Nuclear magnetic resonance T2 spectrum: multifractal characteristics and pore structure evaluation
Yan Jian-Ping1,2, He Xu2, Geng Bin3, Hu Qin-Hong4, Feng Chun-Zhen5, Kou Xiao-Pan5, and Li Xing-Wen5
1. State Key Laboratory of Oil & Gas Reservoir Geology and Exploitation (Southwest Petroleum University), Chengdu 610500, China.
2. School of Geoscience and Technology, Southwest Petroleum University, Chengdu 610500, China.
3. Institute of Exploration and Development, ShengLi Oil Field, SINOPEC, Dongying 257015, China.
4. Department of Earth and Environmental Science, University of Texas at Arlington, Texas, 76019, USA.
5. Changqing Division of PetroChina Logging Company, Xi’an 718500, China.
Abstract Pore structure characteristics are important to oil and gas exploration in complex low-permeability reservoirs. Using multifractal theory and nuclear magnetic resonance (NMR), we studied the pore structure of low-permeability sandstone rocks from the 4th Member (ES4) of the Shahejie Formation in the south slope of the Dongying Sag. We used the existing pore structure data from petrophysics, core slices, and mercury injection tests to classify the pore structure into three categories and five subcategories. Then, the T2 spectra of samples with different pore structures were interpolated, and the one- and three-dimensional fractal dimensions and the multifractal spectrum were obtained. Parameters α (intensity of singularity) and f(α) (density of distribution) were extracted from the multifractal spectra. The differences in the three fractal dimensions suggest that the pore structure types correlate with α and f(α). The results calculated based on the multifractal spectrum is consistent with that of the core slices and mercury injection. Finally, the proposed method was applied to an actual logging profile to evaluate the pore structure of low-permeability sandstone reservoirs.
This work was supported by the National Natural Science Foundation of China (Grant No. 41202110) and Open Fund of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Southwest Petroleum University) (Grant No. PLN201612), the Applied Basic Research Projects in Sichuan Province (Grant No. 2015JY0200) and Open Fund Project from Sichuan Key Laboratory of Natural Gas Geology (Grant No. 2015trqdz07).
Cite this article:
. Nuclear magnetic resonance T2 spectrum: multifractal characteristics and pore structure evaluation[J]. APPLIED GEOPHYSICS, 2017, 14(2): 205-215.
[1]
Avnir, D., Farin D., and Pfeifer P., 1984, Molecular fractal surfaces: Nature, 308(5956), 261-263.
[2]
Chhabra, A., and Jensen, R. V., 1989, Direct determination of the f(α) singularity spectrum: Physical Review Letters, 62(12), 1327-1330.
[3]
Falconer, K. J., 1985, The geometry of fractal sets: Cambridge, England.
[4]
Ge, X. M., Fan, Y. R., Li, J. T., et al., 2015, Pore structure characterization and classification using multifractal theoryAn application in Santanghu basin of western China: Journal of Petroleum Science and Engineering, 127, 297-304.
[5]
Hansen, J. P., and Skjeltorp, A. T., 1988, Fractal pore space and rock permeability implications: Physical Review B, 38(4), 2635-2638.
[6]
Angulo, R. F., Alvaraso, V., and Gonzalea, H., 1992, Fractal dimensions from mercury intrusion capillary tests: The Second Latin American Petroleum Engineering Conference, II LAPEC, of the Society of Petroleum Engineers, SPE 23695, 255-263.
[7]
He, Y. D., Mao,Z. Q., Xiao, L. Z., et al., 2005, An improved method of using NMR T2 distribution to evaluate pore size distribution: Chinese Journal of
[8]
Avnir, D., Farin D., and Pfeifer P., 1984, Molecular fractal surfaces: Nature, 308(5956), 261-263.
[9]
Hu, F. L, Zhou, C., Li, C. L., et al., 2016, Water spectrum method of NMR logging for identifying fluids: Petroleum Exploration and Development, 43(2), 244-252.
[10]
Chhabra, A., and Jensen, R. V., 1989, Direct determination of the f(α) singularity spectrum: Physical Review Letters, 62(12), 1327-1330.
