Paul I think there’s 2 ways to look at it.
The way you’ve already described— wine contact with the oak doesn’t change regardless of size. The oak should not fade at different rates.
And the other — an 8 gal barrel for example. Assuming 1 week per gallon on 1st run— and doubling every subsequent batch.
The barrel would oak 2 batches in 6 months and x3 after 14 months total. 3 batches seems to be the accepted MAX amount of batches a barrel can oak in spite of only going 14 months.
But with a full 53gal barrel — batch #1 at 1year. Batch #2 at 20-24 months. 2 batches and already at 3 year mark and might be oaked out by then.
Obviously it’s understood not all wine needs same amount of oak— and not all barrels give it at same rate.
And even tho it defies logic- the smaller barrels are said to go neutral after about 3 runs—- this is how I understood it to be at least.
As a general statement, those time frames are pretty much what my barrels have exhibited, the five 6 gallons were neutral at 18 months, the 12 gallon about the same time frame.
My 30 gallon French oak barrel has had wine in it for close to a year, and I can't detect the slightest hint of oak in the wine yet. I'd planned on leaving it in for a year, but now am starting to expand the time horizon to include maybe two years.........