Application of full set of two point correlation functions from a pair of 2D cut sections for 3D porous media reconstruction

Abstract

Three dimensional reconstruction of porous media using limited statistical information has attracted a great interest in Earth sciences and petroleum engineering. In this study, a fast and reliable method for 3D reconstruction is proposed based on approximation of correlation functions and phase recovery algorithm using one and two perpendicular cut sections. In the proposed method, initially, full set of two point correlation functions (TPCFs) are extracted from the cut sections. Afterwards, the TPCF vectors are decomposed and then averaged to improve the accuracy of the 3D-TPCFs approximation and improve the capabilities of the reconstruction procedure. To demonstrate the ability of the proposed method to deal with both connectivity and anisotropic issues existed in 3D reconstruction literature, Berea sandstone and a synthetic representative volume element (RVE) are used. Eventually, the reconstruction results of Berea sandstone and the synthetic RVEs are examined based on tortuosity values, autocorrelation function and also porosity distribution in comparison with their corresponding original RVEs. Evaluation of tortuosity values in the original and reconstructed RVEs for both Berea sandstone and the synthetic RVE reveals that for every axis of interest, there is a satisfactory agreement between the original and reconstructed RVEs realized using those two cut sections that contain the direction of interest as their common axis. This point indicates that the proposed approach which used two perpendicular cut sections provides more reliable and robust 3D reconstruction RVEs.