Skip to main content
SpringerLink
Log in

Two-Scale Geomechanics of Carbonates

  • Original Paper
  • Published:
Rock Mechanics and Rock Engineering Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Abbreviations

\({A_{\text{m}}}\) :

Cross-sectional area of the grain with a known mineralogy

\({A_{\text{M}}}\) :

Cross-sectional area of the core-scale model

\({A_{\text{r}}}\) :

Cross-sectional area of the representative element

E m :

Elastic modulus of the mineral

\({E_{\text{M}}}\) :

Elastic modulus of the core-scale model

\(E_{{{\text{Model}}}}^{{{\text{Ave}}}}\) :

Average of the predicted elastic moduli

\(E_{{{\text{Lab}}}}^{{{\text{Max}}}}\) :

Maximum of the measured elastic moduli

\(E_{{{\text{Lab}}}}^{{{\text{Min}}}}\) :

Minimum of the measured elastic moduli

\({E_{\text{r}}}\) :

Elastic modulus of the representative element

Error:

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

\({f_i}\) :

Volume fraction of each mineral

\({G_{\text{m}}}\) :

Shear modulus

\({I_{\text{m}}}\) :

Moment of inertia

\({J_{\text{m}}}\) :

Polar moment of inertia

\({k_{\text{r}}}\) :

Stretching stiffness

\({k_\theta }\) :

Bending stiffness

\({k_\phi }\) :

Torsional stiffness

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

Average size of a solid grain with a known mineralogy

\({L_{\text{M}}}\) :

Length of the core-scale model

\({L_{\text{r}}}\) :

Length of the representative model

M :

Bending load

N :

Axial load

\({N_i}\) :

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

\({N_{\text{t}}}\) :

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

P :

Compressive load

T :

Torsion of a solid medium

\({U_{\text{A}}}\) :

Stretching or compression potential energy

\({U_{\text{M}}}\) :

Bending potential energy

\({U_{\text{r}}}\) :

Stretching energy of a solid medium

\({U_{\text{T}}}\) :

Torsional energy

\({U_{{\text{total}}}}\) :

Total potential energy of the solid medium

\({U_\theta }\) :

Angle bending energy of the solid medium

\({U_\phi }\) :

Torsional energy of the solid medium

\(\alpha\) :

Rotational angle of the solid medium ends

\(\varepsilon\) :

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

\(\sigma\) :

Normal stress of the model

\({\phi _1}\) :

Microporosity

\({\phi _2}\) :

Macroporosity

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

Total porosity

FEM:

Finite element method

Micro-CT:

Micro computed tomography

XRD:

X-ray diffraction

References

  • Ameen MS, Smart BG, Somerville JM, Hammilton S, Naji NA (2009) Predicting rock mechanical properties of carbonates from wireline logs (a case study: Arab-D reservoir, Ghawar field, Saudi Arabia). Mar Pet Geol 26(4):430–444

    Article  Google Scholar 

  • Bakhorji AM (2010) Laboratory measurements of static and dynamic elastic properties in carbonate. PhD dissertation, University of Alberta

  • Bobko C, Ulm FJ (2008) The nano-mechanical morphology of shale. Mech Mater 40(4):318–337

    Article  Google Scholar 

  • Bryant S, Blunt M (1992) Prediction of relative permeability in simple porous media. Phys Rev A 46(4):2004

    Article  Google Scholar 

  • Burchette TP (2012) Carbonate rocks and petroleum reservoirs: a geological perspective from the industry. Geol Soc Lond Spec Publ 370(1):17–37

    Article  Google Scholar 

  • Cantrell DL, Hagerty RM (1999) Microporosity in Arab formation carbonates, Saudi Arabia. GeoArabia 4(2):129–154

    Google Scholar 

  • Cantrell DL, Hagerty RM (2003) Reservoir rock classification, Arab-D reservoir, Ghawar field, Saudi Arabia. GEOARABIA-MANAMA- 8:435–462

    Google Scholar 

  • Cantrell D, Swart P, Hagerty R (2004) Genesis and characterization of dolomite, Arab-D reservoir, Ghawar field, Saudi Arabia. GeoArabia 9(2):11–36

