Estimating 3D elastic moduli of rock from 2D thin-section images using differential effective medium theory

Standard digital rock physics (DRP) has been extensively used to compute rock physical parameters such as permeability and elastic moduli. Digital images are captured using 3D microcomputed tomography scanners that are not widely available and often come with an excessive cost and expensive computation. Alternative DRP methods, however, benefit from the highly available low-cost 2D thin-section images and require a small amount of computer memory use and CPU. We have developed another alternative DRP method to compute 3D elastic parameters based on differential effective medium (DEM) theory. Our investigations indicate that the pore aspect ratio (PAR) is the most crucial factor controlling the elasticmoduli of rock. Based on digital rock modeling in a dry calcite sample with 20% porosity, the bulk modulus is reduced by 51%, 80.7%, and 96.8% for aspect ratios of 1, 0.2, and 0.05, respectively. Similarly, the shear modulus is reduced by 52%, 73.8%, and 92.8% for the same PARs. These findings confirm the importance of the PAR in wave propagation through porous media. Such an evaluation, however, can be very expensive for 3D images because one requires using several of them for drawing a reliable conclusion. Therefore, we aim to capture the PAR distribution from 2D images. This distribution is, then, used to estimate 3D elastic moduli of sample by DEM-equations. Three orthogonal 2D images were used and results indicated that 2D PARs in orthogonal orientations could address pore shapes more effectively. Moreover, a stochastic porous media reconstruction method was also used to generate more scenarios of rock structure and those of which that are not seen in 2D images. Results from Berea sandstone and Grosmont carbonate indicated that using only 2D images our proposed method could effectively estimate 3D elastic moduli of rock samples.