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Article

Pore-Fracture System Distribution Heterogeneity by Using the T2 Spectral Curve under a Centrifugal State

by
Tian Tian
1,
Di Zhang
1,
Yong Shi
1,*,
Fangkai Quan
2,* and
Zhenyuan Qin
3
1
The Second Exploration Team of Shandong Coalfield Geological Bureau, Jining 272000, China
2
School of Safety Science and Engineering, Anhui University of Science and Technology, Huainan 232001, China
3
Department of Mechanical, Materials and Manufacturing Engineering, Faculty of Engineering, University of Nottingham, Nottingham NG7 2RD, UK
*
Authors to whom correspondence should be addressed.
Processes 2024, 12(9), 1812; https://doi.org/10.3390/pr12091812
Submission received: 25 July 2024 / Revised: 17 August 2024 / Accepted: 22 August 2024 / Published: 26 August 2024
(This article belongs to the Special Issue Exploration, Exploitation and Utilization of Coal and Gas Resources)
Browse Figures
Versions Notes

Abstract

:
In this paper, 12 sandstone samples are collected from the Taiyuan Formation in Qinshui Basin, and sample types using the T2 spectral under LF-NMR saturation and centrifugation conditions are classified. Moreover, single and multifractal models were used to calculate fractal parameters of saturated and centrifugal T2 spectra, and the correlation between different fractal parameters, pore structure, T2cutoff value, and pore permeability parameters was studied. The results are as follows. (1) According to the T2 spectrum curves under centrifugation and saturation conditions, all the samples can be divided into three types. There are significant differences in the uniform pore size distribution. However, the non-uniformity of small pore distribution in type B samples is stronger than that of other types, while heterogeneity of large pore distribution is weaker than that of different types. The centrifugal T2 spectrum curve exhibits both single-fold and multifractal characteristics. The results of a single fractal by using a centrifugal T2 spectrum are consistent with those of a saturated T2 spectrum, indicating that single fractal features by using centrifugal and saturated T2 spectra are consistent. Unlike the single fractal parameters, the correlation between the saturation and centrifugal T2 spectrum’s multifractal parameters is weak. This suggests that the physical significance conveyed by the centrifugal T2 spectrum’s multifractal parameters differs from that of the saturated T2 spectrum.

1. Introduction

Different from conventional reservoirs, tight sandstone reservoirs have the characteristics of low resources, low porosity and permeability, low single-well production, and high complexity of pore throat structure. Therefore, micropore structure is the main factor affecting reservoir productivity and permeability. As the most important parameter of pore structure, the heterogeneity of pore size distribution is of great significance in describing the pore structure in detail [1]. At present, many experiments are used to study the pore structure of sandstone, including high-pressure mercury intrusion (HPMI), low-temperature liquid nitrogen adsorption (LPN2-GA) test, argon ion polishing scanning electron microscope (SEM), CT scanning test, and so on. Among them, low-field nuclear magnetic resonance (LF-NMR) technology has the advantages of being fast and non-destructive and has become one of the most common experiments to characterize the pore structure of tight sandstone reservoirs. Based on the T2 spectrum in a saturated state, many studies have utilized fractal theory to quantitatively characterize the non-uniformity of pore size distribution [2,3,4,5,6].
Zhang et al. (2020) showed that the fractal model can be divided into single and multifractal models, and then the single-fractal model can be divided into three fractal dimension parameters, namely D1 (T2 is less than the T2 cutoff value, representing a smaller pore size distribution heterogeneity), D2 (T2 is greater than the T2 cutoff value, which characterizes the pore distribution heterogeneity of larger pores), and D3 (characterizes the total pore size distribution heterogeneity) [7,8]. At the same time, the relationship between different fractal parameters and pore structure, pore permeability parameters, and mineral content is discussed [9,10,11,12]. It shows that D1 is positively correlated with pore volume of smaller pore size, and multifractal parameters have good applicability in characterizing the heterogeneity of pore structure of tight sandstone. It is worth noting that the above fractal calculation results are obtained by using the T2 spectrum in the saturated state [13,14,15].
The T2cutoff value calculated by the T2 spectrum under saturated and centrifugal conditions is a key parameter for calculating irreducible water saturation and permeability [16,17,18,19,20,21]. This suggests that the T2 spectrum in the centrifugal state holds significant importance as well. However, only the T2 spectral parameters (peak value, fractal dimension value) in the saturated state are used to predict the T2cutoff value, which also affects the prediction accuracy of the T2cutoff value. In summary, many studies have calculated the fractal dimension of the T2 spectrum in the saturated state and predicted the T2cutoff value using the fractal parameters.
However, there are still the following problems. First, whether the T2 spectrum in the centrifugal state has fractal characteristics remains to be discussed. At the same time, whether the T2 spectrum fractal parameters of the saturated state and the centrifugal state are correlated remains to be further studied.
In this paper, 12 tight sandstone samples were collected from the Taiyuan Formation in the Qinshui Basin. The heterogeneity of pore distribution was analyzed using LF-NMR technology, and then the samples were classified by the T2 spectrum difference under saturated and centrifugal conditions. At the same time, the fractal parameters of saturated and centrifugal T2 spectra were calculated by single (models 1 and 2) and multifractal models, and the differences in fractal parameters under different water content conditions were compared. On this basis, the correlation between different fractal parameters, pore structure, T2cutoff value, and porosity and permeability parameters were discussed.

