Page 71 - Origin and Prediction of Abnormal Formation Pressures

ORIGIN OF ABNORMAL FORMATION PRESSURES 53

10

%
O"

10 -1

10 -2
10 -1 1 10 100
z/fKt/Ss} 1/2

Fig. 2-19. Dimensionless graph of excess-head pressure distribution in a semi-infinite medium with constant
flux at the boundary. (Modified after Hanshaw and Bredehoeft, 1968, fig. 10, p. 1119; in Rieke and
Chilingarian, 1974, fig. 178, p. 332. Courtesy of the Geol. Soc. Am. Bull.)

distribution in a semi-infinite medium:
02h ' Ss Oh'
(2-47)
Oz 2 K Ot
where 0 < z _< ec

h'(z, 0) - 0 at t--0
h'(oc, 0) -0 att>0
Ohl qo
att>0
Oz z=0 K
It is necessary to define z = 0 at the boundary of the media, which for the core of a
semi-finite medium is at the source layer.
By analogy, the solution is obtained from Carslaw and Jaeger (1959, p. 75):

-- -- Ssz~2 exp -Ssz2 erf ~ - 1 (2-48)
qoz ~ 4Kt /Kt
2

A graphical solution to Eq. 2-48 is presented in Fig. 2-19. The head at the surface,