Ammonia Plant: Temperature, Purge and the Pressure Upgrade
An ammonia plant runs N2(g) + 3H2(g) ⇌ 2NH3(g), ΔH = -92 kJ/mol, at 450 °C and 200 atm over a promoted iron catalyst. Equilibrium conversion of N2 at 200 atm is 26% at 450 °C, 40% at 400 °C and 55% at 350 °C; at 250 atm and 450 °C it is 33%. The measured per-pass conversion is 22%. Ammonia is condensed at -25 °C and unreacted gas is recompressed and recycled. The feed contains 2% argon, and a small purge stream is vented. Raising pressure to 250 atm would increase compressor power by 15% at constant throughput, although the recycle loop carries most of the compression load. Compression uses 22 MW; electricity costs $0.08/kWh and the plant runs 8000 h per year. The catalyst is only active above about 400 °C.
1. Explain why the plant does not simply run at 350 °C to obtain the higher equilibrium conversion, and why the per-pass conversion (22%) is below the equilibrium value (26%).
Read the worked answer
Why not 350 °C
Le Chatelier's principle does favour the lower temperature: the reaction is exothermic, so cooling raises K, exactly as the data show (26% at 450 °C, 55% at 350 °C). But equilibrium says nothing about how quickly it is reached. The promoted iron catalyst needs roughly 400 °C before it chemisorbs N2 fast enough, and that step controls the overall rate. At 350 °C the rate would be negligible and the converter would need an uneconomic volume. The plant also recovers reaction heat as high-pressure steam, which requires a hot outlet gas.
Why 22% is below 26%
The exit gas has not reached equilibrium - contact time is finite and catalyst activity declines between charges, so the outlet is always somewhat short of the equilibrium value. That is normal and not a fault.
What actually matters
The plant sells ammonia, not equilibrium. With recycle, a low per-pass conversion costs compression energy but not raw material, because unreacted N2 and H2 return to the converter; overall conversion of fresh feed still approaches about 98%. The design question is therefore the cheapest combination of temperature, pressure, catalyst activity and recycle ratio, not the highest possible per-pass figure.
2. Explain why the purge stream is necessary and predict the effect of increasing the purge rate on conversion and on operating cost.
Read the worked answer
Why a purge is needed
Argon is inert here: it is not consumed in the converter and is not condensed at -25 °C, so it circulates. In any recycle loop, a species that is never removed accumulates until its removal rate equals its input rate. That is precisely what the purge does.
Without a purge, argon in the loop rises until the partial pressures of N2 and H2 - and therefore both the rate and the equilibrium conversion - are badly reduced, while the compressor moves large volumes of useless gas.
Effect of increasing the purge
- Argon fraction in the loop falls, so partial pressures of reactants rise: per-pass conversion and rate improve slightly.
- More H2 and N2 leave in the purge. Hydrogen is made from natural gas and is the most expensive component, so the reformer must produce more syngas per tonne of ammonia.
Judgement
The purge rate is a trade-off between inert build-up and raw-material loss, set so the argon entering equals the argon leaving at an acceptable loop concentration. A membrane or PSA unit recovering H2 from the purge allows a larger purge without the raw-material penalty, and removing argon from the nitrogen feed upstream is even cheaper if the air separation can do it.
3. Evaluate the proposal to raise the operating pressure from 200 atm to 250 atm. Include an equilibrium argument, an energy-cost calculation and the reliability of the 15% figure.
Read the worked answer
Equilibrium argument
Four moles of gas become two, so raising pressure moves the position right: conversion rises from 26% to 33% at 450 °C. The direction is unambiguous, but the size of the benefit in energy terms is not.
Cost using the quoted figure
- 15% of 22 MW = 3.3 MW
- 3.3 MW × 8000 h = 26 400 MWh per year = 2.64 × 10^7 kWh
- at $0.08/kWh ≈ $2.1 million per year
Why the 15% figure is the wrong number to trust
It applies at constant throughput of the existing gas, but the recycle loop dominates compression. At 22% per-pass conversion the recycle ratio is roughly (1/0.22) - 1 ≈ 3.5 volumes per volume of fresh feed; at 33% it is about 2.0. So the mass of gas compressed per tonne of ammonia falls sharply, and the net compression energy may rise by much less than 15% - possibly even fall. The quoted 15% may therefore overstate the penalty or have the wrong sign at the plant boundary.
Judgement
The proposal is credible but cannot be decided without (i) the breakdown of the 15% between fresh feed and recycle and (ii) the capital cost of a converter and pipework rated at 250 atm, since wall thickness and hydrogen embrittlement rise steeply with pressure. Before committing, check whether a more active catalyst running at 420-430 °C delivers the same gain at 200 atm with no new vessel.