Hey, so I've gone over Kimmeridge in the Domesday sources I have and there's no mention of an oil well on the site. What source are you using? The current oil well at Kimmeridge has been operating since the 1950s.
Crude oil products weren't really used in Medieval Europe. It was extracted in Classical/Medieval MENA, largely due to the fact that it was essentially available on the surface, or with minimal excavation required. By the 9th Century, Persian scientists were distilling crude, largely to produce kerosene for lamps.