Frequency Dispersion of Dielectric Permittivity and Electric Conductivity of Rocks via Two-Scale Homogenization of the Maxwell Equations

We evaluate effective dielectric permittivity and electric conductivity for water-saturated rocks based on a realistic model of a representative cell of the pore space which has periodical structure. We have applied the method of two-scale homogenization of the Maxwell equations, which results in up-scaling coupled equations at the microscale to equations valid at the macroscale. We have analyzed the interfacial Maxwell-Wagner dispersion effect and the Archie law as well.