We introduce a new approach to simulate a virtual mercury intrusion porosimetry (MIP) using neither skeleton computing nor seed-growing methods. Most of the existing methods to determine local pore sizes in a porous medium require to compute the skeleton of the pore space. However, the skeleton computation is a very time consuming process. Instead, our approach uses a particular spatial enumeration encoding of the porous media, a set of disjoint boxes, and an algorithm able to determine the set of boxes invaded by the mercury at each iteration without any need of a previous skeleton computation. The algorithm detects all the pores which must be lled for a given mercury intrusion pressure, which is related to a diameter by the Washburn equation. The presented method is able to detect narrow throats and one-dimensional transitions between pores in order to prevent incorrect full uid invasion of the whole sample. The particular encoding used in this work is a new compact version of an existing model, the Ordered Union of Disjoint Boxes (OUDB). Finally, the pore size distribution of the porous medium and the corresponding pore graph can be obtained from the analyzed sample.