WO2020215524A1 - 一种基于分形理论及ct扫描的煤体孔渗参数预测方法 - Google Patents

一种基于分形理论及ct扫描的煤体孔渗参数预测方法 Download PDF

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WO2020215524A1
WO2020215524A1 PCT/CN2019/098777 CN2019098777W WO2020215524A1 WO 2020215524 A1 WO2020215524 A1 WO 2020215524A1 CN 2019098777 W CN2019098777 W CN 2019098777W WO 2020215524 A1 WO2020215524 A1 WO 2020215524A1
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dimensional
coal
porosity
fractal
fractal dimension
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王刚
程卫民
沈俊男
刘震
倪冠华
刘义鑫
孙路路
刘志远
秦相杰
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山东科技大学
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N15/00—Investigating characteristics of particles; Investigating permeability, pore-volume or surface-area of porous materials
    • G01N15/08—Investigating permeability, pore-volume, or surface area of porous materials
    • G01N15/088—Investigating volume, surface area, size or distribution of pores; Porosimetry
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N23/00—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00
    • G01N23/02—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by transmitting the radiation through the material
    • G01N23/04—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by transmitting the radiation through the material and forming images of the material
    • G01N23/046—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by transmitting the radiation through the material and forming images of the material using tomography, e.g. computed tomography [CT]

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  • the invention belongs to the technical field of coal mine gas disaster prevention and control, and specifically relates to a method for predicting coal pore permeability parameters.
  • coal As a complex porous medium, coal has a large number of irregular pores and cracks of different sizes. Due to the complexity of the internal pore and fissure structure of coal, it is difficult to analyze and describe it with traditional geometric methods. Therefore, relevant researchers have long sought various methods to accurately determine the microscopic pore and fissure structure of coal. Studies have shown that the pore characteristics of porous media affect its physical properties and permeability. Therefore, accurate prediction of coal porosity and permeability is of great significance to the study of gas adsorption and desorption, high-efficiency gas drainage, and coal seam water injection.
  • the purpose of the present invention is to provide a coal body porosity and permeability parameter prediction method based on fractal theory and CT scanning, which can accurately and quickly predict the porosity and permeability of coal samples.
  • a method for predicting coal porosity and permeability parameters based on fractal theory and CT scanning which sequentially includes the following steps:
  • step S1 the specific steps of obtaining a two-dimensional CT slice of a coal sample are: selecting the coal sample to make it into a cylindrical sample, placing the sample on a console for CT scanning, The sample is positioned and rotated through the console. X-rays pass through the sample and receive images through the detector on the console. During scanning, the turntable of the console rotates by 0.9°, and scans once. The two-dimensional coal sample is obtained by CT scanning. CT slices.
  • step S2 the steps of using three-dimensional reconstruction software to accurately perform three-dimensional reconstruction of the real pore and fissure structure of the coal sample include CT image processing steps, noise reduction steps, threshold segmentation steps, and characterization unit body selection. Steps and steps to reconstruct the 3D hole and fracture structure model.
  • a median filter is used for noise reduction during processing, and the selection of the characteristic unit size in the characteristic unit selection step is based on the method of porosity.
  • the three-dimensional data volume is covered by a cube box
  • D is the fractal dimension
  • N( ⁇ ) is the number of boxes containing information in each division of the three-dimensional network
  • ⁇ is the side length of the three-dimensional cube
  • the specific algorithm for calculating the three-dimensional volume fractal dimension is: first construct a cube box with side length a, and then transform different side length values ⁇ to form a number of small boxes correspondingly.
  • the calculation includes the number of small boxes N( ⁇ ), after many times Transformation can get a series of ⁇ -N( ⁇ ) data; then make a scatter plot of the relationship between ln(1/ ⁇ ) and lnN( ⁇ ), and use the least square method to find the slope.
  • the slope is the three-dimensional volume fractal dimension of the coal sample number.
  • step S4 calculates the tortuosity fractal dimension of the three-dimensional space.
  • L T (r) is the actual length of the fluid path, cm;
  • L 0 is the characteristic length of the capillary, cm;
  • D T is the fractal dimension of the average tortuosity of the capillary, dimensionless, 1 ⁇ D T ⁇ 3 ;
  • D T is the fractal dimension of the average tortuosity of the capillary
  • T av is the average tortuosity of the capillary, dimensionless
  • r av is the average capillary radius, ⁇ m
  • L m is a capillary used to characterize the two-dimensional space
  • ⁇ is porosity, %
  • r min is the minimum pore throat radius, ⁇ m
  • D f is the fractal dimension of the coal sample
  • Simultaneous formulas (3)-(6) can obtain the tortuosity fractal dimension of the capillary in the two-dimensional space, and add one to the tortuosity fractal dimension of the three-dimensional space.
