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A Review on Nuclear Magnetic Resonance Logging: Simulation Schemes

자기공명반응 시뮬레이션 해설 및 비교

  • Jang, Jae Hwa (Sejong University, Department of Energy and Mineral Resource Engineering) ;
  • Nam, Myung Jin (Sejong University, Department of Energy and Mineral Resource Engineering)
  • 장재화 (세종대학교 에너지자원공학과) ;
  • 남명진 (세종대학교 에너지자원공학과)
  • Received : 2012.12.13
  • Accepted : 2013.02.20
  • Published : 2013.05.31

Abstract

Nuclear magnetic resonance (NMR) logging has become an important technique for formation evaluation, detecting interaction signals between H protons and applied magnetic fields. Measured decay signals called relaxation, contain important information about density of H protons and different decay rate due to its fluid type in the sensitive area. Thus, petrophysical information such as porosity, permeability and wettability can be estimated through the interpretation of the decay signals. Many researches on random walk simulation have been published, since a simulation method based on random walk for solving exponential decays was adapted in the early of 1950. This study first makes a review on NMR simulation researches, explains two most important methods: simulation with or without considering magnetic field gradient. Lastly, the study makes a comparison between NMR simulation responses with and without magnetic field gradient to show the importance to consider magnetic gradient to analyze the effects of magnetic gradients on NMR responses.

자기공명검층은 수소와 자기장의 상호작용을 측정, 분석하는 물리검층 방법으로 이는 저류층 평가를 위한 중요한 물리검층 방법 중 하나이다. 측정된 감쇠 신호 즉, 이완은 측정지역 내 수소의 밀도에 대한 정보와 유체의 종류에 따른 감쇠속도에 대한 정보를 포함하고 있으며, 이를 바탕으로 공극률, 투과도와 습윤도 등을 예측할 수 있다. 1950년대 초반 랜덤워크로 자기공명의 이완감쇠를 시뮬레이션한 것을 시작으로 자기공명반응에 대한 연구가 급격히 발전되었다. 이 논문에서는 자기공명 시뮬레이션의 연구 동향을 먼저 살펴 보고, 자기공명반응인 이완을 발생시키는 이완메커니즘에 대해 간단히 알아본다. 이에 기초하여 자기공명검층에서 주로 측정하는 횡축이완곡선을 자기장구배를 고려하는 경우와 고려하지 않는 시뮬레이션 방법에 대해 비교분석하고 자기장구배가 이완메커니즘 및 횡축이완곡선에 미치는 영향에 대해 분석한다.

