# Characterization and Prediction of Complex Natural Fractures in the Tight Conglomerate Reservoirs: A Fractal Method

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

^{−2}and 50.0 m·m

^{−2}, with an average of 31.42 m·m

^{−2}. The cumulative frequency distribution of both fracture apertures and areal densities follow power law distribution. The fracture parameters at different scales can be predicted by extrapolating these power law distributions.

## 1. Introduction

_{2}sequestration, gas storage, nuclear waste disposal, etc.) [18,19], or induce geological disasters [18]. Therefore, quantitative characterization and comprehensive evaluation of natural fractures are very important and urgently needed.

## 2. Geological Setting

## 3. Methodology

^{−D},

- Using a core scanner to obtain high-resolution 360° core images (Figure 2);
- Covering the image of the entire core with a mesh composed of square grids with side length of r; counting the number N(r) of boxes containing fractures;
- Gradually changing the side length r of the square grids, and repeatedly counting the corresponding N(r);
- Taking r as the abscissa and N(r) as the ordinate, using the least-square method to perform regression analysis on the statistical data in the double logarithmic coordinate system (Figure 3).

_{f}is the fracture porosity (%); S is the core area (m

^{2}); A

_{i}is the aperture of the ith fracture (m); L

_{i}is the length of the ith fracture (m); K

_{f}is the fracture permeability (mD); and $\overline{A}$ is the average fracture aperture (m).

## 4. Fracture Characterization

#### 4.1. Fracture Type and Characteristics

#### 4.2. Fracture Parameters

^{−2}and 50.0 m·m

^{−2}, with an average of 31.42 m·m

^{−2}(Figure 7b). The fracture porosities are mainly distributed between 0.60% and 1.60%, with an average of 1.26% (Figure 7c), and the fracture permeabilities are mainly distributed between 50 mD and 150 mD (Figure 7d).

## 5. Discussion

#### 5.1. Geological Significance of Fracture Fractal Dimension

#### 5.2. Power-Law Distribution of Fracture Parameters and Fracture Prediction

#### 5.3. Contribution of Fractures

## 6. Conclusions

^{−2}and 50.0 m·m

^{−2}, with an average of 31.42 m·m

^{−2}. The fracture porosities are mainly distributed between 0.60% and 1.60%, with an average of 1.26%, and the fracture permeabilities are mainly distributed between 50 mD and 150 mD. The fracture fractal dimension has an exponential correlation with the fracture areal density and can therefore be used to quantify the fracture intensity. A good exponential correlation also exists between the fracture fractal dimension and the fracture porosity and permeability, which can reflect their contributions to the physical properties of the tight reservoirs. Therefore, the fracture fractal dimension D is a good comprehensive index as a quantitative parameter to characterize the intensity of the complex fracture system and reflect the contributions of fractures to the tight reservoir.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Location of the Jiulongshan gas field in the Western Sichuan Foreland Basin, China. (

**a**) Location of the Western Sichuan Foreland Basin; (

**b**) structure outline map of the northern part of Western Sichuan Foreland Basin; (

**c**) depth contour and fault distribution of top of the Zhenzhuchong Formation, Jiulongshan oil field.

**Figure 2.**Core images, fracture traces and meshes. (

**a**) Image of the surface of core A; (

**b**) fracture traces of core A and the grids for box-counting; (

**c**) image of the surface of core B; (

**d**) fracture traces of core B and the grids for box-counting. The side length of the blue boxes is 1 cm, 2 cm, 3 cm, 5 cm, 8 cm, 10 cm and 15 cm, respectively.

