Ten cases is 240 brews. A full keg is 15 and a half gallons and will crank-out, worst case, about 200 12-ounce servings, and best case will be about 220 cups without too much foam if they're kept on ice well. That equates to about seven more cases of beer. So, two kegs is double that, at least 14 more cases of beer (on the wall, 14 cases of beer...!) And 14 times 24 is (reaches for calculator) = 336 additional brews.
240 + 336 is 576 total beers, divided amongst 22 people is 26 beers apiece (with 4 beers left-over). Figuring some will drink more than others, that should still balance out when all is said and done.
So it all comes down to how long, on average, it will take 22 people to consume 26 beers each. Let's say the beer-run starts on Wednesday afternoon, the party begins, and doesn't end until the last drop is drunk.
I might be able to consume 10 beers the first night 'cause I'm partying with friends and feelin' right, and then, say, 8 beers the next day until the food arrives, then only 3 more after. That's 10+8+3=21 beers, leaving 5 more for the next day, which will be effortless on my part.
So, I'm saying 2 and a half days - final answer!!