Pure and Applied Geophysics

, Volume 176, Issue 4, pp 1467–1485 | Cite as

Effective Stress Coefficient for Seismic Velocities in Carbonate Rocks: Effects of Pore Characteristics and Fluid Types

  • Gautier NjiekakEmail author
  • Douglas R. Schmitt


The concept of effective stress is key for understanding the dependence of rock elastic and compaction behaviors on stress and pore-fluid pressure. Previous studies on the concept largely used data acquired on siliciclastic rocks. Carbonate rocks, however, display elastic and compaction behaviors that can be very different than those of siliciclastic rocks. For example, applying most velocity-to-pore-pressure transforms in the context of carbonate reservoirs can be quite challenging. Our study used an experimental approach (a disequilibrium compaction scenario) to assess effective stress coefficient (n) for velocities in three carbonate samples displaying comparable porosities but different dominant pore types (in terms of shape and compliance). Different saturating fluids (nitrogen and distilled water) were used, one at a time, which allowed us to compare both pore and fluid type effects on the coefficient n between these rocks. We found that n is generally bounded by unity. The exception is with nVs (n derived from shear wave velocities) obtained under nitrogen-saturated conditions; nVs is higher than 1 on the three studied samples. Under nitrogen-saturated conditions, the less compliant the main pore types in a given rock are, the higher the value of nVs is. Higher-than-unity values of nVs indicate a deviation from the behavior predicted by existing theories. This could stem from (i) the fact that theoretical analyses assume a pore fluid whose properties are not comparable to those of nitrogen and/or (ii) the way the bulk volumetric strain (a main factor in elastic wave propagation) is incorporated into those theories.


Effective stress coefficient ultrasonic measurement elastic wave velocity carbonate rock porosity pore space stiffness 



We acknowledge (1) Carbon Management Canada that provided a research grant to Dr. Gautier Njiekak and (2) NSERC and the Canada Research Chair program that supported the development of the measurement system. The samples were provided by the Saskatchewan Core Repository. We thank Randolf S. Kofman for his help in the laboratory and Dr. Tobias Mueller for helpful conversations and comments. We also thank the editor and the anonymous reviewer whose comments helped improve the manuscript.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Physics, Institute for Geophysical Research, CCIS 4-183University of AlbertaEdmontonCanada
  2. 2.Department of Earth, Atmospheric, and Planetary SciencesPurdue UniversityWest LafayetteUSA

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