minerals Article
Characterization of Coal Micro-Pore Structure and Simulation on the Seepage Rules of Low-Pressure Water Based on CT Scanning Data Gang Zhou 1,2,3, *, Qi Zhang 1,2 , Ruonan Bai 1,2 and Guanhua Ni 1,2 1
2 3
*
State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China;
[email protected] (Q.Z.);
[email protected] (R.B.);
[email protected] (G.N.) College of Mining and Safety Engineering, Shandong University of Science and Technology, Qingdao 266590, China Key Laboratory of Coal Mine Gas and Fire Prevention and Control of Ministry of Education, China University of Mining and Technology, Xuzhou 221116, China Correspondence:
[email protected]; Tel.: +86-532-8605-8080
Academic Editor: Kota Hanumantha Rao Received: 27 April 2016; Accepted: 20 July 2016; Published: 26 July 2016
Abstract: This paper used the X-ray three-dimensional (3D) microscope and acquired, through CT scanning, the 3D data of the long-frame coal sample from the Daliuta Coal Mine. Then, the 3D datacube reconstructed from the coal’s CT scanning data was visualized with the use of Avizo, an advanced visualization software (FEI, Hillsboro, OR, USA). By means of a gray-scale segmentation technique, the model of the coal’s micro-pore structure was extracted from the object region, and the precise characterization was then conducted. Finally, the numerical simulation on the water seepage characteristics in the coal micro-pores model under the pressure of 3 MPa was performed on the CFX platform. Results show that the seepage of low-pressure water exhibited preference to the channels with large pore radii, short paths, and short distance from the outlet. The seepage pressure of low-pressure water decreased gradually along the seepage direction, while the seepage velocity of low-pressure water decreased gradually along the direction from the pore center to the wall. Regarding the single-channel seepage behaviors, the seepage velocity and mass flow rate of water seepage in the X direction were the largest, followed by the values of the seepage in the Y direction, and the seepage velocity and mass flow rate of water seepage in the Z direction were the smallest. Compared with the results in single-channel seepage, the dual-channel seepage in the direction of (X + Y) and the multi-channel seepage in the direction of (X + Y + Z) exhibited significant increases in the overall seepage velocity. The present study extends the application of 3D CT scanning data and provides a new idea and approach for exploring the seepage rules in coal micro-pore structures. Keywords: CT; coal microscopic structure model; pores and throats; three-dimensional (3D) data cube; seepage simulation of water-injection
visualization of
1. Introduction Water injection into coal seams is one of the most significant methods to prevent and deal with rock bursts, coal and gas outbursts, and coal dust. However, coal is a complex porous medium which, besides coal matrix, contains many other components, such as pores, fractures, and minerals. The physical properties and micro-pore structure characteristics of coal components directly affect its macroscopic physical and chemical properties, such as adsorptivity and permeability. A thorough knowledge of these micro-properties provides the basis for the research on the seepage characteristics of water and gas in coal pores [1]. Accordingly, it is particularly important to quantitatively characterize Minerals 2016, 6, 78; doi:10.3390/min6030078
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the micro-pore structure with good precision. Computed tomography (CT) has become a dominant technique which is used to investigate the micro-pore structure of coal because of several advantages it offers, such as non-destructive, accurate and quantitative detection, as well as three-dimensional (3D) digitization. Over the past several years, many researchers conducted a great deal of research on the micro-structure of coal. Van et al. [2] gained in-depth insight into the distribution of minerals, macerals, pores and fractures in coals by using the X-CT technique. Simons et al. [3] made quantitative characterization of coals using the CT reconstruction method, in which the precision of characterization was approximately 53 µm. By means of the CT technique, Mazumder et al. [4] investigated the cleats, pore diameters, and spacing in coal seams, and Golab et al. [5] analyzed the occurrence characteristics of the minerals in coals. With the CT imaging method, Karacan et al. [6] examined the adsorption and migration behaviors of gases in the micro-structure of coal and made corresponding assessments. Mathews et al. [7] used a high-resolution CT technique to observe the thermal drying process of subbituminous coals. By means of the micro-CT technique, Meng et al. [8] conducted a quantitative study on the morphological characteristics of the pore structure of coking coals. Yao et al. [9] adopted a quantitative method to characterize the development degrees and spatial distribution characteristics of pores and cracks in coals of various ranks. Song et al. [10] performed 3D scanning imaging on coal samples of different structures and precisely