I have a 06 van with lly and I use to idle it alot like 8-12 hrs at a time at idle. What it is, is unburnt fuel and a little bit of oil getting stuck in the cat then when you start to drive it the cat heats up a you got yourself a smoke machine. when I use to idle for a long period of time it would take atleast 3/4 to 1 mile before it cleared up. I was told by a lot of gm techs to use the high idle switch I have it set at 1000 rpm and it has worked out, now that it is cold out I don't have to idle the van for comfort except for 2 weeks ago I was in southern LA. and it was like 85 degrees out, to hot for me and I kicked the idle swtch on and idled her for about 9 hrs. and when I took off no white smoke, just a little bit of soot. I 1st noticed the white smoke at 3k miles and I now have 128k on it and have taken it to 8 dealerships in 5 different states I stopped taking it in at 90k because it was just a waste of time,and I was told by all the techs it was because I was idling at idle. I hope they are right I drive 120k a year and I need this one to last until atleast 540k.
all's I have had to replace was a #8 injector at 23k because it was running above the specs "running rich"
HOPE THIS HELPS YOU OUT

