That sounds like 9 or 10 cups of boiling water per day. I'd estimate about 50 grams of fuel per day, provided it isn't really windy and you don't let it boil unnecessarily. It would be better if you calibrated this yourself since it varies depending on your stove and pot and exactly what you do.
The medium size canisters are about 220g of fuel each, so that would give you four days per canister, or two of that size for the trip. You could also take one tall one but it's nice to have two so that you can get a better sense for how you're burning through it.
My best guess. Good luck.