2. Experimental Test and Theoretical Analysis

2.1. Experimental Test

The target samples were collected from the Ordos Basin in the western part of the North China Plate. It is a typical superimposed basin on the edge of the craton, with a total area of about 37 × 104 km2. The basin is composed of the western margin thrust belt, Tianhuan sag, Yishan slope, western Shanxi bending fold belt, Yimeng uplift, and Weibei uplift tectonic belt [8]. To study the pore distribution of tight sandstone reservoirs at different depths, a total of 12 samples of the Benxi Formation were collected from different exploration wells, with each sampling depth of 3000~3900 m.
Each tight sandstone sample was prepared into a cylinder with a diameter of 25 mm and a height of 30 mm for LF-NMR testing. Parameters such as T2 cutoff value and irreducible water saturation can be obtained by LF-NMR technology. The detailed process is shown in Reference [8]. The nitrogen permeameter can be used to measure gas porosity and permeability [21]. At the same time, all samples were polished with red epoxy resin, and the mineral composition, structure, pore type, and porosity of sandstone samples were determined by polarized light microscopy [22].

2.2. Fractal Theory

The fractal dimension D refers to the Hausdorff dimension, which is an important parameter for describing the complexity of fractal objects. When the Hausdorff dimension of an object is a fraction, the object is called a fractal, and the D value at this time is the fractal dimension of the fractal, abbreviated as fractal dimension or fractional dimension.
Single fractal model: The expression of the single fractal model is as follows [7]:
lg ( V p ) = ( 3 − D w ) lg ( T 2 ) + ( D w − 3 ) lg T 2 max
In the formula, Vp is the pore volume percentage of the T2 spectrum under saturated water condition, %; T2 max is the maximum transverse relaxation time, ms; and Dw is the fractal dimension in saturated water state, dimensionless.
It is worth noting that the above fractal results are obtained by using the T2 spectrum in the saturated state (Figure 1a). The fractal dimension calculated by the T2 spectrum in the centrifugal state is called Di.
Model 1 (D1 and D2): The cutoff value of T2 is obtained by saturation and centrifugal T2 spectra. Using the T2 cutoff value, the T2 spectrum can be divided into movable water and bound water [23]. The part of T2 less than the cutoff value of T2 corresponds to the distribution of bound water [24]. The part of T2 greater than the T2 cutoff value corresponds to the distribution of movable water [25]. The fractal calculation of these two parts is carried out, and the corresponding heterogeneity of irreducible water and movable water distribution is obtained [8].
Model 2 (D3). The distribution heterogeneity of total pores (including movable water and irreducible water) can be obtained by a full-scale linear fitting of the T2 spectrum.
Multifractal model: Multifractal results include two types of speech. A~f (a) is a set of basic languages describing multifractal local characteristics, which is called multifractal spectrum [26,27]. Another set, q~D (q), is introduced from the perspective of information theory, which is called the generalized fractal dimension (Figure 1d). The detailed description is shown in Reference [7].

