I see this solenoid on various other sides with multiple conflicting specs. Your best bet is to set up a test, use a regulated bench supply good for well over 500mA (
@12vdc) and measure the current.
However, among all the conflicting specs, 4W seems to be the highest one so you could factor for that, 300mA at 12V, is 300mAh for an hour a week. This is within the capability of rechargeable NiHM AA, or of course larger cell sizes, as well as various Li-Ion pack sizes.
One spec I saw showed 12V +/-10%. That seems like a suspiciously round % number to me but if we use it we see it can operate between 13.2V and 10.8V. This becomes a bit of an issue in that 10 x 1.2 NiMH cells have a peak charge closer to 1.4V, so 10 in series would give 14V, above the 13.2V spec. Dropping down to 9 in series, the cells can only drop to 1.2V each before the series reaches the minimum 10.8V, so only half the capacity is used.
This latter case could be acceptable to you, if you merely buy a pack that's double the capacity you'd otherwise need, but then the question becomes how often you want to (need to) recharge it and what method to recharge it?
You mentioned 8 x AA or D cells, but I assume you mean alkaline primary cells to arrive at 12V, but you would only discharge them to 1.35V before reaching the 10.8V minimum so most of the battery capacity is wasted. It is possible the solenoid can operate reliably at a lower voltage than spec'd, but I wouldn't assume it without a bench test, done with the line pressurized to the normal working pressure in case that affects the data.
A 12V lead acid battery would be the closest match for both full charge and discharge voltage levels, yet it is the option with the most weight and fewest recharge cycles before replacement is required, but at least it is rechargeable unlike the more than half wasted alkaline cells.
Another option I would prefer would be to use 4 x NiMH LSD (low self discharge) AA cells, for example Panasonic/Sanyo/Fujitsu (whatever the heck they're calling themselves these days, lol) cells, then a ~$1, ~2amp, boost switching power supply to convert the ~4.8V to 12V. Here is a random example PSU on ebay, but you may be able to drive the cost down more by buying in volume, perhaps on alibaba or another site that deals in bulk:
https://www.ebay.com/itm/3PCS-DC-DC...wer-Supply-Converter-Module-N108/382552336602
This would result in roughly 1A current drain (after factoring for around 80% boost converter efficiency, this is yet another thing to bench test), something a AA NiMH can handle, for roughly 2 hours run time per recharge. This is based on the questionable, yet still peak rating mentioned above of 4W. It might run multiple times that long. This would also allow easily sourcing replacement cells, but they must be LSD if you don't want to have to possibly recharge them very few days before use, especially as they age.
This would also allow using a commonly available 4 bay smart NiMH charger to recharge them, or did you intend to go fancier and create a custom charger and a battery cartridge that the cells are not removed from like many cordless power tools use?
This would also make the battery pack reasonably small and light weight, but again before making a decision I would bench test the solenoid and measure current under the load of the pressurized line. You might be able to get away with using 4x AAA cells (and a boost switching supply still) instead of AA if the average current at 12V is under roughly 150mA.
You could do as described above with alkaline cells but AA alkaline don't have the current capacity, so you'd move up to at least C cells and D even better. I don't see a good reason to do this as it will quickly get more expensive than using rechargeable LSD NiMH, AA cells if the equipment is used more than rarely, unless of course you are selling the product and want to shift the cost of batteries onto the consumer, but you can still do that with NiMH AA rechargeables, let the consumer purchase them since they are so very common in the market, but it's usually considered better form to include rechargeable batteries with a product that uses them.
Suppose the average current measured was 100mA or lower, then you might even be able to have a 4 x AA battery bay, plus the boost converter after it, then the user can choose whether to install alkalines, NiMH, or even lithium primary cells, but not 4 x 14500 (AA sized) Li-Ion cells unless you went to a more elaborate buck/boost converter and suffered some additional efficiency loss. Plus if you say 14500 to most people, their eyes glaze over because they have no idea what you're talking about.
