Mathematical simulation of chemical processes requires deep knowledges of kinetics, thermodynamics, mass transfer, etc. You have to learn basics of heterogeneous reaction kinetics. Learn what is the TurnOver Frequency (TOF)
Directly Fe2O3 wont react with Methane, But Metallic Fe reacts with CH4 to form Fe3C and H2. To know kinetics of Fe2O3 reduction crack methane to form CO and H2. Reduction reactions With CO and H2 sre more effective.
Here is a paper that explains reduction of Iron via partially oxidized methane the CO and H2 formed are the actual reducing agent. Exxon had a large project to demonstrate this technology called the FeOR project back in the late 70's I was not directly involved but I knew several people who were. It was a technical success but an economic failure as I recall