Claims
- 1. A method of measuring a nonlinear property of an earth formation traversed by a borehole having borehole fluid, by utilizing a sonic logging tool having at least one of a monopole and a dipole source, and at least one sonic detector, said method comprising:
- a) at a location in the borehole which is at a first pressure, using the sonic logging tool to generate and measure a first frequency dependent velocity of a Stoneley wave (v.sub.ref.sup.Stoneley);
- b) pressurizing the borehole at said location in the borehole to a second pressure different than said first pressure;
- c) using the sonic logging tool to generate and measure a second frequency dependent velocity of a Stoneley wave (v.sup.Stoneley);
- d) determining an indication of a nonlinear parameter of the earth formation by determining a fractional change (v.sup.Stoneley -v.sub.ref .sup.Stoneley)/v.sub.ref.sup.Stoneley in said Stoneley wave velocities, and subtracting from said fractional change in said Stoneley wave velocities a component related to the borehole fluid and a component related to linear aspects of the formation to provide a nonlinear formation component.
- 2. A method according to claim 1, wherein:
- said nonlinear formation component is provided substantially according to an equation
- (v.sup.Stoneley -v.sub.ref.sup.Stoneley)/v.sub.ref.sup.Stoneley =C.sub.1 N.sub.1 +C.sub.2 N.sub.2 +.DELTA.v/v.vertline..sub.fluid +.DELTA.v/v.vertline..sub.linear
- where .DELTA.P is the difference in pressure between said first pressure and said second pressure, .DELTA.v/v.vertline..sub.linear is said component related to linear aspects of the formation, .DELTA.v/v.vertline..sub.fluid is said component related to the borehole fluid, C.sub.1 and C.sub.2 are volume integrals which are a function of frequency and are calculable in terms of a Stoneley wave solution in an ambient state of the formation, and N.sub.1 and N.sub.2 are nonlinear constants of the formation.
- 3. A method according to claim 2, further comprising:
- solving said equation for N.sub.1 and N.sub.2 by obtaining values for v.sup.Stoneley, v.sub.ref.sup.Stoneley, C.sub.1 and C.sub.2 for at least a first frequency (f1) and a second frequency (f2).
- 4. A method according to claim 3, wherein:
- at least one of said first and second frequencies is chosen from a frequency band of 2.5 kHz to 7 kHz.
- 5. A method according to claim 3, wherein:
- said solving said equation comprises conducting a multifrequency inversion according to AX=B where ##EQU12##
- 6. A method according to claim 2, further comprising:
- measuring a first shear wave velocity and a first compressional wave velocity at said first pressure, wherein C.sub.1 is determined utilizing said first shear wave velocity and said first compressional wave velocity; and
- measuring a second shear wave velocity and a second compressional wave velocity at said second pressure, wherein C.sub.2 is determined utilizing said second shear wave velocity and said second compressional wave velocity.
- 7. A method according to claim 3, further comprising:
- obtaining a database of experimental data relating, in a plurality of other formations, stress in said plurality of other formations to squares of shear wave velocities in said other formations; and
- utilizing said nonlinear constants and said database of experimental data to find at least one of
- (i) stress in said formation, and
- (ii) additional stress required to fracture said formation.
- 8. A method according to claim 7, further comprising:
- choosing from said database of experimental data, a stress-shear velocity squared curve relating to a formation having a lithology substantially similar to the formation in which the logging tool is located; and
- finding a value relating to a slope of said curve in order to find a point along said curve by utilizing said nonlinear constants, Young's modulus for the formation in an ambient reference state, Poisson's ratio for the formation in an ambient reference state, and values of linear parameters of the formation, said point along said curve providing an indication of stress in the formation.
- 9. A method according to claim 9, wherein:
- said value relating to a slope of said curve is found according to at least one of equations ##EQU13## and equations ##EQU14## where V.sub.12 and V.sub.13 are shear wave velocities in said formation having a lithology substantially similar to the formation in which the logging tool is located along a first direction ("1") and polarized along perpendicular directions thereto ("2" and "3" respectively), S is the uniaxial stress along the one of the perpendicular directions, Y is Young's modulus, and .nu. is Poisson's ratio.
