My portable air conditioner's compressor can get quite noisy, it's like a vibrating pulsing grinding noise. Is it possible to reduce this noise?
Check to make sure one of the (presumably plastic) panels that make up the exterior of the unit are not loose. My unit had a "fancy" black plastic border that fastened around the front panel, and it would over time begin to work loose as the compressor vibrated. I ended up wedging a little folded piece of paper between the front panel and the bordering plastic to get it to shut up.
Other than that, put something vibration-absorbing under it if possible, as Ed Beal suggests. There's not a lot to be done. These units are noisy because the usual outdoor bits are now in a box next to you. But if you need cool air, you need cool air!
There should not be any "grinding" but scroll compressors used in AC systems do have a large amount of vibtation they are normally mounted on 3 or 4 rubber vibration isolators for this reason. If you want to dampen a small window unit for example I have used 1/4" rubber sheet under the system to further isolate the noise, I would be cautious about the type of insulation as last year a friend had tried to put fiberglass around his new unit and although it worked he used two muck and the unit fell out and dammaged both the outlet it was plugged into and the condensing coil on the unit that was not repairable.