Numerical simulation of resistivity and investigation of porosity exponent in carbonates

In carbonates, the petrophysical interpretation is strongly controlled by the porosity exponent used in Archie’s Law due to the variety of the pore types, the complexity of the pore geometry and the topology. Traditionally, the petrophysical model modifies the porosity exponent with consideration of the porosity based on experimental resistivity. Additionally, the porosity models can be used to predict porosity exponent based on the equivalent resistance network, in series or parallel or both. However, these models do not consider the intrinsic factors, affecting the porosity exponent, such as pore geometry and topology and simplify the arrangement of pore types. In order to further build the formulation between porosity exponent and these intrinsic factors for accurately predicting porosity exponent, non-destructive pore scale measurement-CT imaging is used to extract pore geometry and topology, and to determine the main pore types. At the same time measurements of porosity exponent in the lab can be used to calibrate the pore scale modelling and used to investigate the influence of the pore geometry, topology and pore type on the porosity exponent. It is found that the key factors affecting porosity exponent are the ratio of pore cross section area ratio to the pore throat cross sectional area ratio (PTAR) and Euler number representing the connectivity. With the increase of the PTAR and Euler number, the porosity exponent increases. Both of them are related to the pore types. Fracture-like (FT) pores can reduce the PTAR and Euler number resulting in the decrease of the formation factor, porosity exponent and the anisotropy while vuggy-like (VG) pores increase PTAR and Euler number resulting in the increase of porosity exponent with less influence on anisotropy. The effect on formation factor is related to the type of VG, whether connected or non-connected. In coquinas from the Morro do Chaves Formation (Lower Cretaceous, NE Brazil) there are many combinations of pore, pore shape and pore connectivity that make numerical modelling of resistivity in these rocks such a useful addition to help explain the laboratory measurements and add an understanding of the dominant pore structure which was found to vary from sample to sample. Some interesting concavo-convex pore systems have been identified