Geology Reference
In-Depth Information
porous bodies, see Paterson and Wong {2005, Sect. 7.3.1, where K
¼
1
=
b
e
and
K
s
¼
1
=
b
s
}.
From the solution of (
3.51
) for a semi-infinite medium with constant D and a
given fluid pressure applied at the surface, the penetration distance in time t is of
the order of
p
Dt
or the time to penetrate a distance x is of the order of x
2
=
D. In the
case of a gas such as argon or water vapor as pore fluid, b * 10
-5
Pa
-1
near
atmospheric pressure and b * 10
-9
Pa
-1
at pressures of the order of 100 MPa,
while g *30.10
-6
Pa s (this value is not very sensitive to pressure in macroscopic
flow, although where the pressure is low, g may be effectively higher because of
the mean free path effect mentioned earlier). Using the approximation b
0
¼
/b
;
the
time needed for a small pressure pulse to penetrate 10 mm into a rock having
k = 10
-19
m
2
and /=0.01 would be of the order of one hour when the fluid
pressure is near atmospheric pressure or one second when the fluid pressure is near
100 MPa, respectively; these intervals suggest timescales for the re-equilibration
of pore pressure in a laboratory specimen of such a rock after a small perturbation.
In the case of large pressure changes, D can no longer be taken as constant because
of the large change in b with pressure and a solution for variable D must be sought.
For numerical solution of (
3.51
) in this case, see Lin (
1982
).
Another effect that may sometimes be of interest is the hydrodynamic dispersion,
represented by the spreading or mixing of a tracer solute introduced at a point in the
system (Bear
1972
, Chap. 10). The effect can be described in terms of a coefficient
of hydrodynamic dispersion which is a function of the velocity of the fluid, the
molecular diffusion coefficient of the solute in the fluid, and a geometrical property
of the porous solid known as its dispersivity, related to but not solely determined by
the permeability.
References
Adda Y, Philibert J (1966) La diffusion dans les solides. Press University, Paris, 1285 pp
Allègre CJ, Le Mouel JL, Provost A (1982) Scaling rules in rock fracture and possible
implications for earthquake prediction. Nature 297:47-49
Allnatt
AR,
Lidiard
AB
(1993)
Atomic
transport
in
solids.
Cambridge
University
Press,
Cambridge 572 pp
Anderson DE (1981) Diffusion in electrolyte mixtures. In: Kinetics of geochemical processes.
Mineral Soc Am, pp 211-260
Anderson DE, Graf DL (1976) Multicomponent electrolyte diffusion. Annual Rev Earth Planet
Sci 4:95-121
Archie GE (1942) The electrical resistivity log as an aid in determining some reservoir
characteristics. Trans AIME 146:54-62
Arrhenius S (1889) Über die Reaktionsgeschwindigkeit bei der Inversion von Rohzucker durch
Saüren. Zeitschrift für physikalische Chemie 4:226-248
Atkins PW (1978) Physical chemistry. Oxford University Press, Oxford, 1018 pp
Atkins PW (1986) Physical chemistry, 3rd edn. Oxford University Press, Oxford, 857 pp
Atkinson A, Taylor RI (1981) The diffusion of 63Ni along grain boundaries in nickel oxide. Phil
Mag A43:979-998
