MEDIAL AXIS ANALYSIS OF VOID STRUCTURE IN 3-DIMENSIONAL TOMOGRAPHIC-IMAGES OF POROUS-MEDIA

We introduce the medial axis as a tool in the analysis of geometric st ructure of void space in porous media, The medial axis traces the fund amental geometry of the void pathways. We describe an algorithm for ge nerating the medial axis of the void structure from digitized three di mensional images of porous media obtained from X ray CAT scans. The me dial axis is constructed during an iterative erosion procedure which, at each step, replaces the image of the void structure with a smaller version obtained by eroding its surface layer of voxels. The algorithm is applied to high (5 mu m) resolution microtomographic images of two rock chips (Berea sandstone and Danish chalk) and a sample pf uniform (100 mu m) diameter, packed glass beads. We statistically investigate several geometrical properties of the structure bf the medial axes ob tained. The first is the distribution of relative volumes in each eros ion layer of the void space. We find the distributions to be exponenti al for the two real rock samples and normal for the packed glass beads . The second property investigated is the distribution of volumes of d isconnected segments of the medial axis which are in one-to-one corres pondence with disconnected void segments of the sample. We find indica tions for a; universal power law behavior governing the distribution o f volumes of the smallest disconnected pieces. The final behavior stud ied is a geometric tortuosity as measured by shortest paths through th e medial axis. This tortuosity distribution appears well described by a gamma distribution.