Rock Mechanics and Rock Engineering

, Volume 44, Issue 5, pp 541–552 | Cite as

Analysis of Pore Pressure and Stress Distribution around a Wellbore Drilled in Chemically Active Elastoplastic Formations

  • Hamid Roshan
  • S. S. Rahman
Original Paper


Drilling in low-permeable reactive shale formations with water-based drilling mud presents significant challenges, particularly in high-pressure and high-temperature environments. In previous studies, several models were proposed to describe the thermodynamic behaviour of shale. Most shale formations under high pressure are expected to undergo plastic deformation. An innovative algorithm including work hardening is proposed in the framework of thermo-chemo-poroelasticity to investigate the effect of plasticity on stresses around the wellbore. For this purpose a finite-element model of coupled thermo-chemo-poro-elastoplasticity is developed. The governing equations are based on the concept of thermodynamics of irreversible processes in discontinuous systems. In order to solve the plastic problem, a single-step backward Euler algorithm containing a yield surface-correction scheme is used to integrate the plastic stress–strain relation. An initial stress method is employed to solve the non-linearity of the plastic equation. In addition, super convergent patch recovery is used to accurately evaluate the time-dependent stress tensor from nodal displacement. The results of this study reveal that thermal and chemical osmosis can significantly affect the fluid flow in low-permeable shale formations. When the salinity of drilling mud is higher than that of pore fluid, fluid is pulled out of the formation by chemical osmotic back flow. Similar results are observed when the temperature of drilling mud is lower than that of the formation fluid. It is found that linear elastic approaches to wellbore stability analysis appear to overestimate the tangential stress around the wellbore and produce more conservative stresses compared to the results of field observation. Therefore, the drilling mud properties obtained from the elastoplastic wellbore stability in shales provide a safer mud weight window and reduce drilling cost.


Thermo-chemo-poro-elastoplasticity Water-active rocks Osmotic flow Wellbore stability analysis 

List of Symbols




Thermal diffusivity


Average diluent mass fraction in formation


Average solute mass fraction in drilling mud


Average solute mass fraction in formation


Elastic modulus tensor


Solute diffusion coefficient


Coefficient of thermal diffusion

Plastic multiplier


Yield function


Shear modulus of rock


Constant isotropic hardening module


First stress invariant


Second invariant of the deviatoric stress




Isotropic hardening parameter


Fluid bulk module


Thermal osmosis coefficient


Solid bulk module


Molar mass of the solute


Number of nodes


Pressure shape functions


Displacement shape functions


Mass fraction shape functions


Temperature shape functions




Initial reservoir pressure

\( \vec{P} \)

Pore pressure vector


Plastic potential


Universal gas constant


Specific fluid entropy


Shale temperature


Drilling mud temperature




Absolute temperature





\( \vec{U} \)

Displacement vector


Biot’s coefficient


Thermal expansion coefficient of fluid


Thermal expansion coefficient of solid


Strain tensor


Variation of the fluid content




Poisson’s ratio

\( \mathop {\rho_{f} }\limits^{ - } \)

Fluid density


Stress tensor

\( \sigma^{\prime}_{p} \)

Plastic effective stress


Initial uniaxial yield stress


Minimum in situ horizontal stress


Maximum in situ horizontal stress




Internal friction


Chemical swelling parameter for solute


Chemical swelling parameters for diluent

Standard solute reflection coefficient


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.School of Petroleum EngineeringUniversity of New South WalesSydneyAustralia

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