3. Result and Discussion

3.1. NMR T2 Spectrum Distribution and Type Division

To realize the quantitative characterization of pore fracture structure, according to the relationship between different relaxation times T2 and pore size, it is divided into small pores (T2 is less than 2.5 ms), medium pores (T2 is 2.5~100 ms), and large pores (T2 is greater than 100 ms). According to the T2 spectrum under saturated and centrifugal conditions, all samples can be divided into three categories. Samples 1, 2, 3, and 4 belong to type A, and the T2 spectrum shows a single peak state (the main body of T2 is distributed in 2.5~100 ms). The peak area of T2 in 2.5~20 ms is about 65%. It shows that the percentage of mesopore volume is high, which belongs to the type of mesopore development (Figure 2a). Like the T2 spectrum in the saturated state, the T2 spectrum in the centrifugal state also shows a single peak state (Figure 2b). Samples 5, 6, 7, and 8 belong to type B, and the T2 spectrum shows a single peak state (the main body of T2 is distributed in 10~1000 ms), indicating that the percentage of macroporous pore volume is high and belongs to macroporous development type (Figure 2c). Like the T2 spectrum in the saturated state, the T2 spectrum in the centrifugal state also shows a single peak state (Figure 2d).
Samples 9, 10, 11, and 12 were C-type, and the T2 spectrum showed a single peak state (the main body of T2 was distributed in 0.01~100 ms). The peak area of T2 in 0.01~20 ms was about 75%. It shows that the percentage of mesopore volume of the small hole is higher, which belongs to the transitional type (Figure 2a). Like the T2 spectrum in the saturated state, the T2 spectrum in the centrifugal state also shows a single peak state (Figure 2b). In general, the mesopores and macropores of the samples in this paper are relatively developed.
Figure 3a shows that samples with higher porosity have relatively higher permeability. Compared to other literature, the relationship between permeability and porosity does not follow a power function, which may be related to the small number of samples. There is no correlation between the T2cutoff value and T2 gm, and there is a weak negative correlation between the T2cutoff value and irreducible water saturation (Siwt). Table 1 shows that the porosity and permeability of the C-type samples are smaller than those of other types of samples because small pores are more developed in C-type samples. At the same time, the T2cutoff of type B is larger than that of other types of samples, and the bound water saturation of this type is much lower than that of the other two types. This is because the percentage of large pore volume in this type of sample is higher, which leads to an increase in this value.

3.2. Fractal Characteristics Based on the Saturated T2 Spectrum

Based on Formula (1), the fractal curves of all samples can be obtained (Figure 4). Figure 4a,c show that the fractal curves of A and C samples can be roughly divided into two stages; that is, the fractal dimension values of small pores and large pores are different, indicating that the pore size distribution of these two types is different. Different from type A and C, the fractal curve of type B can be regarded as a straight line, indicating that the pore heterogeneity in different pore size ranges of this kind of sample is small. In general, the single fractal characteristics of different types of samples are different.
Table 2 shows that the D1s (T2 is lower than the T2cutoff value) of type B samples is greater than that of type A and type C, but the D2s (T2 is greater than the T2cutoff value) of type B samples is less than that of type A and type C, indicating that the non-uniformity of small pore distribution in type B samples is stronger than that of other types, and the non-uniformity of large pore distribution in type B samples is weaker than that of other types. Figure 5c shows that the D3s of type C are larger than those of type A and type B, indicating that the total pore distribution inhomogeneity of type C is greater than that of other types. This is because the B-type sample is a large pore development type, and the more developed the large pores, the lower the heterogeneity of the pore distribution.
The multifractal calculation results are shown in Figure 5. The results show that all samples have multifractal characteristics. The D10 of type A samples was 0.43–0.55, the D10 of type B samples was 0.49–0.65, and the D10 of type C samples was 0.57–0.74, indicating that the D10 of type C samples was larger than that of other types of samples. The D−10 of type A samples was 3.24~5.64, the D−10 of type B samples was 4.42~4.87, and the D−10 of type C samples was 2.77~5.44, indicating that the D−10 of type B samples was smaller than that of other types of samples. The D−10-D0 of type A samples is 2.24~4.64, the D−10-D0 of type B samples is 3.42~3.87, and the D−10-D0 of type C samples is 1.77~4.44, indicating that the distribution of low pore volume area of type B samples is the weakest. Table 2 shows that the D−10-D0, D0-D10, and D−10-D10 of type A samples are larger than those of other types of samples, indicating that the overall pore distribution heterogeneity of type A samples is the strongest. It is worth noting that the single-fold results show that the pore distribution inhomogeneity of type A samples is weaker than that of other types of samples, which is different from Figure 4. This is because the calculation principles of the single fractal model and the multifractal model are different, and the physical meanings of the two are different.
Figure 6a shows that with the increase of D−10, D10 gradually decreases. With the increase of D0-D10, D10 increased linearly (Figure 6b). Figure 6c,d show that there is a significant linear positive correlation between D−10-D0 and D−10-D10; however, there is no significant correlation between D0-D10 and D−10-D10, which indicates that the low-value area of pore volume in this kind of sample controls the overall distribution of pore cracks.