characterized their seepage pore properties. However, due to the limitation in the accuracy of CT equipment, the precise characterization of coal micro-pore structure still exhibits certain errors and needs to be further improved. Based on the knowledge of coal micro-pore structure, many scholars further explored the seepage laws in coal pores with certain progress. Coles et al. [11] conducted an in-depth study on the characteristics of adsorption and migration of the gases in coal pores and cracks. Stauffer and Aharony [12] focused on the seepage mechanism in a single porous medium and concluded that the permeability of this porous medium decreases as the number of isolated pore groups increases. Using the Lattice Boltzmann Method (LBM), Teng [13] and Jin et al. [14] performed simulations on the seepage rules of gas in the coals. Liu et al. [15] established the coupling numerical model of seepage and stress in the media with pores and fractures based on the discrete element method of continuous media. Perera et al. [16] reviewed the effects of coal physical properties and permeability on carbon dioxide sequestration in a coal seam. Despite all of these achievements, there is still a need for comprehensive and thorough understanding of the seepage laws of low-pressure water in coals at the micro-level. Therefore, it is quite necessary to perform scanning and reconstruction on coals using high-precision micro-CT equipment, then construct the coal’s micro-pore structure model and, finally, investigate the seepage rules of pressurized water in coal’s micro-pore structure at the micro-level through simulations. In this paper, coals were firstly scanned using the high-precision X-ray 3D microscope (Nano Voxel-2000, Sanying Precision Instruments Co., Ltd., Tianjin, China) and the 3D reconstruction of coal was visualized by Avizo software so as to precisely characterize the model of the micro-pore structure of coal. Finally, the simulation on the single-channel, dual-channel, and multi-channel seepage behaviors of low-pressure water was conducted based on the geometric model of coal’s micro-pores. The present study offers a new way towards a deeper understanding of coal’s real micro-pore structure and the seepage rules of pressurized water in coals. 2. Principle of CT Scanning According to photoelectric effect, when X-ray or γ-ray passes through an object, the incident photons can be absorbed by the object and thereby the incident intensity decreases, i.e., the intensity of X-ray or γ-ray is attenuated. Taking a uniformly-distributed material with a linear attenuation coefficient of µ as an example, when it is irradiated by X-rays with an incident intensity of I0 ,
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the attenuation of X-rays by the object obeys the Beer-Lambert law and the following expression can be obtained: I “ I0 e´µ4 x (1) where I denotes the intensity of ray attenuated by the object and ∆x denotes the distance the ray travels in the object. For a mixture or a compound material consisting of more than a single element, the following expression can be obtained: ÿ µ“ a i µi (2) i
where µi and ai denote the linear attenuation coefficient and mass percentage of the i-th component, respectively. The following expression can be obtained: řn
I “ I0 e´µ1 ∆x e´µ2 ∆x e´µ3 ∆x . . . e´µn ∆x “ I0 e´
i“1 µi ∆x
(3)
Equation (3) can further be converted into: ˆ ´ ln
I I0
˙
ˆ “ ln
I0 I
˙ ÿ “
ż n i“1 µi ∆x
“ L
µi dx
(4)
Based on Equation (4), one can find that the linear integral of the material attenuation coefficient along the ray transmission path equals to the logarithm of the ratio of input intensity to output intensity. In CT technology, the image is reconstructed through the calculation of the attenuation coefficient based on the projection data related to the ratio in Equation (4). 3. Coal Sample Processing and CT Scanning During CT scanning, the layer with a certain thickness is scanned by the X-ray beam, and the transmitted X-ray signal is received by the detector and then transformed into visible light signal; then, the light signal is converted to electrical signal via photovoltaic conversion, which is then converted to a digital signal via the analog-to-digital (A/D) converter and input to the computer for processing. CT can detect the internal structure of a material in a non-destructive way and generate high density resolution images of the cross-section. In a word, CT exhibits obvious advantages in investigating the micro-pore structure of coal [17–19]. In this paper, the X-ray 3D microscope (Nano Voxel-2000, Sanying Precision Instruments Co., Ltd.) was used for CT scanning, with a resolution up to 0.5 µm. The imaging quality and overall performance of this X-ray 3D microscope have already reached the top level of similar products in the world [20,21]. The equipment can be used for 3D characterization of the internal pore structure of coal and rock at the micro-scale. By using a combination of several types of software for finite-element and discrete-element analysis, such as Avizo, Ansys, COMSOL, EDEM, and Barracuda, the 3D connectivity of the internal pores and throats in the core