High-resolution Xray-CT images are increasingly used to numerically derive petrophysical properties of interest at the pore scale, in particular effective permeability. Current micro Xray-CT facilities typically offer a resolution of a few microns per voxel resulting in a field of view of about 5 mm3 for a 20482 CCD. At this scale the resolution is normally sufficient to resolve pore space connectivity and transport properties. For samples exhibiting heterogeneity above the field of view of such a single high resolution tomogram with resolved pore space, a second low resolution tomogram can provide a larger scale porosity map. The problem then reduces to rock-typing the low resolution Xray-CT image, deriving viable porosity-permeability transforms from the high resolution Xray-CT image(s) for all rock types present, and upscaling of the permeability field to derive a plug-scale permeability.
In this study we characterize spatially heterogeneity using overlapping registered Xray-CT images derived at different resolutions spanning orders of magnitude in length scales. A 38mm diameter carbonate core is studied in detail and imaged at low resolution - and at high resolution by taking four 5mm diameter subsets, one of which is imaged using full length helical scanning. Fine-scale permeability transforms are derived using direct porosity-permeability relationships, random sampling of the porosity-permeability scatter-plot as function of porosity, and structural correlations combined with stochastic simulation. A range of these methods are applied at the coarse scale. We compare various upscaling methods including renormalization theory with direct solutions using a Laplace solver and report error bounds.
We find that for the heterogeneous samples permeability typically increases with scale. Conventional methods using basic averaging techniques fail to provide truthful vertical permeability due to large permeability contrasts. The most accurate upscaling technique is employing Darcy’s law. A key part of the study is the establishment of porosity transforms between high-resolution and low-resolution images to arrive at a calibrated porosity map to constraint permeability estimates for the whole core.