Rock Mechanics and Rock Engineering

, Volume 51, Issue 12, pp 3667–3679 | Cite as

Two-Scale Geomechanics of Carbonates

  • Wenfeng Li
  • A. Sakhaee-PourEmail author
Original Paper


The geomechanical characterization of a carbonate reservoir is required for formation stimulation and hydrocarbon recovery. The pertinent core- or block-scale (large-scale) characterizations are time consuming and expensive, and more importantly, cannot be used for drill cuttings. The present study proposes a two-scale model based on microscale (small-scale) measurements to predict the geomechanical properties of a carbonate formation at the core scale. At the small scale, we develop a physically representative element by accounting for the effective stiffness of a constitutive mineral and of voids. At the large scale, we account for the volume fraction of each mineral, the porosity, and the pore structure of the void space. The elastic deformation of a large-scale model is simulated using a finite element method (FEM), whose results are tested against independent lab measurements. The proposed two-scale model has applications for geomechanical characterization of a formation at the core scale from drill cuttings.


Two-scale model Representative element Pore structure Finite element method (FEM) Drill cutting 

List of Symbols


Cross-sectional area of the grain with a known mineralogy


Cross-sectional area of the core-scale model


Cross-sectional area of the representative element


Elastic modulus of the mineral


Elastic modulus of the core-scale model


Average of the predicted elastic moduli


Maximum of the measured elastic moduli


Minimum of the measured elastic moduli


Elastic modulus of the representative element


Error of the predicted Young’s moduli at the core scale


Volume fraction of each mineral


Shear modulus


Moment of inertia


Polar moment of inertia


Stretching stiffness

\({k_\theta }\)

Bending stiffness

\({k_\phi }\)

Torsional stiffness


Average size of a solid grain with a known mineralogy


Length of the core-scale model


Length of the representative model


Bending load


Axial load


Number of the representative elements relevant to the ith mineral in the core-scale model


Total number of the representative elements in the core-scale model


Compressive load


Torsion of a solid medium


Stretching or compression potential energy


Bending potential energy


Stretching energy of a solid medium


Torsional energy


Total potential energy of the solid medium

\({U_\theta }\)

Angle bending energy of the solid medium

\({U_\phi }\)

Torsional energy of the solid medium


Rotational angle of the solid medium ends


Normal strain of the model

\(\Delta {L_{\text{m}}}\)

Change in the length of the solid medium

\(\Delta r\)

Stretching elastic deformation

\(\Delta \beta\)

Torsion angle of the solid medium

\(\Delta \theta\)

Angle bending elastic deformation

\(\Delta \phi\)

Torsional elastic deformation


Normal stress of the model

\({\phi _1}\)


\({\phi _2}\)


\({\phi _{{\text{total}}}}\)

Total porosity



Finite element method


Micro computed tomography


X-ray diffraction



We are grateful for the constructive comments of the anonymous reviewers and the editor, which helped us improve the paper substantially.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Petroleum EngineeringUniversity of HoustonHoustonUSA

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