Fractal-Based Approaches to Pore Structure Investigation and Water Saturation Prediction from NMR Measurements: A Case Study of the Gas-Bearing Tight Sandstone Reservoir in Nanpu Sag
Abstract
:1. Introduction
2. Methodology
2.1. Pore Structure Investigation of Water-Saturated Tight Sandstone Based on Fractal Analysis from NMR Spectra
2.2. Water Saturation Prediction Method of Gas-Bearing Tight Sandstone Based on Fractal Analysis from NMR Spectra
3. Model Validation
3.1. Pore Structure Characterization Method Based on Fractal Analysis from NMR Spectra
3.2. Water Saturation Prediction Method Based on Fractal Analysis from NMR Spectra
4. Application
5. Discussion and Future Work
5.1. Relationship of the Fractal Dimension from NMR with the Pore Size from the T2 Spectrum
5.2. Relationship of the Fractal Dimension from NMR with Swir and T2lm
5.3. Fractal-Based Water Saturation Prediction Model from NMR
5.4. Future Work
- The fractal dimension of tight sandstone is closely related to its pore structure [34]. The pore structures in the different study areas have their specific fractal features and may be characterized by double [35], triple, or multi-fractals. Launching research to figure out fractal characteristics in a specific study area is necessary;
- The double fractal theory is the basis of the water saturation prediction method based on the fractal dimension from NMR proposed in this paper. In order to improve the accuracy, multi-fractal theory can be introduced to establish the water saturation prediction model;
- At present, 2D NMR logging is widely used in reservoir evaluation, and the research on fractal characteristics of 2D NMR is a new hot spot;
- For T2, the relaxation characteristics of oil-bearing sandstone differ greatly from that of gas-bearing sandstone [36]. The water saturation prediction model for gas-bearing sandstone proposed in this paper cannot be applied in oil-bearing sandstone reservoirs, but it still has reference and guiding significance for deriving a water saturation prediction model for oil-bearing sandstone;
- The T2cut and T2lm are very important parameters for our research results, and lots of factors have significant affection on their values, such as pore size, clay content, pressure, and others. Previous studies have proved that factors leading to the decrease in the T2cut and T2lm include the compressed rock matrix, the growth of clay content, and hydrocarbon limiting in micro-pores. In the extending application of the new method in various types of hydrocarbon-bearing reservoirs, it is necessary to conduct experiments and analysis on the influence factors on the T2cut and T2lm.
6. Conclusions
- (1)
