# The Study of Multi-Scale Specific Surface Area in Shale Rock with Fracture-Micropore-Nanopore

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}; V is volume of the rock sample, cm

^{3}.

## 2. Materials

^{4}–10 cyclothem) inter-salt shale, as it is the most important target layer for exploration. The buried depth is between 1674.0 m and 1684.5 m. The reservoir initial pressure is 21.24 MPa with a pressure coefficient between 1.26 and 1.35. The initial reservoir temperature is around 73.4 °C.

^{4}–10 cyclothem inter-salt shale cores are mostly black, grey-black, and grey-brown with a small amount of grey-white at the bottom, which mainly contains argillaceous dolomite, dolomitic mudstone, argillaceous limestone, and mudstone with glauberite interlayers. Shale laminae are extremely well developed, which are flat and contain no fossils. The distribution of glauberite is relatively dense at the top and bottom with a thickness of approximately 30–50 cm of glauberite interlayer developed at the top, and the mud content increases in the middle and the carbonate increases at the top. This distribution reflects high salinity–low salinity–high salinity lake evolution features. As shown in Figure 1, the lithology of this sample is argillaceous dolomite, and it develops microfracture and matrix pores with the porosity of 10.2% and permeability of 22.2 mD, while the main mineral is dolomite with the content of 62.72%, also, the quartz, illite and sodium feldspar are mixed in it.

## 3. Methodology

#### 3.1. Micro CT Scanning

_{o}is the initial intensity of the X-rays, I is the intensity of the X-rays after passing through the rock, that is, the intensity of the X-rays after they have been attenuated, i represents the rock component in the path through which the rays pass, ${\mu}_{i}$, ${x}_{i}$ are the attenuation coefficient of the ith component to the X-rays and the length of the component in the current path of the X-rays, respectively. The principle of CT imaging is based on the measurement of X-rays passing through a cross-section of the rock, after which a certain reconstruction method is used to calculate the absorption coefficients, thereby recovering structural information about the rock cross-section.

#### 3.2. FIB-SEM Scanning

#### 3.3. Image Processing

- (1)
- Brightness adjustment

- (2)
- Contrast adjustment

- (3)
- Sharpening of images

#### 3.4. Image Segmentation

_{i}, the probability of each gray level is described as follows:

_{1}, …, t

_{n}, …, t

_{m−1}] to classify the image into m classes. These classes are denoted as C

_{0}= [0, 1, …, t

_{1}], …, C

_{n}= [t

_{n}+ 1, t

_{n}+ 2, …, t

_{n}

_{+1}], …, C

_{m}

_{−1}= [t

_{m}

_{−1}+ 1, t

_{m}

_{−1}+ 2, …, L − 1], and the interclass variance is defined as:

_{0}, …, C

_{n}, …, C

_{m}

_{−1}]:

_{1}

^{*}, …, t

_{n}

^{*}, …, t

_{m}

_{−1}

^{*}] is chosen as the optimal threshold, which could let ${\sigma}_{B}^{2}$ achieve the maximum value.

_{0}(microfracture phase), C

_{1}(macro matrix phase) and C

_{2}(macro skeleton phase). While ${C}_{0}=\left[0,1,\dots ,{t}_{1}\right],{C}_{1}=\left[{t}_{1}+1,{t}_{1}+2,\dots ,{t}_{2}\right]$ and ${C}_{2}=\left[{t}_{2}+1,{t}_{2}+2,\dots ,L-1\right]$, the optimal threshold t

_{1}*, t

_{2}* is chosen to obtain the maximum value of ${\sigma}_{B}^{2}$, which could construct the microfracture digital rock.