3.3. Fractal Characteristics Based on Centrifugal T2 Spectrum

Based on equation 1, the fractal curves of all samples can be obtained by using the centrifugal T2 spectrum (Figure 7). Figure 7a,b show that the fractal curves of A and C samples can be roughly divided into two stages; that is, the fractal dimension values of small pores and large pores are different, indicating that the two types of pore size distribution inhomogeneity are significantly different. Different from type A and C, the fractal curve of type B can be regarded as a straight line, indicating that the pore heterogeneity in different pore size ranges of this kind of sample is small. In general, the single fractal characteristics of different types of samples are different. Figure 8 shows that the results of single fractal parameters based on the centrifugal T2 spectrum are consistent with those of the saturated T2 spectrum and show that the fractal characteristics of the T2 spectrum based on the centrifugal and saturated states are consistent.
Figure 9 shows that the curve based on the centrifugal T2 spectrum still shows multifractal characteristics. Comparing Figure 5, the centrifugal T2 spectrum still shows an anti-S type, and Di is greater than Ds under the same sample. Different from the multifractal saturated T2 spectrum, Table 3 shows that the D0-D10 of type A samples is larger than that of other types of samples, indicating that the distribution heterogeneity of the high pore volume area of type A samples is the strongest. It is worth noting that the difference between D−10-D0 and D−10-D10 of the three samples is small, which also shows that the fractal characteristics of the centrifugal T2 spectrum and the saturated T2 spectrum are different.

3.4. Correlation Analysis of Fractal Parameters under Different Water Content Conditions

Figure 10a shows that D1s and D2s have a weak negative linear relationship, and there is no significant correlation between D1s and D3s. At the same time, except for type B, with the increase of D2s, D3s increases linearly. The single fractal model shows that the heterogeneity of the pore distribution of seepage pores controls the heterogeneity of pore fracture structure distribution. Like the saturated T2 spectrum, the D1i and D2i exhibit a weak negative linear correlation, indicating a limited association between these parameters. Conversely, no significant correlation was observed between D1i and D3i, suggesting that these variables are not closely related. At the same time, except for type B, D3i increases linearly with the increase of D2i. This shows that the fractal characteristics in centrifugal and saturated states are consistent.
Figure 11a,c show that there is no obvious relationship between D0-D10S and D−10-D10S, and D−10-D0S increases with the increase of D−10-D10S, indicating that the low-value area of pore volume affects the heterogeneity of full-scale pore-fracture structure distribution (Figure 11b). In the centrifugal water state, Figure 11a,b show that there is no obvious relationship between D0-D10S, D−10-D10S, and D−10-D10S, which indicates that there are differences in multifractal characteristics between centrifugal and saturated states.
Figure 12a shows that there is a linear positive correlation between the pore fractal dimension D1s based on the saturated T2 spectrum and the pore fractal dimension D1i based on the centrifugal T2 spectrum. At the same time, the macroporous fractal dimension D2s based on the saturated T2 spectrum and the macroporous fractal dimension D2i based on the centrifugal T2 spectrum are linearly positively correlated (Figure 12b), which indicates that the fractal characteristics of the T2 spectrum curves under saturated and centrifugal conditions are consistent. However, there is no obvious relationship between the total pore fractal dimension D3s based on the saturated T2 spectrum and the total pore fractal dimension D3i based on the centrifugal T2 spectrum (Figure 12c). Different from the single multifractal parameters, the correlation between the multifractal parameters of the saturated and centrifugal T2 spectra is weak (Figure 12d–f). This also shows that the physical meaning of the multifractal parameters based on the centrifugal T2 spectrum is different from that of the saturated T2 spectrum.

