@sour_grapes presented a formula that is interesting, and probably close to reality.
https://www.winemakingtalk.com/threads/2nd-annual-m-a-n-e-event.66003/post-696470
I agree with
@Johnd on all points.
Sometimes it helps to see numbers to visualize things. The chart below is taken from a barrel FAQ on homebrewing.org
Note that surface area is for a specific barrel design, but is a reasonable approximation for other barrel dimensions.
The key value in the table is
Surface to Volume Ratio. When this ratio is high (smaller barrel), the wine gets more contact with the wood per liter of volume, so the extraction of oak character is higher.
When the value is low (larger barrel), there is more surface through which to evaporate, so we have more evaporation, and I assume micro-oxidation.
@Kitchen, is your question philosophical or practical, meaning are you planning to make a batch that will fit a puncheon?
If so, you need to take into account the amount of evaporation from a larger barrel. I have 54 liter / 14.25 gallon barrels, which evaporate about 10% per year, so for a year's aging I need to start with 16 gallons of wine.
If the evaporation rate was the same with a puncheon, you'd need to start with 150 gallons of wine, and would need an addition 15 for the 2nd year. However if the evaporation rate is greater (which I expect is so) you need even more wine than that.
An alternate is to use neutral barrels of whatever size. You get the concentration effect without imparting too much oak, and can add oak adjuncts to impart as much oak character as you want. This has the advantage that you can mix-n-match oak adjuncts, e.g., French heavy toast + American medium toast.