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

1. A method of evaluating a volume of an earth formation wherein the volume comprises a fluid-saturated rock matrix including clay particles, the method comprising:

making measurements of complex permittivity at a plurality of frequencies using an electromagnetic tool in a borehole penetrating the earth;

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 C EXP applied to the corresponding permittivity of each of the plurality of components, where C EXP is constrained to be a positive rational number, the plurality of parameters comprising a value for C EXP generated as output from the inversion and at least one of: i) water saturation; and ii) resistivity of formation water.

2. The method of claim 1 comprising modeling for electrical effects caused by at least one of: i) a surface conductivity of the clay particles; and ii) a textural property of the clay particles.

3. The method of claim 1 wherein the plurality of parameters comprises at least one of: i) an additional electrical parameter of the volume; and ii) a textural parameter of the volume.

4. The method of claim 1 , wherein the mixing model is derived from a relationship of an effective permittivity of the volume to a corresponding volumetric factor and a corresponding permittivity of each of a plurality of components of the volume.

5. The method of claim 4 , wherein the components comprise at least formation water and at least one of: i) the rock matrix of the formation; and ii) formation hydrocarbons.

6. The method of claim 5 , wherein the plurality of parameters comprises a volumetric factor for at least the formation water and at least one of: i) the rock matrix of the formation; and ii) the formation hydrocarbons.

7. The method of claim 1 , further comprising:

using at least one processor to estimate an effective permittivity and an effective conductivity of the volume.

8. The method of claim 7 , further comprising:

estimating the at least one parameter of interest in dependence upon the effective permittivity; the effective conductivity; an estimated porosity; and an estimated temperature.

9. The method of claim 8 , further comprising:

estimating a permittivity of a rock matrix within the volume using at least one of: i) lithology information, and ii) a volumetric analysis of the volume.

10. The method of claim 1 wherein the at least one parameter of interest comprises at least one of: i) cation exchange capacity (CEC);

ii) a textural parameter of the clay particles; iii) permittivity of formation water; iv) clay type of clay particles.

11. The method of claim 4 , wherein the model relates dispersion between the measurements to the plurality of parameters of interest.

12. The method of claim 1 , wherein the plurality of parameters of interest comprise resistivity of formation water, water saturation, and permittivity of the rock matrix; and wherein estimating the plurality of parameters of interest comprises using the measurements to perform an inversion for a value of the resistivity of formation water, a value of the water saturation, a value of the permittivity of the rock matrix, and a value of the C EXP simultaneously.

13. The method of claim 1 , further comprising using a stochastic correlation library correlating the plurality of parameters of interest to a property of the clay particles to estimate the property.

14. The method of claim 1 , further comprising:

conveying the electromagnetic tool in the borehole.

15. The method of claim 1 , wherein the electromagnetic tool uses electrical induction.

16. The method of claim 1 , wherein estimating the plurality of parameters of interest comprises using measurements from five different frequencies in an inversion.

17. 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 C EXP applied to the corresponding permittivity of each of the plurality of components, where C EXP 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.