**Figure 3.**Schematic diagram for the calculation of fracture fractal dimension (modified from [59]). (

**a**) Calculation of fracture fractal dimension for core A; (

**b**) Calculation of fracture fractal dimension for core B.

**Figure 4.**Fracture types in the tight conglomerates. (

**a**) Well L4, 3164.32 m; (

**b**) Well L102, 3198.35 m. IGF = intra-gravel fracture, TGF = trans-gravel fracture, GEF = Gravel edge fracture.

**Figure 5.**Gravel edge fracture (GEF) and trans-gravel fractures (TGF) in thin sections. (

**a**) Gravel edge fracture (GEF), Well L104, 3175.05 m; (

**b**) trans-gravel fractures (TGF), Well L16, 3159.34 m.

**Figure 6.**Trans-gravel fractures in cores and out crop. (

**a**) Trans-gravel fractures with high dip angle in core, Well L102, 3185.75 m; (

**b**) trans-gravel fractures with low dip angle in core, Well L104, 3174.65 m; (

**c**) conjugate fractures in outcrop, see Figure 1 for outcrop location.

**Figure 7.**Distributions of fracture parameters. (

**a**) Distribution of fracture fractal dimension; (

**b**) distribution of fracture areal density; (

**c**) distribution of fracture porosity; (

**d**) distribution of fracture permeability.

**Figure 8.**Cumulative frequency plots of micro-fracture apertures (blue squares) and macro-fracture apertures (red circles).

**Figure 12.**Cumulative plot of micro-fracture apertures (blue squares) and macro-fracture apertures (red circles). The power law distribution of micro-fractures (blue Equation) was obtained by fitting the solid square data, the power law distribution of macro-fractures (red Equation) was obtained by fitting the solid circle data, the power law distribution of all fractures (black Equation) was obtained by fitting the solid square and solid circle data and the best fitting line is slightly offset to the right for clarity of the plot.

**Figure 13.**Cumulative plot of macro-fracture areal density (red circles) and prediction of micro-fracture areal density (blue square). The Equation was obtained by fitting the solid circle data, the opening squares are predicted areal density of micro-fractures by extrapolating the power law of cumulative areal density distribution of macro-fractures.

**Table 1.**Fracture parameters (fractal dimension, areal density, porosity and permeability) calculated from cores.

Well Name | Interval | Fractal Dimension | Correlation Coefficient | Areal Density (m·m^{−2}) | Porosity (%) | Permeability (mD) | |
---|---|---|---|---|---|---|---|

