Research Papers

Early-Age Stress and Pressure Developments in a Wellbore Cement Liner: Application to Eccentric Geometries

[+] Author and Article Information
Thomas Petersen, Franz-Josef Ulm

Department of Civil and
Environmental Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received April 13, 2016; final manuscript received June 22, 2016; published online July 13, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(9), 091012 (Jul 13, 2016) (11 pages) Paper No: JAM-16-1181; doi: 10.1115/1.4034013 History: Received April 13, 2016; Revised June 22, 2016

This paper introduces a predictive model for the stress and pressure evolutions in a wellbore cement liner at early ages. A pressure state equation is derived that observes the coupling of the elastic changes of the solid matrix, the eigenstress developments in the solid and porespaces, and the mass consumption of water in course of the reaction. Here, the transient constitution of the solid volume necessitates advancing the mechanical state of the poroelastic cement skeleton incrementally and at constant hydration degree. Next, analytic function theory is employed to assess the localization of stresses along the steel–cement (SC) and rock–cement (RC) interfaces by placing the casing eccentrically with respect to the wellbore hole. Though the energy release rate due to complete debonding of either interface is only marginally influenced by the eccentricity, the risk of evolving a microcrack along the thick portion of the sheath is substantially increased. Additionally, it is observed that the risk of microannulus formation is principally affected by the pressure rebound, which is engendered by the slowing reaction rate and amplified for rock boundaries with low permeability.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Ingraffea, A. R. , Wells, M. T. , Santoro, R. L. , and Shonkoff, S. B. C. , 2014, “ Assessment and Risk Analysis of Casing and Cement Impairment in Oil and Gas Wells in Pennsylvania, 2000–2012,” Proc. Natl. Acad. Sci., 111(30), pp. 10955–10960. [CrossRef]
Masoero, E. , Del Gado, E. , Pellenq, R. J.-M. , Yip, S. , and Ulm, F.-J. , 2014, “ Nano-Scale Mechanics of Colloidal C–S–H Gels,” Soft Matter, 10(3), pp. 491–499. [CrossRef] [PubMed]
Bonett, A. , and Pafitis, D. , 1996, “ Getting to the Root of Gas Migration,” Oilfield Rev., 8(1), pp. 36–49.
Albawi, A. , 2013, “ Influence of Thermal Cycling on Cement Sheath, Integrity,” Master's thesis, Faculty of Engineering Science and Technology, Department of Petroleum Engineering and Applied Geophysics, Norwegian University of Science and Technology, Trondheim, Norway.
Ulm, F.-J. , Abuhaikal, M. , Petersen, T. A. , and Pellenq, R. J.-M. , 2014, “ Poro-Chemo-Fracture-Mechanics…Bottom-Up: Application to Risk of Fracture Design of Oil and Gas Cement Sheath at Early Ages,” Computational Modelling of Concrete Structures, CRC Press, Boca Raton, FL, p. 61.
Nabipour, A. , Joodi, B. , and Sarmadivaleh, M. , 2010, “ Finite Element Simulation of Downhole Stresses in Deep Gas Wells Cements,” SPE Deep Gas Conference and Exhibition, Society of Petroleum Engineers, Manama, Bahrain, Jan. 24–26, Paper No. SPE-132156-MS.
Wang, W. , and Taleghani, A. D. , 2014, “ Three-Dimensional Analysis of Cement Sheath Integrity Around Wellbores,” J. Pet. Sci. Eng., 121, pp. 38–51. [CrossRef]
Nur, A. , and Byerlee, J. D. , 1971, “ An Exact Effective Stress Law for Elastic Deformation of Rock With Fluids,” J. Geophys. Res., 76(26), pp. 6414–6419. [CrossRef]
Coussy, O. , 2004, Poromechanics, Wiley, Chichester, UK.
Powers, T. C. , and Brownyard, T. L. , 1946, “ Studies of the Physical Properties of Hardened Portland Cement Paste,” Proc.-Am. Concr. Inst., 43(9), pp. 249–336.
Ulm, F.-J. , and Coussy, O. , 2001, “ What Is a ‘Massive’ Concrete Structure at Early Ages? Some Dimensional Arguments,” J. Eng. Mech., 5(512), pp. 512–522. [CrossRef]
Powers, T. C. , 1935, “ Absorption of Water by Portland Cement Paste During the Hardening Process,” Ind. Eng. Chem., 27(7), pp. 790–794. [CrossRef]
Abdolhosseini Qomi, M. J. , Krakowiak, K. J. , Bauchy, M. , Stewart, K. L. , Shahsavari, R. , Jagannathan, D. , Brommer, D. B. , Baronnet, A. , Buehler, M. J. , Yip, S. , Ulm, F.-J. , Van Vliet, K. J. , and Pellenq, R. J.-M. , 2014, “ Combinatorial Molecular Optimization of Cement Hydrates,” Nat. Commun., 5, p. 4960. [CrossRef] [PubMed]