- 10. A method of measuring a nonlinear property of an earth formation traversed by a borehole having borehole fluid, by utilizing a sonic logging tool having at least one of a monopole and a dipole source, and at least one sonic detector, said method comprising:
- a) at a location in the borehole which is at a first pressure, using the sonic logging tool to generate and measure a first frequency dependent velocity of a flexural wave (v.sub.ref.sup.flexural);
- b) pressurizing the borehole at said location in the borehole to a second pressure different than said first pressure;
- c) using the sonic logging tool to generate and measure a second frequency dependent velocity of a flexural wave (v.sup.flexural);
- d) determining an indication of a nonlinear parameter of the earth formation by determining a fractional change (v.sup.flexural -v.sub.ref.sup.flexural) /v.sub.ref.sup.flexural in said flexural wave velocities, and subtracting from said fractional change in said flexural wave velocities a component related to the borehole fluid and a component related to linear aspects of the formation to provide a nonlinear formation component.
- 11. A method according to claim 10, wherein:
- said nonlinear formation component is provided substantially according to an equation
- (v.sup.flexural -v.sub.ref.sup.flexural)/v.sub.ref.sup.flexural =D.sub.1 N.sub.1 +D.sub.2 N.sub.2 +.DELTA.v/v.vertline..sub.fluid +.DELTA.v/v.vertline..sub.linear
- where .DELTA.P is the difference in pressure between said first pressure and said second pressure, .DELTA.v/v.vertline..sub.linear is said component related to linear aspects of the formation, .DELTA.v/v.vertline..sub.fluid is said component related to the borehole fluid, D.sub.1 and D.sub.2 are volume integrals which are a function of frequency and are calculable in terms of a flexural wave solution in an ambient state of the formation, and N.sub.1 and N.sub.2 are nonlinear constants of the formation.
- 12. A method according to claim 11, further comprising:
- solving said equation for N.sub.1 and N.sub.2 by obtaining values for v.sup.flexural, v.sub.ref.sup.flexural, D.sub.1, and D.sub.2 for at least a first frequency (f1) and a second frequency (f2).
- 13. A method according to claim 12, wherein:
- at least one of said first and second frequencies is chosen from a frequency band of 3.5 kHz to 6 kHz.
- 14. A method according to claim 12, wherein:
- said solving said equation comprises conducting a multifrequency inversion according to AX=B where ##EQU15##
- 15. A method according to claim 11, further comprising:
- measuring a first shear wave velocity and a first compressional wave velocity at said first pressure, wherein D.sub.1 is determined utilizing said first shear wave velocity and said first compressional wave velocity; and
- measuring a second shear wave velocity and a second compressional wave velocity at said second pressure, wherein D.sub.2 is determined utilizing said second shear wave velocity and said second compressional wave velocity.
- 16. A method according to claim 12, further comprising:
- obtaining a database of experimental data relating, in a plurality of other formations, stress in said plurality of other formations to squares of shear wave velocities in said other formations; and
- utilizing said nonlinear constants and said database of experimental data to find at least one of
- (i) stress in said formation, and
- (ii) additional stress required to fracture said formation.
- 17. A method according to claim 16, further comprising:
- choosing from said database of experimental data, a stress-shear velocity squared curve relating to a formation having a lithology substantially similar to the formation in which the logging tool is located; and
- finding a value relating to a slope of said curve in order to find a point along said curve by utilizing said nonlinear constants, Young's modulus for the formation in an ambient reference state, Poisson's ratio for the formation in an ambient reference state, and values of linear parameters of the formation, said point along said curve providing an indication of stress in the formation.
- 18. A method according to claim 17, wherein:
- said value relating to a slope of said curve is found according to at least one of equations ##EQU16## and equations ##EQU17## where V.sub.12 and V.sub.13 are shear wave velocities in said formation having a lithology substantially similar to the formation in which the logging tool is located along a first direction ("1") and polarized along perpendicular directions thereto ("2" and "3" respectively), S is the uniaxial stress along the one of the perpendicular directions, Y is Young's modulus, and .gamma. is Poisson's ratio.
- 19. Apparatus for measuring a nonlinear property of an earth formation traversed by a borehole having borehole fluid therein, comprising:
- a) a sonic borehole tool with a sonic source which generates a first Stoneley wave in the borehole with said borehole at a first pressure, and a sonic detector, wherein said sonic borehole measures an indication of a first frequency dependent velocity of said first Stoneley wave (v.sub.ref.sup.Stoneley) to provide first measurements;
- b) borehole pressurizing means for pressurizing the borehole at a location of said sonic borehole tool in the borehole to a second pressure different than said first pressure, wherein said sonic source of said sonic borehole logging tool generates a second Stoneley wave, and said sonic borehole tool measures indications of a second frequency dependent velocity of said second Stoneley wave (v.sup.Stoneley) with said borehole pressurized at said second pressure to provide second measurements;
- d) processing means for obtaining said first measurements and said second measurements and for determining therefrom an indication of a nonlinear parameter of the earth formation by determining a fractional change (v.sup.Stoneley -v.sub.ref.sup.Stoneley)/v.sub.ref.sup.Stoneley in said Stoneley wave velocities, and subtracting from said fractional change in said Stoneley wave velocities a component related to the borehole fluid and a component related to linear aspects of the formation to provide a nonlinear formation component.
