Nuclear magnetic resonance pulse sequences for use with borehole logging tools

• US 5,023,551 A
• Filed: 12/19/1989
• Issued: 06/11/1991
• Est. Priority Date: 08/27/1986
• Status: Expired due to Term

• Current Assignee: Schlumberger Technology Corporation (Schlumberger NV)
• Original Assignee: Schlumberger-Doll Research Center (Schlumberger NV)
• Inventors: Fukuhara, Masafumi, Sezginer, Abdurrahman, Kleinberg, Robert L.
• Primary Examiner(s): Tokar, Michael J.
• Application Number:
  US07/452,903
• Time in Patent Office: 539 Days
• Field of Search: 324/300, 324/303, 324/307, 324/309, 324/310, 324/311, 324/312, 324/313, 324/314, 324/318, 324/322, 128/653 A
• US Class Current: 324/303
• CPC Class Codes: G01N 24/081 Making measurements of geologic samples, e.g. measurements of moisture, pH, porosity, permeability, tortuosity or viscosity
• CPC Class Codes: G01R 33/341 comprising surface coils
• CPC Class Codes: G01R 33/3671 involving modulation of the quality factor of the RF coil G01R33/3642 takes precedence
• CPC Class Codes: G01R 33/3808 Magnet assemblies for single-sided MR wherein the magnet assembly is located on one side of a subject only; Magnet assemblies for inside-out MR, e.g. for MR in a borehole or in a blood vessel, or magnet assemblies for fringe-field MR
• CPC Class Codes: G01R 33/443 Assessment of an electric or a magnetic field, e.g. spatial mapping, determination of a B0 drift or dosimetry
• CPC Class Codes: G01R 33/448 Relaxometry, i.e. quantification of relaxation times or spin density G01R33/50 takes precedence
• CPC Class Codes: G01V 3/32 operating with electron or nuclear magnetic resonance

Abstract

An NMR pulse sequence for use in the borehole environment is provided which combines a modified fast inversion recovery (FIR) pulse sequence with a series of more than ten, and typically hundreds, of CPMG pulses according to

[W.sub.i -180-τ.sub.i -90-(t.sub.cp -180-t.sub.cp -echo).sub.j ].sub.i

where j is the index of the CPMG echoes gathered, i is the index of the wait times in the pulse sequence, W_i are the wait times, i are the recovery times before the CPMG pulses, and tcp is the Carr-Purcell spacing. Measurements are made of the signals induced in the formation as a result of the magnetic fields. Determinations of M_o and/or T1 are then made from the measurements according to relationships which relate Mp_o, T1 and T2 to the signal magnitude. Other relationships which provide stretched exponentials or multiple exponentials can also be used. From the M_o and/or T1 determinations, formation parameters such as porosity and permeability may be derived according to equations known in the art. In obtaining the most accurate determinations of formation parameters in the least amount of time, the various pulse sequence parameters (I, J, W_i, and τ_i) are optimized prior to logging. Additional accuracy is obtained by integrating a gated portion of the echoes rather than by measuring amplitude, and by utilizing a phase alternated CPMG sequence in repetitive measurements in order to eliminate baseline shift error.

Claims

1. A method for measuring an indication of an attribute of a volume of earth formation with a borehole tool having means for producing static magnetic fields in a volume of a formation, means for producing oscillating magnetic fields in a volume of a formation, and means for measuring an induced magnetic signal, said method comprising:

a) producing a static magnetic field in said volume of formation;

b) producing oscillating magnetic fields according to a pulse sequence

space="preserve" listing-type="equation">[W.sub.i -180-τ

.sub.i -90-(t.sub.cp -180-t.sub.cp -echo).sub.j ].sub.i

where j=1, 2, . . . J, and J is the number of echoes collected in a single Carr-Purcell-Meiboom-Gill (CPMG) sequence, where i=1, . . . I, and I is the number of waiting times used in the pulse sequence,

where W_i are recovery times before a CPMG sequence, and

where τ

_i are recovery times before a CPMG sequence, and

where t_cp is the Carr-Purcell spacing, in order to induce signals in said volume which are measurable by said tool in said borehole; and

c) measuring with said tool said induced signals.

2. A method according to claim 1, further comprising:

d) determining from said measured signals an indication of said attribute of said volume of earth formation.

3. A method according to claim 2, wherein:

J is greater than or equal to ten.

4. A method according to claim 3, wherein:

J is greater than or equal to one hundred.

