## 3 Results and Discussion
### Effect of the Catalyst Activity
#### 3.1.2 Different Inlet Gas Velocities  
In Figure 9, the maximum temperature attained in the filter during the regeneration process, \(\mathrm{T_{max}}\), and the time for filter regeneration, \(\mathrm{t_{reg}}\), are plotted versus \(k\) as obtained from simulations run at different inlet gas velocities (\(\mathrm{V_{in}}=1\) m/s; 3 m/s; 5 m/s).  
Regardless of the inlet velocity, the transition from slow to fast regeneration is gradual. Conversely, in the presence of cake, this transition is rather abrupt [14; 15].  
At \(\mathrm{V_{in}}=1\) m/s, \(\mathrm{T_{max}}\)/\(\mathrm{t_{reg}}\) monotonically increases/decreases with increasing \(k\) from 1 to 10. When \(k\) is further increased (\(k>10\)), the opposite trends have been simulated, and overall the quantitative features of the regeneration dynamics become much less sensitive to variations in catalyst activity. This behavior is due to the fact that, at low catalyst activity, regeneration takes place according to a kinetics-limited mode, whereas at high catalyst activity, it takes place according to an oxygen transport-limited mode.  
In the kinetics-limited mode, regeneration is sensitive to convective heat removal by the gas flowing through the filter. The heat removal increases with increasing inlet gas velocity, thus explaining the trends of decreasing \(\mathrm{T_{max}}\) and increasing \(\mathrm{t_{reg}}\) at low catalyst activity.  
As the inlet gas velocity is increased, the transition from the kinetics-limited mode to the oxygen transport-limited mode shifts towards higher values of \(k\) (in other words, the oxygen-transport limitations start playing a role at higher catalyst activity). This explains the inversion in the trends of \(\mathrm{T_{max}}\) and \(\mathrm{t_{reg}}\) with the inlet gas velocity in going from low to high catalyst activity.  
Figure 8: Time histories of oxygen mole fraction (solid lines) and soot combustion rate (dashed lines) (monitor points of Figure 2): \(k=200\) (\(\mathrm{V_{in}}=1\) m/s).  
In Figure 10, the results of Figure 9 are shown in the operating map of the filter built in the plane T\({}_{\rm max}\) versus t\({}_{\rm reg}\).  
At V\({}_{\rm in}\) = 1 m/s, two branches - upper and lower - are well distinguished. In moving from the upper branch (1 \(\leq k\leq\) 10) to the lower branch (10 \(<k\leq\) 200), we go from the kinetics-limited mode to the oxygen transport-limited mode. Under the conditions of this latter mode, regeneration can be conducted at lower temperatures and/or over shorter times than under the conditions of the kinetics-limited mode.  
Figure 9: Maximum temperature, T\({}_{\rm max}\), and time for filter regeneration, t\({}_{\rm reg}\), versus \(k\) at different inlet gas velocities.  
As the inlet gas velocity is increased (from 1 m/s to 5 m/s), the distance between the upper branch and the lower branch decreases, meaning that the potential gain from working at high catalyst activity under the conditions of the oxygen transport-limited mode decreases as well. At \(\mathrm{V_{in}}\) = 5 m/s, the two branches almost overlap and, thus, there is no substantial gain.