In porous burners, the flame thickness can be smaller than the pore size, resulting in sharp and locally-anchored flame fronts. The presence of such steep gradients at the pore level is a major hurdle for the derivation of volume-averaged models, particularly for the highly non-linear reaction rates. With the intent to address the difficulties associated with volume-averaging for porous media combustion, this work makes use of 3D Pore-Level Direct Numerical Simulations including conjugate heat transfer and complex chemistry in burners of finite length. These detailed 3D simulations are compared to their 1D volume-averaged counterpart, with effective properties estimated directly on the computational domains and of identical thermo-chemical scheme. Discrepancies in terms of burning rate, profiles, and a priori analysis on the reaction rates are discussed. Various pore sizes and geometries are considered. At the pore level, it is shown that preheating, wrinkling and wall quenching are the three main factors driving the global burning rate. Importantly, hydrodynamic dispersion is shown to have an indirect role on combustion processes. From the observations of combustion at pore scale, a new closure for reaction rates based on a flamelet assumption is proposed. It accounts for flame wrinkling and eliminates the unwanted effect of hydrodynamic dispersion on burning rate.