High Pressure Electromagnetic Fractal Behaviour of Sedimentary Rocks

Abstract

The dependence of resistivity on pressure is well known in water saturated porous sedimentary rocks. A new electromagnetic fractal model has been employed successfully to study the fractal parameters for double layer polarisation in the low-to-intermediate frequency range. This model addresses the roughness of the pore space and it has been employed to study the over burden effects on the complex resistivity under in situ conditions in the frequency range 10Hz-100kHz and pressure range 1MPa-40MPa. This model includes three relaxation times: bulk relaxation, double layer relaxation and fractal relaxation of pore roughness surfaces; a grain ratio resistivity relating the resistivity of blocking grains to the electrolyte resistivity; the DC resistivity of the rock; the chargeability; and the fractal frequency exponent given by the fractal nature and roughness of the pore surfaces. The fractal parameters were obtained using a random search method to obtain the best simultaneous fittings for gain and phase experimental curves. The fractal parameters obtained were observed to respond differently at low, intermediate and elevated pressure levels, thus providing a mechanism to gain an insight into the physical processes occurring within the rocks. It is interesting to note that even when the conductivity curves do not show any significant variation, the fractal parameters obtained from both gain and phase curves show pronounced response to the variation of pressure. The encouraging results of this model demonstrate the possibilities for its use in understanding the behaviour of saturated porous rocks at elevated pressures.