Determination of shale content of formation from dispersive multi-frequency dielectric measurements

An apparatus for evaluating a volume of an earth formation wherein the volume comprises a fluid-saturated rock matrix including clay particles, the apparatus comprising:

• a carrier configured to be conveyed in a borehole penetrating the earth formation;
• an electromagnetic tool disposed on the carrier and configured to make measurements of complex permittivity of a volume of the earth formation proximate the tool at a plurality of frequencies;
• and
• at least one processor configured to:
• estimating a plurality of parameters of interest simultaneously by performing an inversion using the measurements at the plurality of frequencies and a mixing model accounting for electrical effects on the measurements caused by the clay particles, wherein the mixing model relates the effective permittivity of the volume to a function of the corresponding permittivity of each of a plurality of components of the volume, the function of the corresponding permittivity of each of the plurality of components of the volume comprising a root of degree CEXP applied to the corresponding permittivity of each of the plurality of components, where CEXP is constrained to be a positive rational number, the plurality of parameters comprising a value for CEXP generated as output from the inversion and at least one of:
• i) water saturation;
• and ii) resistivity of formation water.