- 20. Apparatus according to claim 19, wherein:
- said nonlinear formation component is determined by said processing means substantially according to an equation
- (v.sup.Stoneley -v.sub.ref.sup.Stoneley)/v.sub.ref.sup.Stoneley =C.sub.1 N.sub.1 +C.sub.2 N.sub.2 +.DELTA.v/v.vertline..sub.fluid +.DELTA.v/v.vertline..sub.linear
- where .DELTA.P is the difference in pressure between said first pressure and said second pressure, .DELTA.v/v.vertline..sub.linear is said component related to linear aspects of the formation, .DELTA.v/v.vertline..sub.fluid is said component related to the borehole fluid, C.sub.1 and C.sub.2 are volume integrals which are a function of frequency and are calculable in terms of a Stoneley wave solution in an ambient state of the formation, and N.sub.1 and N.sub.2 are nonlinear constants of the formation.
- 21. Apparatus according to claim 20, wherein:
- said processing means solves said equation for N.sub.1 and N.sub.2 by obtaining values for v.sup.Stoneley, v.sub.ref.sup.Stoneley, and C.sub.2 for at least a first frequency (f1) and a second frequency (f2).
- 22. Apparatus according to claim 21, wherein:
- said processing means solves said equation by conducting a multifrequency inversion according to AX=B where ##EQU18##
- 23. Apparatus according to claim 20 wherein:
- said sonic source generates a first shear wave and a first compressional wave at said first pressure and a second shear wave and a second compressional wave at said second pressure, and sonic detector detects said first shear wave, said first compressional wave, said second shear wave, and said second compressional wave, and
- said processing means determines a first shear wave velocity and a first compressional wave velocity velocity and determines C.sub.1 utilizing said first shear wave velocity and said first compressional wave velocity, and said processing means determines a second shear wave velocity and a second compressional wave velocity, and determines C.sub.2 utilizing said second shear wave velocity and said second compressional wave velocity.
- 24. Apparatus according to claim 21, further comprising:
- a database of experimental data relating, in a plurality of other formations, stress in said plurality of other formations to squares of shear wave velocities in said other formations, wherein
- said processing means utilizes said nonlinear constants and said database of experimental data to find at least one of
- (i) stress in said formation, and
- (ii) additional stress required to fracture said formation.
- 25. Apparatus according to claim 19, wherein:
- said borehole pressurizing means comprises first and second inflatable packer means on said sonic borehole tool with said sonic source and sonic receiver located between said first and second inflatable packers means, said first and second inflatable packer means for inflating to contact and seal with a wall of the borehole, and
- said borehole pressurizing means further includes a fluid storage means for storing fluid in said sonic borehole tool, and a fluid injection means coupled to said fluid storage means for injecting said fluid into said borehole when said first and second inflatable packer means are inflated.
- 26. Apparatus for measuring a nonlinear property of an earth formation traversed by a borehole having borehole fluid therein, comprising:
- a) a sonic borehole tool with a sonic source which generates a first flexural wave in the borehole with said borehole at a first pressure, and a sonic detector, wherein said sonic borehole measures an indication of a first frequency dependent velocity of said first flexural wave (v.sub.ref.sup.flexural) to provide first measurements;
- b) borehole pressurizing means for pressurizing the borehole at a location of said sonic borehole tool in the borehole to a second pressure different than said first pressure, wherein said sonic source of said sonic borehole logging tool generates a second flexural wave, and said sonic borehole tool measures indications of a second frequency dependent velocity of said second flexural wave (v.sup.flexural) with said borehole pressurized at said second pressure to provide second measurements;
- d) processing means for obtaining said first measurements and said second measurements and for determining therefrom an indication of a nonlinear parameter of the earth formation by determining a fractional change (v.sup.flexural -v.sub.ref.sup.flexural)/v.sub.ref.sup.flexural in said flexural wave velocities, and subtracting from said fractional change in said flexural wave velocities a component related to the borehole fluid and a component related to linear aspects of the formation to provide a nonlinear formation component.
