FIG. 2 MECD CHANGE: NORMAL, STRIKE-SLIP FAULTING REGIME
0.84
0.80
0.76
0.72
0.68
0.63
0.59
90
75 60 45
30 15 0 90 75 60 45 30 15
0
Inclination angle, degrees Relative azimuthal angle, degrees
Ma
x
im
u
mE
CD,
g/
c
c
Fluid seepage stresses
Compared with conventional overbalanced drilling, effective
fluid column pressure is lower than the formation pressure
during UBD, showing that formation fluid will flow into the
wellbore and seepage force will be exerted on wellbore rocks
during UBD operations in horizontal wells (Equation 5).
Researchers have already devised the model and boundary conditions to study the effects of fluid seepage on wellbore during UBD of horizontal wells. 8
Building on this allows determination of additional
stresses induced by fluid seepage (radial stress, σfr; tangential stress, σfθ; and axial stress, σfz). Equation 6, where R
is the borehole radius, m; r is the radial distance from the
center of wellbore to a point in the formation, m; Pop is the
original pore pressure, MPa; and re is the radius of external
boundary, m, shows the additional stresses.
At the wellbore wall (r=R), Equation 7 expresses the
stress components (σfr, σfθ, σfz) produced by fluid seepage.
The principal stresses on wellbore rocks are found by linear
addition of Equation 4 and Equation 7, further described in
Equation 8. 9
Wellbore-collapse model
For an easier calculation, maximum principal stress, inter-
mediate principal stress, and minimum principal stress are
assumed to be σe θmax, σe θmin, and σer respectively, in Equa-
tion 8. Using the Mohr-Coulomb mathematical model (ex-
pressed in Equation 9, which considers the principle of ef-
fective stress) yields a new wellbore-collapse model where
σe1 and σe3 denote effective maximum principal stress and
redistribution of circumferential stresses
Since the greatest concern for wellbore stability is at the
borehole wall, stress components in Equation 1 at that loca-
tion can be re-expressed by Equation 2 in the cylindrical
coordinate (τ, θ, z), where θ is the angular position around
the wellbore circumference measured in degrees and ν is
Poisson’s ratio.
From Equation 2, we find that σθ, σz, and τθ z are connected to θ, showing that the stress state of an inclined borehole
varies with the spatial position of wellbore rocks. Because
τθ z is usually not 0, whereas σθ and σz are not the principal
stresses of wellbore rocks, στ is a principal stress. Equation
3 shows the principal stress, σ, and shear stress, τ, consisting of the stress components in Equation 2.
When dσ/dβ = 0, another two principal stresses (σθmax
and σθmin) emerge (Equation 4). Here the principle of effec-
tive stress is taken into account where αe is Biot’s coeficient,
and Pp is pore pressure, MPa.
– – STRESS REGIMES Table 2
Maximum Minimum
horizontal horizontal
Vertical stress stress stress
Regime type ––––––––––––––––— MPa/100m —––––––––––––––––
NF 2. 15 1. 85 1. 65
NF-SS 2. 15 2. 15 1. 65
SS 1. 85 2. 15 1. 65
SS-RF 1. 65 2. 15 1. 65
RF 1. 65 2. 15 1. 85
