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All the time, upstream of the catalytic converter, it helps convert NOx to nitrogen and water. The amount it injects follows engine load, more fuel = more urea injection.
My understanding is DEF is injected when EGTs exceed a certain temperature. I see higher consumption towing and in the winter. I think it is unrelated to DPF regen.
The DEF and DPF are two different animals for two different purposes. Diesel Exhaust Fluid is injected in the exhaust gas stream when Nox emission is to high. It is a chemical reaction.
The Diesel Particulate Filter filters out the soot (black smoke, i.e. rolling coal) from the exhaust gas. When the DPF is full the engine injects raw diesel into the exhaust stroke of the cylinder to fuel a burn-out of the filter. It cremates the particulates from the filter media with fire. This is called a regeneration or regen for short. Yes, we are still cavemen using fire.
Pretty well discussed above.
NOx is created by High Combustion Temps. So when you are idling at 300°F you are not injecting DEF because there is little NOx
When your turbo is at 15 psi boost and you are climbing a 5% grade your EGTs jump to 900°F and you probably are injecting DEF to reduce the NOx created by the higher combustion temps,
The amount of DEF injected is totally dependant on how much NOx is being produced. And that is dependant on the combustion temps in the cylinders
When your DEF is frozen (truck sits overnight with temps less than 12F) you definitely aren't injecting any for a little while!
EGR is used to lower cylinder temps and balance the need for DEF. But essentially, DEF is used all the time to varying "dosing" amounts. I believe the DEF injector is turned off during a regen because it would serve the purpose of lowering exhaust gas temp before it hits the DPF.
My EGTs stay pretty low for most of my driving. I use about 4 jugs (10 gallons) per year (20k miles). It seems that I use more DEF in a 150 mile tow than 1000 miles of commuting unloaded.