- Rock samples having similar pore structures have similar fractal features. The experimental data show that samples have a similar T2 curve monography, although the porosity differs, and and values are centrally distributed. This is the basis for pore structure characterization and classification method based on the fractal dimension from NMR. In addition, is in direct ratio to T2lm and Swir, but has no obvious correlation with these two parameters;
- (2)
- To analyze the relationship between pore size and the fractal dimension from NMR, pore size is divided into five types according to T2 spectra ranges, including (T2 range of 70–900 ms), (T2 range of 20–70 ms), (T2 range of 5–20 ms), (T2 range of 2–5 ms), and (T2 range of 0.1–2 ms). The fractal dimension is inversely proportional to and , increasing and which are occupied by the movable water, leading to decreasing bound water content and fractal dimension . The fractal dimension is in inverse ratio to and , while it is in direct ratio to , increasing and results in decreasing fractal dimension , but increasing leads to increasing fractal dimension ;
- (3)
- In water-saturated rock, when macro-pores fill with gas, residual water-saturated pores are still satisfied with the fractal theory. As the NMR signal of the gas-filling pores is too small to be measured, the fractal dimension from NMR changes. As decreases, increases, but has little variation, and (the increment of ) is directly related to the water saturation of gas-bearing tight sandstone. When decreases to , approximately equals 3. As the pore structure transferred from Type A to Type E, the maximum value of (the difference between under state and that under 100% state) becomes smaller;
- (4)
- Experimental data and application result show that firstly, pore structure evaluation and classification can be achieved based on fractal analysis from NMR spectra; the method can be further applied in reservoir quality evaluation and favorable reservoir prediction. Secondly, the accuracy of calculated water saturation by the new method is higher than that calculated by the Archie model, and the fractal-based water saturation prediction method from NMR extends the application area of NMR logging and also provides a non-electrical idea for the qualitative identification and evaluation of gas-bearing tight sandstone reservoir, it has a reference for the gas-bearing recognition of tight sandstone and carbonate reservoirs.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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No. | T2 Curves Morphology | Porosity v/v | Permeability md | Swir v/v | T2cut ms | T2lm ms | Dva | Dvb | f1 v/v | f2 v/v | f3 v/v | f4 v/v | f5 v/v |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | right unimodal pattern (T2 value of peak: 200 ms) | 12.51 | 23.21 | 16.00 | 14.70 | 74.67 | 2.52 | 1.30 | 0.61 | 0.19 | 0.10 | 0.05 | 0.05 |