    Google Scholar 

  • Cho YS, Jun S, Im S, Kim HG (2005) An improved interface element with variable nodes for non-matching finite element meshes. Comput Methods Appl Mech Eng 194(27):3022–3046

    Article  Google Scholar 

  • Croize D, Ehrenberg SN, Bjorlykke K, Renard F, Jahren J (2010) Petrophysical properties of bioclastic platform carbonates: implications for porosity controls during burial. Mar Pet Geol 27(8):1765–1774

    Article  Google Scholar 

  • De Boer A, Van Zuijlen AH, Bijl H (2007) Review of coupling methods for non-matching meshes. Comput Methods Appl Mech Eng 196(8):1515–1525

    Article  Google Scholar 

  • Dunham RJ (1962) Classification of carbonate rocks according to depositional texture. In: Ham WE (ed) Classification of carbonate rocks, vol 1. American Association of Petroleum Geologists Memoir, pp 108–121

  • Eberli GP, Baechle GT, Anselmetti FS, Incze ML (2003) Factors controlling elastic properties in carbonate sediments and rocks. Lead Edge 22(7):654–660

    Article  Google Scholar 

  • Edgell HS (1997) Significance of reef limestones as oil and gas reservoirs in the Middle East and North Africa. Preprint of the report in the meeting at the Sydney University

  • Edimann K, Somerville JM, Smart BGD, Hamilton SA, Crawford BR (1998) Predicting rock mechanical properties from wireline porosities. In: SPE/ISRM rock mechanics in petroleum engineering. Society of Petroleum Engineers

  • Farquhar RA, Somerville JM, Smart BGD (1994) Porosity as a geomechanical indicator: an application of core and log data and rock mechanics. In: European petroleum conference. Society of Petroleum Engineers

  • Fries TP, Byfut A, Alizada A, Cheng KW, Schröder A (2011) Hanging nodes and XFEM. Int J Numer Methods Eng 86:404–430

    Article  Google Scholar 

  • Ganis B, Mear ME, Sakhaee-Pour A, Wheeler MF, Wick T (2014) Modeling fluid injection in fractures with a reservoir simulator coupled to a boundary element method. Comput Geosci 18(5):613–624

    Article  Google Scholar 

  • Gritto R, Korneev V, Elobaid E, Mohamed F, Sadooni F (2014) Seismic detection of subsurface karst-like structures. In: Qatar foundation annual research conference, no. 1, p EEPP0551

  • Herrmann HJ, Luding S (1998) Modeling granular media on the computer. Continuum Mech Thermodyn 10(4):189–231

    Article  Google Scholar 

  • Hovorka S, Mace RE, Collins EW (1998) Permeability structure of the Edwards Aquifer, south Texas: implications for aquifer management (Vol. 250). Bureau of Economic Geology, University of Texas at Austin

  • Jouini MS, Vega S, Mokhtar EA (2011) Multiscale characterization of pore spaces using multifractals analysis of scanning electronic microscopy images of carbonates. Nonlinear Process Geophys 18(6):941–953

    Article  Google Scholar 

  • Lenormand R, Fonta O (2007) Advances in measuring porosity and permeability from drill cuttings. In: SPE/EAGE reservoir characterization and simulation conference. Society of Petroleum Engineers

  • Lucia FJ (1995) Rock-fabric/petrophysical classification of carbonate pore space for reservoir characterization. AAPG Bull 79(9):1275–1300

    Google Scholar 

  • Lucia FJ (2007) Carbonate reservoir characterization: an integrated approach. Springer Science & Business Media, Berlin

    Google Scholar 

  • Lucia FJ, Jennings JW, Rahnis M, Meyer FO (2001) Permeability and rock fabric from wireline logs, Arab-D reservoir, Ghawar field, Saudi Arabia. GeoArabia 6:619–646

    Google Scholar 

  • Machel HG, Borrero ML, Dembicki E, Huebscher H, Ping L, Zhao Y (2012) The Grosmont: the world’s largest unconventional oil reservoir hosted in carbonate rocks. Geol Soc Lond Spec Publ 370(1):49–81

