Application of Multifractal Theory for Determination of Fluid Movability of Coal-Measure Sedimentary Rocks Using Nuclear Magnetic Resonance (NMR)
Abstract
:1. Introduction
2. Materials and Methods
2.1. Rock Samples
2.2. NMR Measurements
2.3. Multifractal Analysis
3. Results
3.1. Petrophysical Properties
3.2. Mineralogical Compositions
3.3. T2 Distributions
3.4. Multifractal Characteristics
3.5. Free-Fluid Volume Index (FFI)
4. Discussion
4.1. Correlation between Physical Properties and FFI
4.2. Correlation between Clay Minerals and FFI
4.3. Correlation between Multifractal Characteristics and FFI
4.4. FFI Prediction Model
5. Conclusions
- The pore structure and multifractal properties of three typical coal-measure sedimentary rocks from China’s Daqiang Coal Mine were explored utilizing NMR experiments, and a FFI prediction model was created using multifractal theory. The main conclusions are as follows.
- The experimental samples consist primarily of micropores and transition pores, and the range of FFI is 7.65% to 18.36%.
- Different physical parameters and mineral components have multiple effects on the FFI. Porosity, kaolinite content, and FFI exhibit a linear positive correlation, whereas chlorite and illite depict a linear negative correlation, with no apparent correlation between permeability and the FFI.
- The selected samples have prominent multifractal characteristics, in which the multifractal dimension (Dq) is linearly positively correlated with the FFI, and the multifractal subtraction (Dmin − Dmax), the multifractal dimension proportion (Dmin/Dmax), and the singularity strengths (Δα) are negatively correlated with the FFI.
- Utilizing NMR data from eight samples and multifractal theory, a prediction model for FFI was constructed and verified employing experimental data from five samples. The anticipated outcomes correspond closely to the experimental data.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
BVI | bound fluid volume index, % |
Ck | the content of kaolinite, % |
Cc | the content of chlorite, % |
CI | the content of illite, % |
Dq | multifractal dimension |
Dmin − Dmax | multifractal dimension subtraction |
Dmin/Dmax | multifractal dimension proportion |
Dmin − D0 | the breadth of the left branch of the generalized dimension spectrum |
D0 − Dmax | the breadth of the right branch of the generalized dimension spectrum |
D0 | capacity dimension |
D1 | information dimension |
D2 | correlation dimension |
FFI | free-fluid volume index, % |
f(α) | the multifractal singularity spectrum |
K | Permeability, mD |
L | the side length of the box |
Ni(ε) | the total volume of pores in the ith box |
Nα(ε) | the number of boxes with the same α value |
NECH | number of echoes |
Pi(ε) | probability mass function |
P1 | 90° pulse width, μs |
P2 | 180° pulse width, μs |
q | an order of the matrix |
SW | spectral width, KHz |
S/N | signal-noise ratio |
T2 | transverse relaxation time, ms |
T2b | bulk relaxation time, ms |
T2c | transverse relaxation time cutoff value, ms |
T2d | diffusion relaxation time, ms |
T2s | surface relaxation time, ms |
TE | echo time, ms |
TW | waiting time, ms |