2 | 11.30 | 8.74 | 20.78 | 22.59 | 70.64 | 2.56 | 1.21 | 0.60 | 0.18 | 0.12 | 0.06 | 0.04 | |
3 | 10.90 | 4.49 | 25.49 | 14.85 | 52.22 | 2.58 | 1.45 | 0.55 | 0.20 | 0.12 | 0.07 | 0.06 | |
4 | 13.90 | 31.13 | 16.72 | 19.71 | 77.62 | 2.48 | 1.28 | 0.64 | 0.21 | 0.11 | 0.03 | 0.01 | |
5 | 11.20 | 7.03 | 26.21 | 13.66 | 44.08 | 2.59 | 1.36 | 0.43 | 0.27 | 0.15 | 0.08 | 0.07 | |
6 | 11.30 | 6.81 | 26.37 | 17.43 | 43.63 | 2.58 | 1.46 | 0.49 | 0.24 | 0.14 | 0.07 | 0.06 | |
7 | 12.00 | 14.49 | 19.51 | 16.37 | 73.55 | 2.56 | 1.40 | 0.61 | 0.19 | 0.12 | 0.05 | 0.04 | |
Range average value | 10.9–13.9 11.76 | 4.49–31.13 13.7 | 16–26.37 21.58 | 13.66–22.59 17.04 | 43.63–77.62 62.35 | 2.48–2.59 2.55 | 1.21–1.46 1.35 | 0.43–0.64 0.56 | 0.18–0.27 0.21 | 0.1–0.15 0.12 | 0.03–0.08 0.06 | 0.01–0.07 0.05 | |
8 | balanced bimodal pattern | 13.23 | 1.61 | 46.11 | 13.39 | 17.96 | 2.80 | 1.15 | 0.33 | 0.15 | 0.23 | 0.15 | 0.14 |
9 | 12.20 | 1.98 | 49.35 | 10.90 | 18.57 | 2.78 | 1.19 | 0.33 | 0.16 | 0.20 | 0.16 | 0.15 | |
Range average value | 12.2–13.23 12.72 | 1.61–1.98 1.79 | 46.11–49.35 47.73 | 10.9–13.39 12.15 | 17.96–18.57 18.27 | 2.78–2.80 2.79 | 1.15–1.19 1.17 | 0.33–0.33 0.33 | 0.15–0.16 0.155 | 0.2–0.23 0.215 | 0.15–0.16 0.155 | 0.14–0.15 0.145 | |
10 | right unimodal pattern (T2 value of peak: 30 ms) | 8.06 | 0.49 | 50.52 | 17.48 | 15.40 | 2.70 | 1.30 | 0.15 | 0.31 | 0.26 | 0.12 | 0.17 |
11 | 14.10 | 2.49 | 44.17 | 23.98 | 27.89 | 2.73 | 1.54 | 0.36 | 0.25 | 0.21 | 0.09 | 0.09 | |
12 | 14.70 | 1.00 | 48.36 | 19.57 | 18.85 | 2.75 | 1.35 | 0.31 | 0.24 | 0.23 | 0.10 | 0.12 | |
13 | 13.10 | 0.69 | 45.92 | 14.31 | 16.97 | 2.76 | 1.18 | 0.28 | 0.25 | 0.24 | 0.11 | 0.13 | |
14 | 14.80 | 0.66 | 55.01 | 21.27 | 16.66 | 2.78 | 1.45 | 0.28 | 0.25 | 0.23 | 0.09 | 0.15 | |
15 | 15.30 | 1.09 | 48.98 | 16.22 | 15.40 | 2.78 | 1.32 | 0.25 | 0.27 | 0.23 | 0.10 | 0.15 | |
Range average value | 8.6–15.3 13.34 | 0.49–2.49 1.07 | 44.17–55.01 48.83 | 14.31–23.98 18.81 | 15.4–27.89 18.52 | 2.70–2.78 2.75 | 1.18–1.54 1.36 | 0.15–0.36 0.27 | 0.24–0.31 0.26 | 0.21–0.26 0.23 | 0.09–0.12 0.1 | 0.09–0.17 0.13 | |
16 | balanced unimodal pattern (T2 value of peak: 10 ms) | 5.70 | 0.31 | 62.75 | 18.19 | 11.67 | 2.80 | 1.70 | 0.17 | 0.19 | 0.34 | 0.15 | 0.15 |
17 | 8.90 | 0.22 | 58.64 | 15.81 | 11.20 | 2.85 | 1.69 | 0.17 | 0.22 | 0.31 | 0.15 | 0.15 | |
Range average value | 5.7–8.9 7.3 | 0.22–0.31 0.27 | 58.64–62.75 60.7 | 15.81–18.19 17 | 11.2–11.67 11.43 | 2.80–2.85 2.83 | 1.69–1.70 1.69 | 0.17–0.17 0.17 | 0.19–0.22 0.21 | 0.31–0.34 0.325 | 0.15–0.15 0.15 | 0.15–0.15 0.15 | |
18 | left bimodal pattern | 8.75 | 0.15 | 58.72 | 2.58 | 2.69 | 2.89 | 0.59 | 0.28 | 0.05 | 0.12 | 0.15 | 0.41 |
19 | 12.50 | 0.20 | 54.60 | 4.52 | 6.55 | 2.86 | 0.89 | 0.20 | 0.13 | 0.17 | 0.18 | 0.32 | |
