Looking Inside Pores: Polarization by Constrictivity or Pores

Abstract

Mathematical modeling of a little known model of induced polarization (IP) referred to as ``polarization caused by constrictivity of pores' was developed. As all pore structures in sediments are characterized by constrictivity of pores this model must be regarded as the general model of IP occurring in sediments containing no metals. Using heat equations mathematical modeling has been done for complex pore structures. It was shown that the IP processes are different at time off and time on and that there is a non-linear dependence between applied electrical current and IP amplitude. The duration of the polarization process t0 in pores is controlled by the transfer numbers and radii of the connected pores. After time t0 the electrical circuit ruptures and the potential difference between the pore ends becomes constant. Then the definition of the physical means 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'. Two phenomena control the amplitude of potential difference at switch on time: 1. Successive blockage of pores increases the resistivity of sediments and as a result the measured potential difference increases. 2. Excess concentration of electrolyte at the boundaries between pores with different radii provides an additional potential. However during the switch off time only the excess of electrolyte concentration is involved in the diffusion process which tends to level the ion concentrations along the pores. Therefore the physical phenomena of the IP effect that occurs at switch on and switch off time are different. This difference forms the basis of the mathematical consideration of a new model of the IP effect. The blockage of pore channels controls the electrical resistivity of sediments. This model will be used in the interpretation of IP data and laboratory measurements of petrophysical properties of sediments.