X(q,ε) | the partition function |
α | singularity strength |
α(q) | singular strength of the q value |
αmax | the maximum value of singularity strength |
αmin | the minimum value of singularity strength |
αi | the Lipschitz–Hölder singularity exponent |
φ | porosity, |
%ε | equal-size |
References
- Zhang, N.; Wang, S.; Zhao, F.; Sun, X.; He, M. Characterization of the Pore Structure and Fluid Movability of Coal-Measure Sedimentary Rocks by Nuclear Magnetic Resonance (NMR). ACS Omega 2021, 6, 22831–22839. [Google Scholar] [CrossRef]
- Jiang, J.; Yang, W.; Cheng, Y.; Zhao, K.; Zheng, S. Pore structure characterization of coal particles via MIP, N2 and CO2 adsorption: Effect of coalification on nanopores evolution. Powder Technol. 2019, 354, 136–148. [Google Scholar] [CrossRef]
- Zhou, L.; Kang, Z. Fractal characterization of pores in shales using NMR: A case study from the Lower Cambrian Niutitang Formation in the Middle Yangtze Platform, Southwest China. J. Nat. Gas. Sci. Eng. 2016, 35, 860–872. [Google Scholar] [CrossRef]
- Yu, S.; Bo, J.; Fengli, L.; Jiegang, L. Structure and fractal characteristic of micro- and meso-pores in low, middle-rank tectonic deformed coals by CO2 and N2 adsorption. Micropor Mesopor Mat. 2017, 253, 191–202. [Google Scholar] [CrossRef]
- Gao, Z.; Liang, Z.; Qinhong, H.; Jiang, Z.; Xuan, Q. A new and integrated imaging and compositional method to investigate the contributions of organic matter and inorganic minerals to the pore spaces of lacustrine shale in China. Mar. Pet. Geol. 2021, 127, 104962. [Google Scholar] [CrossRef]
- Zhang, N.; Zhao, F.; Guo, P.; Li, J.; Gong, W.; Guo, Z.; Sun, X. Nanoscale Pore Structure Characterization and Permeability of Mudrocks and Fine-Grained Sandstones in Coal Reservoirs by Scanning Electron Microscopy, Mercury Intrusion Porosimetry, and Low-Field Nuclear Magnetic Resonance. Geofluids 2018, 2018, 2905141. [Google Scholar] [CrossRef]
- Yang, S.; Yang, F.; Lyu, C.; Li, C.; Chen, G.; Ma, M.; Xue, L. Variations of Pore Structure and Methane Adsorption of Continental Deformed Shales from Small-Scale Anticline and Syncline: Two Cases Study of the Triassic Yanchang Formation, Ordos Basin and Jurassic Yaojie Formation, Minhe Basin. ACS Omega 2022, 7, 48224–48239. [Google Scholar] [CrossRef]
- Yuchen, F.; Keyu, L. Large-volume FIB-SEM 3D reconstruction: An effective method for characterizing pore space of lacustrine shales. Front. Earth Sci. 2023, 10, 1046927. [Google Scholar] [CrossRef]
- Gu, Y.; Wan, Q.; Li, X.; Han, T.; Yang, S.; Hu, Q. Structure and Evolution of Clay-Organic Nanocomposites in Three Leading Shales in China. J. Earth Sci. 2023, 34, 824–837. [Google Scholar] [CrossRef]
- Zuo, H.; Zhai, C.; Deng, S.; Jiang, X.; Javadpour, F. Lattice Boltzmann modeling of gaseous microflow in shale nanoporous media. Fuel 2023, 337, 127087. [Google Scholar] [CrossRef]
- Liu, W.; Wang, G.; Han, D.; Xu, H.; Chu, X. Accurate characterization of coal pore and fissure structure based on CT 3D reconstruction and NMR. J. Nat. Gas Sci. Eng. 2021, 96, 104242. [Google Scholar] [CrossRef]
