Petroleum hydrocarbons can be treated by bacteria. During, Iraq war bacteria had been used to clean oil spills in the coastal waters. The organic matter present in an anaerobic digester is mostly biodegradable. Bacteria from anaerobic digester can not degrade petroleum hydrocarbons.

That question is hard to answer without further "context" clarification.

Are you feeding petroleum hydrocarbons to the (mostly municipal waste) anaerobic digester or are you taking out the bacteria from the (mostly municipal waste) anaerobic digester and using it as a seed for a different process?

Both answers from Sathiraju & Shalini are correct in a sense.

I want to know the chemical process involved. Are we talking about electron donor/receptor?

 Check if this helps

http://bioinformatica.uab.es/biocomputacio/treballs02-03/RBurgos/dades/Articulos/Anarerobicdegradation.pdf