The Washburn equation is widely accepted for describing capillary imbibition. It has, however, been shown to be insufficient at very short times due partly to the lack of inertial terms. Bosanquet (C. H. Bosanquet, Philos. Mag. ser. 645, 525 (1923)) applied an inertial term via momentum, Szekely et al. (J. Szekely, A. W. Neumann, and Y. K. Chang, J. Colloid Interface Sci.35, 273 (1971)) examined single capillaries based on a revised boundary-condition model, and Sorbie et al. (K. S. Sorbie, Y. Z. Wu, and S. R. McDougall, J. Colloid Interface Sci. 289 (1995)) reviewed and applied Szekely's work to examine the effects of comparative imbibition into a parallel pore doublet. The study here extends the work of Sorbie et al. by applying the equation of Bosanquet to a three-dimensional network model, Pore-Cor. All authors agree that, with the inclusion of inertial terms at short times, smaller radius capillaries will initially fill faster than larger radius capillaries which disagrees with the Washburn equation. It is shown that the aspect ratio of a capillary, defined as its length divided by its radius, plays an important role, in combination with the capillary radii themselves, in determining the filling rate of individual elements. The distribution of this ratio associated with the capillary throat elements within a network structure is investigated. The result is that a preferred pathway of permeation is observed under supersource imbibition conditions in the case where a broad size distribution of capillary elements occurs within a network structure.