- Fang, H.; Wang, Z.; Sang, S.; Liu, S.; Gu, C.; Yang, J.; Li, L.; Huang, Y. Correlation Evaluation and Schematic Analysis of Influencing Factors Affecting Pore and Fracture Connectivity on the Microscale and Their Application Discussion in Coal Reservoir Based on X-ray CT Data. ACS Omega 2023, 8, 11852–11867. [Google Scholar] [CrossRef] [PubMed]
- Liu, S.; Zhang, L.; Su, X.; Zhao, L.; Wang, Y. Micro-CT characterization on pore structure evolution of low-permeability sandstone under acid treatment. Appl. Geochem. 2023, 152, 105633. [Google Scholar] [CrossRef]
- Shi, X.; Xu, H.; Che, M.; Xiao, C.; Ni, H.; Gao, Q. Investigations of fracture behavior and pore structure change in pulse fracturing for cement block. Int. J. Rock. Mech. Min. 2023, 166, 105366. [Google Scholar] [CrossRef]
- Okolo, G.N.; Everson, R.C.; Neomagus, H.W.J.P.; Roberts, M.J.; Sakurovs, R. Comparing the porosity and surface areas of coal as measured by gas adsorption, mercury intrusion and SAXS techniques. Fuel 2015, 141, 293–304. [Google Scholar] [CrossRef]
- Jia, T.; Zhang, S.; Tang, S.; Xin, D.; Zhang, Q.; Zhang, K. Pore Structure and Adsorption Characteristics of Maceral Groups: Insights from Centrifugal Flotation Experiment of Coals. ACS Omega 2023, 8, 12079–12097. [Google Scholar] [CrossRef]
- Zhang, Q.; Zhu, H.; Kang, R.; Zhang, L.; Fang, S.; Hu, L.; Qu, B.; Liao, Q. Insight into the effect of biaxial compression strain on adsorption structure of bituminous coal matrix as well as gas diffusion and permeability properties by macromolecule simulation. Fuel 2023, 338, 127223. [Google Scholar] [CrossRef]
- Li, X.; Kang, Y.; Haghighi, M. Investigation of pore size distributions of coals with different structures by nuclear magnetic resonance (NMR) and mercury intrusion porosimetry (MIP). Measurement 2018, 116, 122–128. [Google Scholar] [CrossRef]
- Li, Y.; Song, D.; Liu, S.; Ji, X.; Hao, H. Evaluation of pore properties in coal through compressibility correction based on mercury intrusion porosimetry: A practical approach. Fuel 2021, 291, 120130. [Google Scholar] [CrossRef]
- Zhang, R.; Jiang, S.; Zhang, L.; Wang, H.; Zhang, T.; Yu, R.; Zhang, L.; Chima, F.U.; Fattah, M. Microscopic Pore Structures and Their Controlling Factors of the Lower Carboniferous Luzhai Shale in Guizhong Depression, China. Geofluids 2023, 2023, 8890709. [Google Scholar] [CrossRef]
- Yao, Y.; Liu, D.; Che, Y.; Tang, D.; Tang, S.; Huang, W. Petrophysical characterization of coals by low-field nuclear magnetic resonance (NMR). Fuel 2010, 89, 1371–1380. [Google Scholar] [CrossRef]
- Gao, J.; Wei, H.; Zhou, R.; Ren, Q.; Tian, T.; Ning, B.; Ding, X.; Zhang, Z.; Fattah, M. Study on the Coupling Law between Pore-Scale Fluid Flow Capacity and Pore-Throat Configuration in Tight Sandstone Reservoirs. Geofluids 2023, 2023, 1693773. [Google Scholar] [CrossRef]
- Hu, T.; Pan, T.; Chen, L.; Li, J.; Liu, Y. Pore structure characterization and deliverability prediction of fractured tight glutenite reservoir based on geophysical well logging. Acta Geophysica 2023. [Google Scholar] [CrossRef]
- Zheng, S.; Sang, S.; Yao, Y.; Liu, D.; Liu, S.; Wang, M.; Feng, G. A multifractal-based method for determination NMR dual T2 cutoffs in coals. J. Pet. Sci. Eng. 2022, 214, 110488. [Google Scholar] [CrossRef]
