This paper presents a critical review and the state of the art of graphene porous membranes, a brand-new technology and backdrop to discuss its potential application for efficient water desalination in low salinity water injection (LSWI). LSWI technology consists in injecting designed, adequately modified, filtered water to maximize oil production. To this end, desalination technologies already available can be further optimized, for example, via graphene membranes, to achieve greater efficiency in water-oil displacement. Theoretical and experimental applications of graphene porous membranes in water desalination have shown promising results over the last 5-6 years. Needless to say, improvements are still needed before graphene porous membranes become readily available. However, the present work simply sets out to demonstrate, at least in principle, the practical potential graphene membranes would have in hydrocarbon recovery processes.