Reconstructing random media. II. Three-dimensional media from two-dimensional cuts

We report on an investigation concerning the utilization of morphological information obtained from a two-dimensional (2D) slice (thin section) of a random medium to reconstruct the full three-dimensional (3D) medium. We apply a procedure that we developed in an earlier paper that incorporates any set of statistical correlation functions to reconstruct a Fontainebleau sandstone in three dimensions. Since we have available the experimentally determined 3D representation of the sandstone, we can probe the extent to which intrinsically 3D information (such as connectedness) is captured in the reconstruction. We considered reconstructing the sandstone using the two-point probability function and lineal-path function as obtained from 2D cuts (cross sections) of the sample. The reconstructions are able to reproduce accurately certain 3D properties of the pore space, such as the pore-size distribution, the mean survival time of a Brownian particle, and the fluid permeability. The degree of connectedness of the pore space also compares remarkably well with the actual sandstone. However, not surprisingly, visualization of the 3D pore structures reveals that the reconstructions are not perfect. A more refined reconstruction can be produced by incorporating higher-order information at the expense of greater computational cost. Finally, we remark that our reconstruction study sheds light on the nature of information contained in the employed correlation functions.