Thomas, J. J. , Jennings, H. M. , and Allen, A. J. , 1998, “ The Surface Area of Cement Paste as Measured by Neutron Scattering: Evidence for Two CSH Morphologies,” Cem. Concr. Res., 28(6), pp. 897–905. [CrossRef]
Barberon, F. , Korb, J.-P. , Petit, D. , Morin, V. , and Bermejo, E. , 2003, “ Probing the Surface Area of a Cement-Based Material by Nuclear Magnetic Relaxation Dispersion,” Phys. Rev. Lett., 90(11), p. 116103. [CrossRef] [PubMed]
Ioannidou, K. , Krakowiak, K. J. , Bauchy, M. , Hoover, C. G. , Masoero, E. , Yip, S. , Ulm, F.-J. , Levitz, P. , Pellenq, R. J.-M. , and Del Gado, E. , 2016, “ Mesoscale Texture of Cement Hydrates,” Proc. Natl. Acad. Sci., 113(8), pp. 2029–2034. [CrossRef]
Dormieux, L. , Kondo, D. , and Ulm, F.-J. , 2006, Microporomechanics, Wiley, Chichester, UK.
Verbeck, G. J. , and Helmuth, R. H. , 1968, “ Structures and Physical Properties of Cement Paste,” 5th International Symposium on the Chemistry of Cement, Tokyo, Japan, Oct. 7–11, pp. 1–32.
Taylor, H. F. W. , 1997, Cement Chemistry, Thomas Telford, London.
Powers, T. C. , 1958, “ Structure and Physical Properties of Hardened Portland Cement Paste,” J. Am. Ceram. Soc., 41(1), pp. 1–6. [CrossRef]
Jeffery, G. B. , 1921, “ Plane Stress and Plane Strain in Bipolar Co-Ordinates,” Philos. Trans. R. Soc., A, 221(582–593), pp. 265–293. [CrossRef]
Muskhelishvili, N. I. , 1953, Some Basic Problems of the Mathematical Theory of Elasticity: Fundamental Equations, Plane Theory of Elasticity, Torsion, and Bending, J. R. M. Radok, trans., Noordhoff International Publishing, Groningen, The Netherlands.
Thiercelin, M. J. , Dargaud, B. , Baret, J. F. , and Rodriquez, W. J. , 1998, “ Cement Design Based on Cement Mechanical Response,” SPE Drill. Completion, 13(4), pp. 266–273. [CrossRef]
DeBruijn, G. G. , Garnier, A. , Brignoli, R. , Bexte, D. C. , and Reinheimer, D. , 2009, “ Flexible Cement Improves Wellbore Integrity in SAGD Wells,” SPE/IADC Drilling Conference and Exhibition, Society of Petroleum Engineers, Amsterdam, The Netherlands, Mar. 17–19, Paper No. SPE-119960-MS.
Ardakani, S. M. , and Ulm, F.-J. , 2013, “ Chemoelastic Fracture Mechanics Model for Cement Sheath Integrity,” J. Eng. Mech., 140(4), p. 04013009. [CrossRef]
Wang, Z. , Lou, Y. , and Suo, Z. , 2016, “ Crack Tunneling in Cement Sheath of Hydrocarbon Well,” ASME J. Appl. Mech., 83(1), p. 011002. [CrossRef]
Petersen, T. A. , and Ulm, F.-J. , 2016, “ Radial Fracture in a Three-Phase Composite: Application to Wellbore Cement Liners at Early Ages,” Eng. Fract. Mech., 154, pp. 272–287. [CrossRef]
Hoover, C. G. , and Ulm, F.-J. , 2015, “ Experimental Chemo-Mechanics of Early-Age Fracture Properties of Cement Paste,” Cem. Concr. Res., 75, pp. 42–52. [CrossRef]
Lecampion, B. , Bunger, A. , Kear, J. , and Quesada, D. , 2013, “ Interface Debonding Driven by Fluid Injection in a Cased and Cemented Wellbore: Modeling and Experiments,” Int. J. Greenhouse Gas Control, 18, pp. 208–223. [CrossRef]
Rice, J. , 1988, “ Elastic Fracture Mechanics Concepts for Interfacial Cracks,” ASME J. Appl. Mech., 55(1), pp. 98–103. [CrossRef]
Hellmich, C. , Ulm, F.-J. , and Mang, H. A. , 1999, “ Consistent Linearization in Finite Element Analysis of Coupled Chemo-Thermal Problems With Exo- or Endothermal Reactions,” Comput. Mech., 24(4), pp. 238–244. [CrossRef]
Petersen, T. A. , 2015, “ Chemo-Poro-Elastic Fracture Mechanics of Wellbore Cement Liners: The Role of Eigenstress and Pore Pressure on the Risk of Fracture,” Master's thesis, Massachusetts Institute of Technology, Cambridge, MA.
Constantinides, G. , and Ulm, F.-J. , 2007, “ The Nanogranular Nature of C–S–H,” J. Mech. Phys. Solids, 55(1), pp. 64–90. [CrossRef]
Ortega, J. A. , Gathier, B. , and Ulm, F.-J. , 2011, “ Homogenization of Cohesive-Frictional Strength Properties of Porous Composites: Linear Comparison Composite Approach,” J. Nanomech. Micromech., 1(1), pp. 11–23. [CrossRef]
Qomi, M. J. A. , Bauchy, M. , Ulm, F.-J. , and Pellenq, R. , 2015, “ Polymorphism and Its Implications on Structure-Property Correlation in Calcium-Silicate-Hydrates,” Nanotechnology in Construction, K. Sobolev and S. P. Shah, eds., Springer, Cham, Switzerland, pp. 99–108.