- Wang, G.; Han, D.; Qin, X.; Liu, Z.; Liu, J. A comprehensive method for studying pore structure and seepage characteristics of coal mass based on 3D CT reconstruction and NMR. Fuel 2020, 281, 118735. [Google Scholar] [CrossRef]
- Zhao, Y.; Sun, Y.; Liu, S.; Wang, K.; Jiang, Y. Pore structure characterization of coal by NMR cryoporometry. Fuel 2017, 190, 359–369. [Google Scholar] [CrossRef]
- Hui, W.; Wang, Y.; Ren, D.; Jin, H. Effects of pore structures on the movable fluid saturation in tight sandstones: A He8 formation example in Sulige Gasfield, Ordos Basin, China. J. Pet. Sci. Eng. 2020, 192, 107295. [Google Scholar] [CrossRef]
- Wang, W.; Yue, D.; Eriksson, K.A.; Liu, X.; Liang, X.; Qu, X.; Xie, Q. Qualitative and quantitative characterization of multiple factors that influence movable fluid saturation in lacustrine deep-water gravity-flow tight sandstones from the Yanchang Formation, southern Ordos Basin, China. Mar. Pet. Geol. 2020, 121, 104625. [Google Scholar] [CrossRef]
- Fu, H.; Tang, D.; Xu, T.; Xu, H.; Tao, S.; Li, S.; Yin, Z.; Chen, B.; Zhang, C.; Wang, L. Characteristics of pore structure and fractal dimension of low-rank coal: A case study of Lower Jurassic Xishanyao coal in the southern Junggar Basin, NW China. Fuel 2017, 193, 254–264. [Google Scholar] [CrossRef]
- Deng, S.; Xiong, F.; Liu, Y.; Jiang, Q. Temperature-Dependent Permeability Model of Granite After Thermal Treatment Based on Energy Dissipation Theory and Fractal Theory. Rock. Mech. Rock. Eng. 2023. [Google Scholar] [CrossRef]
- Liu, S.; Huang, Z. Mesopore Fractal Characteristics in Low-Permeability Sandstone Affected by High Temperature Using NMR. Appl. Magn. Reson. 2023. [Google Scholar] [CrossRef]
- Yang, F.; Wang, F.; Du, J.; Yang, S.; Wen, R. Fractal characteristics of artificially matured lacustrine shales from Ordos Basin, West China. J. Pet. Explor. Prod. Technol. 2023, 13, 1703–1713. [Google Scholar] [CrossRef]
- Yao, Y.; Liu, D.; Tang, D.; Tang, S.; Huang, W. Fractal characterization of adsorption-pores of coals from North China: An investigation on CH4 adsorption capacity of coals. Int. J. Coal. Geol. 2008, 73, 27–42. [Google Scholar] [CrossRef]
- Zhang, N.; Wang, S.; Xun, X.; Wang, H.; Sun, X.; He, M. Pore Structure and Fractal Characteristics of Coal-Measure Sedimentary Rocks Using Nuclear Magnetic Resonance (NMR) and Mercury Intrusion Porosimetry (MIP). Energies 2023, 16, 3812. [Google Scholar] [CrossRef]
- Li, X.; Wei, W.; Wang, L.; Cai, J. Fractal Dimension of Digital 3D Rock Models with Different Pore Structures. Energies 2022, 15, 7461. [Google Scholar] [CrossRef]
- Wang, D.; Xie, Z.; Hu, H.; Wang, T.; Deng, Z. Pore Structure and Fractal Characteristics of Marine–Continental Transitional Black Shales: A Case Study of the Permian Shanxi Formation in the Eastern Margin of the Ordos Basin. Processes 2023, 11, 1424. [Google Scholar] [CrossRef]
- Zhao, P.; Wang, Z.; Sun, Z.; Cai, J.; Wang, L. Investigation on the pore structure and multifractal characteristics of tight oil reservoirs using NMR measurements: Permian Lucaogou Formation in Jimusaer Sag, Junggar Basin. Mar. Pet. Geol. 2017, 86, 1067–1081. [Google Scholar] [CrossRef]
