I finally got around to doing a little math, I don't know the actual ratios you use for the spawns of each pool but these values seem pretty accurate to me from my experience of running the game.
These values assume that you're constantly spawning orbs (ie there's no cap on the number of orbs present, or orbs are always able to merge), and that you're starting from zero orbs each stage.
The formula is simply:
Longest/Shortest Time Required = Tier Orb Value Required / (Min/Max Pool Orb Value * Spawn Rate unlocked by that point)
Hopefully the formatting of this table is readable... (edit: it's not so I've just left the results)
| Orb Tier | Orb Value | Longest Time Required | Shortest Time Required |
|---|---|---|---|
| 1 | 1 | 1.5s | 1.5s |
| 2 | 2 | 2.4s | 2.4s |
| 3 | 4 | 3.6s | 3.6s |
| 4 | 8 | 7.2s | 7.2s |
| 5 | 16 | 7.2s | 7.2s |
| 6 | 32 | 11.2s | 11.2s |
| 7 | 64 | 22.4s | 22.4s |
| 8 | 128 | 22.4s | 22.4s |
| 9 | 256 | 44.8s | 44.8s |
| 10 | 512 | 44.8s | 22.4s |
| 11 | 1'024 | 1m 10.4s | 0m 35.2s |
| 12 | 2'048 | 2m 20.8s | 1m 10.4s |
| 13 | 4'096 | 4m 41.6s | 2m 20.8s |
| 14 | 8'192 | 6m 15.5s | 3m 7.7s |
| 15 | 16'384 | 6m 15.5s | 1m 33.9s |
| 16 | 32'768 | 9m 6.1s | 2m 16.5s |
| 17 | 65'536 | 18m 12.3s | 4m 33.1s |
| 18 | 131'072 | 27m 18.4s | 6m 49.6s |
| 19 | 262'144 | 48m 32.7s | 12m 8.2s |
| 20 | 524'288 | 36m 24.5s | 9m 6.1s |
| 21 | 1'048'576 | 1h 12m 49.1s | 0h 18m 12.3s |
| 22 | 2'097'152 | 2h 25m 38.1s | 0h 36m 24.5s |
| 23 | 4'194'304 | 4h 51m 16.3s | 1h 12m 49.1s |
| 24 | 8'388'608 | 9h 42m 32.5s | 2h 25m 38.1s |
| 25 | 16'777'216 | 9h 42m 32.5s | 1h 12m 49.1s |
| 26 | 33'554'432 | 19h 25m 5.1s | 2h 25m 38.1s |
| 27 | 67'108'864 | 1d 14h 50m 10.1s | 0d 4h 51m 16.3s |
| 28 | 134'217'728 | 3d 5h 40m 20.3s | 0d 9h 42m 32.5s |
| 29 | 268'435'456 | 6d 11h 20m 40.5s | 0d 19h 25m 5.1s |
| 29 | 536'870'912 | 12d 22h 41m 21.1s | 1d 14h 50m 10.1s |
| 30 | 1'073'741'824 | 25d 21h 22m 42.1s | 1d 14h 50m 10.1s |