Quasi-dimensional modeling is used on a wide scale in engine development, given its potential for saving time and resources compared to experimental investigations. Often it is preferred to more complex CFD codes that are much more computationally intensive. Accuracy is one major issue of quasi-dimensional simulations and for this reason sub-models are continuously developed in order to improve predictive capabilities. This study looks into the use of equivalent fluid velocity and characteristic length scales for simulating the processes of fresh charge entrainment and oxidation behind the flame front. Rather than dividing combustion into three different phases (i.e. laminar kernel, turbulent flame propagation and oxidation near the walls), the concept of turbulent heat and mass transfer is imposed throughout the entire process. Within this framework, the calibration of the two coefficients for fresh charge entrainment and oxidation behind the flame front was investigated, based on in-cylinder pressure and flame imaging recorded in a spark ignition (SI) engine fueled with gasoline, ethanol, methane and hydrogen. After the procedure of identifying the pairs of coefficients that ensured good accuracy during flame propagation, a more detailed analysis was performed with respect to the three aforementioned combustion phases. These findings constitute the basis for developing mass transfer sub-models that ensure improved accuracy for multi-fuel operation of SI engines.