We veer away from the more theological to the practical side of preparing the oil of the sick:
20 The matter proper for the sacrament is olive oil or, according to circumstances, other oil derived from plants. (See Roman Pontifical, Rite of Blessing of Oils, Rite of Consecrating the Chrism, Introduction, no. 3 [The Sacramentary Appendix II])
Ordinarily, one uses olive oil. In most places, this is not an issue. But where obtaining olive oil is an issue, the replacement oil must come from a plant, not an animal. Some regulations on who blesses the oil and when:
21 The oil used for anointing the sick must be blessed for this purpose by the bishop or by a priest who has this faculty, either from the law or by special concession of the Apostolic See.
The law itself permits the following, besides a bishop, to bless the oil of the sick:
a) those whom the law equates with diocesan bishops;
b) in case of true necessity, any priest. (See ibid., no. 8)
The oil of the sick is ordinarily blessed by the bishop on Holy Thursday. (See ibid., no. 9)
There is a provision for blessing oil within the rite of anointing. If this is to be done, the priest may bring it or the family may provide it:
22 If a priest, in accord with no. 21 b, is to bless the oil during the rite, he may bring the unblessed oil with him, or the family of the sick person may prepare the oil in a suitable vessel. If any of the oil is left after the celebration of the sacrament, it should be absorbed in cotton and burned.
Oil blessed by a priest for a particular celebration is not to be used for other anointings. Among priests reading this post, how many of you dispose of such oil? Some practical aspects:
If the priest uses oil that has already been blessed (either by the bishop or by a priest), he brings it with him in the vessel in which it is kept. This vessel, made of suitable material, should be clean and should contain sufficient oil (soaked in cotton for convenience). In this case, after celebrating the sacrament the priest returns the vessel to the place where it is kept with proper respect. He should make sure that the oil remains fit for use and should replenish it from time to time, either yearly when the bishop blesses the oil on Holy Thursday or more frequently if necessary.
Many parishes burn holy oils from the previous year in the Easter fire (without fanfare or ritual) or at other times. Some places continue to keep the stock of oil over several years. How does your parish manage
it?
Catholic Sensibility 
As for a disposing of Holy Oils, I’m told that in Cincinnati the archbishop noticed that many parishes seems to have huge amount of Chrism in large jugs, so he assumed that they must never be disposing of the old oil.
So at the most recent Chrism mass, he used a fragrance in the Chrism that slightly darkened its color. That way he could instantly tell when visiting a parish whether or not they dispose of the old Chrism.
I personally thought it was a pretty clever solution.
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