Page 70 - Petroleum Geology

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It must be noted at once that while this formula 3.6 is satisfactory for
shallow depths, to perhaps 2 or 3 km, it cannot be correct because as porosity
is eliminated with depth, the transit time approaches the matrix transit time
(%55 ps/ft, ~180
ps/m. We shall therefore seek a better one.
There is little reliable experimental data on mudstone sonic transit times
and the corresponding porosities, but Magara (1968, p. 2474, table 11) found
a linear relationship. Accepting this, we proceed as follows:
Define At, as the value of At when the porosity is f,;
At* as the dimensionless transit time A t/A to;
A tza as the dimensionless transit time at zero porosity A tma/A to;
and
f* as the relative porosity f/fo.
Then f* = 1 when At* = 1, and f* = 0 when At* = At:,, and we can write:

flfo = (At-Atma)/(At, -Atma)- (3.7a)
The value of At,, is close to 55 ps/ft (180 ps/m) in mudstones. The values
of At, and f, are about 165 ps/ft (540 ps/m) and 0.5 (to one significant
figure) and these figures should be used when there is no reliable data
suggesting others. Again, note carefully that we are concerned with the values
when the mudstone has accumulated into the stratigraphic record, not the
superficial values of 200 ps/ft and porosities of 60% and more.
Magara’s data is plotted on Fig. 3-5, using the above values of the material
constants.

At* = At/At,
0
I

f*

0

Fig. 3-5. Plot of dimensionless time against relative porosity for mudstones. Points are
computed from data of Magara (1968, p. 2474, table 11) using At, = 165 ps/ft, Atrna =
55 ps/ft and f, = 0.5.