A loop that refuses to give up.

Fifteen percent is a failing grade, and it is fine.

Nitrogen is 78% of the air you are breathing and almost nothing alive can use it, because the two atoms are held together by a triple bond worth about 945 kJ per mole. That is one of the strongest bonds in ordinary chemistry. Plants do not break it. Lightning breaks a little of it. For most of history the nitrogen in your food came from manure, guano, or a legume with the right bacteria in its roots.

The Haber Bosch process breaks it on purpose, on an iron catalyst, at around 400 to 450 C and roughly 200 atmospheres. Even with all of that, equilibrium only lets about 15% of what enters the converter come out as ammonia. Push the temperature up and the reaction goes faster but equilibrium gets worse, because making ammonia gives off heat. Push it down and equilibrium improves but the catalyst goes to sleep. 400 C is the truce.

The gap between those last two numbers is the whole design. You do not get to 98% by building a better reactor. You get there by refusing to throw anything away.

The loop, and the valve that decides whether it lives.

Gas leaves the converter hot and only 15% converted. You chill it until the ammonia turns to a liquid and drops out of the bottom of a separator, and everything that did not react goes round again: compressor, converter, cooler, separator, back to the compressor. Fifteen percent per lap, and almost all of it by the end.

There is one problem, and it is the reason this drawing has a thin line going off to the left. The make-up gas carries argon and methane with it. They never react and they never condense, so every lap leaves them behind in the loop. Left alone they build up until the nitrogen and hydrogen are a minority in their own plant and the converter stops doing anything useful. The fix is a purge: bleed a little of the loop gas away, forever.

The numbers move on a steady state inert balance with a make-up gas carrying 1.25 mol% inerts at a tenth of the loop flow, an ammonia converter whose per pass conversion falls with the square of the reactant fraction, and a loop carrying roughly three moles of hydrogen for every mole of nitrogen. It is the shape of the real thing, not a plant model: a real loop is rated against equilibrium at temperature and pressure, with the recycle solved to convergence.

The balance that sets the number.

The purge fraction is not a taste. It falls out of one statement: at steady state, the inert leaving has to equal the inert arriving. Nothing else removes argon.

Inert arrives dissolved in the make-up gas, at some small fraction of it. Inert leaves only in the purge, at whatever fraction the loop has reached. Set those equal and the loop tells you what it will settle at:

Which is why the answer is inversely proportional to how much you purge, and why halving the purge doubles the argon. A conventional steam reforming plant brings in around 1.25 mol% inerts with its make-up, mostly argon out of the process air and unconverted methane. A loop willing to sit at about 12 mol% inerts therefore has to purge roughly a tenth of its make-up gas, and make-up is only about a tenth of what is going round, so the valve ends up bleeding about 1% of the loop gas. Published practice for this service is 0.5 to 2.5 vol% of the loop gas, held so the inerts stay under about 25%. Drag the slider back to 0.5% and watch the inerts hit that ceiling.

Why that one valve is the plant.

Purge too little and the inerts climb. They take up partial pressure that nitrogen and hydrogen are not taking up, per pass conversion falls, the compressor works harder for less, and the loop slowly suffocates on gas that does nothing.

Purge too much and the arithmetic is worse in a way that is easier to miss. The purge stream is mostly hydrogen and nitrogen, not argon. Every mole you bleed is hydrogen you made in a steam reformer, at temperature, from methane you bought. Throwing it away to chase the last of the argon is paying twice.

So the valve sits between two costs that point in opposite directions, and the plant lives in the dip between them. Big plants do not simply accept the loss: they put the purge through a hydrogen recovery unit, a membrane or a cryogenic separation, take the hydrogen back and vent the argon. The valve is still the thing that decides.

This process is about 2% of all the final energy humans use and roughly 70% of its output goes to fertiliser. It is the reason nearly half the people alive eat. One valve, on one loop, held between half a percent and two and a half.

Why the simulator fights you.

Open a flowsheet like this in a steady state simulator and it will not solve on the first run. The reason is structural, not a bug: the converter feed depends on the recycle, and the recycle depends on what the converter did. You cannot compute either one first.

So the simulator cuts the loop. It picks a stream, usually the recycle, and calls it a tear stream. It guesses what is in it, runs the whole flowsheet forward on that guess, arrives back at the cut with a computed value, compares the two, and guesses again. It repeats until the guess and the computed value agree to a tolerance you set.

A bad first guess on a loop this tight can wander for dozens of iterations or walk off somewhere non physical and fail. A recycle with a purge is worse, because the purge fraction and the inert build-up are coupled: change the valve and you change the composition that the tear stream was converging to. Recycle loops are the standard answer to what makes steady state flowsheet convergence hard.

That is the loop we are building agents to close. Reflux Student drives your own Aspen Plus, sets the case up, runs it, reads the result back and tells you what it verified. Try it free on Aspen Plus →