Page 98 - Reservoir Geomechanics

82 Reservoir geomechanics

The total deformation for this Gulf of Mexico sample can now be described in terms
of porosity, effective pressure and time by combining equations (3.18) and (3.19) into
the following:
φ(P c , t) = 0.2456P −0.1518 − (P c /6666.7)t 0.2318 (3.20)
c
As before, the first term of equation (3.20) represents the instantaneous component of
deformation, with φ 0 equal to 0.2456 and the parameter d equal to −0.1518. The second
term describes the time-dependent component of deformation, with the parameters A
equal to 6667 and b equal to 0.2318. Assuming complete drawdown of the producing
reservoir and an approximately 30 year history results in a predicted total vertical
compaction of nearly 10%.
Table 3.2 summarizes the fitting parameters obtained from the creep strain tests and
constant strain rate tests described earlier. The parameters to make note of are the
exponent parameters, b and d. The apparent viscosity of a reservoir sand is captured in

Table 3.2. Creep parameters for two uncemented sands

A b φ 0 d
Reservoir sand (creep) (creep) (instant) (instant) Notes

Wilmington 5410.3 0.1644 0.271 −0.046 Stiffer and more viscous
GOM – Field X 6666.7 0.2318 0.246 −0.152 Softer and less viscous

1.2 × 10 −5

−
1.0 × 10 −5 Cherts, quartzites
Coefficient of thermal expansion ( o C) 6.0 × 10 −6 Sandstones
−6
8.0 × 10
Granitoid rocks
Slates
Andesites
−6
4.0 × 10
Gabbros, basalts, diabase
2.0 × 10

−7
1.0 × 10 −6
0 20 40 60 80 100
Percent of silica
Figure 3.14. Measurements of the coefficient of linear thermal expansion for a variety of rocks as a
function of the percentage of silica (data from Griffith 1936). As the coefficient of thermal
−1
expansion of silica (∼10 −5 ◦ C )isan order of magnitude higher than that of most other rock
−1
forming minerals (∼10 −6 ◦ C ), the coefficient of thermal expansion ranges between those two
amounts, depending on the percentage of silica.