Keywords

References

  1. Adler, P. M., Jacquin, C. G., and Quiblier, J. A., 1990, Flow in simulated porous media, International J. Multiphase Flow, 16(4), 691-712. https://doi.org/10.1016/0301-9322(90)90025-E
  2. Al-Kharusi, A. S., and Blunt, M. J., 2007, Network extraction from sandstone and carbonate pore space images, J. Petroleum Science and Engineering, 56, 219-231. https://doi.org/10.1016/j.petrol.2006.09.003
  3. Arns, C., Knackstedt, M., Pinczewski, W. V., and Martys, N., 2004, Virtual permeametry on micro tomographic images, J. Petroleum Science and Engineering, 45, 41-46. https://doi.org/10.1016/j.petrol.2004.05.001
  4. Arns, C. H., Knackstedt, M. A., and Martys, N., 2005, Crossproperty correlations and permeability estimation in sandstone, Physical Review, 72, 046304.
  5. Arns, C. H., Sheppard, A. P., Saadatfar, M., and Knackstedt, M. A., 2006, Prediction of permeability from NMR response: surface relaxivity heterogeneity, Trans. SPWLA 47th Annual Logging Symposium, GG, 1-13.
  6. Arns, C. H., Sheppard, A. P., Sok, R. M., and Knackstedt, M. A., 2007, NMR petrophysical predictions on digitized core images, Petrophysic, 48(3), 202-221.
  7. Arns, C. H., AlGhamdi, T., and Arns, J. T., 2011, Numerical analysis of NMR relaxation diffusion responses of sedimentary rock, New J. of Physics, 13, 015004. https://doi.org/10.1088/1367-2630/13/1/015004
  8. Bakke, S., and Oren, P. E., 1997, 3D pore-scale modeling of sandstones and flow simulations in the pore networks, SPE Journal, 2, 136-149. https://doi.org/10.2118/35479-PA
  9. Bergman, D. J., Dunn, K. J., Schwartz, L. M., and Mitra, P. P., 1995, Self-diffusion in a periodic porous medium: a comparison of different approaches, Physical Review, 51(4), 3393-3400.
  10. Bloch, F., 1946, Nuclear induction, Physical Review, 70, 460-473. https://doi.org/10.1103/PhysRev.70.460
  11. Bryant, S. L., Mellor, D. W., and Cade, C. A., 1993, Physically representative network models of transport in porous media, AIChE Journal, 39(3), 387-396. https://doi.org/10.1002/aic.690390303
  12. Carr, H. Y., and Purcell, E. M., 1954, Effects of diffusion on free precession in nuclear magnetic resonance experiment, Physical Review, 94(3), 630-638. https://doi.org/10.1103/PhysRev.94.630
  13. Clennell, M. B., Josh, M., Dewhurst, D., Esteban, L., and Raven, M., 2010, Shale petrophysics: electrical, dielectric and NMR methods to Characterize mud rocks and discover relationships to mechanical properties and hydrocarbon affinity, AAPG Search and Discovery, 90122.
  14. Dong, H., Touati, M., and Blunt, M. J., 2007, Pore network modeling: analysis of pore size distribution of arabian core samples, 15th SPE Middle East Oil & Gas Show and Conference, 105156.
  15. Douglass, D., and McCall, D., 1958, Diffusion in paraffin hydrocarbons, J. Physics Chemistry, 62, 1102. https://doi.org/10.1021/j150567a020
  16. Dullien, F. A. L., 1992, Porous media: fluid transport and pore structure, Academic Press.
  17. Dunn, K. J., Bergman, D. J., and LaTorraca, G. A., 2002, Nuclear Magnetic Resonance: Petrophysical and Logging Application, Elsevier Science.
  18. Edmund, S. E., 2007, Nuclear magnetic resonance measurements of fluid-solid interactions in dialysis-membrane materials, Master of Science in Chemical Engineering, Bucknell University.
  19. Evans, M. L., Mulkey, T. J., and Vesper, M. J., 1980, Auxin action on proton influx in corn roots and its correlation with growth, Planta, 148, 510-512. https://doi.org/10.1007/BF02395322
  20. Freidlin, M., 1985, Functional integration and partial differential equation, Princeton University Press.
  21. Grebenkov, D. S., Marcel, F., and Bernard, S., 2003, Spectral properties of the brownian self-transport operator, The European Physical Journal, 36(B), 221-231.
