### Abstract

Many types of mixing model are used widely within the earth sciences to determine the electrical properties of porous media consisting of solid and fluid phases of known conductivities, volume fractions and distributions (i.e. phase connectivities). Most models are valid for two or more conducting phases. However, of the simple models only Archie's law includes a Variable term, the Archie cementation exponent m, that describes the connectivity of the phases. Unfortunately, Archie's law is only valid for one conducting phase distributed within a non-conducting phase, which makes it inapplicable in instances where the rock matrix has a significant conductivity such as for day-rich rocks and in calculations involving partial melting. More complex models exist which account for multiple conducting phases and control over phase conductivity. We have adapted the conventional Archie's law to produce a simple modified Archie's law that can be used with two conducting phases of any conductivity and any volume fraction, while retaining the ability to model variable connectivities within those phases that result from variations in their distribution. The modified model has two exponents (m and p) that describe the connectivity of each of the two phases. The exponents are related through an equation that depends also on the volume fractions of the two phases. The modified and the conventional versions of Archie's law have been tested on a granular analogue porous medium with a conducting matrix and a pore space saturated with a range of saline fluids with different salinities and conductivities. The new model describes the experimentally determined electrical behaviour of the system extremely well, improving greatly on the conventional Archie's law. (C) 2000 Elsevier Science B.V. All rights reserved.

Original language | English |
---|---|

Pages (from-to) | 369-383 |

Number of pages | 15 |

Journal | Earth and Planetary Science Letters |

Volume | 180 |

Publication status | Published - 2000 |

### Keywords

- Archie's law
- electrical conductivity
- partial melting
- mixing
- models
- ELECTRICAL-CONDUCTIVITY
- DIELECTRIC-CONSTANT
- SEDIMENTARY-ROCKS
- POROUS-MEDIA
- UPPER-MANTLE
- CRUST
- PYRENEES
- BOUNDS
- MODEL
- SANDS

### Cite this

*Earth and Planetary Science Letters*,

*180*, 369-383.

**A modified Archie's law for two conducting phases.** / Glover, P W J ; Hole, M J ; Pous, J .

Research output: Contribution to journal › Article

*Earth and Planetary Science Letters*, vol. 180, pp. 369-383.

}

TY - JOUR

T1 - A modified Archie's law for two conducting phases

AU - Glover, P W J

AU - Hole, M J

AU - Pous, J

PY - 2000

Y1 - 2000

N2 - Many types of mixing model are used widely within the earth sciences to determine the electrical properties of porous media consisting of solid and fluid phases of known conductivities, volume fractions and distributions (i.e. phase connectivities). Most models are valid for two or more conducting phases. However, of the simple models only Archie's law includes a Variable term, the Archie cementation exponent m, that describes the connectivity of the phases. Unfortunately, Archie's law is only valid for one conducting phase distributed within a non-conducting phase, which makes it inapplicable in instances where the rock matrix has a significant conductivity such as for day-rich rocks and in calculations involving partial melting. More complex models exist which account for multiple conducting phases and control over phase conductivity. We have adapted the conventional Archie's law to produce a simple modified Archie's law that can be used with two conducting phases of any conductivity and any volume fraction, while retaining the ability to model variable connectivities within those phases that result from variations in their distribution. The modified model has two exponents (m and p) that describe the connectivity of each of the two phases. The exponents are related through an equation that depends also on the volume fractions of the two phases. The modified and the conventional versions of Archie's law have been tested on a granular analogue porous medium with a conducting matrix and a pore space saturated with a range of saline fluids with different salinities and conductivities. The new model describes the experimentally determined electrical behaviour of the system extremely well, improving greatly on the conventional Archie's law. (C) 2000 Elsevier Science B.V. All rights reserved.

AB - Many types of mixing model are used widely within the earth sciences to determine the electrical properties of porous media consisting of solid and fluid phases of known conductivities, volume fractions and distributions (i.e. phase connectivities). Most models are valid for two or more conducting phases. However, of the simple models only Archie's law includes a Variable term, the Archie cementation exponent m, that describes the connectivity of the phases. Unfortunately, Archie's law is only valid for one conducting phase distributed within a non-conducting phase, which makes it inapplicable in instances where the rock matrix has a significant conductivity such as for day-rich rocks and in calculations involving partial melting. More complex models exist which account for multiple conducting phases and control over phase conductivity. We have adapted the conventional Archie's law to produce a simple modified Archie's law that can be used with two conducting phases of any conductivity and any volume fraction, while retaining the ability to model variable connectivities within those phases that result from variations in their distribution. The modified model has two exponents (m and p) that describe the connectivity of each of the two phases. The exponents are related through an equation that depends also on the volume fractions of the two phases. The modified and the conventional versions of Archie's law have been tested on a granular analogue porous medium with a conducting matrix and a pore space saturated with a range of saline fluids with different salinities and conductivities. The new model describes the experimentally determined electrical behaviour of the system extremely well, improving greatly on the conventional Archie's law. (C) 2000 Elsevier Science B.V. All rights reserved.

KW - Archie's law

KW - electrical conductivity

KW - partial melting

KW - mixing

KW - models

KW - ELECTRICAL-CONDUCTIVITY

KW - DIELECTRIC-CONSTANT

KW - SEDIMENTARY-ROCKS

KW - POROUS-MEDIA

KW - UPPER-MANTLE

KW - CRUST

KW - PYRENEES

KW - BOUNDS

KW - MODEL

KW - SANDS

M3 - Article

VL - 180

SP - 369

EP - 383

JO - Earth and Planetary Science Letters

JF - Earth and Planetary Science Letters

SN - 0012-821X

ER -