Classical upscaling methods like spatial averaging or periodic homogenization allow for a description of various transport processes in heterogeneous media from one scale to another. Moreover, the effective parameters appearing in the scaled equations are related to the microgeometry by the associated closure problems, which are generally completed by periodic boundary conditions. This is why these methods are mostly applied to either simple periodic structures (array of spheres for example) or computer-generated media with enforced structural periodicity, for the purpose of obtaining closure relations that can be applied to general media. With the development of imaging techniques like X-rays tomography, it is now possible to access the 3D microstructure of heterogeneous media. In some cases, the traditional periodic closure problem may be used to give an acceptable estimate of the effective properties, but the periodicity conditions may result in dramatic errors in the case of low-porosity materials (like cementious materials for example). We propose here to study another set of boundary conditions, which could allow for a good prediction of the effective diffusivity of a saturated, low-porosity medium. In order to do that, the question of the importance of the periodic boundary conditions appearing in the classical closure problem is investigated. Both analytical and numerical studies on 2D and 3D media show that these periodic conditions could, advantageously, be replaced by homogeneous Dirichlet conditions and that the condition of scale separation seems to be sufficient to achieve a good determination of the effective properties. A simple method is also proposed to dramatically improve the convergence of the non-periodic solution toward reference solution. As an application, the effective diffusivity tensor is computed on 3D image of computer-generated cement paste with very low porosity, showing very good agreement with available experimental data.