A few days ago without warning, my kitchen sink started backing up. From a presumably drained state, it takes about 50 seconds for the water to back up. I've measured the fill rate as one liter in 9 seconds, so the total water that backs up in 50 seconds is 5.64 liters or less, since the drain is slow, not stopped.
My drain pipe seems to be 2" in diameter—though the disposal is much wider than that—so the area of the pipe cross-section is about 16 cm^2. 5.64 liters is 5,640 cm^3, and 5,640 cm^3 / 16 cm^2 is 352 cm, or 3.52 m, or about 11.5 feet if my math is correct.
After trying other things, I removed the P-trap and fed an auger over 20 feet into the drain. No particular debris or residue came out, though there was some black grease on parts of the auger, and the water still backs up at the same rate. With the P-trap off, I am able to hear wind through the drain, so I know for sure that the drain vent is not blocked. If my estimate of the blockage being less than 11.5 feet away is correct, and I fed 20 feet of the auger into the drain, then perhaps my auger went up the vent pipe as in this comment?
Any other suggestions as to what I might try, if I can't locate or identify the obstruction? Is there any benefit to trying any of the liquid drain products? (I believe that I'm not supposed to put them directly into my sink, because of the in-sink disposal, but with the P-trap open I could pour them directly into the drain pipe.) I tend to use enzyme-based build-up remover from time to time, but it's been a while since I've done so, and this began unexpectedly.