The latest Direct Numerical Simulation (DNS) modeling results in flameless combustion suggest interactions between the combustion reaction zones. The New Extended Eddy Dissipation Concept (NE-EDC) model, where model coefficients are calculated based on local Reynolds and Damköhler numbers, was proposed to improve the standard Eddy Dissipation Concept (EDC) model's accuracy when modeling flameless combustion, but this model does not include the interactions between the reaction zones. In this work, a revised version of the NE-EDC model is presented, called here Generalized NE-EDC model, where the chemical time scale is calculated in detail, considering the reaction rates of CH4, H2, O2, CO and CO2, making the interaction between the reaction zones more realistic (in the NE-EDC only a one-step CH4 global reaction mechanism is considered). A comparative study of four global reaction mechanisms is carried out to select the best mechanism for chemical time scale definition: the adjusted Jones & Lindstedt (JL1); the adjusted Westbrook & Dryer (WD1); the adjusted Westbrook & Dryer (WD2); and the one-step CH4 global mechanism (1-step). The four global reaction mechanisms, in combination with the NE-EDC model, are applied to the Delft lab-scale furnace and the modeling results are compared against those experimental measurements. The NE-EDC modeling results, in combination with WD2, present a slight improvement over the other global mechanisms in flameless modeling.