> one might think of pumping it “up”, but really the only hard work is producing the pressure difference P_feed - P_permeate or so — water is buoyant to an extent that almost exactly negates its weight
If you package the permeate in a balloon (hopefully a very strong one!) and let the balloon rise to the surface, buoyancy is very relevant.
If you instead pipe it -- to simplify the analysis, let's say it's going straight up a vertical chimney to the surface -- it doesn't seem like buoyancy is relevant.
Take a vertical water-filled pipe sealed at the bottom and open to the air on top. The water N meters from the top of the pipe will be the same pressure as N meters inside the ocean -- even if the pipe's nowhere near an external body of water! A water column self-pressurizes due to the potential gradient of Earth's gravity.
Now put the bottom of the pipe at the bottom of the ocean, you can unseal it and stick a pump on it.
You put 1 kg of water into the pipe N meters below the surface. You take 1 kg of water out at the surface. And repeat in a cycle. Some part of the system has to be doing enough work to lift 1 kg of water N meters per cycle. That work has to come from the pump -- where else could it come from?
I'm skeptical of any notion that water "floats" to the surface of the pipe "for free"!
If you have two pipes of the same height, one filled with fresh water and one with salt water, the pressure will be greater at the bottom of the salt-water pipe because salt-water is denser. Connect them at the bottom with a pipe and water will flow from salt to fresh until the pressures equalize. But connect them with a membrane, and this is countered by the osmotic pressure of fresh water trying to get to salt water, so you don't get any magic flow for free. You have however got a pressure gradient for free - just not enough to desalinate.
If you put this in the ocean, you can remove the salt pipe and get the same effect. But if you want continuous fresh water, you need to further increase the pressure difference across the membrane by continuously lowering the height of the fresh-water column by pumping water up and out of the top. That takes energy, but not as much as it would take if we had to raise the pressure on the salt-water side.
If you package the permeate in a balloon (hopefully a very strong one!) and let the balloon rise to the surface, buoyancy is very relevant.
If you instead pipe it -- to simplify the analysis, let's say it's going straight up a vertical chimney to the surface -- it doesn't seem like buoyancy is relevant.
Take a vertical water-filled pipe sealed at the bottom and open to the air on top. The water N meters from the top of the pipe will be the same pressure as N meters inside the ocean -- even if the pipe's nowhere near an external body of water! A water column self-pressurizes due to the potential gradient of Earth's gravity.
Now put the bottom of the pipe at the bottom of the ocean, you can unseal it and stick a pump on it.
You put 1 kg of water into the pipe N meters below the surface. You take 1 kg of water out at the surface. And repeat in a cycle. Some part of the system has to be doing enough work to lift 1 kg of water N meters per cycle. That work has to come from the pump -- where else could it come from?
I'm skeptical of any notion that water "floats" to the surface of the pipe "for free"!