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Predicting Permeability in Low-Resolution Micro-CT Images: A Multi-scale Statistical approach
Permeability is a measure of the ability of porous materials to allow the flow of fluids. It has direct impact on topics such as producing oil and gas from subsurface reservoirs, the recharge and discharge of aquifers, contaminant transport, and the geological storage of CO2. In the context of mining it has relevance in acid mine drainage, heap leaching, and in-situ recovery (in-situ leaching) of subsurface ores.

In X-ray microcomputed tomography imaging (micro-CT) sample size and field of view have a direct impact on image resolution. Lower resolution images give larger fields of view, which are therefore more representative of heterogenous systems; however, depending on the sample texture, lower resolution images typically represent connecting pore throats with intermediate gray scale voxels. Unless voxels are rendered as pore space, they are generally not included in the pore network used for permeability simulation; therefore, low-resolution images are often inadequate to accurately compute permeability using simulation methods.

With this project, we investigate statistical methods of estimating permeability in low-resolution images where direct computation is not possible. We use a relatively well-known multi-scale approach (Figure 1) whereby a large core sample (~80mm tall x 25mm diameter) of a relatively clean heterogenous sandstone is imaged twice at low resolution (16 and 64 micron/voxel) to capture sample heterogeneity. A physically cored sub-sample (8mm diameter) is subsequently imaged at high-resolution (5 micron/voxel). 16 micron/voxel resolution is typically achievable on 25mm core plugs, while 64 micron/voxel is achievable at the whole core scale, even though here we imaged a 25 mm core plug.

Figure 1: a) the 25 mm core plug imaged at 16 micron/voxel; b) the 5 micron/voxel image of the 8 mm sub-plug; and the overlap regions from the 16 micron/voxel and 64 micron/voxel images (c and d respectively). The white square indicates the approximate location of the 8 mm sub-plug.

The high-resolution image adequately captures those pore throats controlling fluid flow and is used for direct permeability simulation using an implementation of the Lattice-Boltzmann method. Digital alignment of the high- and low-resolution images allow the computation of rock characteristics such as open pore fraction and formation factor (based on electric conductivity) on the exact same rock volumes from the low resolution images.

Statistical models with simulated permeability from the high-resolution image as response variable and the computed rock characteristics as predictor variables, show that open pore fraction and computed formation factor are good individual predictors of permeability. Open pore fraction is the resolvable pore volume at any given resolution and represents some smaller fraction of the actual porosity of the sample. Critically the correlation between permeability and formation factor relies on the intermediate gray scale voxels in the low-resolution images to be set to permit the flow of electrical current.

The interpretation is that the open pore fraction and formation factor implicitly contain information about the morphology of the critical flow paths. Applying the multiple linear models (containing both open pore fraction and formation factor) to the larger scale low-resolution images shows excellent agreement between predicted permeabilities in the 16 and 64 micron/voxel images (Figure 2). Here we do not have conventional permeability measurements to compare with the predicted values. It is generally very difficult to measure permeability directly on exactly the same volumes used for digital simulation; however, in this instance the agreement between two independently predicted sets of permeability values, using two different sets of input data from the 16 and 64 micron/voxel images, are highly encouraging. The implications of predicting permeability in whole core scale ╬╝CT images are far-reaching. It provides additional information for the interpretation of downhole logging data and serves as an extra step towards populating formation-scale models with fluid flow properties aimed at large-scale dynamic flow simulation.

Figure 2: The predicted permeability of the 25 mm core using predictor characteristics from the 16 and 64 micron/voxel images. Green horizontal stippled lines indicate the boundaries between rock units (identified algorithmically) and the black box indicates the approximate location of the smaller-scale 8mm sub-plug. The scatterplots compare the predicted permeabilities from the 16 and 64 micron/voxel images for the 8 mm sub-plug calibration volume (left) and the 25 mm core plug (right).

Read the full article with the results and discussion of this project:

Botha, P. W. S. K., and A. P. Sheppard (2016). Mapping permeability in low-resolution micro-CT images: A multi-scale statistical approach, Water Resources Research, doi:10.1002/2015WR018454.
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