A modified Archie’s law for two conducting phases

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 clay-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.