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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

Abstract

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.

Keywords

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

List of Symbols

c

Cohesion

cT

Thermal diffusivity

CD

Average diluent mass fraction in formation

CM

Average solute mass fraction in drilling mud

CS

Average solute mass fraction in formation

De

Elastic modulus tensor

D

Solute diffusion coefficient

DT

Coefficient of thermal diffusion

Plastic multiplier

f

Yield function

G

Shear modulus of rock

Hi0

Constant isotropic hardening module

J1

First stress invariant

J2

Second invariant of the deviatoric stress

k

Permeability

κ

Isotropic hardening parameter

Kf

Fluid bulk module

KT

Thermal osmosis coefficient

KS

Solid bulk module

MS

Molar mass of the solute

n

Number of nodes

NP

Pressure shape functions

Nu

Displacement shape functions

NCS

Mass fraction shape functions

NT

Temperature shape functions

p

Pressure

Pi

Initial reservoir pressure

\( \vec{P} \)

Pore pressure vector

QL

Plastic potential

R

Universal gas constant

s0

Specific fluid entropy

Ts

Shale temperature

Tm

Drilling mud temperature

T

Temperature

Ta

Absolute temperature

t

Time

u

Displacement

\( \vec{U} \)

Displacement vector

α

Biot’s coefficient

αf

Thermal expansion coefficient of fluid

αm

Thermal expansion coefficient of solid

ɛ

Strain tensor

ζ

Variation of the fluid content

μ

Viscosity

ν

Poisson’s ratio

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

Fluid density

σ

Stress tensor

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

Plastic effective stress

σy0

Initial uniaxial yield stress

σh

Minimum in situ horizontal stress

σH

Maximum in situ horizontal stress

ϕ

Porosity

φ

Internal friction

ωS

Chemical swelling parameter for solute

ωD

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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