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Estimation of Biot’s effective stress coefficient from well logs

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Abstract

Effective stress governs the mechanical response of rock formations to variations in stress and pore pressure, which affect wellbore stability and reservoir integrity during drilling and production. Biot’s coefficient is employed to calculate effective stresses from total stress and pore pressure. Therefore, the measurement of Biot’s coefficient becomes crucial. However, the laboratory measurement of Biot’s coefficient is expensive and laborious. This paper presents three methods for computing Biot’s coefficient using logging data. The first method calculates Biot’s coefficient using the existing empirical correlations between porosity and Biot’s coefficient. The second and third methods calculate Biot’s coefficient using dynamic rock and solid bulk modulus, computed using rock and solid wave velocities, respectively. However, the second and third methods calculate the necessary solid wave velocities in different ways. The second method calculates solid shear and compressive velocities (V s and V p) using a newly developed correlation between the differential pressure, porosity and wave velocity of sandstone. The third method calculates solid wave velocities based on the significant finding that the V p/V s ratio with respect to the S-wave velocity is constant for sediments including highly compacted sand. Case studies were undertaken using logging data from the Gulf Coast Gas Wells. It was found that Biot’s coefficient calculated using the first method was highly dependent on the chosen relation, while the coefficients calculated using the second and third methods were related to well logs. Results from the third method show that Biot’s coefficient deflects to higher values in situations where gamma ray surveys read low API values. This is in agreement with the phenomenon that rocks with a smaller API should have lower a clay content and bigger value of Biot’s coefficient. Therefore, the third method is more reliable and also requires fewer input parameters.

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Abbreviations

σ eff :

Effective stress [MPa]

σ total :

Total stress [MPa]

α :

Biot’s coefficient [–]

p :

Pore pressure [MPa]

ϕ :

Rock porosity [–]

K rock :

Rock bulk modulus [MPa]

K solid :

Solid bulk modulus [MPa]

E :

Young’s modulus [MPa]

υ :

Poisson’s ratio [–]

V s :

Shear wave velocity [m/s]

V p :

Compressive wave velocity [m/s]

P d :

Differential pressure [MPa]

C :

Clay content [–]

V rockp :

Rock compressive wave velocity [m/s]

V solidp :

Solid compressive wave velocity [m/s]

V rocks :

Rock shear wave velocity [m/s]

V solids :

Solid shear wave velocity [m/s]

V constant :

Constant wave velocity under high confining pressure [m/s]

V solid :

Solid wave velocity [m/s]

R p/s :

Radios between V solidp/s and V constantp/s [–]

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Acknowledgments

The work presented in this paper was funded by the National Natural Science Foundation of China (Grant No. NSFC51374147) and the Chinese Ministry of Science and Technology (Grant 2012DFA60760).

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Authors and Affiliations

  1. Sino-German Energy Research Center, Sichuan University, Chengdu, China

    Xuan Luo & Zhengmeng Hou

  2. Energy Research Centre of Niedersachsen, 38640, Goslar, Germany

    Xuan Luo, Patrick Were & Zhengmeng Hou

  3. State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu, 610065, China

    Jianfeng Liu

  4. Institute of Petroleum Engineering, Clausthal University of Technology, 38678, Clausthal-Zellerfeld, Germany

    Zhengmeng Hou

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  1. Xuan Luo
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Correspondence to Xuan Luo.

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Luo, X., Were, P., Liu, J. et al. Estimation of Biot’s effective stress coefficient from well logs. Environ Earth Sci 73, 7019–7028 (2015). https://doi.org/10.1007/s12665-015-4219-8

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