Numerical and theoretical simulations of the dielectric properties of porous rocks

Accurate determination of the dielectric properties of porous rocks is important for the dielectric exploration methods in a range of applications from water resources to petroleum industry. Carefully controlled laboratory measurements offer the best way of obtaining the dielectric behaviors but they will require relatively large quantity of sample materials prepared in specific shapes, which is not always available. Numerical and theoretical simulations compensate for this weakness and can compute the dielectric dispersion at the pore-scale level on small fragments of rocks. However, whether consistent dielectric results can be obtained from the numerical computation and from the properly developed theoretical models still needs investigation. We introduced in this paper the numerical model based on the three-dimensional finite difference method (3D-FDM) and a range of theoretical models on basis of interfacial polarization for the calculation of the frequency dependent dielectric properties in porous rocks of complex geometry. The numerical and theoretical models were applied to a hypothetical porous rock with ideal shaped grains and to a real synthetic sandstone sample with complex pore and grain structure. Comparison of the simulation results from the two methods showed excellent agreement with each other with squared correlation coefficients better than R2 = 0.98 for both relative permittivity and conductivity of the two example rocks. The consistent numerical and theoretical results provide a complementary way for the numerical and theoretical models to work together for a better simulation of the dielectric properties of porous rocks.