  A local-sensitivity-analysis technique is employed to generate new skeletal
reaction models for methane combustion from the foundational fuel chemistry
model (FFCM-1). The sensitivities of the thermo-chemical variables with respect
to the reaction rates are computed via the forced-optimally time dependent
(f-OTD) methodology. In this methodology, the large sensitivity matrix
containing all local sensitivities is modeled as a product of two low-rank
time-dependent matrices. The evolution equations of these matrices are derived
from the governing equations of the system. The modeled sensitivities are
computed for the auto-ignition of methane at atmospheric and high pressures
with different sets of initial temperatures, and equivalence ratios. These
sensitivities are then analyzed to rank the most important (sensitive) species.
A series of skeletal models with different number of species and levels of
accuracy in reproducing the FFCM-1 results are suggested. The performances of
the generated models are compared against FFCM-1 in predicting the ignition
delay, the laminar flame speed, and the flame extinction. The results of this
comparative assessment suggest the skeletal models with 24 and more species
generate the FFCM-1 results with an excellent accuracy.