can be calculated and the statistical results of porosity, pore size, throat size, and various seepage characteristic parameters can be acquired. Figure 1 displays the photograph of the X-ray 3D microscope. In the present study, a long flame coal sample from the Daliuta Coal Mine, Shenmu County, Shaanxi, was selected, and an ore core with the diameter and length of 2 and 5 mm, respectively, was drilled for further analysis. To avoid the influence of coal shape change induced by water evaporation on the experimental results, the ore core was sealed with wax. After being sealed, the ore core of the coal sample was 3.31 mm in diameter, as shown in Figure 2. Then, the ore core was stuck to the end of a toothpick, placed on the sample stage of the X-ray 3D microscope (which can be rotated by 360˝ ), and fixed by the screw. The main control computer interface was then initiated for adjusting the position of the sample stage to the central position in four dimensions (x, y, z, and r). Then the X-ray source was turned on, and 3D data of the coal sample was acquired viasuper-wide-field scanning. Table 1
then, the light signal is converted to electrical signal via photovoltaic conversion, which is then converted to a digital signal via the analog-to-digital (A/D) converter and input to the computer for processing. CT can detect the internal structure of a material in a non-destructive way and generate high density resolution images of the cross-section. In a word, CT exhibits obvious advantages in investigating the micro-pore structure of coal [17–19]. Minerals 2016, 6, 4 of 16 In78 this paper, the X-ray 3D microscope (Nano Voxel-2000, Sanying Precision Instruments Co., Ltd.) was used for CT scanning, with a resolution up to 0.5 μm. The imaging quality and overall performance of this X-ray 3D microscope have already reached the top level of similar products in world [20,21]. The equipment canCT be used for 3D characterization of the internal pore structure lists thethe specific parameter settings in scanning. A 20ˆ lens detector was used, the number of of frames coal and rock micro-scale. By using a combination of several types it of was software for by 0.4˝ , scanning was setatasthe 900, i.e., the sample stage was scanned once when rotated and discrete-element analysis, such as Avizo, Ansys, COMSOL, EDEM, and and the finite-element duration of exposure equaled to the duration of one full rotation of the sample stage. In Table 1, Barracuda, the 3D connectivity of the internal pores and throats in the core can be calculated and Minerals 2016, 6, 78 4 of 16 SOD denotes the distance between the X-ray source and the detector, and ODD denotes the distance the statistical results of porosity, pore size, throat size, and various seepage characteristic betweenparameters the stagecan sample and the detector. be acquired. Figure 1 displays the photograph of the X-ray 3D microscope. In the present study, a long flame coal sample from the Daliuta Coal Mine, Shenmu County, Shaanxi, was selected, and an ore core with the diameter and length of 2 and 5 mm, respectively, was drilled for further analysis. To avoid the influence of coal shape change induced by water evaporation on the experimental results, the ore core was sealed with wax. After being sealed, the ore core of the coal sample was 3.31 mm in diameter, as shown in Figure 2. Then, the ore core was stuck to the end of a toothpick, placed on the sample stage of the X-ray 3D microscope (which can be rotated by 360°), and fixed by the screw. The main control computer interface was then initiated for adjusting the position of the sample stage to the central position in four dimensions (x, y, z, and r). Then the X-ray source was turned on, and 3D data of the coal sample was acquired viasuper-wide-field scanning. Table 1 lists the specific parameter settings in CT scanning. A 20× lens detector was used, the number of scanning frames was set as 900, i.e., the sample stage was scanned once when it was rotated by 0.4°, and the duration of exposure equaled to the duration of Figure 1. X-ray 3D microscope (NanoVoxel-2000). one full rotation of the sample stage. In Table 1, SOD denotes the distance between the X-ray source Figure 1. X-ray 3D microscope (NanoVoxel-2000). and the detector, and ODD denotes the distance between the stage sample and the detector.
Figure 2. Diameter measurement of the ore core.
Figure 2. Diameter measurement of the ore core. Table 1. Setting of scanning parameters of X-ray 3D microscope. Detector
Detector20×
Table 1. Setting of scanning parameters of X-ray 3D microscope. SOD/ODD Voltage Electric Scanning Exposure
(mm/mm) SOD/ODD 35/13 Voltage (mm/mm) (kV)
(kV) Current (μA) Frame Electric Current Scanning 41 240 900 (µA) Frame
20ˆ4. Visualization 35/13 of the 3D 41Reconstruction 240 of Coal Sample 900
Time (h)
19 (h) Time
19
Penetration Time (s) Rate (%) 65Exposure 57 Penetration Time (s) Rate (%)
65
57
It should be noted that the Nano Voxel-2000X-raysystem is equipped with a set of special 3D reconstruction software and algorithms that can directly convert the 2D scanned images to a 3D 4. Visualization of the 3D Reconstruction of Coal Sample data cube.