- 27. Apparatus according to claim 26, wherein:
- said nonlinear formation component is determined by said processing means substantially according to an equation
- (v.sup.flexural -v.sub.ref.sup.flexural)/v.sub.ref.sup.flexural =D.sub.1 N.sub.1 +D.sub.2 N.sub.2 +.DELTA.v/v.vertline..sub.fluid +.DELTA.v/v.vertline..sub.linear
- where .DELTA.P is the difference in pressure between said first pressure and said second pressure, .DELTA.v/v.vertline..sub.linear is said component related to linear aspects of the formation, .DELTA.v/v.vertline..sub.fluid is said component related to the borehole fluid, D.sub.1 and D.sub.2 are volume integrals which are a function of frequency and are calculable in terms of a flexural wave solution in an ambient state of the formation, and N.sub.1 and N.sub.2 are nonlinear constants of the formation.
- 28. Apparatus according to claim 27, wherein:
- said processing means solves said equation for N.sub.1 and N.sub.2 by obtaining values for v.sup.flexural, v.sub.ref.sup.flexural, D.sub.1, and D.sub.2 for at least a first frequency (f1) and a second frequency (f2).
- 29. Apparatus according to claim 28, wherein:
- said processing means solves said equation by conducting a multifrequency inversion according to AX=B where ##EQU19##
- 30. Apparatus according to claim 27, wherein:
- said sonic source generates a first shear wave and a first compressional wave at said first pressure and a second shear wave and a second compressional wave at said second pressure, and sonic detector detects said first shear wave, said first compressional wave, said second shear wave, and said second compressional wave, and
- said processing means determines a first shear wave velocity and a first compressional wave velocity velocity and determines D.sub.I utilizing said first shear wave velocity and said first compressional wave velocity, and said processing means determines a second shear wave velocity and a second compressional wave velocity, and determines D.sub.2 utilizing said second shear wave velocity and said second compressional wave velocity.
- 31. Apparatus according to claim 28, further comprising: a database of experimental data relating, in a plurality of other formations, stress in said plurality of other formations to squares of shear wave velocities in said other formations, wherein
- said processing means utilizes said nonlinear constants and said database of experimental data to find at least one of
- (i) stress in said formation, and
- (ii) additional stress required to fracture said formation.
- 32. Apparatus according to claim 26, wherein:
- said borehole pressurizing means comprises first and second inflatable packer means on said sonic borehole tool with said sonic source and sonic receiver located between said first and second inflatable packers means, said first and second inflatable packer means for inflating to contact and seal with a wall of the borehole, and
- said borehole pressurizing means further includes a fluid storage means for storing fluid in said sonic borehole tool, and a fluid injection means coupled to said fluid storage means for injecting said fluid into said borehole when said first and second inflatable packer means are inflated.
- 33. A method of characterizing an underground formation surrounding a borehole, comprising:
- a) pressurizing the borehole at a location at a first pressure;
- b) generating a first sonic signal at the location at the first pressure;
- c) measuring a first frequency dependent Stoneley wave velocity at the location at the first pressure;
- d) pressurizing the borehole at the location to a second pressure different to the first pressure;
- e) generating a second sonic signal at the location at the second pressure;
- f) measuring a second frequency dependent Stoneley wave velocity at the location at the second pressure;
- g) determining a frequency dependent acoustoelastic coefficient from the first and second frequency dependent velocities;
- h) obtaining an indication of a nonlinear property of the formation from the frequency dependent acoustoelastic coefficient; and
- i) using the indication of the nonlinear property to characterize the formation.
- 34. A method as claimed in claim 33, comprising using a tool having a monopole source to generate the first and second sonic signals.
- 35. A method as claimed in claim 33, comprising using a tool having a dipole source to generate the first and second sonic signals.
- 36. A method as claimed in claim 33, wherein the frequency dependent acoustoelastic coefficient is derived according to (v.sup.Stoneley -V.sub.ref.sup.Stoneley)/V.sub.ref.sup.Stoneley .DELTA.P, wherein V.sub.ref.sup.Stoneley is the first frequency dependent Stoneley wave velocity, V.sup.Stoneley is the second frequency dependent Stoneley wave velocity and .DELTA.P is the difference between the first and second pressures.
- 37. A method of characterizing an underground formation surrounding a borehole, comprising:
- a) pressurizing the borehole at a location at a first pressure;
- b) generating a first sonic signal at the location at the first pressure;
- c) measuring a first frequency dependent flexural wave velocity at the location at the first pressure;
- d) pressurizing the borehole at the location to a second pressure different to the first pressure;
- e) generating a second sonic signal at the location at the second pressure;
- f) measuring a second frequency dependent flexural wave velocity at the location at the second pressure;
- g) determining a frequency dependent acoustoelastic coefficient from the first and second frequency dependent velocities;
- h) obtaining an indication of a nonlinear property of the formation from the frequency dependent acoustoelastic coefficient; and
- i) using the indication of the nonlinear property to characterize the formation.
