A question about "appurtenances"

[Taylor Kendrick]

Hi there,

I came across a section on appurtenances in my RE course and wanted to explore a hypothetical. First, here's an example of subsurface rights as an appurtenance (from the course):

Example
An oil company buys the rights to the oil beneath a piece of property. The oil company now owns the subsurface rights to that property (one of the property's appurtenances) and can transfer or keep them as they wish. Should that property be sold again in the future, the property owner would convey all rights to the buyer EXCEPT the oil rights that were no longer the landowner's to sell. The new buyer would have to honor the pre-existing oil rights of the oil company.

My question is: is it possible to transfer oil rights but not mineral rights? If I gave oil rights to one entity and mineral rights to another, what would happen if both entities discovered their rightful resource in the same place?