That xwebforum link has some great info and pictures. I did see the 30wt recommendation, up from original 20wt. There are also some fluid volumes listed there, though 250ish ml of fluid is really not a lot.
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From that thread:
The fluid inside comes in a selection of viscosities, roughly from as little as "1 weight" to as much as "40 weight" (and I'm sure there are more). According to the Koni engineer I know, they use their own proprietary blend of fluid (pretty much every dampener maker does). But it really isn't that critical to use their blend. However the viscosity you choose will make a difference on how the unit performs. He said these can use as light as 10 wt to as heavy as 30 wt. The original fluid for mine (remember it can vary from one to the next) was 20 wt, but I went with 30 wt for the stiffer springs I'm using. Another factor is the quantity (volume) of fluid. This actually makes a bigger difference than the viscosity. There needs to be some air space inside these sealed units, the balance of air and fluid changes the dynamics. He told me my fronts should have 240 mL and the rears 230 mL of fluid each, which is interesting because the rears are longer and can hold more fluid. I chose a synthetic fluid but it is available in different blends. The most affordable fluid source is motorcycle supply stores. They carry a wide selection at a great price. Or again you can get the actual Koni stuff for a lot more money.
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Sounds like we'll get some real info via Andy/Lee, but I'll put my thoughts here anyway in case they're useful.
I didn't realize how the twin tubes on these worked, pretty darn cool and simple vs. some of the monotube stuff. During operation the base valve and shock action will generally keep the cartridge full of oil, and there's an external "reservoir" of fluid in the volume between the cartridge and the strut wall to compensate for shaft displacement. the air chamber, like a motorcycle fork or a gas charged shock, is just an expansion space. The more fluid volume you have, the less air volume you have, which will produce an air spring effect that is stronger the more compressed the damper is. This matters a lot on motorcycles, but I'm not sure how much it really matters on a car as long as there is enough fluid to keep it from sucking air into the inner cartridge. What you really want to be sure of is that you don't overfill - the damper will hydraulically lock if it's overfilled and will blow seals out immediately. If it's underfilled, you may not damage anything, but the cartridge will start sucking air and you'll lose damping. So fluid level matters, but there's a range that's typically acceptable.
If I was rebuilding these in the absence of any other information, I would probably fill the cartridge halfway with oil, slide the piston and rod assembly into the cartridge but leave the seal head at the top pulled up, fill the rest of the way with fluid, and push the seal head into the cartridge. Not totally free of air, but close enough for this type of damper. It will probably slowly leak some oil out of the base valve once this is done. To figure how much oil in the outer section before dropping the filled cartridge into the housing, use some geometry to calculate the free space between the cartridge and the body. Then calculate the volume displaced by the strut rod when fully compressed vs fully extended. Now you know the absolute minimum amount of air space you need to leave. I'd probably multiply this by 2 for safety (this is definitely a SWAG number based on dirt bike forks), subtract it from your total available air space, and then you have roughly how much oil to add between chambers to be "safe". If I'm guessing, which I am, I'd think about half of the outer chamber volume will be air, and half will be oil, as that oil is also one of the main ways that heat is transferred from the damping chamber to the outer shock body for cooling.
You'll also be able to verify you're safe once fully assembled - you should easily be able to fully stroke the damper. If it's remarkably hard to fully compress, you've got too much oil and not enough air. Once you assemble it the first time, it is normal to have to cycle the damper several times to purge remaining air and get consistent damping - air will migrate to the outer chamber as the damper cycles. Try to avoid cycling the damper when inverted, it will pump oil out of the cartridge and pump air back in. It will eventually re-purge itself during operation if this happens, though.