (i.e., no distribution) ranged from $3.74/kg to $5.86/kg. So that helps us to factor in the cost of hydrogen into this analysis.

If we assume the low end of the projected production costs of about $4/kg of hydrogen produced, production of 1 ton of fuel will require 294 kg * $4/kg = $1,176 in hydrogen. Add that to the $55.20 for the electricity required to capture the carbon dioxide and the $90.35 in thermal energy per ton of fuel, and the primary raw materials cost $1,322 per ton of fuel.

As noted, a ton of fuel would contain about 352 gallons, so this means the raw materials will cost -- based on the assumptions made here, which are based on data that has been released -- about $3.76 per gallon of diesel produced. The vast majority of that cost is due to the hydrogen, so the assumptions made about hydrogen production are where the greatest sensitivity to price will be.

It is also possible, as noted previously, that if Audi is using the standard water-gas shift reaction to convert carbon dioxide into carbon monoxide, the hydrogen requirement could be around 50 percent higher. That would add another $1.67/gal to the raw material cost for a total of $5.43/gal. In any case, the process economics are dominated by the cost of producing hydrogen.

Keep in mind that these are only the costs for the primary feedstock inputs. They don’t include the cost of capital recovery, nor do they include operating and maintenance costs. These can easily add several more dollars per gallon to the costs. The article anticipates that “the e-diesel will sell to the public for between 1 and 1.50 euros per litre.” This converts to between $4.24/gal to $6.37/gal. While the lower end of this range appears to be overly optimistic, the upper range may be achievable keeping in mind that we have made some very generous assumptions regarding their process. Notably, cheaper U.S. prices were used for key inputs. On the flip side, the current spot price of diesel in the U.S. is under $2/gal.

Conclusions

To sum up, can Audi produce fuel from thin air? Sure. There is no question about technical viability.

However, they are also not the first to make this claim. In 2012 I wrote an article titled "Investors Beware of Fuel From Thin Air," in which I examined very similar claims from a company called Air Fuel Synthesis. The question boils down to economic viability, which appears to be challenging given what has been released about the process.

Also keep in mind that Audi has only done this process at very small scale. These projections were based on lab-scale experiments. Audi has now scaled the process to 160 liters per day, which is about 1 barrel per day. They will now gather data at this scale, and either firm up or contradict some of their assumptions about the process.

If everything works as hoped, they will then need to scale up again to something in the 100 to 1,000 barrels-per-day range. These scale-up steps are like gates that must be successfully passed, and historically, most seemingly promising processes fail to pass through those gates for various reasons. As a result, one should never take too seriously a cost estimate for fuel production from a commercial plant when the data is derived from experiments at a much smaller scale.

It is important to note that because this process is an energy sink, it could exacerbate carbon dioxide emissions. Audi is claiming it doesn't because the company is assuming little to no carbon emissions from the inputs. That’s why the graphic stipulates that the electricity comes “entirely from renewable energy sources.”

It will certainly be difficult to run a plant continuously on intermittent energy inputs, but any fossil-fuel inputs into the plant will have their carbon dioxide emissions magnified. To understand this, consider that it may take 2 or 3 BTUs of energy input for each BTU of energy output. You could possibly pull that off in an environmentally friendly way with 3 BTUs of solar power input and 1 BTU of diesel output, but if you use natural gas instead, then that 1 BTU of diesel output may generate the emissions from 3 BTUs of natural-gas input.

In a case like that, it would be better to use that fossil-fuel input directly in an engine (if possible) than to utilize it to produce a fuel in a process that is an energy sink.

So, circling back to the claim that “carbon-neutral diesel is now a reality” -- I think most would agree that projections of what a process will look like after it has been scaled up two more times don’t constitute reality. They constitute a vision of reality. This claim is no more accurate than if I were to say, “Colonies on Mars are now a reality.”

Finally, please note that the analysis here isn’t meant to demean the work that has been carried out and continues to be done. I consider this very worthwhile and fascinating research. I am simply attempting to offer a more complete and realistic perspective in light of the uncritical reports by the mainstream media.

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Robert Rapier is managing editor and director of analysis at Energy Trends Insider. He is a chemical engineer with 20 years of international engineering experience in the energy business. This article was originally published at Energy Trends Insider and was reprinted with permission.