2D to 3D Geometrical Transform: Estimation of Material Properties from 2D Images

Recent advances in 3D imaging allow us to get high resolution geometry of different porous media. However, 3D imaging is expensive and time consuming compared with 2D imaging. 2D imaging gives us high resolution and quality, quickly and with little economical investment.

In this work we propose a geometrical transformation of thin slices to a 3D volume. This transformation is unique, isotropic, analytical, and given that we obtain a 3D volume with the same geometrical characteristics as the 2D image, it enables us to compute physical properties such as permeability, bulk modulus, and conductivity.

We rely completely in the geometrical information available in 2D images, and use this information to construct a 3D volume that preserves the geometrical measurements in 2D. The result is a 3D volume that has the same porosity as the 2D image, as well as a pore-space, well connected and geometrically isomorphic to the pore space of the original sample.

We test the success of this 2D to 3D transform in its ability to predict the physical properties of the sample, in our case the bulk and shear modulus, conductivity and permeability. Obtaining and excellent match of properties computed in volumes obtained from micro-CT, and those properties obtained just from 2D thin slices. For instance in the figure we can see permeability estimates just from a 2D image, compared with the permeability estimates obtained from the original 3D CT-scan, for REV samples the results from 2D images are comparable to those from 3D images.

In conclusion, we have created a transform that creates a 3D volume from a 2D image, with the same geometrical characteristics, reproducing space connectivity, and providing reliable estimates of properties as permeability using only one thin section.