Fundamental understanding of the water in graphene is crucial to optimally design and operate the sustainable energy, water desalination, and bio-medical systems. A numerous atomic-scale studies have been reported, primarily articulating the surface interactions (interatomic potentials) between the water and graphene. However, a systematic comparative study among the various interatomic potentials is rare, especially for the water transport confmed in the graphene nanostructure. In this study, the effects of different interatomic potentials and gap sizes on water self-diffusivity are investigated using the molecular dynamics simulation at T = 300 K. The water is confmed in the rigid graphene nanogap with the various gap sizes L-z = 0.7 to 4.17 nm, using SPC/E and TIP3P water models. The water self-diffusivity is calculated using the mean squared displacement approach. It is found that the water self diffusivity in the confined region is lower than that of the bulk water, and it decreases as the gap size 'decreases and the surface energy increases. Also, the water self-diffusivity nearly linearly decreases with the increasing surface energy to reach the bulk water self-diffusivity at zero surface energy. The obtained results provide a roadmap to fundamentally understand the water transport properties in the graphene geometries and surface interactions.