The pressure at the bottom of the ocean will need to push thru the column of water as well as the membrane - there's not enough energy to do that (otherwise, there'd be spontaneous water sprouts in the ocean!).
You pump out the top x feet of water from the pipe. The equalizing levels of inside and outside the pipe is what drives the upward flow through the membrane.
Perhaps the advantage is that you can lift in multiple stages, so each pump doesn't bear the full column pressure. Also the pumps aren't exposed to salt.
Am I missing something here?
The pressure at the membrane will only ever be the difference. It has nothing to do with the depth the membrane is actually under the water.
Air pressure increases slightly as you descend a well, but not enough to change the outcome.
What you’re saying would imply that the Titan submersible would be at the same pressure whether under an ocean of water, or in a well the same depth. No. The former is 375atm, the latter is a bit more than 1atm.
You only need to lift the top layer of water a little bit. The rest of the water column would come up after it. Of course, you cannot lift the top of the siphon more than 10m above sea level.
While operating, it's basically a deep open well with a bit of water at the bottom. You need to pump that water out to keep the process going.
It is incontrovertible that this system would have to push the water up from below.
I don't think the math works out all that spectacularly though. The pressure difference would be a about 1.1 MPa, and desalination of seawater takes ~6MPa, so by running a pipe down to the bottom of Monterey Canyon you could... save almost 20% of the energy costs.
Which makes sense. You can't build a perpetual motion machine by sticking a pipe with a membrane at the bottom and a turbine at the top into the ocean. Even if it's a very long pipe.
If we can run those for hundreds of miles through water, pumping thick sludge that is crude oil....