New model of polarization of rocks: Theory and application
Mathematical modeling of a little known model of induced polarization (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. During the polarization process, all contacts between pores of different transfer numbers will be blocked and the electrical current will flow through the remaining channels. Diffusion equations with different specified boundary conditions for time-on and time-off have been used to develop the base of this model. The new algorithm was tested on laboratory measurements. Several samples were selected: shale, mudstone, tillite, hematite, lava, and manganese ore. Each theoretical model includes pores of more than 40 different sizes sporadically distributed in the sample. The obtained data show good agreement with theory and provide new information about pore size distribution in samples, prevalent pore radius, and effect of anisotropy.
Bibliogr. 16 poz.
- Anderson, L.A., and G.V. Keller (1964), A study in induced polarization, Geophysics 29, 5, 848-864.
- Bockris, J. O’M., and A.K.N. Reddy (1998), Modern Electrochemistry 1, 2nd ed., Ionics, Plenum Press, New York, 769 pp.
- Evans, D.A.D., J. Gutzmer, N.J. Beukes, and J.L. Kirschvink (2001), Paleomagnetic constraints on ages of mineralization in the Kalahari manganese field, South Africa, Econ. Geol. 96, 3, 621-631.
- Fridrikhsberg, D.A., and Yu.P. Shishkin (1972), Calculation of Φ1-potential and specific conductivity of double electric layer. In: D.A. Fridrikhsberg (ed.), Electro-Surface Phenomena in Disperse Systems, Moscow, Nedra, 3-15 (in Russian).
- Ishido, T., and H. Mizutani (1981), Experimental and theoretical basis of electrokinetic phenomena in rock-water systems and its applications to geophysics, J. Geophys. Res. 86, B3, 1763-1775.
- Kobranova, V.N. (1986), Petrophysics, Nedra, Moscow, 392 pp. (in Russian).
- Kormiltsev, V.V. (1995), Electrokinetical phenomena in porous rocks, AN SSSR, Ural Branch, Sverdlovsk, 192-B95 (in Russian).
- Koshlyakov, N.S., E.B. Gliner, and M.M. Smirnov (1970), Partial Differentiation of Equations in Mathematical Physics, Vysshaya Shkola, Moscow, 710 pp. (in Russian).
- Marshall, D.J., and T.R. Madden (1959), Induced polarization, a study of its causes, Geophysics 24, 4, 790-816.
- Pipe, H., L. Riere, and J.R. Schopper (1987), Theory of semi-similar network structures in sedimentary and igneous rocks and their investigations with microscopical and physical methods, J. Microscopy 2, 121-147.
- Schön, J. (1996), Physical Properties of Rocks: Fundamentals and Principles of Petrophysics. Handbook of Geophysical Exploration. Vol. 18, New York, Pergamon Press Inc., 583 pp.
- Titov, K., V. Komarov, V. Tarasov, and A. Levitski (2002), Theoretical and experimental study of time domain-induced polarization in water saturated sands, J. Appl. Geophys. 50, 4, 417-433.
- Ward, S.H. (1990), Resistivity and induced polarization methods. In: S.H. Ward (ed.), Geotechnical and Environmental Geophysics – Investigation in Geophysics No. 5, Vol. 1, SEG, 169-189.
- Zadorozhnaya, V.Yu. (2008), Resistivity measured by direct and alternating current: why are they different? Adv. Geosci. 19, 45-59.
- Zadorozhnaya, V.Yu., and M.E. Hauger (2007), Membrane polarization on rocks and measured resistivity. In: V.V. Spichak (ed.), Earth Electromagnetic Investigations. III International School-Seminar on Electromagnetic Sounding of the Earth (EMS-2007), Lecture, Moscow, 149-167.
- Zadorozhnaya, V.Yu., and M.H. Hauger (2009), Mathematical modeling of membrane polarization occurring in rocks due to applied electrical field, Izv. –Phys. Solid Earth 45, 12, 1038-1054.