  22. Gillen, M., Murphy, E., and Benavides, S., 2004, Technology update: higher levels of fluid typing and speed deliver robust answers from Nuclear Magnetic Resonance technology, J. Petroleum Technology, 56(8), 28-29.
  23. Hahn, E., 1950, Spin Echo, Physical Review, 80, 580-594. https://doi.org/10.1103/PhysRev.80.580
  24. Hazlett, R. D., 1995, Simulation of capillary-dominated displacements in microtomographic images of reservoir rocks, Transport Porous Media, 20(1-2), 21-35. https://doi.org/10.1007/BF00616924
  25. Hidajat, I., Singh, M., Cooper, J., and Mohanty, K. K., 2002, Permeability of porous media from simulated NMR response, Transport in Porous Media, 48, 225-247. https://doi.org/10.1023/A:1015682602625
  26. Hidajat, I., Singh, M., and Mohanty, K. K., 2003, NMR response of porous media by random walk algorithm: a parallel implementation, Chemical Engineering Science, 190(12), 1661-1680.
  27. Idowu, N. A., 2009, Pore-scale modeling: stochastic network generation and modeling of rate effects in water flooding, PhD thesis, Imperial College London.
  28. Ioannidis, M. A., Kwiecien, I., Chatzis, I., MacDonald, I. F., and Dullien, F. A. L., 1997, Comprehensive pore structure characterisation using 3D computer reconstruction and stochastic modeling, SPE Technical Conference and Exhibition, 38713.
  29. Jang, J. H., and Nam, M. J., 2012, A review on nuclear magnetic resonance logging: fundamental theory and measurements, Jigu-Mulli-wa-Mulli-Tamsa, 15(4), 235-244.
  30. Jang, J. H., and Nam, M. J., 2013, A review on nuclear magnetic resonance logging: data interpretation, The Korean Society for Geosystem Engineering, 50, 144-155.
  31. Jin, G., Patzek, T. W., and Silin, D. B., 2003, Physics-based reconstruction of sedimentary rocks, SPE Western Regional/AAPG Pacific Section Joint Meeting, 83587.
  32. Kenyon, W. E., 1992, Nuclear magnetic resonance as a petrophysical measurement, Nuclear Geophysics, 6(2), 153-171.
  33. Kenyon, W. E., 1997, Petrophysical principles of applications of NMR logging, Log Analyst, 38, 21-43.
  34. Kim, I. C., Cule, D., and Torquato, S., 2000, Walker diffusion method for calculation of transport properties of composite materials, Physical Review, 61(4), 4659-4660. https://doi.org/10.1103/PhysRevB.61.4659
  35. Liang, Z. R., Fernandes, C. P., Magnani, F. S., and Philippi, P. C., 1998, A reconstruction technique for 3D porous media using image analysis and fourier transforms, J. Petroleum Science and Engineering, 21, 273-283. https://doi.org/10.1016/S0920-4105(98)00077-1
  36. Liang, Z., Ioannidis, M. A., and Chatzis, I., 2000, Geometric and topological analysis of three-dimensional porous media: pore space partitioning based on morphological skeletonization, J. Colloid and Interface Science, 221, 13-24. https://doi.org/10.1006/jcis.1999.6559
  37. Lindquist, W .B., Lee, S. M., Coker, D. A., Jones, K. W., and Spanne, P., 1996, Medial axis analysis of void structure in three-dimensional tomographic images of porous media, J. Geophysical Research, 101, 8297-8310. https://doi.org/10.1029/95JB03039
  38. Mendelson, K. S., 1990, Percolation model of nuclear magnetic relaxation in porous media, Physical Review, 41, 562-567.
  39. Mohnke, O., Ahrenholz, B., and Klitzsh, N., 2011, Joint numerical microscale simulations of muti-phase flow and NMR relaxation behavior in porous media, EGU General Assembly, 13, 2011-11141-2.
  40. Okabe, H., and Blunt, M. J., 2004, Prediction of permeability for porous media reconstructed using multiple-point statistics, Physical Review, 70, 066135.
  41. Oren, P. E., and Bakke, S., 2003, Reconstruction of Berea sandstone and pore-scale modeling of wettability effects, J. Petroleum Science and Engineering, 39, 177-199. https://doi.org/10.1016/S0920-4105(03)00062-7