4. Conclusions

In this paper, 12 tight sandstone samples were collected from the Taiyuan Formation in the Qinshui Basin. The heterogeneity of pore distribution was analyzed using LF-NMR technology, and then the samples were classified by T2 spectrum difference under saturated and centrifugal conditions. At the same time, the fractal parameters of saturated and centrifugal T2 spectra are calculated by single and multifractal models, and the differences in fractal parameters under different water content conditions are compared. On this basis, the correlation between different fractal parameters, pore structure, T2 cutoff value, and porosity and permeability parameters are discussed. The conclusions are as follows.
(1) According to the T2 spectrum curves under centrifugal and saturated conditions, the samples can be divided into three categories. The T2 spectrum of type A is unimodal (the main body of T2 is 2.5~100 ms), which is a mesoporous development type. The T2 spectrum of type B is unimodal (the main body of T2 is distributed in 10~1000 ms), which is a macropore development type. The C-type T2 spectrum is in an unimodal state (the main body of T2 is distributed in 0.01–100 ms), and the volume percentage of small pores and mesopores is high, which is a transitional type. Like the saturated T2 spectrum, the centrifugal T2 spectrum shows a single peak.
(2) The single fractal results of the saturated T2 spectrum show that the fractal dimension values of small pores and large pores of A and C samples are different, indicating that the two types of pore size distribution inhomogeneity have obvious differences. However, the non-uniformity of small pore distribution in type B samples is stronger than that of other types, and the non-uniformity of large pore distribution is weaker than that of other types. The multifractal results of the saturated T2 spectrum show that there is a significant linear positive correlation between D−10-D0 and D−10-D10. However, there is no significant correlation between D0-D10 and D−10-D10, which indicates that the low pore volume area controls the heterogeneity of pore fracture distribution.
(3) The centrifugal T2 spectrum showed single and multifractal characteristics. The results of a single fractal based on the centrifugal T2 spectrum are consistent with those of the saturated T2 spectrum; that is, the single fractal characteristics based on the centrifugal and saturated T2 spectrum are consistent. Different from the single multifractal parameter, the correlation between the multifractal parameters of the saturated and centrifugal T2 spectra is weak, which indicates that the physical meaning of the multifractal parameters based on the centrifugal T2 spectrum is different from that of the saturated T2 spectrum.

Author Contributions

Methodology, T.T. and D.Z.; validation, Y.S. and Z.Q.; analysis, F.Q.; writing—review and editing, T.T., D.Z. and F.Q. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Research Fund of Scientific Research Foundation for High-level Talents of Anhui University of Science and Technology No. 2023yjrc70; National Natural Science Foundation of China (42402175).

