You need to examine various ways of controlling the temperature in the MSR because the catalyst is sensitive to high temperatures and it has been reported that elevated temperatures lead to the production of unacceptable by-products. In the analysis, suppose that the feed gas to the MSR is 5 mole% methane, 25% CO, 5 % CO₂, and the remainder hydrogen, and that the MSR operates at 7.5 MPa. Take K_ϕ13.3 = K_ϕ13.5 = 1.0.

a. Determine the temperature of the stream leaving the MSR if no heat is removed from the reactor (i.e., it is operated adiabatically), the CO conversion is 45%, the CO₂ conversion is 30%, and all of the feed enters the top of the MSR at 210 C and 7.5 MPa.

b. How much heat must be removed from the MSR in part (a) to ensure that the temperature does not exceed 250°C? Give your answer in kJ/kmol of feed.

c. Repeat the calculations in part (a) if 70% of the total feed to the MSR enters as quench streams (see the Process Description) at 130°C and 7.5 MPa, while the remainder enters the top of the converter at 210°C. Assume the exit pressure is 7.5 MPa.

d. Suppose that 70% of the feed to the MSR enters as quench streams at 130 C and 7.5 MPa, while the remainder of the feed enters at the top of the converter at 210°C. Determine the equilibrium conversions of CO and CO₂ if the MSR is to operate adiabatically.