Top (m) | Bottom (m) | ||||||

L4 | 3069.39 | 3069.55 | 1.38 | 0.9910 | 40.29 | 1.26 | 133.98 |

L4 | 3069.64 | 3069.72 | 1.22 | 0.9891 | 26.59 | 0.99 | 38.62 |

L4 | 3069.77 | 3069.78 | 1.22 | 0.9884 | 25.85 | 0.83 | 74.93 |

L4 | 3069.98 | 3070.11 | 1.28 | 0.9901 | 27.87 | 1.51 | 81.98 |

L4 | 3070.22 | 3070.29 | 1.31 | 0.9920 | 26.58 | 0.82 | 90.48 |

L4 | 3070.49 | 3070.57 | 1.40 | 0.9908 | 40.54 | 0.96 | 106.12 |

L4 | 3070.80 | 3070.93 | 1.43 | 0.9898 | 36.80 | 1.22 | 88.98 |

L4 | 3071.01 | 3071.12 | 1.10 | 0.9914 | 24.98 | 0.59 | 32.00 |

L4 | 3071.36 | 3071.56 | 1.24 | 0.9905 | 32.81 | 0.95 | 74.75 |

L4 | 3071.71 | 3071.80 | 1.58 | 0.9897 | 39.29 | 1.27 | 138.58 |

L4 | 3071.91 | 3072.12 | 1.17 | 0.9914 | 21.30 | 0.76 | 80.85 |

L4 | 3072.24 | 3072.41 | 1.01 | 0.9893 | 17.95 | 0.50 | 39.93 |

L10 | 3080.74 | 3080.91 | 1.15 | 0.9877 | 24.22 | 0.71 | 52.18 |

L10 | 3101.61 | 3101.80 | 1.28 | 0.9927 | 26.99 | 0.74 | 67.63 |

L10 | 3101.88 | 3102.07 | 1.03 | 0.9922 | 24.19 | 0.62 | 34.91 |

L10 | 3102.13 | 3102.34 | 1.65 | 0.9933 | 56.49 | 1.81 | 245.25 |

L10 | 3102.55 | 3102.71 | 1.24 | 0.9894 | 24.77 | 0.83 | 82.18 |

L10 | 3102.81 | 3102.95 | 1.31 | 0.9896 | 40.64 | 1.15 | 79.94 |

L10 | 3103.30 | 3103.42 | 1.24 | 0.9923 | 31.86 | 1.09 | 94.35 |

L10 | 3103.49 | 3103.53 | 1.33 | 0.9879 | 32.42 | 1.77 | 90.54 |

L10 | 3103.61 | 3103.79 | 1.36 | 0.9900 | 40.62 | 1.42 | 143.99 |

L10 | 3103.88 | 3103.93 | 1.40 | 0.9876 | 35.68 | 1.54 | 58.35 |

L10 | 3104.07 | 3104.18 | 1.37 | 0.9875 | 36.02 | 1.27 | 120.48 |

L10 | 3104.26 | 3104.37 | 1.36 | 0.9895 | 28.56 | 1.17 | 166.58 |

L102 | 3087.20 | 3087.34 | 1.46 | 0.9884 | 34.29 | 2.18 | 114.94 |

L102 | 3087.51 | 3087.57 | 1.35 | 0.9887 | 30.49 | 1.05 | 103.49 |

L102 | 3087.75 | 3087.85 | 1.50 | 0.9886 | 45.50 | 1.38 | 139.29 |

L102 | 3087.94 | 3088.08 | 1.55 | 0.9875 | 50.57 | 1.78 | 191.51 |

L102 | 3088.23 | 3088.33 | 1.04 | 0.9903 | 24.69 | 0.73 | 55.77 |

L102 | 3088.60 | 3088.70 | 1.05 | 0.9886 | 18.00 | 0.69 | 55.13 |

L102 | 3089.01 | 3089.17 | 1.51 | 0.9909 | 43.76 | 1.93 | 218.89 |

L102 | 3089.17 | 3089.28 | 1.10 | 0.9880 | 26.70 | 1.06 | 93.28 |

L102 | 3089.39 | 3089.55 | 1.08 | 0.9918 | 20.01 | 0.58 | 52.04 |

L103 | 3117.23 | 3117.38 | 1.24 | 0.9889 | 30.60 | 1.11 | 128.42 |

L103 | 3117.45 | 3117.54 | 1.43 | 0.9924 | 47.72 | 1.75 | 191.26 |

L103 | 3117.70 | 3117.84 | 1.44 | 0.9906 | 41.50 | 1.24 | 90.64 |

L103 | 3117.99 | 3118.05 | 1.28 | 0.9901 | 39.06 | 1.26 | 75.31 |

L103 | 3118.15 | 3118.26 | 1.39 | 0.9895 | 47.30 | 1.08 | 88.36 |

L103 | 3118.36 | 3118.58 | 1.19 | 0.9928 | 28.91 | 1.21 | 79.01 |

L103 | 3118.67 | 3118.82 | 1.22 | 0.9882 | 33.35 | 0.76 | 35.99 |

L103 | 3118.98 | 3119.03 | 1.41 | 0.9924 | 43.21 | 1.35 | 111.74 |

L103 | 3119.09 | 3119.21 | 1.19 | 0.9894 | 28.88 | 0.95 | 60.14 |

L103 | 3119.30 | 3119.40 | 1.56 | 0.9929 | 67.27 | 2.14 | 169.61 |

L103 | 3119.58 | 3119.72 | 1.15 | 0.9909 | 24.14 | 0.80 | 78.47 |

L103 | 3119.92 | 3120.16 | 1.31 | 0.9915 | 34.79 | 0.79 | 59.60 |

L103 | 3120.32 | 3120.50 | 1.44 | 0.9930 | 48.27 | 1.53 | 90.03 |

L103 | 3128.18 | 3128.37 | 1.52 | 0.9923 | 39.17 | 1.44 | 208.87 |

L103 | 3128.57 | 3128.71 | 1.24 | 0.9905 | 25.29 | 1.1 | 148.97 |

Number | Full Diameter Cores | Core Plugs | Φ_{1}/Φ_{2} | K_{1}/K_{3} | |||
---|---|---|---|---|---|---|---|