Data Availability Statement

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

Author Tian Tian, Di Zhang and Yong Shi were employed by The Second Exploration Team of Shandong Coalfield Geological Bureau. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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Figure 1. Fractal model calculation pattern. (a) T2 spectral morphology under saturated and bound water conditions; (b) Fractal curve based on model 1; (c) Fractal curve based on model 2; (d) Fractal curve based on model 3.
Figure 1. Fractal model calculation pattern. (a) T2 spectral morphology under saturated and bound water conditions; (b) Fractal curve based on model 1; (c) Fractal curve based on model 2; (d) Fractal curve based on model 3.
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Figure 2. Distribution characteristics of the T2 spectrum under saturated and centrifugal conditions. (a,b) T2 spectra of type A samples under saturation and centrifugation conditions; (c,d) T2 spectra of type B samples under saturation and centrifugation conditions; (e,f) T2 spectra of type C samples under saturation and centrifugation conditions.
Figure 2. Distribution characteristics of the T2 spectrum under saturated and centrifugal conditions. (a,b) T2 spectra of type A samples under saturation and centrifugation conditions; (c,d) T2 spectra of type B samples under saturation and centrifugation conditions; (e,f) T2 spectra of type C samples under saturation and centrifugation conditions.
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Figure 3. Correlation of reservoir parameters. (a) the relationship between porosity and permeability; (b) the relationship between the T2cutoff value and other parameters.
Figure 3. Correlation of reservoir parameters. (a) the relationship between porosity and permeability; (b) the relationship between the T2cutoff value and other parameters.
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Figure 4. Single fractal curves of different types of samples based on the saturated T2 spectrum. (a) Single fractal curves of type A samples based on the saturated T2 spectrum; (b) Single fractal curves of type B samples based on the saturated T2 spectrum; (c) Single fractal curves of type C samples based on the saturated T2 spectrum.
Figure 4. Single fractal curves of different types of samples based on the saturated T2 spectrum. (a) Single fractal curves of type A samples based on the saturated T2 spectrum; (b) Single fractal curves of type B samples based on the saturated T2 spectrum; (c) Single fractal curves of type C samples based on the saturated T2 spectrum.
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Processes 12 01812 g005
Figure 5. Multifractal curves of different types of samples based on the saturated T2 spectrum. (a) Multifractal curves of type A samples based on the saturated T2 spectrum; (b) Multifractal curves of type B samples based on the saturated T2 spectrum; (c) Multifractal curves of type C samples based on the saturated T2 spectrum.
Figure 5. Multifractal curves of different types of samples based on the saturated T2 spectrum. (a) Multifractal curves of type A samples based on the saturated T2 spectrum; (b) Multifractal curves of type B samples based on the saturated T2 spectrum; (c) Multifractal curves of type C samples based on the saturated T2 spectrum.
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Processes 12 01812 g006
Figure 6. Correlation analysis of multifractal parameters based on the saturated T2 spectrum. (a) Correlation analysis of D10 and D−10; (b) Correlation analysis of D10 and D0-D10; (c) Correlation analysis of D−10-D0 and D−10-D10; (d) Correlation analysis of D0-D10 and D−10-D10.
Figure 6. Correlation analysis of multifractal parameters based on the saturated T2 spectrum. (a) Correlation analysis of D10 and D−10; (b) Correlation analysis of D10 and D0-D10; (c) Correlation analysis of D−10-D0 and D−10-D10; (d) Correlation analysis of D0-D10 and D−10-D10.
