A Method for Improving Permeability Accuracy of Tight Sandstone Gas Reservoirs Based on Core Data and NMR Logs
Abstract
:1. Introduction
2. Data
2.1. Study Area
2.2. Well logs and Core Data
3. Methodology
3.1. Regression Analysis
3.2. D Value Solution
3.3. Calculation Procedure
- (1)
- An empirical equation similar to Equation (1) is obtained by fitting the core data.
- (2)
- The value of D is obtained by subtracting the permeability by Equation (1) from the permeability of all core samples at the same porosity. The initial values of m and n are given arbitrarily, and the ΔRQI values are calculated by Equation (6).
- (3)
- Regression analysis using ΔRQI and D values, with the m and n values changing, the optimum m and n values are determined when the correlation coefficient of polynomial function is the highest.
- (4)
- Regression analysis using the independent and dependent variables of Equation (8), when the optimized m and n values remain constant. The initial values of a and b are given arbitrarily, with the a and b values changing, the optimum a and b values are determined when the correlation coefficient of the power function is the highest.
- (5)
- When the optimum values of a, b, m, and n are determined, Equation (8) can be derived from Equation (7), D can be calculated from Equation (7), and more accurate permeability can be obtained from Equation (2).
4. Result and Discussion
4.1. Parameter Prediction and Model Establishment
4.2. Results Evaluation and Analysis
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
GR | Natural gamma-ray logging, API |
SP | Spontaneous-potential logging, mv |
CAL | Borehole diameter, cm |
RD | Deep lateral resistivity, Ω.m |
RS | Shallow lateral resistivity, Ω.m |
CNL | Compensated neutron logging, % |
DT | Acoustic transit time, μs/m |
DEN | Density logs, g/cm3 |
TG | Total hydrocarbon content, % |
T2 | NMR transverse relaxation time, ms |
BVI | Bulk volume irreducible, % |
MFFI | Bulk volume moveable, % |
Φ | Porosity, % |
POR_core | Porosity obtained from core analysis, % |
Fs | shape factor |
τ | tortuosity |
Sgv | surface area per unit grain volume, μm−1 |
Fsτ2 | Kozeny constant |
K | Permeability, mD |
K_core | Permeability obtained from core analysis, mD |
K_NMR | Permeability obtained by NMR logs, mD |
Swi | Irreducible water saturation,% |
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No. | Φ-Helium | K-Helium | Φ-NMR | Swi | T2cutoff | MFFI | BVI |
---|---|---|---|---|---|---|---|
(%) | (mD) | (%) | (%) | (ms) | (%) | (%) | |
1 | 10.8 | 0.620 | 10.6 | 49.1 | 14.28 | 5.5 | 5.3 |
2 | 15.1 | 1.819 | 14.6 | 34.4 | 14.60 | 9.9 | 5.2 |
3 | 13.4 | 2.080 | 13.2 | 31.9 | 18.51 | 9.1 | 4.3 |
4 | 14.1 | 1.423 | 13.9 | 36.6 | 13.34 | 8.9 | 5.2 |
5 | 13.9 | 1.054 | 13.4 | 32.2 | 9.66 | 9.4 | 4.5 |
6 | 13.7 | 1.269 | 13.5 | 29.0 | 11.03 | 9.7 | 4.0 |
