Page 83 - Reservoir Geomechanics

67 Basic constitutive laws

a.
Stress = Force/Area Total
S = F/A
T
(Acting outside an impermeable
boundary)

b.
Stresses acting on grains
A T

s c
A c
t
P p c

Pore pressure acting in pore space
t

c.
1

0.9
DRY OTTOWA SAND
f = 0.33
0.8

Alpha 0.7

0.6

DRY FOUNTAINEBLEAU SANDSTONE
0.5 f = 0.15

0.4
0 10 20 30 40 50 60
Pressure (MPa)

Figure 3.5. (a) Schematic illustration of a porous solid with external stress applied outside an
impermeable boundary and pore pressure acting within the pores. (b) Considered at the grain scale,
the force acting at the grain contact is a function of the difference between the applied force and
the pore pressure. As A c /A T goes to zero, the stress acting on the grain contacts is given by the
Terzaghi effective stress law (see text). (c) Laboratory measurements of the Biot coefficient, α, for
a porous sand and well-cemented sandstone courtesy J. Dvorkin.