A reconstruction technique for three-dimensional porous media using image analysis and Fourier transforms

A truncated gaussian method based on Fourier transforms is proposed to gene rate periodic 3D porous structure from a 2D image of the sample. This techn ique improves a previous method developed by Quiblier [Quiblier, J.A., 1984 . A new three-dimensional modeling technique for studying porous media. J. Colloid Interface Sci 98, 84-102] and Adler et al. [Adler, P.M., Jacquin, C .G., Quiblier, J.A., 1990. Flow in simulated porous media. Int. J. Multipha se Flow 16 (4), 691-712]. The difference between the present method and pre vious work [Adler, P.M., 1992. Porous Media: Geometry and Transports. Butte rworth-Heinemann, New York] is that the gaussian field is directly generate d from its autocorrelation function and the use of a linear filter transfor m is avoided. It is not required to solve a set of nonlinear equations asso ciated with this transform. In addition, memory requirements are reduced be cause non-correlated gaussian field data are not needed. Porous structure i s described by the porosity and autocorrelation function, which are measure d from a 2D binarized image of a thin section of the sample. When the autoc orrelation function is positive-definite, the corresponding gaussian field can be generated using Fourier transforms. Phase angle distribution is assu med to be random and does not affect the autocorrelation function. 3D porou s media are generated by truncating the gaussian distribution. Using the fa st Fourier transform makes this algorithm more efficient. Both processing t ime and computer memory requirements are improved. Results for a Berea sand stone sample show that the mean pore size distribution, obtained taking sev eral serial cross-sections of the reconstructed 3D porous structure into ac count, is in good agreement with the original thresholded 2D image. (C) 199 8 Elsevier Science B.V. All rights reserved.