Chemical equilibration with a bulk reservoir is the crucial problem in computer simulations of liquids in confined geometries. The Gibbs ensemble simulation method is used in the present paper to solve this problem for water in pores. MC simulations of TIP4P water in spherical cavities with smooth surfaces and radii from 6 to 15 Angstrom were done in equilibrium with bulk water at T=300 and 350 K. Chemical equilibration between confined and bulk water was obtained by an essential number of molecular transfers. To our knowledge this is the first application of the Gibbs ensemble simulation method for the equilibration of two dense liquid water systems. As most important result we find that liquid water exists in a cavity only if the water-substrate interaction exceeds some critical value. An increase of the average water density by about 20% with the strengthening of the interaction is observed. For all systems there are two prominent water layers near the cavity surface which exhibit strong orientational ordering. The pair correlation functions evidence a strong distortion of the tetrahedral water structure in the first, outer layer towards a square lattice arrangement. The diffusivity of the water in the cavity always decreases with respect to the bulk.