Dear Julien
Would you please tell me what is exactly your problem.
As I understand, your one of your burners has been broken and it seems that its stack has failed. Doesn't it?
You wanna fix it without Plant Shut down. OK?
and in addition you want to take it down to repair. OK?
So, please clarify the below items:
1- Which signals from burner go to DCS? In most burners as far as I know, the burner section is located at the bottom of the equipment unlike flare which ignator and burners are located at the top of the stack on ".flare tip".
Please let us have a schematic sketch of your burner and clarify which variables send signal to DCS.
2- If you have a spare burner which capacity is enough for normal operation, you can continue your production during the reconstruction of your burner.
3- You should exactly clarify on the sketch that which part has been broken.
if the stack was broken may be online welding could solve the problem.
If other parts are broken and you can manufacture them via detailed drawing of them, so first rebuild them and replace in the least time.
Mahdi