Computing heterogeneous core sample velocity using Digital Rock Physics: A multiscale approach

Digital Rock Physics (DRP) is an effective approach to compute physical properties of rock using high-resolution 3D images. Although micro-scale structures are well studied in DRP, micro computed tomography (mu CT) scanners are still not widely available and imaging could be both expensive and time consuming. Moreover, there is always a trade-off between image resolution and sample size. The later issue is crucial especially in heterogeneous samples such as carbonates. in this study, we propose a multiscale procedure and computed wave velocity of three heterogeneous travertine (calcite) samples with the exact core size of 55 mm diameter. This procedure is conducted using relatively cheap and widely available imaging tools, namely medical CT scanner and conventional microscope. In a low-resolution step, 3D CT-images with 200 mu m resolution are obtained and used to compute porosity cubes by a three-phase segmentation (mineral, pore and sub-resolution). In a high-resolution step, elastic moduli are computed using 2D microscopic images with 1 mu m resolution and converted into 3D properties using a 2D-to-3D DRP method. The obtained micro-trends of effective elastic moduli are analytically approximated using the modified Differential Effective Medium (DEM) model. Low-resolution porosity cubes and high-resolution micro-trends are combined to obtain 3D cubes of elastic moduli and density. Finally, a dynamic Finite Difference Method (FDM) is used to propagate P- and S-waves through these samples for velocity computations. Comparison of lab and computed results showed that the errors of P- and S-wave velocities vary from 3.4% to 7% and from 6.7% to 11.1%, respectively.