refined GAC was developed for air purification. but i can remember 50yrs ago when it was called by it's low quality name of carbon. this was basically what can be easily made. very limited in it's abiltity to adsorb.
GAC if used in water with a lot of organics or turbity will load up very quickly. in short order it becomes nothing more than a nitrifiying bed. it is excellent because of it's porosity to colonize bacteria.

if you have seen electron microscopic photos of an RO membrane after having been in service you will have seen colonies of bacteria.

water purification is a very complex process if one is trying to produce a truely pure product. RO, DI (cation, anion resins) nanofiltration, UV (which is worthless in water with heavy organics or turbity), ozone, GAC, specific minerals, coagulators, percipitators and on and on.

basic filtration for minimal potable filtration is slow sand. then if you should have carbon available as a last step run it through. look inside of a wine or whiskey cask this is why they are charred.

you can construct a large slow sand filter if you have the resources and equipment.