- Wang, W.; Wang, R.; Wang, L.; Qu, Z.; Ding, X.; Gao, C.; Meng, W. Pore Structure and Fractal Characteristics of Tight Sandstones Based on Nuclear Magnetic Resonance: A Case Study in the Triassic Yanchang Formation of the Ordos Basin, China. ACS Omega 2023, 8, 16284–16297. [Google Scholar] [CrossRef]
- Zhao, D.; Guo, Y.; Wang, G.; Guan, X.; Zhou, X.; Liu, J. Fractal Analysis and Classification of Pore Structures of High-Rank Coal in Qinshui Basin, China. Energies 2022, 15, 6766. [Google Scholar] [CrossRef]
- Zhang, P.; Lu, S.; Li, J.; Chen, C.; Xue, H.; Zhang, J. Petrophysical characterization of oil-bearing shales by low-field nuclear magnetic resonance (NMR). Mar. Pet. Geol. 2018, 89, 775–785. [Google Scholar] [CrossRef]
- Halsey, T.C.; Jensen, M.H.; Kadanoff, L.P.; Procaccia, I.I.; Shraiman, B.I. Fractal measures and their singularities: The characterization of strange sets. Phys. Rev. A Gen. Phys. 1986, 33, 1141–1151. [Google Scholar] [CrossRef] [PubMed]
- Chhabra, A.; Jensen, R.V. Direct determination of the f( alpha ) singularity spectrum. Phys. Rev. Lett. 1989, 62, 1327–1330. [Google Scholar] [CrossRef]
- Zheng, S.; Yao, Y.; Liu, D.; Cai, Y.; Liu, Y.; Li, X. Nuclear magnetic resonance T2 cutoffs of coals: A novel method by multifractal analysis theory. Fuel 2019, 241, 715–724. [Google Scholar] [CrossRef]
- Hou, X.; Zhu, Y.; Chen, S.; Wang, Y.; Liu, Y. Investigation on pore structure and multifractal of tight sandstone reservoirs in coal bearing strata using LF-NMR measurements. J. Pet. Sci. Eng. 2019, 187, 106757. [Google Scholar] [CrossRef]
- Zhu, J.; Zhang, Y.; Zhang, R.; Zhang, B.; Tang, J.; He, F. Surface fractal dimensions as a characterization parameter for methane adsorption–induced coal strains. Arab. J. Geosci. 2020, 13, 997. [Google Scholar] [CrossRef]
- Liu, K.; Ostadhassan, M.; Kong, L. Fractal and Multifractal Characteristics of Pore Throats in the Bakken Shale. Transp. Porous Med. 2018, 126, 579–598. [Google Scholar] [CrossRef]
- Zhao, P.; Wang, X.; Cai, J.; Luo, M.; Zhang, J.; Liu, Y.; Rabiei, M.; Li, C. Multifractal analysis of pore structure of Middle Bakken formation using low temperature N2 adsorption and NMR measurements. J. Pet. Sci. Eng. 2019, 176, 312–320. [Google Scholar] [CrossRef]
Attribute | Parameter φ (%) |
---|---|
Spectrometer frequency (SF) | 12 MHz |
The constant magnetic field strength of NMR | 0.12 T |
Pulse sequence | Carr–Purcell–Meiboom–Gill (CMPG) |
90° pulse width (P1) | 14.80 μs |
180° pulse width (P2) | 28.8 μs |
Spectral width (SW) | 250 KHz |
Waiting time (TW) | 3000 ms |
Echo time (TE) | 0.18 ms |
Number of echoes (NECH) | 14,000 |
Signal–noise ratio (S/N) | 200 |
Sample No. | Density (cm3/g) | He Porosity (%) | NMR Porosity (%) | Permeability (mD) |
---|---|---|---|---|
SS-1 | 2.53 | 9.27 | 9.12 | 0.0070 |
SS-2 | 2.48 | 10.24 | 9.87 | 0.0030 |
SH-1 | 2.52 | 4.15 | 3.85 | 0.0050 |
SH-2 | 2.51 | 7.75 | 7.45 | 0.0030 |
SH-3 | 2.69 | 9.89 | 10.13 | 0.0010 |
SH-4 | 2.37 | 4.95 | 5.05 | 0.0020 |
SH-5 | 2.42 | 4.21 | 4.03 | 0.0010 |
MS-1 | 2.43 | 9.15 | 9.4 | 0.0020 |
MS-2 | 2.45 | 10.73 | 10.69 | 0.0030 |