Range average value | 8.75–12.5 10.63 | 0.15–0.20 0.18 | 54.6–58.72 56.66 | 2.58–4.52 3.55 | 2.69–6.55 4.62 | 2.86–2.89 2.88 | 0.59–0.89 0.74 | 0.2–0.28 0.24 | 0.05–0.13 0.09 | 0.12–0.17 0.14 | 0.15–0.18 0.16 | 0.41–0.32 0.36 |
No | Sw | T2lm | Dva | Dvb | ΔDva | No | Sw | T2lm | Dva | Dvb | ΔDva |
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 100.00 | 74.67 | 2.52 | 1.30 | 0.00 | 10 | 100.00 | 15.40 | 2.70 | 1.30 | 0.00 |
48.75 | 25.88 | 2.73 | 1.38 | 0.21 | 93.49 | 13.86 | 2.70 | 1.39 | 0.00 | ||
29.67 | 10.08 | 2.81 | 1.30 | 0.29 | 77.48 | 9.18 | 2.75 | 1.24 | 0.05 | ||
18.56 | 4.90 | 2.94 | 1.38 | 0.42 | 54.70 | 4.90 | 2.90 | 1.28 | 0.20 | ||
16.00 | 3.60 | 2.97 | 1.23 | 0.44 | 50.52 | 4.25 | 2.93 | 1.21 | 0.23 | ||
2 | 100.00 | 70.64 | 2.56 | 1.21 | 0.00 | 11 | 100.00 | 27.89 | 2.73 | 1.54 | 0.00 |
58.08 | 31.57 | 2.73 | 1.38 | 0.17 | 89.04 | 22.11 | 2.75 | 1.49 | 0.02 | ||
34.31 | 9.82 | 2.87 | 1.36 | 0.31 | 59.55 | 9.39 | 2.86 | 1.42 | 0.13 | ||
22.10 | 6.08 | 2.94 | 1.28 | 0.38 | 44.17 | 4.94 | 2.92 | 1.38 | 0.19 | ||
20.78 | 4.74 | 2.96 | 1.15 | 0.40 | 12 | 100.00 | 18.85 | 2.75 | 1.35 | 0.00 | |
3 | 100.00 | 52.22 | 2.58 | 1.45 | 0.00 | 93.46 | 17.33 | 2.77 | 1.46 | 0.02 | |
69.00 | 38.75 | 2.68 | 1.59 | 0.10 | 71.52 | 8.60 | 2.83 | 1.27 | 0.09 | ||
40.66 | 10.13 | 2.79 | 1.28 | 0.21 | 55.14 | 5.86 | 2.96 | 1.50 | 0.21 | ||
26.55 | 5.58 | 2.95 | 1.18 | 0.37 | 48.36 | 4.12 | 2.96 | 1.62 | 0.22 | ||
25.49 | 4.48 | 2.95 | 1.14 | 0.37 | 13 | 100.00 | 16.97 | 2.76 | 1.18 | 0.00 | |
4 | 100.00 | 77.62 | 2.48 | 1.28 | 0.00 | 94.66 | 15.28 | 2.78 | 1.52 | 0.02 | |
46.61 | 28.15 | 2.74 | 1.22 | 0.27 | 73.95 | 9.95 | 2.85 | 1.11 | 0.09 | ||
28.11 | 12.88 | 2.83 | 1.17 | 0.35 | 51.64 | 4.72 | 2.96 | 1.44 | 0.20 | ||
18.32 | 7.52 | 2.96 | 1.05 | 0.48 | 45.92 | 3.41 | 2.97 | 1.10 | 0.21 | ||
16.72 | 6.34 | 2.98 | 1.34 | 0.50 | 14 | 100.00 | 16.66 | 2.81 | 1.45 | 0.00 | |
5 | 100.00 | 44.08 | 2.59 | 1.36 | 0.00 | 94.67 | 16.12 | 2.81 | 1.62 | 0.00 | |
68.41 | 26.51 | 2.70 | 1.22 | 0.11 | 79.11 | 10.57 | 2.89 | 1.56 | 0.08 | ||
40.90 | 9.60 | 2.83 | 1.29 | 0.24 | 61.14 | 5.35 | 2.97 | 1.43 | 0.16 | ||
29.71 | 6.54 | 2.94 | 1.33 | 0.35 | 55.01 | 4.32 | 2.98 | 1.49 | 0.18 | ||
26.21 | 5.32 | 2.95 | 1.40 | 0.36 | 15 | 100.00 | 15.40 | 2.78 | 1.32 | 0.00 | |
6 | 100.00 | 43.63 | 2.58 | 1.46 | 0.00 | 93.39 | 13.86 | 2.78 | 1.43 | 0.00 | |
69.91 | 22.94 | 2.72 | 1.31 | 0.14 | 71.08 | 9.18 | 2.85 | 1.31 | 0.07 | ||
41.15 | 9.46 | 2.88 | 1.41 | 0.30 | 53.60 | 4.90 | 2.95 | 1.32 | 0.16 | ||
30.44 | 5.62 | 2.95 | 1.40 | 0.36 | 48.98 | 4.25 | 2.96 | 1.23 | 0.18 | ||
26.37 | 4.85 | 2.96 | 1.52 | 0.38 | 17 | 100.00 | 11.20 | 2.85 | 1.69 | 0.00 | |
7 | 100.00 | 73.55 | 2.56 | 1.40 | 0.00 | 89.70 | 8.79 | 2.88 | 1.45 | 0.02 | |
60.01 | 34.41 | 2.69 | 1.31 | 0.13 | 84.80 | 7.82 | 2.89 | 1.48 | 0.04 | ||
