The properties of water in pores depend strongly on its average density, which is determined by the equilibrium with a bulk reservoir. In the present paper, Gibbs ensemble simulations were used for the equilibration of water in spherical pores with smooth surfaces and radii from 9 to 20 Angstrom and bulk liquid water at T = 300 K and P = 1 bar. The water density profile along the pore radius shows in all cases two prominent water layers near the pore surface. The oxygen-oxygen radial distribution functions evidence a clear distortion of the tetrahedral water structure in the first (outermost) layer towards a quasi-planar square- or hexagonal-like arrangement. An analysis of the non-short-circuited hydrogen-bond polygons evidences the existence of quasi-planar polygons in the first layer. Increasing the pore radius improves the water-water interaction between the two outer water layers, destroys the quasi-planar polygons and speeds up water diffusivity in the pore. The radial distribution functions of the hexagons evidence some distortion of the inner water in the pore towards the structure of cubic ice.