First, a few preliminaries to put things in context. I have a Devillbiss Intellipap, standard edition. My pressure setting is nine. The ramp up is five minutes. My hose is unheated. On the advice of my physician, I did not use the humidifier. He does not think I need it in the summer. HOWEVER, your situation may be different, so check with your provider. If you get the thumbs up, try it for a few nights to be sure you like it.
The main finding is counter-intuitive, at least for wilderness camping: several small batteries are better than one big one. For me the ideal battery was a 3.2 pound 7.8 amp hour 12 volt sealed lead acid battery. A two-pack I bought on the net cost $34. I ended up buying three, intending to rotate them using a solar charger.
I went through a few solar chargers during home trials and never found one at a reasonable price that would charge a 12v battery. You have to go over $100. Anyone who has found and tested one that costs less please jump in. What I found were many good chargers, but all were configured for USB, which outputs considerably less than 12v and hence will not work. A few purport to output 12v, but I found they did not charge or their output was so low they were worthless.
The other reason for wanting to keep the cost of a charger under $100 was as soon as you get up to $150 or so you enter the territory of the proprietary systems sold on many web sites.
In addition to the three batteries, I rigged up my own charging unit with a surplus DC tip from a wall wart that fit the DC plug on the machine. I attached to this some connectors I insulated to prevent any inadvertent shorts in the middle of the night during a rainstorm or whatever. To this connecting cable I added a cheap digital volt meter purchased from an auction site for $5. Total cost for three batteries plus meter: about $60.
If you do do any research you will find a 24 amp hour battery will cost considerably more-- but also weigh A LOT. My three 7.8ah batteries weighed less than a 14ah I purchased as a backup. Another advantage of the smaller batteries is they pack easier. All mine went in individual waterproof bags.
You also may want to purchase a decent charger that will work with SLA batteries. This is VERY important. You cannot charge an SLA with a wall wart or many car battery chargers. Mine cost $35, but will charge a lot more than just my CPAP batteries.
What I experienced surprised me. First, using the voltmeter and charger meter I checked the new batteries and found all were under-charged. It took awhile to "top them off" which ended up being about 13.8 volts. THIS STEP IS CRUCIAL!
I decided to go without CPAP the first night for several reasons. If it did not work out I had the batteries for backup. If something serious developed, I was close enough to civilization to get out. It also gave me an idea of how I would do without CPAP in case something happened to the batteries. This "test night" is the second critical ingredient. Again, I checked with my doctor to be sure it was OK to skip one night.
After that I used the batteries. They lasted me five nights, for a total of six, good enough for a decent wilderness trip. One battery lasted two nights, the other two a little less than two. The volt meter said they drained slightly as days passed. Not a lot, but enough.
What I found, not surprisingly was that when the charge in the batteries dropped below 12v the CPAP quit. Usually 11.7 was the shutoff point. I mention this because all of us with car batteries know they will start a vehicle if a little low. Not so with CPAP.
What surprised me was how little the machine drained the batteries. I don't know if these were from an exceptional manufacturer (they do rate the highest--and are by far the lightest). A 3.4 pound 7.8ah battery could last two nights. That was all I got out of the 14ah battery from a different manufacturer that weighed 11+ pounds.
Maybe someone can explain this apparent anomaly. Checking the machine when I returned home I found it was working the entire night.
So how much did I sleep? The average was seven-plus hours. I find that is all I need. One night I slept almost nine hours.
The machine, which I packed in an old waterproof, padded camera container and the batteries survived torrential rain storms, sitting in the bottom of a canoe (of course the packs were water proof/repellant). They survived running and walking rapids, numerous portages and enough mosquitoes to pick the whole rig up and carry it away.
So what is the summary:
SLA is best due to cost/weight factor
Go with several small, light ones not one big one. In addition to weight, they make packing easier.
7.8 hours appeared to be the magic number. Larger sizes up to 14ah weigh more and cost more.
Be sure and have a voltmeter
When solar gets cheaper it will make wilderness CPAP camping feasible for weeks, not days.
Good luck to everyone venturing into the backcountry! This experience prooves you can do it for an additional cost of $60-$80. Go for it!