Choosing Ammonia Plant Conditions
An ammonia plant must choose operating conditions. At 450 °C and 200 atm, equilibrium conversion of N2 and H2 is 28%; at 400 °C and 200 atm it is 36%, but the catalyst produces only 60% of its rated activity at 400 °C. Lowering pressure to 150 atm reduces conversion by 4 percentage points at either temperature. Electricity for compression costs $0.09/kWh, and the plant earns $420 per tonne NH3. A 10 °C drop in reactor temperature saves $1.10 per tonne NH3 in energy but reduces catalyst activity by 8%. The plant has one catalyst charge and cannot replace it for 12 months. Management wants the highest annual profit, not the highest conversion.
1. Recommend an operating temperature and justify it with a trade-off calculation, stating any assumption.
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Do not choose 400 °C on conversion alone. Moving from 450 to 400 °C raises equilibrium conversion from 28% to 36%, but catalyst activity falls from rated to 60%, a 40% loss, and the charge cannot be replaced for 12 months. Each 10 °C step saves $1.10/t but cuts activity 8%; five steps save $5.50/t and cut activity 40%. Without reactor kinetics, the profit-maximising temperature cannot be fixed: 400 °C is attractive only if the reactor has enough excess catalyst volume and recycle capacity to absorb the rate loss. Otherwise 450 °C is safer. Recommend 450 °C unless a pilot test shows the low-temperature rate is adequate; request catalyst activity and reactor volume data.
2. A junior engineer proposes 150 atm to save compression. Evaluate the proposal using the data.
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Le Chatelier predicts lower pressure favours the side with more gas moles, so NH3 yield falls; the data confirm a 4-percentage-point drop. At 28% conversion, 4 points is about a 14% relative loss in NH3 made per pass. At $420/t, that is about $59 of lost product per tonne of current output, before extra recycle costs. Compression savings would need to exceed that. With electricity at $0.09/kWh, the saving depends on compressor work, which is not given. Reject 150 atm unless a compressor audit shows savings above $59/t plus recycle penalties.
3. Explain why highest conversion and highest profit diverge here, naming two variables.
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Conversion measures how far equilibrium is pushed per pass; profit subtracts energy, catalyst replacement, compression, and recycle costs. A lower temperature raises conversion but lowers catalyst activity, so the plant may need more catalyst or recycle, consuming energy and capital. Higher pressure raises conversion but increases compression electricity. Thus the optimum is where marginal revenue from extra NH3 equals the marginal cost of extra energy and catalyst degradation. The two named variables are catalyst activity and compression energy; recycle ratio and product separation are additional variables.