Experimental investigation of the effect of water vapor on non-catalyzed carbon oxidation with NO2 has shown a promoting effect of about a factor 2. The promoting effect of water increases with decreasing temperature. Similarly, water was observed to promote carbon oxidation with molecular oxygen. Furthermore, a synergistic effect was observed when NO2, water and oxygen were all present in the gas phase. Evidences have been found suggesting that the promoting effect of water proceeds via an interaction with surface oxygen complexes. Implementing the results of this study in the control unit of diesel vehicles will increase the efficiency of filter regeneration. Therefore, the fuel penalty associated with active regeneration cycles can be minimized. To this end, a global kinetic model was developed that can successfully fit the observed reaction rates over the entire range of carbon conversion. The model can be used to optimize filter regeneration by predicting the required exhaust condition for maintaining a balance between soot accumulation and burn-off. A population balance model was formulated that makes it possible to keep track of age distribution in a reactor channel or in a soot filter.