Prompts:
1)​ Can you list all the concepts listed in this problem
2)​ can you generate a chemical engineering problem utilizing some of these
concepts?
3)​ can you regenerate the problem, making it unlike the problem I gave you? you can
even use other concepts covered in chemical engineering
Problem Statement: Methanol Synthesis in an Adiabatic Fixed-Bed Reactor
Background
Methanol is produced via the catalytic hydrogenation of carbon monoxide and carbon dioxide in
a fixed-bed reactor. The reactions are:
1. Primary Reaction:
[ CO + 2H_2 ←→ CH_3OH quad (Delta H^circ_298 = -90.1 kJ/mol) ]
2. Secondary Reaction (Reverse Water-Gas Shift):
[ CO_2 + H_2 ←→CO + H_2O quad (Delta H^circ_298 = +41.2 kJ/mol) ]
The reactor operates adiabatically at 50 bar with a Cu/ZnO/Al₂O₃ catalyst. The feed is a 3:1
molar ratio of H₂:CO₂ at 220°C, and the product exits at 280°C. Due to equilibrium limitations,
only 60% of CO₂ is converted.
Given Data
- Feed flow rate: 100 mol/s (total).
- Heat capacities ((C_p)):
- (H_2 = 29 J/mol·K), (CO = 30 J/mol·K), (CO_2 = 37 J/mol·K),
- (CH_3OH = 43 J/mol·K), (H_2O = 34 J/mol·K).
- Equilibrium constants at 280°C:
- (K_eq1 = 0.008) (methanol synthesis),
- (K_eq2 = 1.5) (RWGS).
Tasks
1. Material Balance:
- Calculate the molar composition of the product stream.
- Determine the extent of reactions ((xi_1, xi_2)).
2. Energy Balance:
- Compute the heat released/absorbed by the reactions.
- Verify if the adiabatic temperature rise (220°C → 280°C) aligns with the energy balance.
3. Reactor Design:
- Propose how to increase methanol yield (e.g., cooling, feed ratio adjustments).
4. Optional (Advanced):
- If the reactor were non-adiabatic with a heat exchanger (cooling to 250°C), recalculate the
product composition.