The application of nanofluids in direct solar absorption, heat transfer or direct solar steam generation entails carrying out a comprehensive study taking into account several physical quantities. Long-term stability, rheological, thermophysical and optical properties of dispersions must be known to assess their potential for envisaged applications. Two low-concentration nanofluids, 0.005 and 0.05 wt%, of sulfonic acid-functionalized and polycarboxylate chemically modified graphene nanoplatelets in water were considered in this work. Elemental analyses of the nanopowders and pH evaluations of the colloids were carried out. The rheological behaviour of dispersions at different temperatures was studied by rotational rheometry. Thermal conductivities were measured by the transient hot wire method and densities by the oscillating U-tube technique. Additionally, a brief report of the optical properties was included to provide a comprehensive physical analysis.