longitudinal dispersion in nonuniform isotropic porous media

110
deviations for these distributions may be assigned (as discussed for
the grain size distributions). The values of a SO for the uniform and
nonuniform media are 0.0679mm and 0.074Smm, respectively. The nominal
geometric standard deviations for the uniform and nonuniform media are
1.14 and 1.8S, respectively.
When the sample has been drained to its residual saturation, it 1S
transferred from the Buchner funnel to a beaker. The sample is then
weighed and placed in an oven to dry the sample completely. After
drying, the sample is weighed. The weight loss during drying
determines the volume of water, V , contained in the sample at residual
w
saturation. The residual saturation for both porous media is found to
be about 10% of the total saturation volume. The dry weight of the
sample gives the volume of sand, V s ' by assuming the sand density to be
2.6Sg/cc. The total porosity, 0 = V I(v + V ), 1S found to be 0.313
wsw
for the uniform medium and 0.291 for the nonuniform medium.
To compute the cumulative probability distribution for pore S1zes
according to the frequency of occurrence, we follow a procedure similar
to the analysis of the grain size distribution. The measured
distribution is interpolated to provide the pore radii at 1000 equally
spaced values in the cumulative distribution. For probabilities beyond
the range of the experimentally determined values, the radius is set to
the maximum or minimum pore size measured. The cumulative distribution
for the occurrence of pore sizes according to frequency 1S derived by
noting that (see equation (3.49))