Synthesis gas composed of CO, CO₂, H₂, and H O is sent to a plug-flow reactor, R-1101, through a feed valve for producing methanol as shown in Figure E17.4(a). The following reactions take place [10, 11]:

The corresponding rate laws for these reactions are [10, 11]

where C_i is the concentration of the species i in kmol/m³.

A coolant with a constant temperature of 350°C and the overall heat transfer coefficient is 80 W/m °C. The reactor effluent is sent to E-1102 where it is cooled to 40°C at steady state. At steady state, the feed composition (mole fraction) and feed flowrate are

The catalyst particle density is 1800 kg/m³, and the bed voidage is 0.45. The reactor length is 5 m, and the diameter is 1 m. At steady state, the feed valve is 50% open. The feed valve is closed to 25% in a single step. Compare the dynamic responses of the methanol and H₂ concentrations at the reactor outlet by using various explicit methods (such as the explicit Euler and Runge- Kutta methods) and implicit methods (such as the implicit Euler and Gear’s method of various orders).

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Syngas Feed 250°C 3 bar 100 kmol/h (FC) FC-1102 CV-1104 Coolant In 2 (a) R-1101 L = 5m D = 1 m (3) Coolant Out E-1102 40°C 4 Vapor Product