5. A method according to claim 4, wherein:

I is greater than or equal to two and less than or equal to sixty.

6. A method according to claim 3, wherein:

said induced signals comprise at least CPMG echoes, and said step of measuring said induced signals comprises integrating at least portions of said CPMG echoes.

7. A method according to claim 6, wherein:

said step of measuring said induced signals comprises gating the measurements measured by said tool, and integrating only desired of said portions of said CPMG echoes.

8. A method according to claim 1, further comprising:

repeating steps b and c for said volume of said formation, wherein in a first said pulse sequence, said 90 degree pulse is a 90(+x) pulse, and in a pulse sequence during said repeated step b, said 90 degree pulse is a 90(-x) pulse, where +x and -x denote the phase of the Larmor frequency of the carrier of the pulse with respect to a continuous wave Larmor frequency signal, and wherein results measured in step c and repeated step c are subtracted from each other to provide a corrected measurement.

9. A method according to claim 8, further comprising:

producing oscillating magnetic fields according to a pulse sequence W_i -180-τ

_i -90(+x) and measuring with said tool signals induced thereby, and producing oscillating magnetic fields according to a pulse sequence W_i -180-τ

_i -90(-x) and measuring with said tool signals induced thereby, wherein the measurements from said W_i -180-τ

_i -90(-x) are subtracted from said W_i -180-τ

_i -90(+x) measurement to provide a first difference, and said first difference is subtracted from said corrected measurement to provide a further corrected measurement.

10. A method according to claim 2, wherein:

said step of determining an indication of an attribute of said formation comprises determining at least a value for a spin-lattice relaxation time (T1) of said formation from said measured induced signals according to a relationship which relates at least T1 to the magnitude of said induced signals.

11. A method according to claim 10, further comprising:

before producing magnetic fields in said formation, choosing values for at least two of a group of variables consisting of I, J, W_i, and τ

_i, wherein said relationship which relates at least said spin-lattice relaxation time to the magnitude of said induced signals includes at least said two of a group of variables therein, and wherein the values of said at least two of a group of variables are chosen by optimizing said at least two of a group of variables in said relationship to reduce the variance of an estimate of T1 to a minimum.

12. A method according to claim 11, wherein:

said at least two of a group of variables are optimized by minimizing a cost function which includes a measurement time multiplied by a function of the uncertainty in estimates of at least T1, wherein the measurement time is a function of the variables of optimization.

13. A method according to claim 12, wherein:

said cost function ,is ##EQU8## where M_o is proportional to the equilibrium value of the longitudinal magnetization, CRLB denotes the Cramer-Rao lower bound for the variances of the estimates based on said measurements resulting from said pulse sequence, (Meas.time) is the time it takes to complete one pulse sequence, T1(1), T1(2), . . . ,T1(M) are logarithmically spaced time covering the expected range of T1, and c_o, c₁, and c₂ are predetermined coefficients.

14. A method according to claim 13 wherein:

n equals 8, c_o =1, and c₁ and c₂ =0.01.

15. A method according to claim 13, wherein:

said at least two of a group of variables are W_i and τ

_i.

16. A method according to claim 13, wherein:

said at least two of a group of variables are all of W_i, τ

_i, I and J.

17. A method according to claim 2, wherein:

said step of determining an indication of an attribute of said formation comprises determining at least a value for an amplitude parameter M_o of said formation from said measured induced signals according to a relationship which relates at least M_o to the magnitude of said induced signals, where M_o is proportional to the equilibrium value of the longitudinal magnetization.

18. A method according to claim 10, wherein:

said relationship relates T1, T2, and M_o, to said induced signal, wherein T2 is the spin-spin relaxation time, and M_o is proportional to the equilibrium value of the longitudinal magnetization.

19. A method according to claim 17, wherein:

said relationship relates T1, T2 and M_o to said induced signal, wherein T2 is the spin-spin relaxation time, and T1 is the spin-lattice relaxation time.

20. A method according to claim 19, wherein:

said relationship which relates T1, T2, and M_o to said induced signal is

space="preserve" listing-type="equation">f.sub.ij =Mo{1+(exp(-τ

.sub.i T1))(c-1-c(exp(-W.sub.i /T1)))}exp(-2t.sub.cp j/T2)

where f_ij is said induced signal at the j'"'"'th echo after the i'"'"'th recovery time, and c is a constant relating to said borehole tool.