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Processes 12 01812 g007
Figure 7. Single fractal curves of different types of samples based on the centrifugal state T2 spectrum. (a) Single fractal curves of types A samples based on the centrifugal state T2 spectrum; (b) Single fractal curves of types C samples based on the centrifugal state T2 spectrum.
Figure 7. Single fractal curves of different types of samples based on the centrifugal state T2 spectrum. (a) Single fractal curves of types A samples based on the centrifugal state T2 spectrum; (b) Single fractal curves of types C samples based on the centrifugal state T2 spectrum.
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Processes 12 01812 g008
Figure 8. Single fractal comparison of different types of samples based on the centrifugal state T2 spectrum. (a) Single fractal comparison of D1i based on the centrifugal state T2 spectrum; (b) Single fractal comparison of D2i based on the centrifugal state T2 spectrum; (c) Single fractal comparison of D3i based on the centrifugal state T2 spectrum.
Figure 8. Single fractal comparison of different types of samples based on the centrifugal state T2 spectrum. (a) Single fractal comparison of D1i based on the centrifugal state T2 spectrum; (b) Single fractal comparison of D2i based on the centrifugal state T2 spectrum; (c) Single fractal comparison of D3i based on the centrifugal state T2 spectrum.
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Processes 12 01812 g009
Figure 9. Multifractal curves of different types of samples based on the centrifugal T2 spectrum. (a) Multifractal curves of types A samples based on the centrifugal T2 spectrum; (b) Multifractal curves of types B samples based on the centrifugal T2 spectrum.
Figure 9. Multifractal curves of different types of samples based on the centrifugal T2 spectrum. (a) Multifractal curves of types A samples based on the centrifugal T2 spectrum; (b) Multifractal curves of types B samples based on the centrifugal T2 spectrum.
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Processes 12 01812 g010aProcesses 12 01812 g010b
Figure 10. Correlation analysis of single fractal parameters based on the centrifugal and saturated T2 spectra. (a) Correlation analysis of D1s and D2s; (b) Correlation analysis of D1s and D3s; (c) Correlation analysis of D2s and D3s; (d) Correlation analysis of D1i and D2i; (e) Correlation analysis of D1i and D3i; (f) Correlation analysis of D2i and D3i.
Figure 10. Correlation analysis of single fractal parameters based on the centrifugal and saturated T2 spectra. (a) Correlation analysis of D1s and D2s; (b) Correlation analysis of D1s and D3s; (c) Correlation analysis of D2s and D3s; (d) Correlation analysis of D1i and D2i; (e) Correlation analysis of D1i and D3i; (f) Correlation analysis of D2i and D3i.
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Figure 11. Correlation analysis of multifractal parameters based on the centrifugal and saturated T2 spectra. (a) Correlation analysis of D0-D10S and D−10-D0S; (b) Correlation analysis of D−10-D0S and D−10-D10S; (c) Correlation analysis of D0-D10i and D−10-D0i; (d) Correlation analysis of D−10-D0i and D−10-D10i.
Figure 11. Correlation analysis of multifractal parameters based on the centrifugal and saturated T2 spectra. (a) Correlation analysis of D0-D10S and D−10-D0S; (b) Correlation analysis of D−10-D0S and D−10-D10S; (c) Correlation analysis of D0-D10i and D−10-D0i; (d) Correlation analysis of D−10-D0i and D−10-D10i.
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Processes 12 01812 g012
Figure 12. Correlation analysis of fractal parameters based on the centrifugal and saturated T2 spectra. (a) Correlation analysis of D1s and D1i; (b) Correlation analysis of D2s and D2i; (c) Correlation analysis of D3s and D3i; (d) Correlation analysis of D−10-D0s and D−10-D0i; (e) Correlation analysis of D0-D10s and D0-D10i; (f) Correlation analysis of D−10-D10s and D−10-D10i.