It should be noted thatisthe Nano Voxel-2000X-raysystem is equipped with a set of and special 3D Avizo™ software a set of all-in-one visual tools and can visually display, process, reconstruction that canprovides directlypowerful convertdata the processing 2D scanned images interpret software engineeringand andalgorithms scientific data. Avizo ability, and itto a 3D has an easy-to-use and user-friendly graphical interface. These features allow it to deal with data cube. complex 3D data. has strong abilities image information processing, geometry Avizo™ software is aAvizo set ofalso all-in-one visual tools in and can visually display, process, and interpret calculation, and reconstruction of high-resolution 3D images. Owing to its particular high-efficiency engineering and scientific data. Avizo provides powerful data processing ability, and it has an algorithm, Avizo can accurately reconstruct 3D image based on the data of slices collected by CT easy-to-use and user-friendly interface. These features allow it to deal with complex equipment, MRT equipment,graphical 3D ultrasonic equipment, and confocal microscope. 3D data. Avizo has strong abilities image information processing, calculation, In the also present study, the used NanoinVoxel-2000 system has the resolution ofgeometry 1 μm × 1 μm × 1 μm. The 3D of data acquired by scanning were imported software for the visualizationalgorithm, of and reconstruction high-resolution 3D images. OwingtotoAvizo its particular high-efficiency 3D reconstruction, and the digital bodybased with the of real collected pore structure then Avizo can accurately reconstruct 3D coal image oncharacteristics the data of slices by was CT equipment, acquired. The voxel size of the digital coal body was 1024 × 1024 × 1024 while the actual size of it MRT equipment, 3D ultrasonic equipment, and confocal microscope. was 1.024 mm × 1.024 mm × 1.024 mm. Two profile images on the XY and ZY planes, respectively, In the present study, the used Nano Voxel-2000 system has the resolution of 1 µm ˆ 1 µm ˆ 1 µm. were selected for observation. Figure 3a shows four images of the reconstructed 3D model from The 3Ddifferent data acquired scanning imported Avizo software foronthe angles of by view. Figure 3b were displays the profileto image of the 512th layer thevisualization XY plane and of 3D reconstruction, and thethe digital Figure 3c displays profilecoal imagebody of thewith 420th the layercharacteristics on the ZY plane. of real pore structure was then acquired. The voxel size of the digital coal body was 1024 ˆ 1024 ˆ 1024 while the actual size of it was 1.024 mm ˆ 1.024 mm ˆ 1.024 mm. Two profile images on the XY and ZY planes, respectively,
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were selected for observation. Figure 3a shows four images of the reconstructed 3D model from different angles of view. Figure 3b displays the profile image of the 512th layer on the XY plane and Figure 3c displays the profile image of the 420th layer on the ZY plane. Minerals 2016, 6, 78 5 of 16 Minerals 2016, 6, 78 Minerals 2016, 6, 78
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(a)
(b)
(c)
Figure 3. Profile image of the reconstructed 3D model: (a) Four-View; (b) 512th layer(c) profile on the (b) (a) Figure 3. Profile(a) image of the reconstructed 3D model: Four-View; (b) 512th layer profile on the XY (a)(c) 420th layer profile on the ZY plane. (b) (c) XY plane; and plane;Figure and (c) 420th layer on the ZY plane. 3. Profile imageprofile of the reconstructed 3D model: (a) Four-View; (b) 512th layer profile on the Figure 3. Profile image of the reconstructed 3D model: (a) Four-View; (b) 512th layer profile on the
XY plane; andimage (c) 420th profile on the ZYselected plane. for further analysis. One can clearly observe The profile on layer the XY plane was XY plane; and (c) 420th layer profile on the ZY plane. The profile image on the XY plane was selected for as further canmore clearly observe the distribution of organic matter, minerals, and pores, shownanalysis. in FigureOne 4. For precise The profile image on the XY plane was selected for further analysis. One can clearly observe the distribution of organic and as shown in Figure 4. clearly Forplane morewas precise characterization of the micro-pore structure coal,pores, anfor original profile image the XY The profile image onmatter, the XY minerals, plane wasofselected further analysis. Oneon the distribution of organic matter, minerals, andborder