Thermoelastic logging

1. A method for thermoelastic logging in a borehole of a subterranean formation, comprising:

generating, by a computer processor, a reference dispersion based on a borehole wave dispersion measurement of the borehole, wherein the reference dispersion represents far-field elastic properties in the subterranean formation;

analyzing, by the computer processor, a difference between the reference dispersion and the borehole wave dispersion measurement based on a thermoelastic model of the subterranean formation to generate an analysis result; and

determining, by the computer processor and based on the analysis result, a temperature dependent parameter of the subterranean formation.

2. The method of claim 1 , further comprising:

displaying the temperature dependent parameter of the subterranean formation.

3. The method of claim 1 , further comprising:

performing a field operation based at least on the temperature dependent parameter of the subterranean formation.

4. The method of claim 1 ,

wherein the temperature dependent parameter comprises a thermoelastic parameter of the subterranean formation.

5. The method of claim 1 , further comprising:

determining, based on the temperature dependent parameter, a temperature of the subterranean formation as a function of a radial distance from the borehole.

6. The method of claim 1 , further comprising:

generating, by varying a depth of a bottom hole assembly (BHA) in the borehole, a borehole log comprising the temperature dependent parameter as a function of a depth in the borehole, wherein the borehole wave dispersion measurement is obtained from the BHA; and

detecting a feature of the subterranean formation based on the borehole log.

7. The method of claim 6 , further comprising:

introducing borehole fluid into the borehole from a wellsite,

wherein the feature of the subterranean formation comprises a fracture containing the borehole fluid entered therein from the borehole,

wherein the borehole fluid and the subterranean formation have different temperatures to cause radially varying amounts of thermal stresses that affect propagation characteristics of elastic waves along an axis of the borehole, and

wherein the thermoelastic model models the thermal stresses, the propagation characteristics of the elastic waves, and the temperature dependent parameter of the subterranean formation.

8. The method of claim 1 , further comprising:

performing a steam injection operation using an injection well adjacent to the borehole;

identifying, based on the temperature dependent parameter, a location of a steam injection front of the steam injection operation; and

adjusting the steam injection operation based on the location of the steam injection front,

wherein the steam injection operation causes radially varying amounts of thermal stresses that affect propagation characteristics of elastic waves along an axis of the borehole, and

wherein the thermoelastic model models the thermal stresses, the propagation characteristics of the elastic waves, and the temperature dependent parameter of the subterranean formation.

9. A system for thermoelastic logging in a borehole of a subterranean formation, comprising:

a sonic tool in the borehole to obtain a borehole wave dispersion measurement of the borehole;

a processor and memory storing instructions, when executed by the processor comprising functionalities to:

generate a reference dispersion based on the borehole wave dispersion measurement, wherein the reference dispersion represents far-field elastic properties in the subterranean formation;

analyze a difference between the reference dispersion and the borehole wave dispersion measurement based on a thermoelastic model of the subterranean formation to generate an analysis result; and

determine, based on the analysis result, a temperature dependent parameter of the subterranean formation; and

a repository storing the borehole wave dispersion measurement.

10. The system of claim 9 , further comprising:

a display device configured to display the temperature dependent parameter of the subterranean formation.

11. The system of claim 9 , further comprising:

an apparatus configured to perform a field operation based at least on the temperature dependent parameter of the subterranean formation.

12. The system of claim 9 ,

wherein the temperature dependent parameter comprises a thermoelastic parameter of the subterranean formation.

13. The system of claim 9 , the instructions, when executed by the processor further comprising functionalities to:

determine, based on the temperature dependent parameter, a temperature of the subterranean formation as a function of a radial distance from the borehole.

14. The system of claim 9 , the instructions, when executed by the processor further comprising functionalities to:

generate, by varying a depth of a bottom hole assembly (BHA) in the borehole, a borehole log comprising the temperature dependent parameter as a function of a depth in the borehole, wherein the borehole wave dispersion measurement is obtained from the BHA; and

detect a feature of the subterranean formation based on the borehole log.

15. The system of claim 14 , further comprising:

a temperature sensor adjacent to the sonic tool and configured to measure a borehole fluid temperature of borehole fluid introduced into the borehole,

wherein the feature of the subterranean formation comprises a fracture containing the borehole fluid entered therein from the borehole,

wherein the borehole fluid temperature is different from a formation temperature of the subterranean formation to cause radially varying amounts of thermal stresses that affect propagation characteristics of elastic waves along an axis of the borehole, and

wherein the thermoelastic model models the borehole fluid temperature, the formation temperature, the thermal stresses, the propagation characteristics of the elastic waves, and the temperature dependent parameter of the subterranean formation.

16. The system of claim 14 , the instructions, when executed by the processor further comprising functionalities to:

identify, based on the temperature dependent parameter, a location of a steam injection front from an injection well adjacent to the borehole; and

adjust a steam injection operation of the injection well based on the location of the steam injection front,

wherein the steam injection operation causes radially varying amounts of thermal stresses that affect propagation characteristics of elastic waves along an axis of the borehole, and

wherein the thermoelastic model models the thermal stresses, the propagation characteristics of the elastic waves, and the temperature dependent parameter of the subterranean formation.

17. A non-transitory computer readable medium storing instructions for thermoelastic logging in a borehole of a subterranean formation, the instructions when executed causing a computer processor to:

generate a reference dispersion based on a borehole wave dispersion measurement of the borehole, wherein the reference dispersion represents far-field elastic properties in the subterranean formation;

analyze a difference between the reference dispersion and the borehole wave dispersion measurement based on a thermoelastic model of the subterranean formation to generate an analysis result; and

determine, based on the analysis result, a temperature dependent parameter of the subterranean formation.

18. The non-transitory computer readable medium of claim 17 , the instructions when executed further causing the computer processor to:

determine, based on the temperature dependent parameter, a temperature of the subterranean formation as a function of a radial distance from the borehole.

19. The non-transitory computer readable medium of claim 17 , the instructions when executed further causing the computer processor to:

generate, by varying a depth of a bottom hole assembly (BHA) in the borehole, a borehole log comprising the temperature dependent parameter as a function of a depth in the borehole, wherein the borehole wave dispersion measurement is obtained from the BHA; and

detect a feature of the subterranean formation based on the borehole log.

20. The non-transitory computer readable medium of claim 17 , the instructions when executed further causing the computer processor to:

identify, based on the temperature dependent parameter, a location of a steam injection front from an injection well adjacent to the borehole; and

adjust a steam injection operation of the injection well based on the location of the steam injection front,

wherein the steam injection operation causes radially varying amounts of thermal stresses that affect propagation characteristics of elastic waves along an axis of the borehole, and

wherein the thermoelastic model models the thermal stresses, the propagation characteristics of the elastic waves, and the temperature dependent parameter of the subterranean formation.