A new theoretical interpretation of Archie's saturation exponent
This paper describes the extension of the concepts of connectedness and conservation of connectedness that underlie the generalized Archie's law for <i>n</i> phases to the interpretation of the saturation exponent. It is shown that the saturation exponent as defined originally by...
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2017-07-01
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| Series: | Solid Earth |
| Online Access: | https://www.solid-earth.net/8/805/2017/se-8-805-2017.pdf |
| Summary: | This paper describes the extension of the concepts of connectedness and
conservation of connectedness that underlie the generalized Archie's law for
<i>n</i> phases to the interpretation of the saturation exponent. It is shown that
the saturation exponent as defined originally by Archie arises naturally from
the generalized Archie's law. In the generalized Archie's law the saturation
exponent of any given phase can be thought of as formally the same as the
phase (i.e. cementation) exponent, but with respect to a reference subset of
phases in a larger <i>n</i>-phase medium. Furthermore, the connectedness of each
of the phases occupying a reference subset of an <i>n</i>-phase medium can be
related to the connectedness of the subset itself by <i>G</i><sub><i>i</i></sub> = <i>G</i><sub>ref</sub><i>S</i><sub><i>i</i></sub><sup><i>n</i><sub><i>i</i></sub></sup>. This leads naturally to the idea of the term <i>S</i><sub><i>i</i></sub><sup><i>n</i><sub><i>i</i></sub></sup> for each phase <i>i</i> being a fractional connectedness, where the fractional
connectednesses of any given reference subset sum to unity in the same way
that the connectednesses sum to unity for the whole medium. One of the
implications of this theory is that the saturation exponent of any phase can
be now be interpreted as the rate of change of the fractional connectedness
with saturation and connectivity within the reference subset. |
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| ISSN: | 1869-9510 1869-9529 |