pores, as shown in Figure 4.can For more observe precise arbitrarily selected, and the part on the yellow was enlarged, as shown in Figure 5. The characterization of the micro-pore structure of coal, an original profile image on the XY plane was the distribution of of the organic matter,structure minerals,ofand pores, as shown in image Figureon 4. the For XY more precise characterization micro-pore coal, an original profile plane was pores were marked in black in the originally measured data. To facilitate the identification and arbitrarily selected, and the part on the yellowofborder enlarged, shown Figure 5. The pores characterization of the micro-pore structure coal, anwas original profileasimage onin the plane arbitrarily and thethe part on the yellow border was enlarged, as segmentation shown in XY Figure 5. was The ofinselected, the single pore, pore image was processed using an image technique. were analysis marked black in the originally measured data. To facilitate the identification and analysis of arbitrarily selected, and the part on the yellow border was enlarged, as shown in Figure 5. The pores were marked in black the originally measured data. facilitate the identification Figure 6 shows the pore imagein after such processing, where theTo pores were marked in white soand as pores were marked in black in the originally measured data. To facilitate the identification and the single pore, the pore image was processed using an image segmentation technique. Figure 6 shows analysis of the single pore, poredistribution image was processed using segmentation technique. to more directly analyze thethe overall and relative sizesan of image the pores on each cross-section. analysis of the single pore, the pore image was using an image segmentation technique. the pore image after such processing, where the processed poreswhere were marked in white so asintowhite more Figure 6 shows the pore image after such processing, the pores were marked sodirectly as The single pore was calibrated and measured with the measurement toolwere of the software. Figure 6 shows the pore image after such processing, where the pores marked in white so as pore to more directly distribution analyze the overall distribution relative sizes the cross-section. pores on each cross-section. analyze the overall and relative sizesand of the pores onof each The single to more directly analyze the overall distribution and relative sizes of tool the pores each cross-section. The single pore was calibrated and with the measurement of theon software. was calibrated and measured with themeasured measurement tool of the software. The single pore was calibrated and measured with the measurement tool of the software.
Figure 4. Component distribution. Figure 4. Component distribution. Figure 4. Component distribution. Figure 4. Component distribution.
Figure 5. Original Pore image. Figure 5. Original Pore image. Figure5.5.Original Original Pore Figure Poreimage. image.
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Figure Figure 6. 6. Pore Pore image image after after processing. processing.
5. of of Structure 6.Model Pore image after processing. 5. Construction Constructionand andOptimization OptimizationFigure ofthe the Model ofMicro-Pore Micro-Pore Structureof ofCoal Coal Figure 6. Pore image after processing.
High-precision characteristics ofof the pore resolution lay basis and provides guarantee High-precision characteristics of the pore resolution lay thethe basis and thethe guarantee for 5. Construction and Optimization the Model of Micro-Pore Structure of provides Coal for the construction of the micro-pore structure model based on the actual pore structure. 5. Construction and Optimization of the Model of Micro-Pore Structure of Coal the construction of the micro-pore structure model basedlay onthe thebasis actual structure. Meanwhile, High-precision of the pore resolution andpore provides the guarantee Meanwhile, tocalculation reduce characteristics theload calculation load induced by oversized data in mesh generation and to reduce the induced by oversized data in mesh generation and analysis, a data High-precision of the pore resolution laybased the basis the guarantee for the constructioncharacteristics of the micro-pore structure model on and the provides actual pore structure. analysis, a data cube with the size of 60 pixel × 60 pixel × 60 pixel was selected in the reconstructed cube for withthe theconstruction