  • the porosity described in formula (4) and formula (6), the minimum pore throat radius described in formula (5), and the fractal dimension of the coal sample in formula (6) can be obtained by CT three-dimensional reconstruction Out.
  • the present invention is based on the high-precision CT image of the coal body, applies the various forms of algorithms of the three-dimensional reconstruction software to perform the three-dimensional reconstruction of the coal body, uses Matlab to write a program based on the three-dimensional box dimension algorithm, and imports the reconstructed three-dimensional hole and fracture structure into the calculation
  • the fractal dimension program the volume fractal dimension of the three-dimensional pore and crack structure is obtained, and the tortuosity fractal dimension is calculated by the formula, and the fitting function of the coal porosity, permeability and tortuosity fractal dimension is obtained, and then
  • the method of the present invention avoids the limitation of the laboratory testing of the coal body's porosity and permeability parameters, and obtains data more quickly and accurately.
  • Fig. 1 is a process flow chart of the method for predicting coal pore permeability parameters of the present invention.
  • the present invention proposes a method for predicting coal porosity and permeability parameters based on fractal theory and CT scanning.
  • the experimental instrument used in this micro-CT scanning experiment is the Xradia 510 Versa high-resolution 3D X-ray microscope produced by ZEISS X-ray Microscopy.
  • the specific instrument parameters are shown in Table 1.
  • the sample is placed on the console, the sample is positioned and rotated with high precision through the console, X-rays pass through the sample, and the detector is used to receive the image.
  • the turntable was rotated by 0.9° and scanned once, and the final CT scan obtained a two-dimensional CT slice of the coal sample.
  • the median filter algorithm is used to denoise the CT image, and then the analysis of the characterizing unit volume is performed. Any point on the image is selected, a cube with a certain side length is selected with the voxel point as the center, and the porosity of the cube is calculated; Side length, calculate the porosity of the cube coal sample under the side length; repeat the above steps to calculate the porosity of the cube coal sample with different side lengths.
  • the results show that with the continuous increase of the side length of the cube, the porosity of the coal sample gradually tends to be stable.
  • the minimum size under the stable condition is selected, and the physical unit size is 500 ⁇ 500 ⁇ 500 voxels. The properties are almost no longer affected by size. Therefore, in the research of this paper, for the consideration of calculation storage and calculation speed, the representative volume is 500 ⁇ 500 ⁇ 500 voxels, and the physical size of the experiment is 1mm ⁇ 1mm ⁇ 1mm.
  • the threshold of the image must be determined.
  • the threshold selection of human-computer interaction is realized through the high-resolution CT gray image and the three-dimensional visualization software AVIZO.
  • the original uncut CT picture was selected and processed for the pore Rate calculation.
  • the threshold size to segment the image the segmentation results of pores and cracks can be observed in real time through the view window. Different thresholds correspond to the segmentation results of different pores and cracks. Compare the measured porosity with the simulated porosity. When the porosity of is the closest to the measured porosity, the threshold at that point is taken as the best value for threshold segmentation, and finally the threshold is selected as 106 to segment the image.
  • the fast watershed algorithm based on topological theory is used to obtain the watershed line of the connected pores, and each pore is distinguished independently, and then the cyclic color illumination model is rendered, which is equivalent to each pore is attached with a unique
  • the tags can easily extract the corresponding pore and fissure structure for quantitative analysis. The specific parameters are shown in Table 2.
  • the principle of three-dimensional volume fractal dimension is based on the method of box-counting dimension. For three-dimensional data volume, it is covered by a cube box.
  • D is the fractal dimension
  • N( ⁇ ) is the number of boxes containing information in the three-dimensional network each time
  • ⁇ is the side length of the three-dimensional cube
  • the specific algorithm for calculating the three-dimensional fractal dimension is: first construct a diameter a Small balls (or cube boxes with side length a), and then transform different side length values ⁇ to form several small balls (small boxes). The calculation includes the number of small boxes N( ⁇ ). After multiple transformations, one Series ⁇ -N( ⁇ ) data. Then make a scatter plot of the relationship between ln(1/ ⁇ ) and lnN( ⁇ ), and use the least square method to find the slope.
  • the slope is the volume fractal dimension.