Φ_{1} (%) | K_{1} (mD) | K_{2} (mD) | Φ_{2} (%) | K_{3} (mD) | |||

1 | 3.90 | 214.50 | 0.0145 | 0.29 | 0.0021 | 13.45 | 102,142.86 |

2 | 3.74 | 201.69 | 0.0007 | 0.64 | 0.0084 | 5.84 | 24,010.71 |

3 | 3.80 | 166.57 | 0.0689 | 0.51 | 0.0056 | 7.45 | 29,744.64 |

4 | 3.12 | 5.75 | 0.0237 | 1.51 | 0.0105 | 2.07 | 547.62 |

5 | 2.61 | 83.58 | 0.0123 | 0.93 | 0.0096 | 2.81 | 8706.25 |

6 | 4.05 | 3.17 | 0.5917 | 1.60 | 0.0191 | 2.53 | 165.97 |

7 | 3.04 | 7.25 | 0.4628 | 1.26 | 0.0084 | 2.41 | 863.10 |

8 | 3.19 | 21.40 | 0.2450 | 1.09 | 0.0047 | 2.93 | 4553.19 |

9 | 3.06 | 32.30 | 0.4930 | 0.89 | 0.0079 | 3.44 | 4088.61 |

10 | 3.01 | 40.40 | 0.6730 | 0.95 | 0.0127 | 3.17 | 3181.10 |

Average | 3.52 | 77.7 | 0.2586 | 0.97 | 0.0089 | 4.61 | 17,800.40 |

_{1}and Φ

_{2}are the porosities of the full-diameter cores and the core plugs respectively; K

_{1}and K

_{2}are horizontal permeability and vertical permeability of the full-diameter cores respectively; K

_{3}is the permeability of the core plugs.

Fracture Length (mm) | Fracture Areal Density | Absolute Error (m·m^{−2}) | Relative Error (%) | |
---|---|---|---|---|

Measured (m·m^{−2}) | Predicted (m·m^{−2}) | |||

10 | 50.35 | 50.14 | −0.21 | 0.42 |

9 | 51.89 | 52.71 | 0.82 | 1.58 |

8 | 56.05 | 55.74 | −0.31 | 0.55 |

7 | 60.48 | 59.39 | –1.09 | 1.80 |

6 | 62.36 | 63.91 | 1.55 | 2.48 |

5 | 67.07 | 69.69 | 2.62 | 3.90 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Gong, L.; Fu, X.; Gao, S.; Zhao, P.; Luo, Q.; Zeng, L.; Yue, W.; Zhang, B.; Liu, B.
Characterization and Prediction of Complex Natural Fractures in the Tight Conglomerate Reservoirs: A Fractal Method. *Energies* **2018**, *11*, 2311.
https://doi.org/10.3390/en11092311

**AMA Style**

Gong L, Fu X, Gao S, Zhao P, Luo Q, Zeng L, Yue W, Zhang B, Liu B.
Characterization and Prediction of Complex Natural Fractures in the Tight Conglomerate Reservoirs: A Fractal Method. *Energies*. 2018; 11(9):2311.
https://doi.org/10.3390/en11092311

**Chicago/Turabian Style**

Gong, Lei, Xiaofei Fu, Shuai Gao, Peiqiang Zhao, Qingyong Luo, Lianbo Zeng, Wenting Yue, Benjian Zhang, and Bo Liu.
2018. "Characterization and Prediction of Complex Natural Fractures in the Tight Conglomerate Reservoirs: A Fractal Method" *Energies* 11, no. 9: 2311.
https://doi.org/10.3390/en11092311