The MBR process (Membrane Biological Reactor) is an activated sludge system that uses a physical membrane for liquid-solids separation.
The activated sludge process is used to remove soluble organic matter from wastewater.
Having said that, you would have to pretreat oil wastewater to remove oils before treatment with an MBR process.
There are other membrane processes used to remove oils from water, but the MBR process is not one of them.