Accuracy of formation factors for three-dimensional pore-scale images of geo-materials estimated by renormalization technique

The formation factor, the dimensionless electric resistivity of porous rock/sediment saturated with conductive fluid, is an important quantity in geophysical exploration for petroleum reservoirs and groundwater aquifers. The renormalization technique is a promising approximation method for the quick estimation of the formation factors from large three-dimensional images of porous geo-materials obtained by X-ray microtomography. In the present study, we applied the renormalization technique to various pore-scale image sets of real geo-materials (sandstones, pumice, lava, and sandy sediments). The purpose is to explore the factors controlling the estimation accuracy of the formation factor. The results revealed that the accuracy increases with increasing (i) porosity, (ii) degree of the pore elongation along the direction of the applied electric field, and (iii) size of the initial subsystem with which the renormalization step starts and with decreasing (iv) pore or grain size. Most importantly, a high degree of elongation of the pore structure along the applied field ensures good accuracy even if the porosity is low, the initial subsystem is small, and the pore or grain size is large.