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62 Reservoir geomechanics

SANDSTONE LIMESTONE SHALE
10 10 10
Porosity
8 8 8
<8%
8–16%
>16%
6 6 6
4 4 4

2 2 2

0 0 0
0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100
E (GPa) E (GPa) E (GPa)
10 10 10

8 8 8

6 6 6

4 4 4

2 2 2

0 0 0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
n n n
15 15 15

10 10 10

5 5 5

0 0 0
0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35
f (%) f (%) f (%)

Figure 3.4. Typical values of static measurements of Young’s modulus, E, and Poisson’s ratio, ν,
for sandstone and limestone and porosity, φ (from Lama and Vutukuri 1978).

The shear modulus of a fluid is obviously zero. The fifth common elastic modulus,
Lame’s constant, λ, does not have a straightforward physical representation. In a mat-
erial in which Poisson’s ratio is equal to 0.25 (a Poisson solid), λ = G.
Figure 3.4 is a compilation of static laboratory measurements of E and ν for sand-
stone, limestone and shale samples for which porosity was also measured (Lama and