Figure 12. Correlation analysis of fractal parameters based on the centrifugal and saturated T2 spectra. (a) Correlation analysis of D1s and D1i; (b) Correlation analysis of D2s and D2i; (c) Correlation analysis of D3s and D3i; (d) Correlation analysis of D−10-D0s and D−10-D0i; (e) Correlation analysis of D0-D10s and D0-D10i; (f) Correlation analysis of D−10-D10s and D−10-D10i.
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Table 1. Sample basic information table.
Table 1. Sample basic information table.
TypeSampleDepth
(m)		Φnitrogen (%)Permeability (mD)Φwatet (%)ΦNMR
(%)		T2 cutoff Value (ms)T2gm
(ms)		Swi (%)
I13540.102.800.112.622.504.643.0963.28
23526.757.500.328.107.882.68 4.85 29.15
33908.599.630.469.859.252.282.2549.02
43802.085.340.035.935.664.082.1261.84
II53834.686.160.306.025.9857.2061.0037.38
63383.36.570.317.157.0264.8553.1242.94
73027.686.500.326.756.5440.0147.4038.02
83177.645.720.326.055.8260.9062.4739.06
III93802.085.340.035.935.664.082.1261.84
103801.224.890.034.964.903.381.4865.34
113801.83.650.133.733.573.38 2.4256.09
123810.93.210.033.423.382.451.52 61.05
Table 2. Summary table of single and multifractal parameters based on the saturated state.
Table 2. Summary table of single and multifractal parameters based on the saturated state.
TypeSampleD1sD2sD3sD10D−10D2D−10-D0D0-D10f10-f−10D−10-D10
I11.44 2.93 2.29 0.55 3.24 0.71 2.24 0.45 0.07 2.69
21.28 2.87 2.12 0.43 5.46 0.48 4.46 0.57 0.23 5.03
31.11 2.93 2.22 0.47 5.64 0.55 4.64 0.53 0.03 5.17
41.44 2.94 2.33 0.57 5.44 0.67 4.44 0.43 0.44 4.88
II52.32 2.71 2.32 0.53 4.48 0.59 3.48 0.47 −0.27 3.95
62.25 2.69 2.37 0.65 4.87 0.78 3.87 0.35 −0.16 4.22
71.88 2.78 2.09 0.49 4.42 0.57 3.42 0.51 −0.62 3.92
82.23 2.68 2.29 0.56 4.57 0.64 3.57 0.44 −0.32 4.00
III91.47 2.94 2.33 0.57 5.44 0.67 4.44 0.43 0.44 4.88
101.40 2.95 2.37 0.73 5.29 0.75 4.29 0.27 0.65 4.57
111.34 2.91 2.32 0.68 3.09 0.75 2.09 0.32 0.73 2.40
121.28 2.93 2.37 0.74 2.77 0.77 1.77 0.26 0.42 2.03
Table 3. Based on the summary table of single and multifractal parameters in the centrifugal state.
Table 3. Based on the summary table of single and multifractal parameters in the centrifugal state.
TypeSampleD1sD2sD3sD10D−10D2D−10-D0D0-D10f10-f−10D−10-D10
I11.40 2.98 2.30 0.54 4.73 0.61 3.73 0.46 −0.07 4.19
21.28 2.92 2.21 0.31 3.44 0.44 2.44 0.69 0.33 3.13
31.22 2.95 2.33 0.63 5.22 0.66 4.22 0.37 0.12 4.59
41.04 2.97 2.19 0.61 5.11 0.64 4.11 0.39 0.12 4.51
II52.07 2.88 2.32 0.62 4.38 0.74 3.38 0.38 −0.68 3.76
61.86 2.87 2.15 0.68 3.55 0.82 2.55 0.32 0.11 2.88
71.95 2.97 2.21 0.51 5.31 0.59 4.31 0.49 0.26 4.81
82.20 2.85 2.37 0.63 4.45 0.75 3.45 0.37 −0.43 3.83
III91.08 2.97 2.19 0.61 5.11 0.64 4.11 0.39 0.12 4.51
101.31 2.99 2.37 0.72 4.78 0.79 3.78 0.28 0.04 4.06
111.36 2.98 2.37 0.70 4.68 0.76 3.68 0.30 0.11 3.97
121.12 2.98 2.34 0.68 4.53 0.76 3.53 0.32 −0.01 3.84
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Tian, T.; Zhang, D.; Shi, Y.; Quan, F.; Qin, Z. Pore-Fracture System Distribution Heterogeneity by Using the T2 Spectral Curve under a Centrifugal State. Processes 2024, 12, 1812. https://doi.org/10.3390/pr12091812

AMA Style

Tian T, Zhang D, Shi Y, Quan F, Qin Z. Pore-Fracture System Distribution Heterogeneity by Using the T2 Spectral Curve under a Centrifugal State. Processes. 2024; 12(9):1812. https://doi.org/10.3390/pr12091812

Chicago/Turabian Style

Tian, Tian, Di Zhang, Yong Shi, Fangkai Quan, and Zhenyuan Qin. 2024. "Pore-Fracture System Distribution Heterogeneity by Using the T2 Spectral Curve under a Centrifugal State" Processes 12, no. 9: 1812. https://doi.org/10.3390/pr12091812

APA Style

Tian, T., Zhang, D., Shi, Y., Quan, F., & Qin, Z. (2024). Pore-Fracture System Distribution Heterogeneity by Using the T2 Spectral Curve under a Centrifugal State. Processes, 12(9), 1812. https://doi.org/10.3390/pr12091812

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