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Christoph H. Arns, Mark A. Knackstedt,
W. Val Pinczewski,
and Edward J. Garboczi
2 January 2004
(1) School of Petroleum Engineering, University of New South Wales,
Sydney, NSW 2052, Australia
(2) Department of Applied Mathematics, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia
(3) Building Materials Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.
Elastic property-porosity relationships are derived directly from microtomographic images. This is illustrated for a suite of 4 samples of Fontainebleau sandstone with porosities ranging from 7.5% to 22%. A finite element method is used to derive the elastic properties of digitized images. By estimating and minimizing several sources of numerical error, very accurate predictions of properties are derived in excellent agreement with experimental measurements over a wide range of the porosity. We consider the elastic properties of the digitized images under dry, water- and oil-saturated conditions. The observed change in the elastic properties due to fluid substitution is in excellent agreement with the exact Gassmann's equations. This shows both the accuracy and the feasibility of combining microtomographic images with elastic calculations to accurately predict petrophysical properties of individual rock morphologies. We compare the numerical predictions to various empirical, effective medium and rigorous approximations used to relate the elastic properties of rocks to porosity under different saturation conditions.