  • D T is the fractal dimension of the average tortuosity of the capillary
  • T av is the average tortuosity of the capillary, dimensionless
  • r av is the average capillary radius, ⁇ m
  • L m is a characteristic length of the capillary in the two-dimensional space coefficient.
  • ⁇ is the porosity, %.
  • r min is the minimum pore throat radius, ⁇ m
  • D f is the fractal dimension of the coal sample.
  • Simultaneous formulas (2)-(5) can be used to obtain the tortuosity fractal dimension of the capillary in the two-dimensional space. Add 1 to the tortuosity fractal dimension of the two-dimensional space to obtain the tortuosity fractal dimension of the three-dimensional space. Among them, the porosity, minimum pore throat radius, and fractal dimension D f existing in the formula can all be obtained by CT three-dimensional reconstruction.
  • the obtained volume fractal dimension and tortuosity fractal dimension are respectively brought into the fitting function to obtain the porosity and permeability of the coal body.

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Abstract

一种基于分形理论及CT扫描的煤体孔渗参数预测方法，包括：首先对煤样进行CT扫描实验，获取煤样的二维CT切片；利用三维重建软件准确的对煤样的真实孔裂隙结构进行三维重建，分别得到6种煤样的三维孔裂隙结构模型，统计出各煤样微观参数；然后利用Matlab程序导入三维孔裂隙结构数据体，并计算各煤样的三维体积分形维数；最后，基于CT三维重建得到的孔裂隙结构参数结合迂曲度分形数学模型求得三维空间的迂曲度分形维数，得到孔隙率、渗透率与分形维数的拟合函数，进而准确预测孔隙率、渗透率。

Description

一种基于分形理论及CT扫描的煤体孔渗参数预测方法 技术领域
本发明属于煤矿瓦斯灾害防治技术领域，具体涉及一种煤体孔渗参数的预测方法。
背景技术
我国作为一个矿产资源大国，蕴藏着丰富的煤矿资源，产量占世界煤炭总产量的36.5％。拥有煤矿数量比世界其它产煤国的总和还多。但我国同时也是煤矿安全形势最为严峻的国家之一，其中因瓦斯事故引起的灾害事故发生频繁，后果也最为严重。
煤作为一种复杂的多孔介质，内部存在大量不规则的，不同尺度的孔隙、裂隙。由于煤体内部孔裂隙结构的复杂性，故难以用传统的几何等方法进行解析描述，因此长期以来相关研究者们寻求各种方法以准确地确定煤体的微观孔裂隙结构。研究表明，多孔介质孔隙特征影响其物理性能及渗透性能，因此，准确预测煤体孔隙率、渗透率对研究瓦斯吸附解吸和高效瓦斯抽采以及煤层注水等瓦斯防治问题具有重要意义。
发明内容
本发明的目的在于提供一种基于分形理论及CT扫描的煤体孔渗参数预测方法，其可以准确快速的预测煤样的孔隙率、渗透率。
其技术解决方案包括：
一种基于分形理论及CT扫描的煤体孔渗参数预测方法，依次包括以下步骤：
S1、对煤样进行CT扫描实验，获取煤样的二维CT切片；
S2、利用三维重建软件准确的对煤样的真实孔裂隙结构进行三维重建，分别得到6种煤样的三维孔裂隙结构模型，统计出各煤样微观参数；
S3、利用Matlab程序导入三维孔裂隙结构数据体，并计算各煤样的三维体积分形维数；