21. A method according to claim 20, wherein:

said step of determining a value for at least T1 comprises conducting a non-linear least squares fit to find values for T1, T2, and M_o which fit said induced signal measurements to said relationship.

22. A method according to claim 19, further comprising:

e) from said determination of M_o determining the porosity of said formation according to a second relationship which relates M_o to porosity.

23. A method according to claim 2, wherein:

said step of determining an indication of an attribute of said formation comprises determining a spin-lattice relaxation time (T1k) of at least one component of said formation from said measured induced signals according to a relationship which relates T1k'"'"'s to the magnitude of said induced signals.

24. A method according to claim 23, wherein:

said relationship relates T1k, T2k and M_ok to said induced signal, according to ##EQU9## wherein k varies from one to at least two, T2k are the spin-spin relaxation times associated with the respective components of said formation, the sum of M_ok is proportional to the equilibrium value of the longitudinal magnetization, f_ij is said induced signal at the j'"'"'th echo after the i'"'"'th recovery time, and c is a constant relating to said borehole tool

25. A method according to claim 24, wherein:

said step of determining a value for at least T1k comprises conducting a non-linear least squares fit to find values for T1k, T2k, and M_ok which fit said induced signal measurements to said relationship.

26. A method according to claim 25, further comprising:

e) from said determinations of M_ok, determining the porosity of said formation according to a second relationship which relates M_ok '"'"'s to porosity.

27. A method according to claim 25, further comprising:

e) from said determinations of T1k, determining the permeability of said formation according to a second relationship which relates T1k to permeability.

28. A method according to claim 25, further comprising:

e) from said determinations of M_ok, determining the irreducible water saturation of said formation according to a second relationship which relates Mok'"'"'s to irreducible water saturation.

29. A method according to claim 2, wherein:

said step of determining an indication of an attribute of said formation comprises determining at least a value for one of the stretch exponential spin-lattice relaxation time (T1α

) of said formation and an amplitude M_o parameter of said formation from said measured induced signals according to a relationship which relates said T1α and

M_o to the magnitude of said induced signals.

30. A method according to claim 29, wherein:

said relationship relates T1α

, T2α

, α

1, α

2, and M_o, to said induced signal, according to

space="preserve" listing-type="equation">f.sub.ij =M.sub.o {exp[-(2t.sub.cp j/T2α

).sup.α

2 ]+(c-1)exp[-((τ

.sub.i /T1α

)+(2t.sub.cp j/T2α

)).sup.α

1 ]-c exp[-(((τ

.sub.i W.sub.i)/T1α

)+(2t.sub.cp j/T2α

)).sup.α

1 ]}

wherein T2α

is the stretched exponential spin-spin relaxation times associated with said formation, α

1 and α

2 are the stretch exponents, M_o is proportional to the equilibrium value of the longitudinal magnetization, f_ij is said induced signal at the j'"'"'th echo after the i'"'"'th recovery time, and c is a constant relating to said borehole tool

31. A method according to claim 30, wherein:

said step of determining a value for at least T1α

comprises conducting a non-linear least squares fit to find values for T1α

, T2α

, α

1, α

2, and M_o which fit said induced signal measurements to said relationship.

32. A method according to claim 29, wherein said step of determining a value comprises determining at least M_o, said method further comprising:

e) from said determination of M_o, determining the porosity of said formation according to a second relationship which relates M_o to porosity.

33. A method according to claim 29, wherein said step of determining a value comprises determining at least T1α

, said method further comprising;

e) from said determination of T1α

, determining the permeability of said formation according to a second relationship which relates T1α

to permeability.

34. A method according to claim 20, further comprising:

before producing magnetic fields in said formation, choosing values for variables I, J, W_i, and τ

_i, wherein said relationship which relates at least said spin-lattice relaxation time to the magnitude of said induced signals includes said variables therein, and wherein said variables are chosen by optimizing the values of said variables in said relationship to reduce the variance of at least an estimate of T1 to a minimum.

35. A method according to claim 34, wherein:

values for said variables are optimized by minimizing a cost function ##EQU10## where M_o is proportional to the equilibrium value of the longitudinal magnetization, CRLE denotes the Cramer-Rao lower bound for the variances of the estimates based on said measurements resulting from said pulse sequence, (Meas.time) is the time it takes to complete one pulse sequence, T1(1), T1(2), . . . , T1(M) are logarithmically spaced time covering the expected range of T1, and c_o, c₁, and c₂ are predetermined coefficients.

