Method for estimating anisotropic mechanical properties of a reservoir using sonic logging data

1. A method for estimating elastic constants within a formation, the method comprising:

applying acoustic waves to the formation, wherein the formation is heterogeneous;

detecting acoustic waves to acquire acoustic data;

determining (i) at least one of elastic constant C 13 using a fast-dipole dispersion and elastic constant C 23 using a slow-dipole dispersion, (ii) elastic constant C 33 , (iii) at least one of elastic constant C 44 and elastic constant C 55 , and (iv) elastic constant C 66 using the acquired acoustic data;

determining elastic constant C 11 using (i) elastic constant C 33 , (ii) at least one of elastic constant C 44 and elastic constant C 55 , (iii) elastic constant C 66 , and (iv) a relationship between Thomsen parameter gamma and Thomsen parameterepsilon;

determining minimum and maximum horizontal stresses for the formation using (i) elastic constant C 11 , (ii) at least one of elastic constant C 13 and elastic constant C 23 , (iii) elastic constant C 33 , and (iv) elastic constant C 66 ; and

determining placement of a lateral wellbore along a vertical pilot well using the minimum and maximum horizontal stresses for the formation,

wherein the elastic constants C 11 , C 13 , C 23 , C 33 , C 44 , C 55 , and C 66 are in Voigt form.

2. The method of claim 1 , wherein (i) elastic constant C 13 is determined and (ii) elastic constant C 33 , (iii) elastic constant C 55 , and (iv) elastic constant C 66 are determined using a fast-dipole dispersion.

3. The method of claim 1 , wherein (i) elastic constant C 23 is determined and (ii) elastic constant C 33 , (iii) elastic constant C 44 , and (iv) elastic constant C 66 are determined using a slow-dipole dispersion.

4. The method of claim 1 , wherein elastic constant C 33 is determined using a measured compressional velocity.

5. The method of claim 1 , wherein elastic constant C 66 is determined using a Stoneley dispersion.

6. The method of claim 1 , further comprising:

determining a vertical Young's modulus, horizontal Young's modulus, a horizontal Poisson's ratio, and two vertical Poisson's ratios using (i) elastic constant C 11 , (ii) at least one of elastic constant C 13 and elastic constant C 23 , and (iii) elastic constant C 33 .

7. The method of claim 1 , wherein the acoustic waves are applied to the formation using a wellbore tool that is disposed within a wellbore that traverses the formation; and

acoustic waves are detected using the wellbore tool.

8. The method of claim 1 , wherein the formation is an unconventional hydrocarbon reservoir.

9. A method for estimating elastic constants within a formation, the method comprising:

applying acoustic waves to the formation, wherein the formation is heterogeneous;

detecting acoustic waves to acquire acoustic data;

determining (i) elastic constant C 11 , (ii) at least one of elastic constant C 13 using a fast-dipole dispersion and elastic constant C 23 using a slow-dipole dispersion, (iii) at least one of elastic constant C 44 and elastic constant C 55 , and (iv) elastic constant C 66 using the acquired acoustic data;

determining elastic constant C 33 using (i) elastic constant C 11 , (ii) at least one of elastic constant C 44 and elastic constant C 55 , (iii) elastic constant C 66 , and (iv) a relationship between Thomsen parameter gamma and Thomsen parameterepsilon;

determining a vertical Young's modulus, horizontal Young's modulus, a horizontal Poisson's ratio, and two vertical Poisson's ratios using (i) elastic constant C 11 , (ii) at least one of elastic constant C 13 and elastic constant C 23 , and (iii) elastic constant C 33 ; and

determining placement of completions along a lateral wellbore using at least one of the three Poisson's ratios,

wherein the elastic constants C 11 , C 13 , C 23 , C 33 , C 44 , C 55 , and C 66 are in Voigt form.

10. The method of claim 9 , wherein (i) elastic constant C 13 is determined and (ii) elastic constant C 44 , and (iii) elastic constant C 66 are determined using a fast-dipole dispersion.

11. The method of claim 9 , wherein (i) elastic constant C 23 is determined and (ii) elastic constant C 55 is determined using a slow-dipole dispersion.

12. The method of claim 9 , wherein elastic constant C 11 is determined using a measured compressional velocity.

13. The method of claim 9 , further comprising:

determining placement of fractures along a lateral wellbore using at least one of the three Poisson's ratios.

14. The method of claim 9 , wherein the acoustic waves are applied to the formation using a wellbore tool that is disposed within a wellbore that traverses the formation; and

acoustic waves are detected using the wellbore tool.

15. The method of claim 9 , wherein the formation is an unconventional hydrocarbon reservoir.

16. A system for estimating elastic constants within a formation, comprising:

a plurality of acoustic sources for applying acoustic waves to the formation wherein the formation is heterogeneous;

an array of receivers for detecting acoustic waves to acquire acoustic data;

a processor system having:

a memory to record waveforms of the acoustic waves; and

a processor used to evaluate the waveforms to determine (i) elastic constant C 11 , (ii) at least one of elastic constant C 13 using a fast-dipole dispersion and elastic constant C 23 using a slow-dipole dispersion, (iii) at least one of elastic constant C 44 and elastic constant C 55 , and (iv) elastic constant C 66 using the acquired acoustic data, to determine elastic constant C 33 using (i) elastic constant C 11 , (ii) at least one of elastic constant C 44 and elastic constant C 55 , (iii) elastic constant C 66 , and (iv) a relationship between Thomsen parameter gamma and Thomsen parameter epsilon, to determine a vertical Young's modulus, horizontal Young's modulus, a horizontal Poisson's ratio, and two vertical Poisson's ratios using (i) elastic constant C 11 , (ii) at least one of elastic constant C 13 and elastic constant C 23 , and (iii) elastic constant C 33 , and to determine placement of fractures along a lateral wellbore using at least one of the three Poisson's ratios,

wherein the elastic constants C 11 , C 13 , C 23 , C 33 , C 44 , C 55 , and C 66 are in Voigt form.