S4、基于CT三维重建得到的孔裂隙结构参数结合迂曲度分形数学模型求得三维空间的迂曲度分形维数，得到孔隙率、渗透率与分形维数的拟合函数，进而准确预测孔隙率、渗透率。
作为本发明的一个优选方案，步骤S1中，获取煤样的二维CT切片的具体步骤为：选取煤样将其制成圆柱形的样品，将样品放置在控制台上进行CT扫描，所述的样品通过控制台做定位和旋转，X射线穿过样品，且通过控制台上的探测器接收图像，扫描时控制台的转台旋转0.9°，扫描1次，经CT扫描获得煤样的二维CT切片。
作为本发明的另一个优选方案，步骤S2中利用三维重建软件准确的对煤样的真实孔裂隙结构进行三维重建的步骤依次包括CT图像处理步骤、降噪步骤、阈值分割步骤、表征单元体选取步骤及重建三维孔裂隙结构模型的步骤。
进一步的，所述的CT图像处理步骤在处理时采用中值滤波器进行降噪处理，所述的表征单元体选取步骤中选择表征单元体尺寸是基于孔隙率的方法进行选取。
进一步的，步骤S3中煤样的三维体积分形维数的计算方法为：
基于计盒维数的方法，对于三维的数据体利用立方体盒子覆盖，
当ε→0时，
Figure PCTCN2019098777-appb-000001
式(1)中：D是分形维数，N(ε)是每次划分三维网络中包含信息的盒子数，ε是三维立方体的边长；
计算三维体积分形维数的具体算法为：先构造一个边长为a的立方体盒子，然后变换不同边长值ε，对应形成若干小盒子，计算包含有小盒子数N(ε)，经过多次变换可得到一系列ε-N(ε)数据；再作ln(1/ε)与lnN(ε)关系的散点图，采用最小二乘法求其斜率，斜率即为煤样的三维体积分形维数。
进一步的，步骤S4中三维空间的迂曲度分形维数的计算方法为：
当流体通过随机且复杂的孔隙结构时，满足如下分形关系式(2)
Figure PCTCN2019098777-appb-000002
式(2)中：L T(r)为流体路径的实际长度，cm；L 0为毛细管的特征长度，cm；D T为毛细管平均迂曲度分形维数，无量纲，1<D T<3；
计算求取煤样的毛细管平均迂曲度的分形维数(D T)，其取值范围为1＜D T＜3，计算公式(3)为
Figure PCTCN2019098777-appb-000003
式(3)中：D T为毛管平均迂曲度的分形维数；T av为毛管的平均迂曲度，无量纲；r av为平均毛管半径，μm；L m为一个用于表征二维空间毛管特征长度的系数，其中，后面3个参数的表达式(4)、(5)分别为
Figure PCTCN2019098777-appb-000004
式(4)中：φ为孔隙度，％；
Figure PCTCN2019098777-appb-000005
式(5)中：r min为最小孔喉半径，μm；D f为煤样的分形维数；
Figure PCTCN2019098777-appb-000006
式(6)中：φ为孔隙度，％；r max为最大孔喉半径，μm；D f为煤样的分形维数，无量纲，1<D f<3；
联立公式(3)-(6)即可求得二维空间的毛细管迂曲度分形维数，将得到的二维空间的迂曲度分形维数加一即为三维空间的迂曲度分形维数。
进一步的，式(4)和式(6)中所述的孔隙度、式(5)中所述的最小孔喉半径及式(6)中煤样的分形维数均可通过CT三维重建得出。
与现有技术相比，本发明带来了以下有益技术效果：
本发明基于高精度煤体的CT图像，应用三维重建软件的多种形态的算法对煤体进行三维重建，利用Matlab编写了基于三维盒维数算法的程序，将重建的三维孔裂隙结构导入计算分形维数的程序中，求得三维孔裂隙结构的体积分形维数并通过公式计算得到迂曲度分形维数，得出煤体孔隙率、渗透率与迂曲度分形维数的拟合函数，进而预测煤体的孔隙率、渗透率，本发明方法避免了实验室测煤体孔渗参数的局限性，获得数据更加快速、准确。
附图说明
下面结合附图对本发明做进一步说明：
图1为本发明煤体孔渗参数预测方法的工艺流程图。
具体实施方式
本发明提出了一种基于分形理论及CT扫描的煤体孔渗参数预测方法，为了使本发明的优点、技术方案更加清楚、明确，下面结合具体实施例对本发明做详细说明。
选取工作面中的煤样，将煤样取芯后将上下断面磨平，制备成直径9mm，高度为16mm的圆柱形煤样，并将煤样进行干燥处理。
本次显微CT扫描实验所使用的实验仪器是ZEISS X-ray Microscopy公司生产的Xradia 510 Versa高分辨率3D X射线显微镜，具体的仪器参数见表1。实验时，将样品放置在控制台上，样品通过控制台做高精度的定位和旋转，X射线穿过样品，探测器用于接收图像。扫描时转台旋转0.9°，扫描1次，最终CT扫描获得煤样的二维CT切片。