22.44 | 6.67 | 2.90 | 1.10 | 0.34 | 64.74 | 4.88 | 2.97 | 1.30 | 0.12 | ||
19.51 | 5.32 | 2.95 | 1.34 | 0.40 | 58.64 | 3.79 | 2.98 | 1.39 | 0.13 | ||
9 | 100.00 | 18.57 | 2.78 | 1.19 | 0.00 | 19 | 100.00 | 6.55 | 2.86 | 0.89 | 0.00 |
82.37 | 12.66 | 2.84 | 1.26 | 0.06 | 95.26 | 5.95 | 2.87 | 0.86 | 0.01 | ||
64.92 | 6.62 | 2.91 | 1.26 | 0.13 | 87.57 | 4.74 | 2.89 | 0.80 | 0.03 | ||
51.24 | 3.73 | 2.97 | 1.13 | 0.19 | 56.65 | 1.60 | 2.98 | 0.80 | 0.12 | ||
49.35 | 3.36 | 2.97 | 1.03 | 0.19 | 54.60 | 1.55 | 2.97 | 0.83 | 0.11 |
Layer | RT (ohm.m) | POR (%) | PERM (md) | Sw_Archie (v/v) | Swir_nmr (v/v) | SW_T2 (v/v) | Dva0 | Dvb | Dva | Type | Production |
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 38 | 10.1 | 0.34 | 0.65 | 0.64 | 0.89 | 2.649 | 1.254 | 2.663 | II | -- |
2 | 16 | 4.3 | 0.03 | 1 | 0.76 | 0.91 | 2.804 | 2.069 | 2.846 | III/IV | -- |
3 | 31 | 11.2 | 0.87 | 0.69 | 0.55 | 0.58 | 2.594 | 0.875 | 2.733 | I/III | -- |
4 | 30 | 13.2 | 1.6 | 0.6 | 0.37 | 0.48 | 2.429 | 0.954 | 2.638 | I/II | |
5 | 41 | 10.7 | 0.45 | 0.65 | 0.41 | 0.51 | 2.558 | 1.104 | 2.699 | I/II/IV | Gas 1.1 × 104 m3, no water |
6 | 31 | 10.2 | 0.22 | 0.64 | 0.5 | 0.53 | 2.646 | 2.288 | 2.702 | I/II | |
7 | 36 | 7.7 | 0.08 | 0.71 | 0.91 | 0.97 | 2.863 | 1.763 | 2.966 | IV/V | -- |
8 | 31 | 6.5 | 0.01 | 1 | 0.8 | 0.83 | 2.75 | 1.085 | 2.797 | IV/V | -- |
9 | 10 | 7.3 | 0.05 | 1 | 0.9 | 0.82 | 2.86 | 0.29 | 2.89 | V | -- |
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Xie, W.; Yin, Q.; Zeng, J.; Wang, G.; Feng, C.; Zhang, P. Fractal-Based Approaches to Pore Structure Investigation and Water Saturation Prediction from NMR Measurements: A Case Study of the Gas-Bearing Tight Sandstone Reservoir in Nanpu Sag. Fractal Fract. 2023, 7, 273. https://doi.org/10.3390/fractalfract7030273
Xie W, Yin Q, Zeng J, Wang G, Feng C, Zhang P. Fractal-Based Approaches to Pore Structure Investigation and Water Saturation Prediction from NMR Measurements: A Case Study of the Gas-Bearing Tight Sandstone Reservoir in Nanpu Sag. Fractal and Fractional. 2023; 7(3):273. https://doi.org/10.3390/fractalfract7030273
Chicago/Turabian StyleXie, Weibiao, Qiuli Yin, Jingbo Zeng, Guiwen Wang, Cheng Feng, and Pan Zhang. 2023. "Fractal-Based Approaches to Pore Structure Investigation and Water Saturation Prediction from NMR Measurements: A Case Study of the Gas-Bearing Tight Sandstone Reservoir in Nanpu Sag" Fractal and Fractional 7, no. 3: 273. https://doi.org/10.3390/fractalfract7030273
APA StyleXie, W., Yin, Q., Zeng, J., Wang, G., Feng, C., & Zhang, P. (2023). Fractal-Based Approaches to Pore Structure Investigation and Water Saturation Prediction from NMR Measurements: A Case Study of the Gas-Bearing Tight Sandstone Reservoir in Nanpu Sag. Fractal and Fractional, 7(3), 273. https://doi.org/10.3390/fractalfract7030273