Resistivity measured by direct and alternating current: Why are they different?

Abstract

Mathematical modeling of a little known model of IP referred to as "induced polarization caused by constrictivity of pores" was developed. Polarization occurs in all types of rocks if surface areas and transfer numbers are different for connected pores. The duration of the polarization process depends on two parameters: pore radii of connected capillaries and transfer numbers. During the polarization process all contacts between pores of different transfer numbers will be blocked and the electrical current will flow through the remaining canals. Two phenomena control the amplitude of potential difference at time-on: 1. Successive blockage of pores increases the resistivity of sediments and results in increased measured potential difference. 2. Excess concentration of electrolyte at the boundaries between pores with different radii provides an additional potential. The amplitude of the potential difference (voltage) of such rocks not only depends on solutions filling pore spaces, porosity and tourtuosity of pores channels, but also on ion mobility, diffusion coefficient, and difference of transfer numbers. During time-on a voltage is occurred due to flowing currentUcurr (t) and excess concentrationUexcess (t) at the contacts. However during the time-off only the excess of concentrationUexcess (t) is involved in the diffusion process which tends to level the ion concentration along the pores. It was found that the measured chargeability is proportional to the porosity. Blockage of pores and excess/loss ions at the contacted pores control this physical parameter. However the relationship between resistivity and porosity is very complicated. Mathematical modeling and laboratory measurements both confirmed the membrane IP effect diminishing with increasing salinity of fluid filled pores of rocks. Membrane polarization does not exist on high frequency of electrical current. As a result the resistivity measured by direct and alternating current is different. The new algorithm was tested on laboratory measurements data showing its good agreement with theory. The calculation of pore size distribution using IP laboratory data has been presented. The definition of the membrane IP effect is: "Membrane IP is the successive blockage of inter-pore connections due to the excess distribution of ions during current flow".