Page 330 - Origin and Prediction of Abnormal Formation Pressures

ABNORMALLY LOW FORMATION PRESSURES 299

permafrost, or tectonic uplift and erosion. The temperature changed in response to the
change in the global Earth's surface temperature or to the change in depth.
Such changes may create volumetric changes in (1) rocks, (2) pore space, and (3) the
interstitial water. Relative pore volume change dVp/Vp and pore water volume change
dVw/Vw with respect to a change in temperature can be expressed as follows (Dobrynin,
1970):

Vp -- j~r d(a - p) + fis dp - as dT (11-5)
dVw = flw dp - O~w dT (11-6)
Vw
where fir, fis, and fiw, are the coefficients of compressibility of pore volume, solids and
water, respectively; and O~s, and O~w are the coefficients of thermal expansion of solids
(minerals) and water, respectively. In the case of static pore water (full hydrodynamic
isolation of pores), a relative change in the volume of pores must be equal to the relative
change of pore water volume:
dVr dVw
= (11-7)
Vr Vw
Equating the right-hand sides of Eqs. 11-5 and 11-6, one obtains"
flw dp - Oew dT -- fir d(a - p) + fis dp - Ors dT (11-8)
Thus, the change in pore pressure (dp) that occurs during a change in the thermody-
namic conditions of a deposit is equal to:

fir lYw -- tYs
dp - da + dT 11-9
/~r -'[- flw -- fls fir -[- flw -- fls
1
2
The average normal stress (a) for horizontal layers is a -- 5ax + 5az, where ax is
the horizontal component of stress (and ax -- ay), and az is the vertical component of
stress. Using the mean lateral compression:
l)
~ a
Crx -- Oy = 1_ v z (11-10)
The total overburden stress is equal to"

a z (11-11)
a 3 1-v
-
-
where v is Poisson's ratio.
Differentiating Eq. 11-11 one obtains:
1 [l+V]d, (11-12)
da--~ 1-v
where da z is the change in the vertical component of stress during sedimentation or
erosion. Expressing da z in terms of change in sedimentary overburden, one obtains:

1 [l+VlgprAh (11-13)
da-~ 1-v