7 | 15.4 | 4.625 | 14.7 | 22.8 | 9.50 | 11.9 | 3.5 |
8 | 11.7 | 4.195 | 11.4 | 26.9 | 11.68 | 8.5 | 3.2 |
9 | 8.4 | 0.195 | 8.2 | 41.5 | 14.22 | 4.9 | 3.5 |
10 | 10.3 | 0.992 | 10.1 | 28.7 | 7.05 | 7.3 | 3.0 |
11 | 7.2 | 0.522 | 7.1 | 46.0 | 13.08 | 3.9 | 3.3 |
12 | 11.9 | 0.606 | 11.5 | 29.9 | 15.25 | 8.3 | 3.6 |
13 | 8.6 | 0.306 | 8.2 | 34.8 | 6.10 | 5.6 | 3.0 |
14 | 11.1 | 0.565 | 10.9 | 38.2 | 8.77 | 6.9 | 4.2 |
15 | 3.3 | 0.161 | 3.5 | 47.8 | 7.27 | 1.7 | 1.6 |
16 | 9.8 | 2.656 | 9.6 | 19.2 | 22.92 | 7.9 | 1.9 |
17 | 7.8 | 1.600 | 7.8 | 20.7 | 14.48 | 6.2 | 1.6 |
18 | 7.5 | 0.206 | 7.0 | 35.0 | 15.04 | 4.9 | 2.6 |
19 | 15.3 | 10.879 | 14.5 | 6.4 | 22.59 | 14.3 | 1.0 |
20 | 13.8 | 8.250 | 13.5 | 7.1 | 19.75 | 12.8 | 1.0 |
21 | 10.4 | 7.350 | 9.7 | 10.0 | 16.38 | 9.4 | 1.0 |
Type | Equation | a | b | R2 |
---|---|---|---|---|
Polynomial | y = −0.0006x2 + 0.1629x − 0.632 | 1.82 | 0.90 | 0.9236 |
Linear | y = 7.0798x − 8.7781 | 0.35 | 0.26 | 0.8874 |
Logarithmic | y = 18.464ln(x) − 1.3917 | 0.20 | 0.19 | 0.8440 |
Power | y = 0.0397x1.2803 | 1.70 | 0.70 | 0.8169 |
Exponential | y = 0.0666e0.5298x | 0.90 | 0.16 | 0.8019 |
No. | Depth | K_core | K_NMR | K_Equation (1) | K_Equation (2) | K_Equations (10) and (11) |
---|---|---|---|---|---|---|
(m) | (mD) | (mD) | (mD) | (mD) | (mD) | |
1 | 3046.35 | 0.0910 | 0.0014 | 0.5776 | 0.0797 | 0.0789 |
2 | 3046.72 | 0.0604 | 0.0012 | 0.6603 | 0.0421 | 0.0402 |
3 | 3047.25 | 0.0162 | 0.0010 | 0.7973 | 0.0232 | 0.0042 |
4 | 3047.55 | 0.0261 | 0.0035 | 1.0892 | 0.0190 | 0.0029 |
5 | 3049.56 | 0.2625 | 0.0246 | 1.3989 | 0.1892 | 0.1615 |
6 | 3050.05 | 0.4431 | 0.0325 | 1.0486 | 0.2690 | 0.2570 |
7 | 3050.24 | 0.4130 | 0.0323 | 0.9896 | 0.2368 | 0.2233 |
8 | 3053.05 | 0.7330 | 0.1245 | 0.6313 | 0.9260 | 0.9357 |
9 | 3053.15 | 0.9921 | 0.1216 | 0.6466 | 1.3298 | 1.3375 |
10 | 3053.34 | 1.9752 | 0.1247 | 0.6533 | 1.9686 | 1.9826 |
11 | 3053.82 | 2.1580 | 0.1490 | 0.6651 | 1.9212 | 1.9340 |
12 | 3054.13 | 1.0473 | 0.1088 | 0.6589 | 1.7083 | 1.7154 |
13 | 3054.45 | 0.9310 | 0.0806 | 0.7757 | 0.6505 | 0.6550 |
Correlation coefficient | 0.8959 | 0.4019 | 0.9419 | 0.9418 |
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Liu, L.; Pan, H.; Deng, C.; Huang, G. A Method for Improving Permeability Accuracy of Tight Sandstone Gas Reservoirs Based on Core Data and NMR Logs. Energies 2019, 12, 2859. https://doi.org/10.3390/en12152859
Liu L, Pan H, Deng C, Huang G. A Method for Improving Permeability Accuracy of Tight Sandstone Gas Reservoirs Based on Core Data and NMR Logs. Energies. 2019; 12(15):2859. https://doi.org/10.3390/en12152859
Chicago/Turabian StyleLiu, Liang, Heping Pan, Chengxiang Deng, and Guoshu Huang. 2019. "A Method for Improving Permeability Accuracy of Tight Sandstone Gas Reservoirs Based on Core Data and NMR Logs" Energies 12, no. 15: 2859. https://doi.org/10.3390/en12152859