Sanoa

I understand you can't separate the chimney from the coil.
If that is so, you might want to screw the coil into the base.
Remove the silicone cap.
Then try again, you might want to apply some force as one is easier to remove then the other.
If you can't get it of this way you can use pliers but look out for squeezing the chimney.

Use force but be gentle.