Page 95 - Reservoir Geomechanics

79 Basic constitutive laws

a.
1
Well-log data
0.9 Ultrasonic
data
0.8
0.7 Quasi-static load cycling data
Normalized bulk modulus 0.5 reservoir lifespan Data
0.6
Extrapolate to
30-year simulated
S.L.Solid
0.4
Burger’s
0.3
Mean pressure = 22.5 MPa Power/Maxwell
0.2
Pressure amplitude = 5 MPa
0.1
0
1.00E−09 1.00E−07 1.00E−05 1.00E−03 1.00E−01 1.00E+01 1.00E+03 1.00E+05
Frequency (Hz)

b.
1.00E+02
data
1.00E+01 S.L.Solid
Burger’s
Power/Maxwell
1.00E+00
Attenuation (1/Q) 1.00E−01

1.00E−02
Mean pressure = 27.5 MPa
1.00E−03 Pressure amplitude = 5 MPa

1.00E−04
1.00E−06 1.00E−05 1.00E−04 1.00E−03 1.00E−02 1.00E−01
Frequency (Hz)

Figure 3.13. (a) Low-frequency bulk modulus dispersion predicted using parameters derived from
fitting the creep strain curves compared with experimental results. The standard linear solid and
Burger’s solid models provide the best fit to the quasi-static data, but fail to predict reasonable
results at time-periods associated with the life of a reservoir. The power law–Maxwell mixed model
reproduces the overall trend of the data, and predicts a physically reasonable value of stiffness at
long time-periods. The error bars represent the inherent uncertainty of the measurements (from
Hagin and Zoback (2004c). (b) Low-frequency attenuation predicted using the parameters derived
from the creep strain data compared with experimental results.