A new non-Archie model for pore structure: numerical experiments using digital rock models

Tortuosity is a key parameter for investigating the pore structure of sedimentary rock. The conventional model for calculating the tortuosity is derived from Archie's law which is only valid for one conductive phase contained in a porous rock. However, there have been increasingly cases to show the non-Archie phenomenon in instances where the rock matrix has extra conductive phases such as surface conductivity caused by the electrical double layer. Therefore, such model may be inapplicable in these cases and in calculations involving partial melting. We investigated the relation between formation factor and porosity (F-phi) over a wide range of porosities by the lattice-gas automata method (LGA) with the electrical double layer. The digital rock samples were constructed by packing up solid grains with different shapes and size distribution, as previously measured in the laboratory on real rock specimens. Our purpose was to identify the origin of non-Archie behaviour of the F-phi relation sometimes observed. The simulations show that Archie's law may only be an approximation of the F-phi relation in a high porosity range. Based on our LGA simulations and additional laboratory experimental data, we developed new equations for non-Archie F-phi relation and tortuosity potentially useful for improving the evaluation of pore structure.