Back of the envelope calculation

A project log for Improve the Haber process

See if ultrasonic cavitation can be used to fixate atmospheric Nitrogen less expensively than the Haber process.

peter-walshPeter Walsh 04/05/2015 at 00:490 Comments

Improving the Bosch-Haber process is a challenging problem, so before I embark on any particular action it's probably a good idea to see if there's any chance of succeeding.

As the saying goes, four hours in the lab will save you an hour in the library...

NB: I am not actually a chem major, so if you see an error in the analysis, please let me know!

Where to find information

Several researchers have looked into ultrasonic nitrogen fixation. For the technical reader, "Sonochemical Fixation of Nitrogen" by Supeno is a good starting point. The paper reviews the previous research and explains the various processes, including cavitation, chemical reactions, solubility, kinematics, and so on.

If you want more information on the problem I'm trying to solve, that's a good place to start.

For a good overview of the ways nitrogen may be fixed, try "Fixation Of Atmospheric Nitrogen" by Frank Ernst. Published in 1928, it gives a little of the history of nitrate usage, and explains in detail the various methods of producing it.

Chapter 1 (history) has an interesting take on WWI:

It is quite generally believed that Germany declared war in 1914 only after assuring herself that she had a suitable source of fixed nitrogen within her own borders. The rate of consumption of nitrogen in explosives during this war was undoubtedly far beyond the expectations of any individual or nation. In order to meet this demand it was necessary, even with the enormous expansion of the rather young atmospheric nitrogen fixation industry, to stint agriculture. How great an effect this had on the eventual result is rather difficult to appraise, but there Is no doubt that the people of several of the warring nations suffered materially and still show the effects of malnutrition.

If you just want the basics of the Bosch-Haber process, this link is pretty good.

For more detail on why ammonia fixation plants are so expensive, check out "Chemical Reactor Design For Process Plants, Vol II" by Howard F. Rase. It's an Ammonia fixation plant case study, and has all the gory details. Not for the faint of heart, guaranteed to make your head spin.

Energy required for Bosch-Haber

According to this link, Nitrogen from the Bosch-Haber process requires 34.5 Gigajoules per metric ton (mt) of nitrogen produced. I can't tell if that's nitrogen produced or ammonia produced, but it doesn't matter because they weigh about the same and this calculation is only approximate.

\color{White} \large \color{White} \large \color{White} \large \color{White} \large 34.5 \times 10^{9} \frac{Joule}{mt} \times 1 \frac{mt}{1000 kg} \times 1 \frac{kg}{1000g} \times 17 \frac{g}{mole} = 586500 \frac{J}{mole}

So Bosch-Haber requires over half a million joules to create one mole of ammonia.

To put this in perspective, 1 mole of ammonia weighs 17 grams, and that many joules will run a 100 watt incandescent bulb for over 90 minutes. Yow.

And this for a chemical reaction that gives off energy in the process. Quite a lot of it, actually:

\color{White} \large \color{White} \large N_{2} + 3 H_{2} \rightarrow 2 NH_{3} + 91800 J

To put that in perspective, this is about a third of the energy you would get from burning the same mass of wood.

The reason the reaction doesn't easily happen - the reason we can't simply ignite the gases like so much paper - has to do with the interplay of the activation energy (breaking the N2 apart) and the entropy. When you heat the gases enough to start the reaction, the reaction is no longer favored and the reverse reaction happens instead. Ammonia breaks down into nitrogen.

This is actually a good thing, otherwise a lightning strike would ignite the atmosphere, oxidizing all the nitrogen and turning rain into nitric acid.

I'll post a more complete explanation in a future log. For now, the target to beat appears to be about half a million joules per mole.

Energy required for sonication

According to another Supeno paper, the maximum rate of ammonia produced was 4 nmol/min/W. Converting to Joules and moles:

\color{White} \large 4 \times 10^{-9} \frac{mol}{W\times minute} \Rightarrow 2.5 \times 10^{8}\frac{W\times minute}{mol}

\color{White} \large 2.5 \times 10^{8}\frac{Watt\times minute}{mol} \times 60 \frac{seconds}{minute} \times 1 \frac{Joule}{Watt \times second} = 1.5 \times 10^{10} \frac{Joules}{mole}

Target for this project

Comparing the Bosch and sonification energies:

\color{White} \large \frac{1.5\times 10^{10}}{586500} = 25575

So for purposes of this project, I need to improve the efficiency of sonification by a factor of about 25,000.

This isn't quite as bad as it looks.

For one thing, I think I can get a factor of 10 (and maybe as much as 100) using a highly tuned transducer horn. It wasn't clear from Supeno's paper, but from his description it looks like he's using a water bath, similar to an ultrasonic cleaner, and he makes no mention of tuning the chamber or transducer. Even if he's running the system at resonance, he may not be running the transducer at resonance, and this will reduce his efficiency.

There's also an interesting quote from his abstract:

The decrease in the rate with bulk temperature suggests that kinetics, rather than thermodynamics, is the limiting condition for sonochemical synthesis of ammonia.

There seems to be no chemical or physical reason why sonification can't work, and the comment above seems to indicate that changes in the experimental setup (geometry, reaction profile, and such) might affect the efficiency.

I'm quite looking forward to trying.