I have no clue what kind of graphene they are testing/using (synthetic/natural) - but promising research at least.

http://mashable.com/2017/04/11/graphene-oxide-desalination-membrane/

via 

http://www.graphene.manchester.ac.uk/discover/latest-findings/

http://science.sciencemag.org/content/343/6172/752.full

Precise and Ultrafast Molecular Sieving Through Graphene Oxide Membranes

Abstract

Graphene-based materials can have well-defined nanometer pores and can exhibit low frictional water flow inside them, making their properties of interest for filtration and separation. We investigate permeation through micrometer-thick laminates prepared by means of vacuum filtration of graphene oxide suspensions. The laminates are vacuum-tight in the dry state but, if immersed in water, act as molecular sieves, blocking all solutes with hydrated radii larger than 4.5 angstroms. Smaller ions permeate through the membranes at rates thousands of times faster than what is expected for simple diffusion. We believe that this behavior is caused by a network of nanocapillaries that open up in the hydrated state and accept only species that fit in. The anomalously fast permeation is attributed to a capillary-like high pressure acting on ions inside graphene capillaries.

On the Fast Track

Membranes based on graphene can simultaneously block the passage of very small molecules while allowing the rapid permeation of water. Joshi et al. (p. 752; see the Perspective by Mi) investigated the permeation of ions and neutral molecules through a graphene oxide (GO) membrane in an aqueous solution. Small ions, with hydrated radii smaller than 0.45 nanometers, permeated through the GO membrane several orders of magnitude faster than predicted, based on diffusion theory. Molecular dynamics simulations revealed that the GO membrane can attract a high concentration of small ions into the membrane, which may explain the fast ion transport.