(Being asked as a theoretical question. Obviously everyone should ask their LOR.)
There is a water filter (or purifier) that works in the following way: The water flows into a part where there is some sort of "chemical" (in the shape of round white balls) that help to "clean the water". The water then pours from there out going through a normal sort of filtering part. If we look at the water is the "ochel" (food) and the white balls as the "pasules" (not good part) is there a problem of borer in the fact that the water (the "ochel" in this case) passes through this filter, "separating" it from the white balls (the "pasoles" in this case.) Perhaps this is "borer b'cli" (separating with a vessel) and would be prohibited on Shabbos.
I'm pointing this out because it's not a "normal case" of using a filter where the water simply passes through a sort of sifting part (which could be muter on Shabbos if a person would drink this water without having used the filter.) The water is getting mixed together with some sort of chemical then "separated" from that so in regards to the chemical we have a "mixture" of "ochel and pasoles".)