Complex pore geometry modeling by continuously varying inclusions (CI) method for elastic parameter prediction using inclusion models

1. A method for predicting elastic parameters of a subsurface, the method comprising:

generating models for changes in shear modulus and changes in bulk modulus of the subsurface as a combination of a host medium shear modulus and host medium bulk modulus and a plurality of inclusion shear moduli and inclusion bulk moduli, each inclusion shear modulus and inclusion bulk modulus comprising an unique inclusion geometry; and

using an inclusion-based rock physical model to solve the models for changes in shear modulus and changes in bulk modulus to predict an effective shear modulus of the subsurface and an effective bulk modulus of the subsurface;

wherein the effective shear module and the effective bulk module are used to generate an image of the subsurface, the image being usable for selecting drilling sites, monitoring well production and/or designing fracking operations.

2. The method of claim 1 , wherein each inclusion shear modulus and each inclusion bulk modulus contributes to changes in the shear modulus and changes in the bulk modulus independent of contributions from other inclusion shear and inclusion bulk modulus terms.

3. The method of claim 1 , wherein the generating of the models for changes in the shear modulus and changes in the bulk modulus further comprises modelling changes in the shear modulus and changes in the bulk modulus as a combination of a plurality of change terms, each change term comprising the host medium shear modulus and host medium bulk modulus and one of the plurality of inclusion shear moduli and inclusion bulk moduli.

4. The method of claim 3 , wherein each change term further comprises a volume fraction within the subsurface of the unique inclusion geometry of the inclusion shear modulus and inclusion bulk modulus in that change term.

5. The method of claim 4 , wherein the volume fractions of all change terms comprise a total volume of inclusions in the subsurface.

6. The method of claim 3 , wherein the combination comprises summation of the plurality of change terms.

7. The method of claim 3 , wherein:

the combination comprises an integral of the change terms over a continuous path parameter; and

the inclusion shear modulus and the inclusion bulk modulus comprising a function of the continuous path parameter.

8. The method of claim 7 , wherein the integral further comprises an inclusion phase density, the inclusion phase density comprising a function of the continuous path parameter.

9. The method of claim 8 , wherein the inclusion phase density conserves at least one of mass and pore volume in the subsurface.

10. The method of claim 1 , further comprising obtaining the host medium shear modulus and host medium bulk modulus.

11. The method of claim 1 , wherein the inclusion-based rock physics models comprise Kuster-Toksoz, differential effective medium or self-consistent approximation.

12. A computer-readable medium containing computer-executable code that when read by a computer causes the computer to perform a method for predicting elastic parameters of a subsurface, the method comprising:

generating models changes in shear modulus and changes in bulk modulus of the subsurface as a combination of a host medium shear modulus and host medium bulk modulus and a plurality of inclusion shear moduli and inclusion bulk moduli, each inclusion shear modulus and inclusion bulk modulus comprising an unique inclusion geometry; and

using an inclusion-based rock physical model to solve the models for changes in shear modulus and changes in bulk modulus to predict an effective shear modulus of the subsurface and an effective bulk modulus of the subsurface, wherein the effective shear module and the effective bulk module are used to generate an image of the subsurface, the image being usable for selecting drilling sites, monitoring well production and/or designing fracking operations.

13. The computer-readable medium of claim 12 , wherein the generating of the models for changes in the shear modulus and changes in the bulk modulus further comprises modelling changes in the effective shear modulus and changes in the effective bulk modulus as a combination of a plurality of change terms, each change term comprising the host medium shear modulus and host medium bulk modulus and one of the plurality of inclusion shear moduli and inclusion bulk moduli.

14. The computer-readable medium of claim 13 , wherein:

each change term further comprises a volume fraction within the subsurface of the unique inclusion geometry of the inclusion shear modulus and inclusion bulk modulus in that change term; and

the volume fractions of all change terms comprise a total volume of inclusions in the subsurface.

15. The computer-readable medium of claim 13 , wherein the combination comprises summation of the plurality of change terms.

16. The computer-readable medium of claim 13 , wherein:

the combination comprises an integral of the change terms over a continuous path parameter; and

the inclusion shear modulus and inclusion bulk modulus comprising a function of the continuous path parameter.

17. The computer-readable medium of claim 16 , wherein the integral further comprises an inclusion phase density, the inclusion phase density comprising a function of the continuous path parameter.

18. The computer-readable medium of claim 17 , wherein the inclusion phase density conserves at least one of mass and pore volume in the subsurface.

19. A computing system for predicting elastic parameters of a subsurface, the computing system comprising:

a storage device storing host medium shear modulus and host medium bulk modulus and a plurality of inclusion shear moduli and inclusion bulk moduli for the subsurface; and

a processor in communication with the storage device and configured to:

generate models for changes in shear modulus and changes in bulk modulus of the subsurface as a combination of a host medium shear modulus and host medium bulk modulus and a plurality of inclusion shear moduli and inclusion bulk moduli, each inclusion shear modulus and inclusion bulk modulus comprising an unique inclusion geometry; and

use an inclusion-based rock physical model to solve the models for changes in shear modulus and changes in bulk modulus to predict an effective shear modulus of the subsurface and an effective bulk modulus of the subsurface,

wherein the effective shear module and the effective bulk module are used to generate an image of the subsurface, the image being usable for selecting drilling sites, monitoring well production and/or designing fracking operations.

20. The computing system of claim 19 , wherein the generating of models for changes in the effective shear modulus and changes in the effective bulk modulus further comprises modelling changes in the shear modulus and changes in the bulk modulus as a combination a plurality of change terms, each change term comprising the host medium shear modulus and host medium bulk modulus and one of the plurality of inclusion shear moduli and inclusion bulk moduli;

the combination comprises an integral of the change terms over a continuous path parameter;

the inclusion shear modulus and inclusion bulk modulus comprising a function of the continuous path parameter; and

the integral further comprising an inclusion phase density, the inclusion phase density comprising a function of the continuous path parameter.