size 60 pixel ˆcalculation 60 pixel ˆload 60structure pixel wasmodel selected in the reconstructed digital coal ofthethe micro-pore based on thein actual pore structure. Meanwhile, toofreduce induced by oversized data mesh generation andbody, digital coal body, as shown in Figure 7. The actual size of the selected coal body is 60 μm × 60the μm × Meanwhile, to 7. reduce thethe calculation induced oversized data in µm mesh generation as shown in Figure Thewith actual size selected body is 60was µm ˆ 60 60 µm. Withand use analysis, a data cube size of of the 60 load pixel × 60 coal pixelby × 60 pixel selected inˆthe reconstructed 60 μm. With the use of the gray-scale segmentation technique, the digital coal body was segmented a data cube with the size of 60 pixel × 60 pixel × 60 pixel wassegmented selected reconstructed digital coal body, as shown intechnique, Figure 7. The size of the selected coal bodyinisthe 60 μm 60 μm ×of the of theanalysis, gray-scale segmentation theactual digital coal body was and the× model and the model of the micro-pore structure of coal was acquired, as shown in Figure 8a. Using digital coal body, as shown in Figure 7. The actual size of the selected coal body is 60 μm × 60 μmnormal × the 60 μm. With the use of the gray-scale segmentation technique, the digital coal body was segmented micro-pore structure of coal was acquired, as shown in Figure 8a. Using the option of vertical option of vertical normal surface optimization inof the software, the model ofcoal micro-pore structure of 60 μm. With the the gray-scale segmentation technique, the digital coal body was segmented and the model ofuse the micro-pore structure of coal was acquired, as shown Figure 8a.optimized Using the and, surface optimization in of the software, the model micro-pore structure ofin was and the ofand, the micro-pore structure of coal was acquired, as shown in Figure 8a.structure Using the option ofmodel vertical normal surface optimization inwith the software, thesurface model of micro-pore of still coal was optimized thus, the pore model smoother was constructed. What thus, the pore model with smoother surface was constructed. What still needs to be explained is, here, option of vertical normal optimization the software, the model of effects. micro-pore structure of coal was optimized and, surface thus, the pore modelinwith smoother surface was constructed. What still needs to be explained only in terms of visual Figure 9b structure displays the optimization is onlyis,inhere, termsthe of optimization visual effects. is Figure 9b displays the model of micro-pore coal was optimized and, thus, the pore model with smoother surface was constructed. What still needs to be explained is, here, the optimization is only in terms of visual effects. Figure 9b displays the model micro-pore structure of coal after the optimization. of coal afterofthe optimization. needs to beofexplained is, structure here, the of optimization is only in terms of visual effects. Figure 9b displays the model micro-pore coal after the optimization. the model of micro-pore structure of coal after the optimization.
Figure 7. Data cube selected in the reconstructed digital coal body.
Figure 7. Data Data cube cube selected selected in the the reconstructed digital coal body. Figure 7. Data cube selected in in the reconstructed digital coal body.
(a) (a)
(b) (b)
Figure 8. Model of micro-pore structure: (a) Before the optimization; and (b) after the optimization. (a) (b) Figure 8. Model of micro-pore structure: (a) Before the optimization; and (b) after the optimization.
Figure 8. Model of micro-pore structure: (a) Before the optimization; and (b) after the optimization. Figure 8. Model of micro-pore structure: (a) Before the optimization; and (b) after the optimization.
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(a)
(b)
(c)
(d)
(e)
(f)
Figure 9. Optimization Optimizationofof coal micro-pore model and mesh generation on theplatform:(a) ICEM platform: Figure 9. coal micro-pore model and mesh generation on the ICEM Repair (a) Repair on the micro-pore structure model; (b) segmentation of islands; (c) deletion of islands; on the micro-pore structure model; (b) segmentation of islands; (c) deletion of islands;(d) establishment (d) establishment of topological (e) setting of theconditions; import and export conditions; and (f) of topological structure; (e) settingstructure; of the import and export and (f) mesh generation. mesh generation.
