Microseismic Monitoring and Geomechanical Modelling of CO2 - bris

5.3. NUMERICAL MODELLING
5.3.1 Fluid-flow simulation
Any attempt to model geomechanical deformation of hydrocarbon reservoirs must begin by modelling
the movement of fluid, the properties of the fluids, and the changes in pore pressure. Fortunately,
such problems have long been of interest to the hydrocarbon industry, and so a range of commercial
fluid-flow simulators are available. Most have good records of reliability for dealing with reservoir fluid
flow processes. All are similar and can in theory be coupled to geomechanical simulators. Throughout
this work I will be using MORE as the fluid-flow simulator, because of the ease with which it can be
coupled using a bespoke Message Passing Interface (MPI) developed as part of the IPEGG project.
5.3.2 Geomechanical modelling
In order to model the geomechanical deformation, I use a finite element code, ELFEN, developed
by Swansea University and Rockfield Ltd.
ELFEN uses a CamClay constitutive model - this is
described in detail by Crook et al. (2006) and is summarised below. In the elastic regime, the material
deformation is modelled according to Hooke’s law. The limits of elastic behaviour are defined by a
yield surface (shown schematically in Figure 5.3) which is a smooth surface defined in p − q space.
The equation of the yield surface is given by
F (σ, ε p v) = g(θ, p)q + (p − p t ) tan β
( p − pc
p t − p c
) 1/n
, (5.11)
where θ is the Lode angle, p t and p c are respectively the tensile and compressive intersects with the p
axis, β is the friction angle, n is a material parameter. g(θ, p) describes a correction for the deviatoric
plane,
(
g(θ, p) =
1
1 − β π (p)
(1 + β π (p) r3
q 3 )) N
π
N π is a material constant, and β π is defined as a function of p as
( )
β π (p) = β0 π exp β1 π p p0 c
p c
(5.12)
(5.13)
β π 0 and β π 1 are further material constants, and r 3 = 27J ′ 3/2, where J ′ 3 is the third deviatoric stress
invariant.
The evolution of the yield surface (strain hardening or softening) is computed as a function of the
volumetric plastic strain, ε p v, following
p c = p 0 c exp
( vε
p
v
(λ − κ)
)
, p t = p 0 t exp
( ) v(ε
p
v ) max
, (5.14)
(λ − κ)
where v is the specific volume, and λ and κ are the slopes of the normal compression and unloadingreloading
lines (Crook et al., 2006), and (ε p v) max is the maximum volumetric plastic strain encountered
by an element.
Inside the yield surface the deformation is elastic, controlled by the Young’s modulus E and
Poisson’s ratio ν, which are given as a function of porosity, Φ and p,
( ) e p + A
E = E 0 (Φ) c , ν = ν min + (ν max − ν min )(1 − exp(−mp)). (5.15)
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