reservoir geomecanics

296 Reservoir geomechanics
a.
b.
500
500
1000
1000
1500
P p
S v
1500
2000
2000
Measured depth (m)
2500
3000
S hmin
Measured depth (m)
2500
3000
3500
3500
4000
4000
4500
4500
10 15 20 25 30
Stress (ppg)
0 0.2 0.4 0.6 0.8 1
Figure 9.17. (a) Measurements of stress at specific depths need to be extended over depth in order
to be used for many applications such as wellbore stability. (b) One method for interpolation and
extrapolation of the measured stress values is to utilize a smoothly varying effective stress ratio
with depth. In this case with four measurements of S hmin and continuous profiles of P p and S v , one
could estimate S hmin at other depths by utilizing a function of σ hmin /σ v similar to what is shown.
it would be reasonable to interpolate or extrapolate the S hmin measurements, but not
necessarily S Hmax .
One reasonable approach to the problem of extrapolation of measured stress values
is based on relatively constant effective principal stress ratios. An example of this is
illustrated in Figure 9.17, where pore pressure is hydrostatic. The measurements of
S hmin in Figure 9.17a indicate values that are not in frictional equilibrium for normal
faulting. Hence, one cannot use equation (4.45)toestimate values at depths less than or
deeper than the measured values. By first calculating the ratio of the minimum effective
horizontal stress to the vertical effective stress, we can utilize these data to extrapolate
beyond the range of measured values and establish a continuous profile of stress with