- 38. A method as claimed in claim 37, comprising using a tool having a monopole source to generate the first and second sonic signals.
- 39. A method as claimed in claim 37, comprising using a tool having a dipole source to generate the first and second sonic signals.
- 40. A method as claimed in claim 37, wherein:
- the frequency dependent acoustoelastic coefficient is derived according to (V.sup.flexural -V.sub.ref.sup.flexural)/V.sub.ref.sup.flexural .DELTA., wherein V.sub.ref.sup.flexural is the first frequency dependent flexural wave velocity, V.sup.flexural is the second frequency dependent flexural wave velocity and .DELTA.P is the difference between the first and second pressures.
- 41. Apparatus for characterizing an underground formation surrounding a borehole, comprising:
- a) a sonic borehole tool positionable at a location in the borehole;
- b) means for pressurizing the borehole at the location to a first pressure and a second pressure which is different from the first pressure;
- c) a monopole sonic signal source in the tool for generating first and second sonic signals at the first and second pressures respectively;
- d) a detector in the tool for measuring first and second frequency dependent Stoneley wave velocities at the first and second pressures respectively;
- e) means for determining a frequency dependent acoustoelastic coefficient from the first and second frequency dependent velocities; and
- f) means for obtaining an indication of a nonlinear property of the formation from the frequency dependent acoustoelastic coefficient so as to characterize the formation.
- 42. Apparatus as claimed in claim 41, wherein:
- said means for pressurizing the borehole comprises first and second packers on the sonic borehole tool and means for setting said first and second packers so as to contact and seal with a wall of the borehole, said monopole source and said detector being positioned between said first and second packers.
- 43. Apparatus as claimed in claim 42, wherein:
- said means for pressurizing the borehole comprises fluid storage means in said sonic borehole tool, and fluid injection means connected to the fluid storage means for injecting fluid from said fluid storage means into the borehole between said first and second packers when set.
- 44. Apparatus for characterizing an underground formation surrounding a borehole, comprising:
- a) a sonic borehole tool positionable at a location in the borehole;
- b) means for pressurizing the borehole at the location to a first pressure and to a second pressure which is different from the first pressure;
- c) a dipole sonic signal source in the tool for generating first and second sonic signals at the first and second pressures respectively;
- d) a detector in the tool for measuring first and second frequency dependent flexural wave velocities at the first and second pressures respectively;
- e) means for determining a frequency dependent acoustoelastic coefficient from the first and second frequency dependent velocities; and
- f) means for obtaining an indication of a nonlinear property of the formation from the frequency dependent acoustoelastic coefficient so as to characterize the formation.
- 45. Apparatus as claimed in claim 44, wherein:
- said means for pressurizing the borehole comprises first and second packers on said sonic borehole tool and means for setting said first and second packers so as to contact and seal with a wall of the borehole, said dipole source and said detector being positioned between said first and second packers.
- 46. Apparatus as claimed in claim 44, wherein:
- said means for pressurizing the borehole comprises fluid storage means in said sonic borehole tool, and fluid injection means connected to said fluid storage means for injecting fluid from said fluid storage means into the borehole between said first and second packers when set.
Parent Case Info
This application is a continuation-in-part of U.S. Ser. No. 08/154,645 filed on Nov. 19, 1993, and of U.S. Ser. No. 08/225,016 filed Apr. 8, 1994 and now issued as U.S. Pat. No. 5,398,215, both of which are hereby incorporated by reference herein in their entireties. This application also relates to U.S. Ser. No. 08/298,919 entitled "Measurement of Formation Characteristics Using Acoustic Borehole Tool Having Sources of Different Frequencies", and U.S. Ser. No. 08/298,718, entitled "Measurement of Predicting Mechanical Failure in Formation Utilizing Stress Derivatives Which Measure Formation Nonlinearity" which are filed on even date herewith and also incorporated by reference herein in their entireties.
US Referenced Citations (3)
Non-Patent Literature Citations (3)
Entry |
Petricola et al, 5th ABU PHABI Nat Oil Co./SPE ABU PHABI Petrol. Conf., May 18, 1992, pp. 561-572, abst. only herewith. |
Nicholaev, A. V.; Phys. Earth Planetary Interiors, v. 50, #1, pp. 1-7, Jan. 1988; abst only herewith. |
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Related Publications (1)
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225016 |
Apr 1994 |
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Continuation in Parts (1)
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154645 |
Nov 1993 |
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