Grahic Jump Location
Fig. 1

Diagram of a wellbore cement liner

Grahic Jump Location
Fig. 2

The cement poroelastic constants in function of thehydration degree (G = 11.1 GPa and N = 174.3 GPa; see Table 2 in Appendix C for the calculation of the volume fractions and the upscaling of the poroelastic constants). The inset shows the evolution of the primary cement phases.

Grahic Jump Location
Fig. 3

Plots depicting the (a) driving forces of the bulk stress developments and (b) the pressure evolution p̂=p/p0 for low and high permeability formations. Herein, the solid eigenstress σ* was assumed to evolve linearly with ξ. As a validation of concept, the black contours in (b) show smoothed, nondimensionalized pressure-log data for a well of undisclosed identity provided by Schlumberger (solid) and the pressure evolution simulated by our model (dashed) for a cement with w/c = 0.45.

Grahic Jump Location
Fig. 4

Bulk effective radial ((a) and (b)) and tangential ((c) and (d)) stress development along the SC interface ((a) and (c)) and the RC interface ((b) and (d)). At complete hydration, a residual Δp remains in the system. Thus, the dashed contours show the asymptotic values of the effective stress, once the pressure has fully recovered to the reference value p = p0.

Grahic Jump Location
Fig. 5

Contour plots of the influence of the shear modulus ratio between rock and cement Gr/Gc and the Newton coefficient λfl on the effective radial stress along SC (left column of panel) and RC (right column) at complete hydration (top row) and once the pressure has completely recovered (bottom row). The casing placement is assumed concentric with the borehole.

Grahic Jump Location
Fig. 6

Diagram of the bilinear transformation that maps the eccentric contours SC and RC in the z-plane to concentric contours in the s-plane

Grahic Jump Location
Fig. 7

(a) The evolution of the energy release rate for a vertically propagating microannulus in a concentric geometry for λfl = 1 × 10−5 s−1; values normalized by Ĝ=GGc∞/2πriΣrr∞2, where i = 1 along the SC and i = 2 along RC. The dashed contours show the energy release rate once the pressure has fully recovered. (b) The normalized energy release rate at t in function of the rock-to-cement shear modulus ratio.

Grahic Jump Location
Fig. 8

The top panels show the distribution of work done along (a) SC and (b) RC to produce a microannulus along the respective interface for different degrees of casing eccentricity. The bottom panels display the energy release rate for a microcrack Gi, i.e., the risk of crack initiation, along (c) SC and (d) RC. dG¯/dθ and G¯i have been normalized with respect to the uniform values in a concentric geometry.

Grahic Jump Location
Fig. 9

The energy release rate for a microcrack along SC and RC G¯i(θ)=Giecc(θ)/Gicent in function of different Gr/Gc



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In