There is a lot going on here with all of the comments. If a person gets back to basics, might the following be what a person should expect? --
1000 gallons of water weighs 8340 pounds, and it takes 8340 btu's (assuming no loss) to raise the temperature of a 1000 gallon tank of water 1F, or 834,000 btu's to raise the tank 100F, say from 70 to 170F. A 500 gallon tank would take 1/2 that. A gasification boiler should operate in the 80%+ efficiency range, meaning that it can convert to usable heat 80%+ of the heat energy available in the wood being burned.
I use 6040 btu/lb of usable heat energy in 20% moisture content wood. That is based on 400F stack temperature. If net boiler efficiency is 80%, then heat content of 4832 btu/lb of wood should be delivered to the system by the boiler. If 85% efficiency, then 5134 btu/lb heat content is available. Measured efficiency on my Tarm is at about the 85% mark.
If the only heat load is the tank, no other draws on the system (and tank is well insulated), then it should take 173 lbs of wood to raise the tank temperature from 70 to 170F at 80% efficiency, or 162 lbs of wood at 85% efficiency. Depending on the type of wood burned, 162 - 173 lbs of wood likely translates to 2 - 3 loads of wood in most gasification boilers.
Next, in experience with my Tarm, average boiler output is in the 70-75% range of rated output. That means from starting a load of wood to burning to low/medium coals, and then reloading again. So if rated output is 140,000 btuh, as it is with the Tarm Solo 40, average output is 98,000 - 105,000 btuh. Using 100,000 btuh for simplification, that means it should take 8.34 hours of burning to raise the tank 100F. And if a load of wood burns in 4 hours, it should take 8 hours of burning to raise the tank 100F for two 80-85 lb loads of wood, or 12 hours of burning for loads of wood in the 55-60 lb range. Of course, if a load of wood is burned in less than 4 hours, time would decrease.
I have an effecta lambda 35 (122,000) boiler and 1,000 gallons of storage and fired things up a few weeks ago.
I was able to raise my 1,000 gallons from 70 to 160 with 3 loads of the boiler (approx. 15 hours) with no load going to the house.
Applying the analysis to this situation (not picking on this one, but this quote had enough information to use the analysis), 122,000 btuh rating, 85,000 - 91500 average output, it should take 9-10 hours of burning to raise the tank 100F or about 8.5 hours to raise the tank 90F. If loads other than the tank were active, these times would increase.
I assume every boiler is a little different. The Tarm Solo 40 has been around for a long time, and some of the newer gasification boilers may have a better draft/control system which should operate to improve efficiency over what the Solo 40 delivers, so I think my experience with the Solo 40 might be close to the minimum that a boiler should deliver.
For those interested in really determining how their boiler performs and avoid speculation, being too conservative or exaggerating, it would be a good exercise to shut off all loads and heat only the tank with weighed wood burns. This will provide some very factual information on boiler performance.