Investigating Textural Controls on Archie’s Porosity Exponent Using Process-Based, Pore-Scale Modelling

Archie’s law is an important empirical relationship linking the electrical resistivity of geological materials to their porosity. It has been found experimentally that the porosity exponent  m  in Archie’s law in sedimentary rocks might be related to the degree of cementation, and therefore  m  is termed as “cementation factor” in most literatures. Despite it has been known for many years, there is lack of well-accepted physical interpretations of the porosity exponent. Some theoretical and experimental evidences have also shown that  m  may be controlled by the particle and/or pore shape. In this study, we conduct a pore-scale modeling of the porosity exponent that incorporates different geological processes. The evolution of  m  of eight synthetic samples with different particle sizes and shapes are calculated during two geological processes, i.e., compaction and cementation. The numerical results show that in dilute conditions,  m  is controlled by the particle shape. As the samples deviate from dilute conditions,  m  increases gradually due to the strong interaction between particles. When the samples are at static equilibrium,  m  is noticeably larger than its values at dilution condition. The numerical simulation results also show that both geological compaction and cementation induce a significant increase in  m . In addition, the geometric characteristics of these samples (e.g., pore space/throat size, and their distributions) during compaction and cementation are also calculated. Preliminary analysis shows a unique correlation between the pore size broadness and porosity exponent for all eight samples. However, such a correlation is not found between  m  and other geometric characteristics.