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

Abstract

A truncated gaussian method based on Fourier transforms is proposed to generate periodic 3D porous structure from a 2D image of the sample. This technique 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. Multiphase Flow 16 (4), 691–712]. The difference between the present method and previous work [Adler, P.M., 1992. Porous Media: Geometry and Transports. Butterworth-Heinemann, New York] is that the gaussian field is directly generated from its autocorrelation function and the use of a linear filter transform is avoided. It is not required to solve a set of nonlinear equations associated with this transform. In addition, memory requirements are reduced because non-correlated gaussian field data are not needed. Porous structure is described by the porosity and autocorrelation function, which are measured from a 2D binarized image of a thin section of the sample. When the autocorrelation function is positive–definite, the corresponding gaussian field can be generated using Fourier transforms. Phase angle distribution is assumed to be random and does not affect the autocorrelation function. 3D porous media are generated by truncating the gaussian distribution. Using the fast Fourier transform makes this algorithm more efficient. Both processing time and computer memory requirements are improved. Results for a Berea sandstone sample show that the mean pore size distribution, obtained taking several serial cross-sections of the reconstructed 3D porous structure into account, is in good agreement with the original thresholded 2D image.