Your question is a difficult one. If you did not find any microkinetic model (mechanism) for methane PO over your catalyst, you have to then compile your own mechanism based on some experimental data. Experimental data can be the number of active sites measured by CO, but even better CH4, chemisorption. You can then feed this information into your modeling software.
You could probably check the works of this group: http://www.itcp.kit.edu/deutschmann/290.php
Probably some helpful work will be there for you. I had a quick look and stumbled upon this paper, for example:
K. Herrera Delgado, H. Stotz, L. Maier, S. Tischer, A. Zellner, O. Deutschmann. Surface Reaction Kinetics of Steam- and CO2-Reforming as well as Oxidation of Methane over Nickel-based Catalysts. Catalysts 5 (2015) 871-904.