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The Effect of Effective Pressure on the Relationship Between Static and Dynamic Young’s Moduli and Poisson’s Ratio of Naparima Hill Formation Mudstones

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Abstract

Static elastic properties, derived from stress–strain data, and dynamic elastic properties, derived from P- and S-wave velocities, are significantly different for rocks. Most rocks are deformed nearly statically (due to tectonic forces and reservoir compaction during production of the reservoir) but static measurements are not as readily available as dynamic measurements. Hence, empirical relationships between the static and dynamic elastic properties are needed to convert the dynamic elastic properties to static values. In this study, the static and dynamic Young’s moduli and Poisson’s ratio were measured simultaneously for dry and fluid-saturated mudstone samples. The samples were axially loaded only within the elastic region to determine the static elasticity. The samples were from four different lithofacies within the Naparima Hill Formation, Trinidad, West Indies. Experiments were carried out at effective pressures up to 130 MPa to determine if the relationship, if any, is influenced by effective pressure. The results show that the dynamic Young’s modulus is greater than the static Young’s moduli. Saturation of the samples causes a decrease in the Young’s modulus and an increase in Poisson’s ratio. Saturation also increases the difference between the static and dynamic Young’s moduli and Poisson’s ratio. A linear relationship with high correlation (R2 greater than 0.9) was established between the static and dynamic Young’s moduli. The gradient of the linear relationship increases, while the intercept decreases, with increasing effective pressure and axial loading. No clear trend was observed between the static and dynamic Poisson’s ratio.

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Abbreviations

V p :

P-wave velocity

V s :

S-wave velocity

L :

Length of the sample

T :

Travel time of the waves

E dynamic :

Dynamic Young’s modulus

v dynamic :

Dynamic Poisson’s ratio

ρ :

Density of the sample

\(\varepsilon_{v}\) :

Volumetric strain

\(\varepsilon_{\text{axial}}\) :

Axial strain

\(\varepsilon_{\text{radial}}\) :

Radial strain

σx, σy, σz :

Normal stresses in the x, y, z direction

\(\in_{x} , \in_{y} , \in_{z}\) :

Normal strains in the x, y, z direction

τyz, τzx, τxy :

Shear stresses in the yz, xz, xy coordinate planes

γyz, γzx, γxy :

Shear strains in the yz, xz, xy coordinate planes

C11, C12, C13 ….. C66 :

Material parameters

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Acknowledgements

We would like to thank the Ministry of Energy and Energy Industries, Trinidad and Tobago, Engineering Institute, Faculty of Engineering, and Campus Research and Publication Fund Committee, University of the West Indies, St. Augustine Campus, for funding this research.

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Authors and Affiliations

  1. Petroleum Geoscience, Department of Chemical Engineering, University of the West Indies, St. Augustine, Trinidad and Tobago

    O. O. Blake, R. Ramsook & U. C. Iyare

  2. Department of Earth, Ocean and Ecological Sciences, University of Liverpool, Liverpool, UK

    D. R. Faulkner

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  1. O. O. Blake
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  2. R. Ramsook
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  3. D. R. Faulkner
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  4. U. C. Iyare
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Correspondence to O. O. Blake.

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Blake, O.O., Ramsook, R., Faulkner, D.R. et al. The Effect of Effective Pressure on the Relationship Between Static and Dynamic Young’s Moduli and Poisson’s Ratio of Naparima Hill Formation Mudstones. Rock Mech Rock Eng 53, 3761–3778 (2020). https://doi.org/10.1007/s00603-020-02140-0

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