I have a window well in a basement where I'd like to setup a portable AC unit (~10000 BTUs). There is a cover that I need to keep in place to avoid water collecting in the window well, but I could possibly keep this open a bit. How do I calculate the threshold for the exhaust of this hot air?
You would be far better off building a roof type structure over the window well that is well above the window well and projects far enough out around the edges of the well that rain water does not enter the well.
Trying to jury rig a scheme to keep an existing lid open "just enough" sounds like a recipe waiting for disaster. Either it will be left closed with the AC unit on and it will overheat and kill itself due to inadequate air flow. Or the lid will be left open an flood of water will enter the well and try flooding through the AC unit creating a potential safety hazard.
I think I'd suggest looking for alternatives which don't involve that window well. Perhaps a ducted A/C would let you install the ducts through the wall above the sill (as you would a dryer's output).