_{0}(micropore phase), C’

_{1}(micro matrix phase) and C’

_{2}(micro skeleton phase). While ${C}_{0}^{\prime}=\left[0,1,\dots ,{{t}^{\prime}}_{1}\right],{C}_{1}^{\prime}=\left[{t}_{1}^{\prime}+1,{t}_{1}^{\prime}+2,\dots ,{t}_{2}^{\prime}\right]$ and ${C}_{2}^{\prime}=\left[{t}_{2}^{\prime}+1,{t}_{2}^{\prime}+2,\dots ,{L}^{\prime}-1\right]$, the optimal threshold t’

_{1}*, t’

_{2}* is chosen to obtain the maximum value of ${{\sigma}^{\prime}}_{B}^{2}$, which could construct the micropore digital rock.

_{0}(nanopore phase) and C”

_{1}(nano-skeleton phase). While ${C}_{0}^{\u2033}=\left[0,1,\dots ,{t}^{\u2033}\right]$, ${C}_{1}=\left[{t}^{\u2033}+1,{t}^{\u2033}+2,\dots ,{L}^{\u2033}-1\right]$, the optimal threshold t″

^{*}is chosen to obtain the maximum value of ${{\sigma}^{\u2033}}_{B}^{2}$, which could construct the nanopore digital rock.

## 4. Results and Discussions

^{2}/cm

^{3}. ${\mathrm{\Phi}}_{m1}$ denotes the percentage of macro matrix phase in the microfracture digital rock, %. ${S}_{mp}$ denotes the specific surface area of micropore digital rock m

^{2}/cm

^{3}. ${\mathrm{\Phi}}_{m2}$ denotes the percentage of micro matrix phase in micropore digital rock, %. ${S}_{np}$ denotes the specific surface area of nanopore digital rock, m

^{2}/cm

^{3}.

^{2}/cm

^{3}. It can be found that, the specific surface area of both microfracture and micropores are small, while their specific surface area is 2~3 orders of magnitude smaller than that of the nanopores, the specific surface area of shale rock is mainly contributed by nanopores. Moreover, the large specific surface area of the nanopores could store a large amount of gas as an adsorbed state, and will increase the flow resistance, which is not conducive to gas flow.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Micro-CT and FIB-SEM scanning image with different resolutions: (

**a**) microfracture sample; (

**b**) micropore subsample; and (

**c**) nanopore subsample.

**Figure 3.**Multi-threshold segmentation of micro/nanoscale gray image: (

**a**) Three-phase segmentation; (

**b**) three-phase segmentation; and (

**c**) two-phase segmentation.

**Figure 4.**Construction of shale multiscale digital rock: (

**a**) microfracture sample; (

**b**) micropore subsample; and (

**c**) nanopore subsample.

**Figure 5.**Extraction of shale multiscale network model: (

**a**) microfracture; (

**b**) micropore; and (

**c**) nanopore.

Percentage | Specific Surface Area, m^{2}/cm^{3} | ||
---|---|---|---|

Micro-fracture digital rock | Micro-fracture | 2.02% | 0.0011 |

Macro matrix | 93.03% | ||

Micropore digital rock | Micropore | 2.13% | 0.0167 |

Micro matrix | 86.67% | ||

Nanopore digital rock | Nanopore | 7.56% | 4.4241 |

Shale multi-scale digital rock | 10.10% | 3.5837 |

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**MDPI and ACS Style**

Hu, R.; Wang, C.; Zhang, M.; Zhang, Y.; Zhao, J.
The Study of Multi-Scale Specific Surface Area in Shale Rock with Fracture-Micropore-Nanopore. *Processes* **2023**, *11*, 1015.
https://doi.org/10.3390/pr11041015

**AMA Style**

Hu R, Wang C, Zhang M, Zhang Y, Zhao J.
The Study of Multi-Scale Specific Surface Area in Shale Rock with Fracture-Micropore-Nanopore. *Processes*. 2023; 11(4):1015.
https://doi.org/10.3390/pr11041015

**Chicago/Turabian Style**

Hu, Rongrong, Chenchen Wang, Maolin Zhang, Yizhong Zhang, and Jie Zhao.
2023. "The Study of Multi-Scale Specific Surface Area in Shale Rock with Fracture-Micropore-Nanopore" *Processes* 11, no. 4: 1015.
https://doi.org/10.3390/pr11041015