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Advances_247_253_Baue+ - Eawag-Empa Library

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Measuring Local<br />

under Stress<br />

Tomography<br />

Strains<br />

with<br />

Andreas Bauer*, Eelco Verhulp**, Stan Schoofs*<br />

in Sandstones<br />

Micro-computed<br />

*Shell International Exploration & Production, Kesslerpark 1, 2288 GS Rijswijk,<br />

The Netherlands<br />

a.bauer@shell.com<br />

stan.schoofs@shell.com<br />

**Department of Biomedical Engineering, Eindhoven University of Technology,<br />

Den Dolech 2,5600 ME Eindhoven, The Netherlands<br />

e. verhulp@tue.nl<br />

ABSTRACT: We report on micro-computed tomography (peT) measurements of Bentheim<br />

sandstone under stress using a specially designed triaxial pressure cell. First results<br />

demonstrate the feasibility of measuring local deformations and strains in sandstones with<br />

mstrain sensitivity. Data analysis includes segmentation of three-dimensional peT images,<br />

grain partitioning, and application of a cross-correlation technique for determining<br />

displacements and rotations of single grains.<br />

KEYWORDS: Micro-computed tomography, sandstones, stress-strain relationship.


Micro structure 249<br />

Figure 1 a shows a drawing of the pressure cell. The sample has a diameter of 5<br />

mm and a length of 14 mm and is clamped between two pistons, by which axial<br />

stress is applied to the sample. The upper piston is moveable and driven<br />

hydraulically. The lower piston is fixed. The sample is surrounded by a relatively<br />

thick poly-ether-ether-ketone (PEEK) mantle (wall thickness 7 rom, outer diameter<br />

21 mm) that can sustain stresses up to 400 bar both along the symmetry axis and<br />

radially. PEEK is a machinable and rather strong material, and, more importantly for<br />

f.LCT applications, it shows only little x-ray absorption as compared to the rock<br />

sample (for typical x-ray energies of 70 keY, the x-ray absorption of the PEEK<br />

mantle is less than 5%). The small annulus between sample and mantle can be filled<br />

by hydraulic oil for radial confinement. Here, a thin rubber sleeve forms a seal<br />

between sample and confinement oil. Small holes in the upper and lower piston<br />

allow for adjustment of pore-fluid pressures and fluid flow (drainage, etc.). The tube<br />

that connects the pore-fluid line in the upper piston slides within the piston, with an<br />

O-ring between tube and piston acting as a seal.<br />

00=20 bar<br />

Figure 1. (A) Schematic drawing of the cylindrical triaxial pressure cell for micro-CTand<br />

(B) resulting J1CT images of a Bentheim sandstone sample at different uniaxial stresses.<br />

The rubber sleeve around the sample is also visible in the images. Before failure at 200<br />

bar, grains and pores can easily be tracked (see circles) although there might be overall<br />

displacements from one image to the other<br />

B


Micro structure <strong>253</strong><br />

Knackstedt M.A., AIDs C.H., Ghous A., Sakellariou A., Senden T.J., Sheppard A.P., Sok<br />

R.M., Nguyen V., and Pinczewski W.V., "3D imaging and characterization of the pore<br />

space of carbonate core; implications to single and two phase flow properties", to be<br />

published, 2006.<br />

Klein E. and Reuschle T., "A model for the mechanical behaviour of Bentheim sandstone in<br />

the brittle regime", Pure and Applied Geophysics 160, p. 833-849, 2003.<br />

Saadatfar M., Turner M.L., Ams C.H., Averdunk H., Senden T.J., Sheppard A.P., Sok R.M.,<br />

Pinczewski W.V., Kelly 1. and Knackstedt M.A., "Rock fabric and texture from digital<br />

core analysis", SPWLA 46th Annual Logging Symposium, p. 1-16, June 26-29 2005.<br />

Saito T. and Toriwaki 1.1., "New algorithms for Euclidean distance transformation of an ndimensional<br />

digitized picture with applications", Pattern Recognition 27, p. 1551-1565,<br />

1994.<br />

Shapiro S.A. and Kaselow A., "Porosity and elastic anisotropy of rocks under tectonic stress<br />

and pore-pressure changes", Geophysics 70, p. N27-N38, 2005.<br />

Takemura T., Oda M., and Takahashi M., "Microstructure observation in deformed<br />

geomaterials using microfocus x-ray computed tomography", in: X-ray CT for<br />

Geomaterials: Soils, Concrete, Rocks, Otani & Obara (Eds.) (Taylor & Francis, Oxford),<br />

p. 299-304, 2004.<br />

Verhulp E., van Rietbergen B. and Huiskes R., "A three-dimensional digital image correlation<br />

technique for strain measurements in microstructures", Journal of Biomechanics 37, p.<br />

1313-1320, 2004.<br />

Viggiani G., Lenoir N., Besuelle P., Di Michiel M., Marello S., Desrues J., Kretzschmer M.,<br />

"X-ray microtomography for studying localized deformation in fine-grained geomaterials<br />

under triaxial compression", C.R. Mechanique 332, p. 819-826,2004.

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