Both pore and throat were defined based on the ball-and-stick network model. The maximum Both pore and throat were defined based on the ball-and-stick network model. The maximum ball algorithm was used in this study for the construction of the ball-and-stick model. The specific ball algorithm was used in this study for the construction of the ball-and-stick model. The specific procedure is described below. For any voxel point in the pore space, the inscribed sphere in this space procedure is described below. For any voxel point in the pore space, the inscribed sphere in this with the maximum volume whose center is located at this voxel point, is firstly found; accordingly, space with the maximum volume whose center is located at this voxel point, is firstly found; the pore space is full of these spheres. It should be noted that these spheres overlap with each other accordingly, the pore space is full of these spheres. It should be noted that these spheres overlap and are mutually included. The included small spheres are then deleted, and the remaining spheres are with each other and are mutually included. The included small spheres are then deleted, and the divided into two types—primary spheres and secondary spheres—to describe the pore space. Finally, remaining spheres are divided into two types—primary spheres and secondary spheres—to all of the primary spheres with local maximum volumes can be regarded as the pores while the spheres describe the pore space. Finally, all of the primary spheres with local maximum volumes can be connecting the adjacent pores are used for characterizing the throats. This algorithm can accurately regarded as the pores while the spheres connecting the adjacent pores are used for characterizing reflect the structural features of coal’s micro-pore space and, thus, quantitatively characterize the pore’s the throats. This algorithm can accurately reflect the structural features of coal’s micro-pore space micro-structural parameters [22]. and, thus, quantitatively characterize the pore’s micro-structural parameters [22]. Figure 9 clearly shows the 3D distribution of the micro-pore structure of coal, from which we Figure 9 clearly shows the 3D distribution of the micro-pore structure of coal, from which we can observe that the channels of pores were extended in a complicated manner and the pores with can observe that the channels of pores were extended in a complicated manner and the pores with different sizes exhibit local differences along different directions; additionally, most of the pores were different sizes exhibit local differences along different directions; additionally, most of the pores formed horizontally and only a minority of pores were formed vertically. In order to gain in-depth were formed horizontally and only a minority of pores were formed vertically. In order to gain knowledge of the microscopic size of the micro-pore model, the ball-and-stick model was developed in-depth knowledge of the microscopic size of the micro-pore model, the ball-and-stick model was using the digital core analysis software Sypicore provided by Nano Voxel-2000, and then the statistics developed using the digital core analysis software Sypicore provided by Nano Voxel-2000, and then on the coal’s micro-structural parameters was conducted using the ’MEASURE’ function of Avizo. the statistics on the coal’s micro-structural parameters was conducted using the ’MEASURE’ The results indicate that the number of pores in this micro-pore model was 219, the maximum pore function of Avizo. The results indicate that the number of pores in this micro-pore model was 219, radius was 4.36 µm, the maximum pore volume was 3336 µm3 , the mean pore radius was 1.17 µm, the maximum pore radius was 4.36 μm, the maximum pore volume was 3336 μm3, the mean pore 3 the mean pore volume was 124.23 µm , and the bulk porosity was 15.47 % (including all of the pores, radius was 1.17 μm, the mean pore volume was 124.23 μm3, and the bulk porosity was 15.47 % throats, and fractures). Table 2 lists the qualitative analysis results of the throat size. (including all of the pores, throats, and fractures). Table 2 lists the qualitative analysis results of the throat size.
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Table 2. Quantitative analysis results of the throat size. Minerals 2016, 6, 78 Maximum Throat Number Radius of Throats (µm)
Mean Maximum Mean Maximum Mean Throat Throat Throat Pore-Throat Pore-Throat Length Length Radius Ratio Ratio Table 2. Quantitative analysis the throat size. (µm) results of (µm) (µm)
Maximum Throat Volume (µm3 )
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311 2.77 0.62 13.89 2.32 20.50 2.08 518 14.67 Mean Maximum Mean Maximum Maximum Number Mean Maximum Mean Throat Throat Throat Throat Throat of Throat Pore-Throat Pore-Throat Volume Radius Radius Length Volume Throats Length (μm) Ratio Ratio The acquired pore-structure model was imported into ICEM CFD software (μm3) Inc., (μm) (μm) (μm) (μm3) (ANSYS 311 2.77 13.89 2.32 20.50 2.08through 518 14.67 mesh Canonsburg, PA, USA) for 0.62 further optimization. The model was meshed high-quality
generation and set with boundary conditions. Accordingly, the single-channel and multi-channel The acquired pore-structure model was imported ICEM CFD software (ANSYS Inc., seepage characteristics of low-pressure water in the modelinto of the micro-pore structure of coal can be Canonsburg, PA, USA) for further optimization. The model was meshed through high-quality mesh simulated. Specifically, the optimization process included three steps: the repair of the micro-pore generation and set with boundary conditions. Accordingly, the single-channel and multi-channel structure model (i.e., to delete the redundant points, lines and surfaces, within the allowable tolerance seepage characteristics of low-pressure water in the model of the micro-pore structure of coal can be of 0.05), the segmentation of islands (here, the islands refer tosteps: the pore geometries that were not simulated. Specifically, the optimization process included three the repair of the micro-pore connected to the maximum pore connected cluster and existed independently in the micro-pore structure model (i.e., to delete the redundant points, lines and surfaces, within the allowable model, while the maximum pore connected cluster refers to the portion with the greatest connected tolerance of 0.05), the segmentation of islands (here, the islands refer to the pore geometries that were not coal connected to themodel) maximum poredeletion connected cluster and existedinindependently in the volume in the micro-pore and the of islands, as shown Figure 9a–c, respectively. micro-pore model, while theachieved maximum pore to the portion with the The segmentation of islands was using theconnected setting ofcluster ‘break refers by connectivity’ on the micro-pore greatest connected volume in the process coal micro-pore model) and the of islands,model as shown model. Figure 9 displays the whole of the optimization ofdeletion coal micro-pore andinmesh Figure on 9a–c, The segmentation of islands was achieved using the setting of ‘break by generation therespectively. ICEM platform. connectivity’ on the micro-pore model. Figure 9 displays the whole process of the optimization of Due to the irregularity of coal pore structure, the global automatic mesh generation was coal micro-pore model and mesh generation on the ICEM platform. firstly adopted; then the quality of meshes was checked and the low-quality meshes were deleted Due to the irregularity of coal pore structure, the global automatic mesh generation was firstly (i.e., the meshes the quality lower 0.4).and After being repaired, the meshes were adopted; thenwith the quality of meshes wasthan checked the low-quality meshes were deleted (i.e., checked, the and the irrelevant mesh points were deleted, through which the grid quality was further enhanced. meshes with the quality lower than 0.4). After being repaired, the meshes were checked, and the irrelevant mesh points were deleted, through which the grid quality was further enhanced.
