Microseismic Monitoring and Geomechanical Modelling of CO2 - bris

CHAPTER 5.
GEOMECHANICAL SIMULATION OF CO 2 INJECTION
subvertically, and I shall use σ ′ 3 to denote this term, with σ ′ 1 and σ ′ 2 referring to the subhorizontal
principal stresses.
5.2.1 Mean and differential stress
The mean stress, p, is defined as the mean of the principal stresses,
p = (σ ′ 1 + σ ′ 2 + σ ′ 3)/3, (5.2)
and the differential stress, q, is defined as the difference between the maximum and minimum principal
stresses,
q = σ ′ 3 − σ ′ 1. (5.3)
High differential stresses will increase shear stresses and cause fractures to develop.
5.2.2 Mohr circles
During injection, a pore pressure increase will lead to an evolution of the effective stress tensor due
to changes both in P fl and in σ ij ,
∆σ ′ ij = ∆σ ij − β w I ij ∆P fl . (5.4)
In order to visualise stress evolution, I will use Mohr circle plots, plotted in σ ′ n − τ space. τ is the
shear stress, and σ ′ n is the normal stress, acting on any 2D planar surface in the rock. Each point on
the circumference of the Mohr circle defines σ ′ n and τ for a plane at the given angle. The shear stress,
τ, is maximum when the plane is at 45 ◦ to the principal stress, is given by
τ = q/2 = σ′ 3 − σ ′ 1
, (5.5)
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The Mohr circle can be defined by the maximum and minimum principal effective stresses. For any
surface in the rock mass, shear failure will occur if the stresses exceed the Mohr-Coulomb envelope,
given by
where m is the coefficient of friction and χ is the cohesion.
τ = mσ ′ n + χ, (5.6)
The stress evolution in the reservoir
during CO 2 injection is shown schematically in Figure 5.1 - if any point on the circle exceeds the yield
envelope then shear failure can occur. m is often given in terms of an angle of friction,
m = tan ϕ f (5.7)
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