Kevin your overview of how the diesel Particulate filter system functions is correct.
The point I was making is that you imply the additive only plays a very small part in the regeneration process, this is not true.
In the normal operating conditions of a modern car diesel engine , the conditions needed to allow regeneration to happen would never be meet.
That's were the additive comes into play.
The particulate filter will trap carbon particles and if not cleaned it would become blocked.
The only way to remove the carbon particles is to burn them off.
unfortunately the ignition temperature of the particulates is about 750-850°C.
Exhaust gas temperatures at this level are only achieved on diesel engines at full throttle for prolong periods.
By introducing the additive, the ignition temperature of the carbon particles is reduced to approx 500°c.
Now if you combine the additive with , injection after the period of main injection the exhaust gas temperature will rise and the carbon particles in the PAF will burn off.
These means the regeneration process can take place at a more relaxed throttle opening and at much lower engine speeds.
I believe the forced regeneration process has now been removed from the O/E tools and is not a option anymore.
So to sum up , you implied the additive played a small part in the regeneration process. But in reality is play a big part and if missing the Process would never happen under normal driving condition.