36. A method according to claim 24, wherein:

before producing magnetic fields in said formation, choosing values for variables I, J, W_i, and τ

_i, wherein said relationship which relates at least said spin-lattice relaxation times to the magnitude of said induced signals includes said variables therein, and wherein said variables are chosen by optimizing the values of said variables in said relationship to reduce the variances of at least one of the T1k'"'"'s to a minimum.

37. A method according to claim 32, wherein:

before producing magnetic fields in said formation, choosing values for variables I, J, W_i, and τ

_i, wherein said relationship which relates at least said stretched spin-lattice relaxation time to the magnitude of said induced signals includes said variables therein, and wherein said variables are chosen by optimizing the values of said variables in said relationship to reduce the variance of at least an estimate of T1α

to a minimum.

38. A method according to claim 37, wherein:

values for said variables are optimized by minimizing a cost function ##EQU11## where M_o is proportional to the equilibrium value of the longitudinal magnetization, CRLB denotes the Cramer-Rao lower bound for the variances of the estimates based on said measurements resulting from said pulse sequence, (Meas.time) is the time it takes to complete one pulse sequence, T1(1), T1(2), . . . ,T1(M) are logarithmically spaced time covering the expected range of T1α

, and c_o, c₁, and c₂ are predetermined coefficients.

39. A method according to claim 34, wherein:

J is greater than or equal to ten;

I is greater than or equal to two and less than or equal to sixty; and

said induced signals comprise at least CPMG echoes, and said step of measuring said induced signals comprises integrating at least portions of said CPMG echoes.

40. A method according to claim 36

J is greater than or equal to ten;

I is greater than or equal to two and less than or equal to sixty; and

said induced signals comprise at least CPMG echoes, and said step of measuring said induced signals comprises integrating at least portions of said CPMG echoes.

41. A method according to claim 38, wherein:

J is greater than or equal to ten;

I is greater than or equal to two and less than or equal to sixty; and

said induced signals comprise at least CPMG echoes, and said step of measuring said induced signals comprises integrating at least portions of said CPMG echoes.

42. A method for measuring an indication of an attribute of a volume of earth formation with a borehole tool having means for producing static magnetic fields in a volume of a formation, means for producing oscillating magnetic fields in a volume of a formation, and means for measuring an induced magnetic signal, said method comprising:

a) producing a static magnetic field in said volume of formation;

b) producing oscillating magnetic fields according to a pulse sequence

space="preserve" listing-type="equation">[τ

.sub.i -90-(t.sub.cp -180-t.sub.cp -echo).sub.j ].sub.i

where j=1, 2, . . . ,J, and J is the number of echoes collected in a single Carr-Purcell-Meiboom-Gill (CPMG) sequence, J being greater than or equal to ten,

where i=1, . . . I, and I is the number of recovery times in the pulse sequence,

where τ

_i are recovery times, and

where t_cp is the Carr-Purcell spacing,

in order to induce signals in said volume which are measurable by said tool in said borehole; and

c) measuring with said tool said induced signals.

43. A method according to claim 42, further comprising:

d) determining from said measured signals an indication of said attribute of said volume of earth formation.

44. A method according to claim 43, wherein:

said induced signals comprise at least CPMG echoes, and said step of measuring said induced signals comprises integrating desired portions of said CPMG echoes.

45. A method according to claim 42, further comprising:

repeating steps b and c for said volume of said formation, wherein in a first said pulse sequence, said 90 degree pulse is a 90(+x) pulse, and in a pulse sequence during said repeated step b, said 90 degree pulse is a 90(-x) pulse, where +x and -x denote the phase of the Larmor frequency of the carrier of the pulse with respect to a continuous wave Larmor frequency signal, and wherein results measured in step c and repeated step c are subtracted from each other to provide a corrected measurement.

46. A method according to claim 43, wherein:

said step of determining an indication of an attribute of said formation comprises determining at least a value for at least one of a spin-lattice relaxation time (T1) of said formation and an amplitude M_o of said formation from said measured induced signals according to a relationship which relates at least T1 and M_o to the magnitude of said induced signals, wherein M_o is proportional to the equilibrium value of the longitudinal magnetization.

47. A method according to claim 46, further comprising:

before producing magnetic fields in said formation, choosing values for at least two of a group of variables consisting of I, J, and τ

_i, wherein said relationship which relates at least said spin-lattice relaxation time to the magnitude of said induced signals includes at least said two of a group of variables therein, and wherein the values of said at least two of a group of variables are chosen by optimizing said at least two of a group of variables in said relationship to reduce the variance of an estimate of T1 to a minimum.