[11]
Katz, A. J., and Thompson, A. H., 1985, Fractal sandstone pores: Implications for conductivity and pore formation: Physical Review Letters, 54(12), 1325-1328.
[12]
Falconer, K. J., 1985, The geometry of fractal sets: Cambridge, England.
[13]
Krohn, C. E., 1988, Sandstone fractal and euclidean pore volume distributions: Journal of Geophysical Research-Solid Earth and Planets, 93(B4), 3286-3296.
[14]
Ge, X. M., Fan, Y. R., Li, J. T., et al., 2015, Pore structure characterization and classification using multifractal theoryAn application in Santanghu basin of western China: Journal of Petroleum Science and Engineering, 127, 297-304.
[15]
Li, J. H., and Zheng B., 2015, A New method for fractal characterization of microscopic pores and its application in shale reservoirs: Natural Gas Industry, 2015, 35(5), 52-59.
[16]
Mandelbrot, B. B., 1977, Fractals: Form, Chance and Dimension, San Francisco, W. H. Freeman.
[17]
Pape, H., Riepe, L., and Schopper, J. R., 1982, A pigeon-holemodel for relating permeability to specific surface: The Log Analyst, 23(1), 5-13.
[18]
Hansen, J. P., and Skjeltorp, A. T., 1988, Fractal pore space and rock permeability implications: Physical Review B, 38(4), 2635-2638.
[19]
He, Y. D., Mao,Z. Q., Xiao, L. Z., et al., 2005, An improved method of using NMR T2 distribution to evaluate pore size distribution: Chinese Journal of
[20]
Peng, R. D., Yang Y. C., Ju, Y., et al., 2011, Computation of fractal dimension of rock pores based on gray CT images: Chinese Science Bulletin, 56(26), 2256-2266.
[21]
Pfeifer, P., and Avnir, D., 1983, Chemistry in noninteger dimensions between two and three, fractal theory of heterogenous surface: Journal of Chemical Physics, 79(7), 3558-3565.
[22]
Subhakar, D., and Chandrasekhar, E., 2016, Reservoir characterization using multifractal detrended fluctuation analysis of geophysical well-log data: Physica A, 445(1), 57-65.
[23]
Tan, M. J., Mao, K. Y., Song, X. D., et al., 2015, NMR petrophsical interpretation method of gas shale on core NMR experiment: Journal of Petroleum Science and Engineering, 136, 100-111.
[24]
Tsakiroglou, C. D., and Fleury, M., 1999, Resistivity index of fractional wettability porous media: Journal of Petroleum Science and Engineering, 22, 253-274.
[25]
Volokitin, Y., Looyestigin, W. J., and Slijkerman, W. F. J., et al., 2001, A practical approach to obtain primary drainage capillary pressure curves from NMR core and log data: Petrophysics, 42(4), 334-343.
[26]
Hu, F. L, Zhou, C., Li, C. L., et al., 2016, Water spectrum method of NMR logging for identifying fluids: Petroleum Exploration and Development, 43(2), 244-252.
[27]
Wang, K.W., and Li, N., 2008, Numerical simulation of rock pore throat structure effects on NMR T2 distribution, Applied Geophysics, 5(2), 86-91.
[28]
Wen, H. M., 2003, Study of Fractal Log Interpretation Theory and Method: PhD Thesis, Chengdu University of Technology, Chengdu.
[29]
Xiao, L. Z., 2007, Frontiers Investigation in Well Logging Science: Petroleum Industry Press, Beijing.
[30]
Xiao, L. Z., and Zhang, W., 2008, A new method to construct reservoir capillary pressure curves using NMR log data and its application: Applied Geophysics, 5(2), 92-98.
[31]
Xie, S. Y., He, Z. L., Qiang, Y. X., et al., 2015, Multifractality of 3D pore structures of carbonate rocks based on CT images: Journal of Geology, 39(1), 4653.
[32]
Xu, Z. X., 2014, Heterogeneity of shale reservoirs based on CT images: Lithologic Reservoirs, 26(6), 46-49.
[33]
Yun, H. Y., Zhao, W. J., Liu, B. K., et al., 2002, Researching Rock Pore Structure with T2 Distribution: Well Logging Technology, 26(1), 18-21.
