--> Complex Resistivity Spectra and Fractal Pore Geometries in Relation to Flow Properties in Carbonate Rocks
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Complex Resistivity Spectra and Fractal Pore Geometries in Relation to Flow Properties in Carbonate Rocks

Abstract

Amplitude and Previous HitphaseNext Hit shift of complex resistivity are analyzed on 150+ brine-saturated carbonate core plug samples in a log sweep of 15 frequency steps from 0.1 – 100,000 Hz at varying reservoir pressures. In the measured dolomites the dispersive behavior of resistivity is between 100 – 100,000 Hz and is directly related to the porosity of the sample. Spectral analysis of complex resistivity is the study of the dispersive behavior of resistivity that is the change of resistance of a medium at different frequencies. Complex resistivity consists of the amplitude and the Previous HitphaseNext Hit shift, which is the delay between the induced voltage signal and the resulting current signal. The delay can be attributed to polarization effects of a medium that is exposed to an alternating current. The Previous HitmagnitudeNext Hit of polarization is dependent on surface chemical and pore geometrical properties. The samples of this study are all carbonates, and, thus, surface chemistry effects can be omitted, leaving the pore geometry as sole influencing factor. Consequently, the dispersion of complex resistivity can be used to estimate pore geometric and hence rock petrophysical properties. For example, in the high-porosity samples, amplitudes are low across the frequency Previous HitspectrumNext Hit. In the low-porosity samples, amplitudes are high but drop significantly at frequencies above 1,000 Hz. Previous HitPhaseNext Hit shifts display more variance in all of the samples. Focusing on the 100 – 2,000 Hz range we see a characteristic slope in the Previous HitphaseTop shift dispersion, which correlates with the permeability of the sample. Using the slope, porosity, and cementation factor, calculated from the amplitude at 720 Hz, we are able to predict permeability with high correlation coefficient of R2 = 0.82. Additionally, pore geometries of the samples are quantified and parameterized with digital image analysis (DIA) on thin-sections. We observe trends of larger and less complex pores resulting in higher cementation factors. The extracted pores are also used to analyze the pore size distribution, which shows a power-law behavior in all samples when plotted on log-log scale using non-linear binning, indicating fractal scaling of the pore space.