表1 Xradia 510 Versa所使用的参数
Figure PCTCN2019098777-appb-000007
采用中值滤波算法对CT图像进行降噪处理，然后进行表征单元体的分析，选取图像上任意一点，以该体素点为中心选取一定边长的正方体，计算该正方体的孔隙率；然后扩大边长，计算该边长下正方体煤样的孔隙率；重复上述步骤计算不同边长正方体煤样的孔隙率。结果表明，随着正方体边长的不断增大，煤样的孔隙率逐渐趋于稳定，选取趋于稳定情况下的最小尺寸，最终表征单元体尺寸选取500×500×500体素时，其物理性质几乎不再受尺寸的影响。因此，在本文研究中，出于计算存储和计算速度的考虑，选取代表元体积为500×500×500体素，实验的物理尺寸为1mm×1mm×1mm。
图像处理完成后，要确定图像的阈值。在已知实测孔隙率的情况下，通过高分辨率的CT灰度图像以及三维可视化软件AVIZO实现了人机交互的阈值选取。为保证实测煤样与三维重建煤样的一致性，使实测与模拟的孔隙率在对比分析时更有说服力，因此选用原始的未裁剪的CT图片，将其进行图像处理之后，用于孔隙率的计算。调整阈值大小对图像进行分割的过程中，通过视图窗口可以实时观察到孔裂隙的分割结果，不同的阈值对应不同的孔裂隙的分割结果，将实测孔隙率与模拟孔隙率进行比较，当模拟得到的孔隙率与实测孔隙率最接近时，取该点的阈值作为最佳值进行阈值分割，最终选取阈值为106对图像进行分割。
阈值分割完成后，采用基于拓扑理论的快速分水岭算法来获得连通孔隙的分水岭线，将每个孔隙独立区分开来，再经循环颜色光照模型的渲染，相当于每个孔隙都贴上了独有的标签，可以很方便地提取对应的孔裂隙结构以进行定量分析。具体的参数见表2。
表2不同煤体结构煤孔隙参数分析结果
Figure PCTCN2019098777-appb-000008
三维体积分形维数原理是基于计盒维数的方法，对于三维的数据体则是利用立方体盒子覆盖的，当ε→0时，
Figure PCTCN2019098777-appb-000009
式中D是分形维数，N(ε)是每次划分三维网络中包含信息的盒子数，ε是三维立方体的边长；计算三维分形维数的具体算法为：先构造一个直径为a的小球(或边长为a的立方体盒子)，然后变换不同边长值ε，对应形成若干个小球(小盒子)，计算包含有小盒子数N(ε)，经过多次变换可得到一系列ε-N(ε)数据。再作ln(1/ε)与lnN(ε)关系的散点图，采用最小二乘法求其斜率，斜率即为体积分形维数。
迂曲度分形维数的计算为：
当流体通过随机且复杂的孔隙结构时，满足如下分形关系式(1)
Figure PCTCN2019098777-appb-000010
式中：L T(r)为流体路径的实际长度，cm；L 0为毛细管的特征长度，cm；D T为毛细管平均迂曲度分形维数，无量纲，1<D T<3。
计算求取煤样的毛细管平均迂曲度的分形维数(D T)，其取值范围为1＜D T＜3，计算公式(2)为
Figure PCTCN2019098777-appb-000011
式中：D T为毛管平均迂曲度的分形维数；T av为毛管的平均迂曲度，无量纲；r av为平均毛管半径，μm；L m为一个用于表征二维空间毛管特征长度的系数。其中，后面3个参数的表达式(3-5)分别为
Figure PCTCN2019098777-appb-000012
式中：φ为孔隙度，％。
Figure PCTCN2019098777-appb-000013
式中：r min为最小孔喉半径，μm；D f为煤样的分形维数。
Figure PCTCN2019098777-appb-000014
式中：φ为孔隙度，％；r max为最大孔喉半径，μm；D f为煤样的分形维数，无量纲，1<D f<3。
联立公式(2)-(5)即可求得二维空间的毛细管迂曲度分形维数，将得到的二维空间的迂曲度分形维数加1即为三维空间的迂曲度分形维数。其中，公式中存在的孔隙度、最小孔喉半径、分形维数D f都可通过CT三维重建得出。
将得到的体积分形维数与迂曲度分形维数分别带入拟合函数中即可得到煤体的孔隙率、渗透率。
本发明中未述及的部分借鉴现有技术即可实现。
需要说明的是，在本说明书的教导下本领域技术人员所做出的任何等同方式，或明显变 型方式均应在本发明的保护范围内。

Claims (7)

  1. 一种基于分形理论及CT扫描的煤体孔渗参数预测方法，其特征在于，依次包括以下步骤：
    S1、对煤样进行CT扫描实验，获取煤样的二维CT切片；
