So it can be said that I contributed *something* useful to this thread, let's do some math.
You just ran out of air on the bottom and your buddy disappeared into the ethos. You are (rightly so) somewhat freaked out about this occurrence. Your breathing rate skyrockets...probably at first to 1.5cft/min or more, but it will settle down once you have something to breathe. Let's assume a 1cft/min breathing rate from the bottom (at 100ft) to the surface, including a 30 ft/min ascent rate, and safety stop at 15 ft. The 1cft/min is reasonable considering that your breathing rate will spike initially and then slowly calm down to a somewhat normal rate.
Figure that you will need to spend a minute or so on the bottom dealing with the problem, and getting settled down. That's 4 ATA, so 4 cft in one minute.
Then, you start your 30 ft/min ascent. You will reach 15 ft in basically 3 minutes at an average depth of roughly 60 ft, or 3 ATA. That's 9 cft (3 ATA * 3 mins). We are up to 13 cft already, with a 13 cft tank, you just ran out of gas (for the second time) at 15 ft.
Now you are going to spend 3 minutes at 15 ft (1.5 ATA). That's another 4.5 cft, plus a 1 minute ascent to the surface...call that another 1.5 cft. Our total is 4 + 9 + 4.5 + 1.5, which is 19 cft. The 19cft tank will probably just squeek in as enough gas to make it from 100 ft with a 'normal' ascent. I would want more than what is the absolute minimum. When deco diving, we plan to carry 1.5x the 'required' amount of deco gas for the dive, just in case things don't go exactly as planned.
Obviously, I'm doing a bit of conservative rounding, but it's not unreasonably so.