48. A method according to claim 47, wherein:

said at least two of a group of variables are optimized by minimizing a cost function which includes the product of a measurement time multiplied by a function of the uncertainty in estimates of at least T1, wherein the measurement time is a function of the variables of optimization.

49. A method according to claim 48, wherein:

said cost function is ##EQU12## where M_o is proportional to the equilibrium value of the longitudinal magnetization, CRLB denotes the Cramer-Rao lower bound for the variances of the estimates based on said measurements resulting from said pulse sequence, (Meas.time) is the time it takes to complete one pulse sequence, T1(1), T1(2), . . . ,T1(M) are logarithmically spaced time covering the expected range of T1, and c_o, c₁, and c₂ are predetermined coefficients.

50. A method according to claim 48, wherein:

said at least two of a group of variables are all of τ

_i, I and J.

51. A method according to claim 46, wherein:

said relationship relates T1, T2, and M_o to said induced signal, wherein T2 is the spin-spin relaxation time, and T1 is the spin-lattice relaxation time.

52. A method according to claim 51, wherein

said relationship which relates T1, T2, and M_o to said induced signal is

53. A method according to claim 52, wherein:

said step of determining a value for at least one of T1 and M_o comprises conducting a non-linear least squares fit to find values for T1, T2, and M_o which fit said induced signal measurements to said relationship.

54. A method according to claim 53, further comprising:

e) from said determination of at least one of T1 and M_o, determining one of the porosity and permeability of said formation according to a second relationship which relates one of T1 and M_o to one of porosity and permeability.

55. A method according to claim 43, wherein

said step of determining an indication of an attribute of said formation comprises determining either a spin-lattice relaxation time (T1k) of at least one component of said formation or an amplitude parameter (M_ok) from said measured induced signals according to a relationship which relates spin-lattice relaxation times and amplitudes to the magnitude of said induced signals, wherein the sum of M_ok '"'"'s is equal to the equilibrium value of the longitudinal magnetization

56. A method according to claim 43, wherein

said relationship relates T1k, T2k and M_ok, to said induced signal, according to ##EQU13## wherein k varies from one to at least two, T2k are the spin-spin relaxation times associated with respective components of said formation, the sum of M_ok is proportional to the equilibrium value of the longitudinal magnetization, f_ij is said induced signal at the j'"'"'th echo after the i'"'"'th recovery time, and c is a constant relating to said borehole tool.

57. A method according to claim 56, wherein:

said step of determining a value for at least T1k comprises conducting a non-linear least squares fit to find values for T1k, T2k, and M_ok which fit said induced signal measurements to said relationship.

58. A method according to claim 57, further comprising:

e) from said determinations of at least one of T1k and M_ok, determining at least one of the porosity, permeability, and irreducible water saturation of said formation according to a second relationship which relates one of T1k and M_ok to one of porosity, permeability, and irreducible water saturation.

59. A method according to claim 43, wherein:

said step of determining an indication of an attribute of said formation comprises determining at least a value for one of the stretch exponential spin-lattice relaxation time (T1α

) of said formation and an amplitude M_o parameter of said formation from said measured induced signals according to a relationship which relates said T1α and

M_o to the magnitude of said induced signals.

60. A method according to claim 59, wherein:

said relationship relates T1α

, T2α

, α

1, α

2, and M_o, to said induced signal, according to

space="preserve" listing-type="equation">f.sub.ij =M.sub.o {exp[-(2t.sub.cp j/T2α

).sup.α

2 ]-exp[-((τ

.sub.i /T1α

)+(2t.sub.cp j/T2α

)).sup.α

]}

wherein T2 is the stretched exponential spin-spin relaxation times associated with said formation, 1 and 2 are the stretch exponents, M_o is proportional to the equilibrium value of the longitudinal magnetization, f_ij is said induced signal at the j'"'"'th echo after the i'"'"'th recovery time, and c is a constant relating to said borehole tool.

61. A method according to claim 60, wherein:

said step of determining a value for at least T1α

comprises conducting a non-linear least squares fit to find values for T1α

, T2α

, α

1, α

2, and M_o which fit said induced signal measurements to said relationship.

62. A method according to claim 61, further comprising:

e) from said determination of at least one of T1α

, and M_o, determining at least one of the porosity and permeability of said formation according to a second relationship which relates at least one of T1α

, and M_o to one of porosity and permeability.