Direct Numerical Simulations (DNS) have been conducted to study the response of initially laminar spherical premixed methane-air flame kernels to successively higher turbulence intensities at five different equivalence ratios. The numerical experiments include a 16-species/25-step skeletal mechanism for methane oxidation and a multicomponent molecular transport model. Highly turbulent conditions (with integral Reynolds numbers up to 4 513) have been accessed. The effect of turbulence on the physical properties of the flame, in particular its consumption speed S c , which is an interesting measure of the turbulent flame speed S T has been investigated. Local quenching events are increasingly observed for highly turbulent conditions, particularly for lean mixtures. The obtained results qualitatively confirm the expected trend regarding correlations between u ′ /S L and the consumption speed: S c first increases, roughly linearly, with u ′ /S L (low turbulence zone), then levels off (bending zone) before decreasing again (quenching limit) for too intense turbulence. For a fixed value of u ′ /S L , S c /S L varies with the mixture equivalence ratio, showing that additional parameters should probably enter phenomenological expressions relating these two quantities.