    S2、利用三维重建软件准确的对煤样的真实孔裂隙结构进行三维重建，分别得到6种煤样的三维孔裂隙结构模型，统计出各煤样微观参数；
    S3、利用Matlab程序导入三维孔裂隙结构数据体，并计算各煤样的三维体积分形维数；
    S4、基于CT三维重建得到的孔裂隙结构参数结合迂曲度分形数学模型求得三维空间的迂曲度分形维数，得到孔隙率、渗透率与分形维数的拟合函数，进而准确预测孔隙率、渗透率。
  2. 根据权利要求1所述的一种基于分形理论及CT扫描的煤体孔渗参数预测方法，其特征在于：步骤S1中，获取煤样的二维CT切片的具体步骤为：选取煤样将其制成圆柱形的样品，将样品放置在控制台上进行CT扫描，所述的样品通过控制台做定位和旋转，X射线穿过样品，且通过控制台上的探测器接收图像，扫描时控制台的转台旋转0.9°，扫描1次，经CT扫描获得煤样的二维CT切片。
  3. 根据权利要求2所述的一种基于分形理论及CT扫描的煤体孔渗参数预测方法，其特征在于：步骤S2中利用三维重建软件准确的对煤样的真实孔裂隙结构进行三维重建的步骤依次包括CT图像处理步骤、降噪步骤、阈值分割步骤、表征单元体选取步骤及重建三维孔裂隙结构模型的步骤。
  4. 根据权利要求3所述的一种基于分形理论及CT扫描的煤体孔渗参数预测方法，其特征在于：所述的CT图像处理步骤在处理时采用中值滤波器进行降噪处理，所述的表征单元体选取步骤中选择表征单元体尺寸是基于孔隙率的方法进行选取。
  5. 根据权利要求4所述的一种基于分形理论及CT扫描的煤体孔渗参数预测方法，其特征在于：步骤S3中煤样的三维体积分形维数的计算方法为：
    基于计盒维数的方法，对于三维的数据体利用立方体盒子覆盖，
    当ε→0时，
    Figure PCTCN2019098777-appb-100001
    式(1)中：D是分形维数，N(ε)是每次划分三维网络中包含信息的盒子数，ε是三维立方体的边长；
    计算三维体积分形维数的具体算法为：先构造一个边长为a的立方体盒子，然后变换不同边长值ε，对应形成若干小盒子，计算包含有小盒子数N(ε)，经过多次变换可得到一系列ε-N(ε)数据；再作ln(1/ε)与lnN(ε)关系的散点图，采用最小二乘法求其斜率，斜率即为煤样的 三维体积分形维数。
  6. 根据权利要求5所述的一种基于分形理论及CT扫描的煤体孔渗参数预测方法，其特征在于：步骤S4中三维空间的迂曲度分形维数的计算方法为：
    当流体通过随机且复杂的孔隙结构时，满足如下分形关系式(2)
    Figure PCTCN2019098777-appb-100002
    式(2)中：L T(r)为流体路径的实际长度，cm；L 0为毛细管的特征长度，cm；D T为毛细管平均迂曲度分形维数，无量纲，1<D T<3；
    计算求取煤样的毛细管平均迂曲度的分形维数(D T)，其取值范围为1＜D T＜3，计算公式(3)为
    Figure PCTCN2019098777-appb-100003
    式(3)中：D T为毛管平均迂曲度的分形维数；T av为毛管的平均迂曲度，无量纲；r av为平均毛管半径，μm；L m为一个用于表征二维空间毛管特征长度的系数，其中，后面3个参数的表达式(4)、(5)分别为
    Figure PCTCN2019098777-appb-100004
    式(4)中：
    Figure PCTCN2019098777-appb-100005
    为孔隙度，％；
    Figure PCTCN2019098777-appb-100006
    式(5)中：r min为最小孔喉半径，μm；D f为煤样的分形维数；
    Figure PCTCN2019098777-appb-100007
    式(6)中：
    Figure PCTCN2019098777-appb-100008
    为孔隙度，％；r max为最大孔喉半径，μm；D f为煤样的分形维数，无量纲，1<D f<3；
    联立公式(3)-(6)即可求得二维空间的毛细管迂曲度分形维数，将得到的二维空间的迂曲度分形维数加一即为三维空间的迂曲度分形维数。
  7. 根据权利要求6所述的一种基于分形理论及CT扫描的煤体孔渗参数预测方法，其特征在于：式(4)和式(6)中所述的孔隙度、式(5)中所述的最小孔喉半径及式(6)中煤 样的分形维数均可通过CT三维重建得出。
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