  42. Ramakrishnan, T. S., Schwartz, L. M., Fordham, E. J., Kenyon, W. E., and Wilkinson, D. J., 1999, Forward models for nuclear magnetic resonance in carbonate rocks, The Log Analyst, 40, 260-270.
  43. Robertson, B., 1966, Spin-echo decay of spins diffusing in a bounded region, Physical review, 155(1), 273-277.
  44. Sheppard, A. P., Sok, R. M., and Averdunk, H., 2005, Improved pore network extraction methods, The Society of Core Analysts, 2005-20.
  45. Sigal, R., and Odusina, E., 2010, NMR gas relaxation signature for organic shale reservoir rocks, AAPG Hedberg Conference, 90122.
  46. Silin, D. B., Guodong, J., and Patzek, T. W., 2003, Robust determination of the pore space morphology in sedimentary rocks, SPE Annual Technical Conference and Exhibition, 84296.
  47. Silin, D., and Patzek, T., 2006, pore space morphology using maximal inscribed spheres, Physica, 371(A), 336-360.
  48. Smolen, J. J., 1996, Cased hole and production log evaluation, PennWell Books.
  49. Swiet, T. M., and Sen, P. N., 1994, Decay of nuclear magnetization by bounded diffusion in a constant field gradient, J. Chemical Physics, 100, 5597. https://doi.org/10.1063/1.467127
  50. Talabi, O., 2008, Pore-scale simulation of NMR response in porous media, PhD thesis, Imperial College London.
  51. Torrey, H., 1956, Bloch equation with diffusive terms, Physical Review, 104, 563-565. https://doi.org/10.1103/PhysRev.104.563
  52. Toumelin, E., 2002, Monte Carlo simulations of NMR measurements in carbonate rocks under a constant magnetic field gradient, Master's thesis, The University of Texas at Austin.
  53. Toumelin, E., Torres-Verdín, C., Chen, S., and Fischer, D. M., 2004a, reconciling NMR measurements and numerical simulations: assessment of temperature and diffusive coupling effects on two-phase carbonate samples, Petrophysics, 44(2), 91-107.
  54. Toumelin, E., Torres-Verdín, C., Sun, B., and Dunn, K. J., 2004b, A numerical assessment of modern borehole NMR interpretation techniques, SPE Technical Conference and Exhibition, 90539.
  55. Toumelin, E., Torres-Verdín, C., Sun, B., and Dunn, K. J., 2006, Limits of 2D NMR interpretation techniques to quantify pore size, wettability, and fluid type: a numerical sensitivity study, SPE Journal, 11, 354-363. https://doi.org/10.2118/90539-PA
  56. Toumelin, E., Torres-Verdín, C., Sun, B., and Dunn, K. J., 2007, Random-walk technique for simulating NMR measurements and 2D NMR maps of porous media with relaxing and permeable boundaries, J. Magnetic Resonance, 188, 83-96. https://doi.org/10.1016/j.jmr.2007.05.024
  57. Torquato, S., and Kim, I. C., 1989, Efficient simulation technique to compute effective properties of heterogeneous media, Applied Physics Letters, 55, 1847-1849. https://doi.org/10.1063/1.102184
  58. Valvatne, P. H., 2004, Predictive pore scale modeling of multiphase flow, PhD thesis, Imperial College London.
  59. Vivek, A., and Hirasaki, G. J., 2007, Diffusional coupling between micro and macroporosity for NMR relaxation in sandstones and grainstones, Petrophysics, 48(4), 289-307.
  60. Wayne, R. C., and Cotts, R. M., 1966, Nuclear magnetic resonance study of self-diffusion in a bounded medium, Physical Review, 151, 264. https://doi.org/10.1103/PhysRev.151.264
  61. Yao, Y. B., Liu, D., Cai, Y. D., and Li, J. Q., 2010a, Advanced characterization of pores and fractures in coals by nuclear magnetic resonance and x-ray computed tomography, Science China, 53, 854-862.
  62. Yao, Y. B., Liu, D., Che, Y., Tang, D., Tang, S., and Huang, W., 2010b, Petrophysical characterization of coals by low-field nuclear magnetic resonance, Fuel, 89, 1371-1380. https://doi.org/10.1016/j.fuel.2009.11.005
  63. Zheng, L. H., and Chiew, Y. C., 1989, Computer-simulation of diffusion-controlled reactions in dispersions of spherical sinks, J. Chemical Physics, 90, 322-327. https://doi.org/10.1063/1.456532