[34]
Katz, A. J., and Thompson, A. H., 1985, Fractal sandstone pores: Implications for conductivity and pore formation: Physical Review Letters, 54(12), 1325-1328.
[35]
Krohn, C. E., 1988, Sandstone fractal and euclidean pore volume distributions: Journal of Geophysical Research-Solid Earth and Planets, 93(B4), 3286-3296.
[36]
Li, J. H., and Zheng B., 2015, A New method for fractal characterization of microscopic pores and its application in shale reservoirs: Natural Gas Industry, 2015, 35(5), 52-59.
[37]
Mandelbrot, B. B., 1977, Fractals: Form, Chance and Dimension, San Francisco, W. H. Freeman.
[38]
Pape, H., Riepe, L., and Schopper, J. R., 1982, A pigeon-holemodel for relating permeability to specific surface: The Log Analyst, 23(1), 5-13.
[39]
Peng, R. D., Yang Y. C., Ju, Y., et al., 2011, Computation of fractal dimension of rock pores based on gray CT images: Chinese Science Bulletin, 56(26), 2256-2266.
[40]
Pfeifer, P., and Avnir, D., 1983, Chemistry in noninteger dimensions between two and three, fractal theory of heterogenous surface: Journal of Chemical Physics, 79(7), 3558-3565.
[41]
Subhakar, D., and Chandrasekhar, E., 2016, Reservoir characterization using multifractal detrended fluctuation analysis of geophysical well-log data: Physica A, 445(1), 57-65.
[42]
Tan, M. J., Mao, K. Y., Song, X. D., et al., 2015, NMR petrophsical interpretation method of gas shale on core NMR experiment: Journal of Petroleum Science and Engineering, 136, 100-111.
[43]
Tsakiroglou, C. D., and Fleury, M., 1999, Resistivity index of fractional wettability porous media: Journal of Petroleum Science and Engineering, 22, 253-274.
[44]
Volokitin, Y., Looyestigin, W. J., and Slijkerman, W. F. J., et al., 2001, A practical approach to obtain primary drainage capillary pressure curves from NMR core and log data: Petrophysics, 42(4), 334-343.
[45]
Wang, K.W., and Li, N., 2008, Numerical simulation of rock pore throat structure effects on NMR T2 distribution, Applied Geophysics, 5(2), 86-91.
[46]
Wen, H. M., 2003, Study of Fractal Log Interpretation Theory and Method: PhD Thesis, Chengdu University of Technology, Chengdu.
[47]
Zhang, C. M., Chen, Z. B., Zhang, Z. S., et al., 2007, Fractal Characteristics of Reservoir Rock Pore Structure based on NMR T2 Distribution: Journal of Oil and Gas Technology, 29(4), 80-86.
[48]
Xiao, L. Z., 2007, Frontiers Investigation in Well Logging Science: Petroleum Industry Press, Beijing.
[49]
Xiao, L. Z., and Zhang, W., 2008, A new method to construct reservoir capillary pressure curves using NMR log data and its application: Applied Geophysics, 5(2), 92-98.
[50]
Xie, S. Y., He, Z. L., Qiang, Y. X., et al., 2015, Multifractality of 3D pore structures of carbonate rocks based on CT images: Journal of Geology, 39(1), 4653.
[51]
Zhou, L., and Kang, Z., 2016, Fractal characterization of pores in shales using NMR: A case study from the Lower Cambrian Niutitang Formation in the Middle Yangtze, Platform, Southwest China: Journal of Natural Gas Science and Engineering, 35(Part A), 860-872.
[52]
Xu, Z. X., 2014, Heterogeneity of shale reservoirs based on CT images: Lithologic Reservoirs, 26(6), 46-49.
[53]
Yun, H. Y., Zhao, W. J., Liu, B. K., et al., 2002, Researching Rock Pore Structure with T2 Distribution: Well Logging Technology, 26(1), 18-21.
[54]
Zhou, S., Liu, D., M., Cai, Y. D., et al., 2016, Fractal characterization of pore-fracture in low-rank coals using a low-field NMR relaxation method: Fuel, 181, 218-226.