Oil based perfumes does not have do not have as long shelf life as alcohol-based. Therefore, they are sold in smaller volumes. They can still keep the fragrance for up to a year, so you will have enough time to use it up.
Another difference to perfumes containing alcohol is that perfume oils stay longer on the skin. Extracting fragrances with oil is an old method and there are writings from 300 BC. Aristotle's disciple Theofrastus there mentions perfume production with oil as a medium.
Grease dissolves fragrances very well. If you ever put a sliced onion or garlic in the fridge next to the butter, you know it will absorb the taste.