In the method of volume averaging, the difference between ordered and disordered porous media appears at two distinct points in the analysis, i.e. in the process of spatial smoothing and in the closure problem. In the closure problem, the use of spatially periodic boundary conditions is consistent with ordered porous media and the fields under consideration when the length-scale constraint, r0 much-less-than L is satisfied. For disordered porous media, spatially periodic boundary conditions are an approximation in need of further study. In the process of spatial smoothing, average quantities must be removed from area and volume integrals in order to extract local transport equations from nonlocal equations. This leads to a series of geometrical integrals that need to be evaluated. In Part II we indicated that these integrals were constants for ordered porous media provided that the weighting function used in the averaging process contained the cellular average. We also indicated that these integrals were constrained by certain order of magnitude estimates for disordered porous media. In this paper we verify these characteristics of the geometrical integrals, and we examine their values for pseudo-periodic and uniformly random systems through the use of computer generated porous media.