Geomechanics Research at Northwestern University
Compaction Bands in Sandstone
Evidence from recent laboratory experiments and field observations on porous rocks (and other materials) has indicated that compaction does not necessarily occur homogeneously, but, instead, is localized in narrow planar zones. These zones are typically nearly perpendicular to the maximum compressive stress. Because the permeability of these zones is reduced by several orders of magnitude, they present barriers to fluid flow across them. Hence their formation in reservoirs or aquifers can adversely affect attempts to inject or withdraw fluids, and are relevant to diverse applications such as sequestration of carbon dioxide, energy recovery and storage, aquifer management and waste isolation Because the zones are narrow, they will be difficult to detect from the surface and, as a result, it is important to understand the conditions for their formation and extension.
We have combined analytical, computational and observational approaches to better understand the structure and formation of compaction bands. An analytical approach, similar to that used for shear bands, has identified the range of material parameters for band formation that is consistent with experimental observations. A simple model for band extension as an “anti-crack” yields a length vs. thickness relation that agrees with field observations. This model also yields an energy required for advance of the band a unit area that is consistent with laboratory observations.
Although the results for band formation are qualitatively consistent with observations, quantitative comparison depends on details of material parameters that are difficult to determine from experiments. Consequently, we are combining very detailed measurements with computational multi-scale methods to relate macroscopic material and transport properties to pore structure. Of particular interest are changes in key macroscopic properties such as permeability and strength due to changes in microstructure.
Pore-scale tomography images with micron resolution have been obtained using synchrotron rays to quantify topological features of the material that can then be linked to macroscopic properties. The micron-resolution images are used to construct faithful representations of the 3D porous network on samples of Aztec sandstone from the Valley of Fire, NV, where natural compaction bands are found. Preliminary calculations using the lattice Boltzmann method show a contrast in permeability of several orders of magnitude between the inside and outside of compaction bands. These changes are not captured by classical methods, such as Kozeny-Carman. These findings will allow us, for the first time, to directly link the changes imposed on continuum properties due to 3D micromechanical changes.
The presence or formation of compaction bands in porous formations intended for sequestration of CO2 could be a serious impediment to economic and efficient use of this technology to mitigate adverse effects on the climate.
1. B. C. Haimson and J. W. Rudnicki, The effect of the intermediate principal stress on fault formation and fault angle in siltstone, Journal of Structural Geology, Special Issue on Fault Zones, in press, 2009.
2. J. E. Andrade and X. Tu. Multiscale framework for behavior prediction in granular media. Mechanics of Materials. 41:652-669, 2009.
3. J. E. Andrade and R. I. Borja. Modeling deformation banding in dense and loose fluid-saturated sands. Finite Elements in Analysis and Design. 43:361-383, 2007.
4. N. Lenoir, J. E. Andrade, W. C. Sun and J. W. Rudnicki. In situ permeability measurements inside compaction bands using X-ray CT and lattice Boltzmann calculations, In 3rd International Workshop on X-Ray CT for Geomaterials, March 1-3, 2010, New Orleans. To appear.
5. J. W. Rudnicki, “Models for compaction band propagation,” Chapter 8 in Rock Physics and Geomechanics in the Study of Reservoirs and Repositories (eds. C. David and M. Le Ravelec-Dupin), Geological Society, London, Special Publications, 284, pp. 107-125, doi: 10.1144/SP284.8, 2007.