MS-3 | 2.38 | 9.18 | 9.73 | 0.0010 |
MS-4 | 2.44 | 10.01 | 10.45 | 0.0017 |
MS-5 | 2.41 | 9.62 | 10.17 | 0.0012 |
MS-6 | 2.42 | 9.73 | 9.85 | 0.0026 |
Sample No. | Dmin | D−2 | D−1 | D0 | D1 | D2 | Dmax | Dmin − Dmax | Dmin/Dmax | Δα |
---|---|---|---|---|---|---|---|---|---|---|
SS-1 | 2.267 | 1.677 | 1.343 | 0.977 | 0.860 | 0.741 | 0.671 | 1.596 | 3.378 | 1.845 |
SS-2 | 2.144 | 1.611 | 1.343 | 0.980 | 0.860 | 0.748 | 0.679 | 1.464 | 3.155 | 1.701 |
SH-1 | 1.494 | 1.186 | 1.073 | 0.923 | 0.830 | 0.745 | 0.669 | 0.825 | 2.234 | 0.995 |
SH-2 | 1.596 | 1.187 | 1.075 | 0.926 | 0.840 | 0.741 | 0.667 | 0.929 | 2.394 | 0.998 |
SH-3 | 2.332 | 1.704 | 1.314 | 0.865 | 0.790 | 0.720 | 0.667 | 1.666 | 3.498 | 1.922 |
SH-4 | 1.946 | 1.605 | 1.392 | 1.000 | 0.880 | 0.751 | 0.683 | 1.263 | 2.848 | 1.418 |
SH-5 | 1.954 | 1.602 | 1.299 | 0.848 | 0.770 | 0.699 | 0.649 | 1.305 | 3.011 | 1.717 |
MS-1 | 1.350 | 1.043 | 0.912 | 0.782 | 0.730 | 0.683 | 0.631 | 0.719 | 2.140 | 0.872 |
MS-2 | 2.655 | 1.952 | 1.516 | 0.873 | 0.770 | 0.677 | 0.624 | 2.032 | 4.258 | 2.317 |
MS-3 | 1.822 | 1.345 | 1.072 | 0.791 | 0.730 | 0.677 | 0.625 | 1.197 | 2.913 | 1.398 |
MS-4 | 2.384 | 1.750 | 1.352 | 0.852 | 0.770 | 0.691 | 0.638 | 1.747 | 3.740 | 2.006 |
MS-5 | 1.438 | 1.113 | 0.955 | 0.797 | 0.740 | 0.692 | 0.639 | 0.799 | 2.249 | 0.951 |
MS-6 | 1.820 | 1.348 | 1.075 | 0.804 | 0.740 | 0.680 | 0.627 | 1.192 | 2.901 | 1.394 |
Sample No. | T2 (ms) | FFI (%) | BVI (%) | FFI/BVI |
---|---|---|---|---|
SS-1 | 2.23 | 13.42 | 86.58 | 0.155 |
SS-2 | 2.77 | 13.02 | 86.98 | 0.150 |
SH-1 | 1.86 | 10.16 | 89.84 | 0.113 |
SH-2 | 1.55 | 14.46 | 85.54 | 0.169 |
SH-3 | 2.83 | 8.81 | 91.19 | 0.097 |
SH-4 | 4.64 | 11.59 | 88.41 | 0.131 |
SH-5 | 1.55 | 12.07 | 87.93 | 0.137 |
MS-1 | 2.48 | 7.93 | 92.07 | 0.086 |
MS-2 | 2.97 | 10.56 | 89.44 | 0.118 |
MS-3 | 2.95 | 8.34 | 91.66 | 0.091 |
MS-4 | 2.87 | 8.65 | 91.35 | 0.095 |
MS-5 | 2.51 | 12.44 | 87.56 | 0.142 |
MS-6 | 2.71 | 11.59 | 88.41 | 0.131 |
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Zhang, N.; Wang, S.; Li, Z.; Guo, S.; Wang, R. Application of Multifractal Theory for Determination of Fluid Movability of Coal-Measure Sedimentary Rocks Using Nuclear Magnetic Resonance (NMR). Fractal Fract. 2023, 7, 503. https://doi.org/10.3390/fractalfract7070503
Zhang N, Wang S, Li Z, Guo S, Wang R. Application of Multifractal Theory for Determination of Fluid Movability of Coal-Measure Sedimentary Rocks Using Nuclear Magnetic Resonance (NMR). Fractal and Fractional. 2023; 7(7):503. https://doi.org/10.3390/fractalfract7070503
Chicago/Turabian StyleZhang, Na, Shuaidong Wang, Zheng Li, Shuhui Guo, and Ruochen Wang. 2023. "Application of Multifractal Theory for Determination of Fluid Movability of Coal-Measure Sedimentary Rocks Using Nuclear Magnetic Resonance (NMR)" Fractal and Fractional 7, no. 7: 503. https://doi.org/10.3390/fractalfract7070503
APA StyleZhang, N., Wang, S., Li, Z., Guo, S., & Wang, R. (2023). Application of Multifractal Theory for Determination of Fluid Movability of Coal-Measure Sedimentary Rocks Using Nuclear Magnetic Resonance (NMR). Fractal and Fractional, 7(7), 503. https://doi.org/10.3390/fractalfract7070503