    Article  Google Scholar 

  • Mavko G, Mukerji T, Dvorkin J (2009) The rock physics handbook: tools for seismic analysis of porous media. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Mousavi MA, Prodanovic M, Jacobi D (2012) New classification of carbonate rocks for process-based pore-scale modeling. SPE J 18(02):243–263

    Article  Google Scholar 

  • Neveux L, Grgic D, Carpentier C, Pironon J, Truche L, Girard JP (2014) Experimental simulation of chemomechanical processes during deep burial diagenesis of carbonate rocks. J Geophys Res Solid Earth 119(2):984–1007

    Article  Google Scholar 

  • Rogen B, Fabricius IL, Japsen P, Hoier C, Mavko G, Pedersen JM (2005) Ultrasonic velocities of North Sea chalk samples: influence of porosity, fluid content and texture. Geophys Prospect 53(4):481–496

    Article  Google Scholar 

  • Sakhaee-Pour A (2009a) Elastic properties of single-layered graphene sheet. Solid State Commun 149(1):91–95

    Article  Google Scholar 

  • Sakhaee-Pour A (2009b) Elastic buckling of single-layered graphene sheet. Comput Mater Sci 45(2):266–270

    Article  Google Scholar 

  • Sakhaee-Pour A, Bryant S (2012) Gas permeability of shale. SPE Reserv Eval Eng 15(04):401–409

    Google Scholar 

  • Sakhaee-Pour A, Bryant SL (2014) Effect of pore structure on the producibility of tight-gas sandstones. AAPG Bull 98(4):663–694

    Article  Google Scholar 

  • Sakhaee-Pour A, Bryant SL (2015) Pore structure of shale. Fuel 143:467–475

    Article  Google Scholar 

  • Sakhaee-Pour A, Tran H (2017) The permeability of a representative carbonate volume with a large vug. Transp Porous Media 120(3):515–534

    Article  Google Scholar 

  • Santos ES, Ferreira FH (2010) Mechanical behavior of a Brazilian off-shore carbonate reservoir. In: 44th US rock mechanics symposium and 5th US-Canada rock mechanics symposium. American Rock Mechanics Association

  • Sayers CM (2008) The elastic properties of carbonates. Lead Edge 27(8):1020–1024

    Article  Google Scholar 

  • US EIA (2017) Annual energy outlook 2017 with projections to 2050. Energy Information Administration, United States Department of Energy, Washington DC

    Google Scholar 

  • Walton G, Arzua J, Alejano LR, Diederichs MS (2015) A laboratory-testing-based study on the strength, deformability, and dilatancy of carbonate rocks at low confinement. Rock Mech Rock Eng 48(3):941–958

    Article  Google Scholar 

  • Wang HF (2017) Theory of linear poroelasticity with applications to geomechanics and hydrogeology. Princeton University Press, Princeton

    Google Scholar 

  • Weger RJ, Eberli GP, Baechle GT, Massaferro JL, Sun YF (2009) Quantification of pore structure and its effect on sonic velocity and permeability in carbonates. AAPG Bull 93(10):1297–1317

    Article  Google Scholar 

  • White WB (2002) Karst hydrology: recent developments and open questions. Eng Geol 65(2):85–105

    Article  Google Scholar 

  • Xu S, Payne MA (2009) Modeling elastic properties in carbonate rocks. Lead Edge 28(1):66–74

    Article  Google Scholar 

  • Yale DP, Jamieson WH Jr (1994) Static and dynamic mechanical properties of carbonates. In: 1st North American rock mechanics symposium. American Rock Mechanics Association

Download references

Acknowledgements

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

Author information

Authors and Affiliations

  1. Department of Petroleum Engineering, University of Houston, Houston, TX, 77204, USA

    Wenfeng Li & A. Sakhaee-Pour

Authors
  1. Wenfeng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Sakhaee-Pour
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Sakhaee-Pour.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, W., Sakhaee-Pour, A. Two-Scale Geomechanics of Carbonates. Rock Mech Rock Eng 51, 3667–3679 (2018). https://doi.org/10.1007/s00603-018-1536-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00603-018-1536-8

Keywords

Search

Navigation