Laboratory Tests - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 407

by the displacement of an equivalent volume of a liquid that is non-reactive with the
rock powder (e.g. toluene) in a fl ask (ISRM 1979b). Its grain density ρ s can be cal-

culated from m S and V S according to (14.4). The total porosity then is calculated by
solving (14.4) for n:

(14.10)

It should be noted, however, that for samples containing clay minerals incomplete dry-
ing may lead to porosities lying somewhere between total and effective porosity.
There are different methods for determining effective porosity described in ISRM
(1979b) including caliper and saturation, mercury displacement and Boyle's law tech-
niques. A further currently widely used method for determining effective porosity is the
gas compression/extension method described in Tiab & Donaldson (2004).

All these methods, however, presume that only pore radii greater than 50 nm exist.
Smaller pores can only be detected using the mercury porosimetry also referred to as
“mercury injection porosimetry” or “mercury intrusion porosimetry”. Here, the sample
is placed in a high-pressure cell initially fi lled with mercury. During the test the pressure
is increased stepwise up to 210 MPa or 420 MPa and pore radii down to 4 nm or 2 nm,
depending on the type of porosimeter, can be penetrated by the mercury. The pore ra-
dius can be determined from a force balance equation based on the capillary pressure
needed to force the mercury into a pore against the opposing force of the mercury's
surface tension. Assuming a cylindrical pore model the pore radius r P can be calculated
using Washburn's equation (Washburn 1921):

(14.11)

where is the contact an-

gle between mercury and the pore surface and p is the injection pressure. Since the
injection pressure is inversely related to the pore radius a cumulative pore size distri-
bution is obtained from the pressure levels applied during the test. The volume of the
injected mercury allows the determination of the effective porosity of the sample. A
detailed description of this method may be found in Hennicke & Sturhahn (1969) and
ASTM (1998).
In Table 14.1, effective porosity values of intact rocks reported by Farmer (1968) and
Wittke (1990) are compiled. The porosity values entered in the right-hand column are
determined by mercury porosimetry (Wittke 1990). The table indicates relative large
bandwidths of porosity values for the same rock types. For pure rock salt consisting of
nearly 100% NaCl (halite) a consistently low porosity of n

γ = 0.476 N/m is the surface tension of mercury at 20°C, θ

≈ 0.002 = 0.2% is reported in

literature (Tollert 1964, Spiers et al. 1986).