In the present work, the fluctuations of equivalence ratio in the PRECCINSTA combustor are investigated via large eddy simulations (LES). Four isothermal flow cases with different combinations of global equivalence ratios (0.7 or 0.83) and grids (1.2 or 1.8 million cells) are simulated to study the mixing process of air with methane, which is injected into the inlet channel through small holes. It is shown that the fluctuations of equivalence ratio are very large, and their ranges are [0.4, 1.3] and [0.3, 1.2] for cases 0.83 and 0.7, respectively. For simulating turbulent partially premixed flames in this burner with the well-known dynamically thickened flame (DTF) combustion model, a suitable multistep reaction mechanism should be chosen aforehand. To do that, laminar premixed flames of 15 different equivalence ratios are calculated using three different methane/air reaction mechanisms: 2S_CH4_BFER, 2sCM2 reduced mechanisms and GRI-Mech 3.0 detailed reaction mechanism. The variations of flame temperature, flame speed and thickness of the laminar flames with the equivalence ratios are compared in detail. It is demonstrated that the applicative equivalence ratio range for the 2S_CH4_BFER mechanism is [0.5, 1.3], which is larger than that of the 2sCM2 mechanism [0.5, 1.2]. Therefore, it is recommended to use the 2S_CH4_BFER scheme to simulate the partially premixed flames in the PRECCINSTA combustion chamber.