6. Simulation on the Seepage Characteristics of Low-Pressure Water in Coal Micro-Pore Structure Model on the Seepage Characteristics of Low-Pressure Water in Coal Micro-Pore 6. Simulation Structure Model using CFX software, the numerical simulation on the characteristics of In this section, In thisand section, using CFX software, numerical on water the characteristics of single-channel multi-channel seepage was the performed for simulation low-pressure in a coal micro-pore single-channel and multi-channel seepage was performed for low-pressure water in a coal structure model. The simulation was based on the transient Navier-Stokes Equation, in which micro-pore structure model. The model simulation based onand the transient a k-epsilon standard turbulence waswas adopted the fluidNavier-Stokes was set as Equation, water atinroom which a k-epsilon standard turbulence model was adopted and the fluid was set as water at room temperature, in terms of material property. In addition, the inlet pressure was set as 3.1 MPa and temperature, in terms of material property. In addition, the inlet pressure was set as 3.1 MPa and the outlet pressure was set as 0.1 MPa. For a coal micro-pore structure model, the characteristics of the outlet pressure was set as 0.1 MPa. For a coal micro-pore structure model, the characteristics of single-channel, dual-channel, and multi-channel seepage were simulated both separately in three single-channel, dual-channel, and multi-channel seepage were simulated both separately in three directions (X, Y, Z) and comprehensively directions. directions (X,and Y, and Z) and comprehensivelyin inthe the combined combined directions.
6.1. Numerical Simulations on on Single-Channel Along Z Directions 6.1. Numerical Simulations Single-ChannelSeepage Seepage Characteristics Characteristics Along thethe X, X, Y, Y, andand Z Directions Figures 10 and display the distributions of pressure and seepage velocityvelocity subject tolow-pressure Figures 10 11 and 11 display the distributions of pressure and seepage subject to water along ainsingle-channel in X, Y, and Z directions. waterlow-pressure along a single-channel X, Y, and Z directions.
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Figure 10. Distributions of pressure subject to low-pressure water along a single-channel in X, Y,
Figure 10. Distributions of pressure subject to low-pressure water along a single-channel in X, Y, and Z and Z directions: (a) X direction; (b) Y direction; and (c) Z direction. directions: (a) X direction; (b) Y direction; and (c) Z direction.
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Figure 11. Distributions of seepage subject to low-pressure waterwater along single-channel in X, Figure 11. ofseepage seepagevelocity velocity subject to low-pressure single-channel Figure 11. Distributions Distributions of velocity subject to low-pressure water along along single-channel in X, Y, and Z directions: (a) X direction; (b) Y direction; and (c) Z direction. in Y, X, and Y, and Z directions: X direction; Y direction; and (c) Z direction. Z directions: (a) X(a) direction; (b) Y(b) direction; and (c) Z direction.
One can observe that, although the pressure drops in three directions (X, Y, and Z) are One can observe that, although pressure drops in three directions Z) are One can observe that, although the the pressure drops in three directions Y, (X, andY, Z)and areinidentical identical (∆P = 3 MPa), the 3D distributions of the single-channel seepage(X, pressure fields three identical (∆P = 3 MPa), the 3D distributions of the single-channel seepage pressure fields in three (∆Pdirections = 3 MPa),are thedifferent 3D distributions ofextent. the single-channel seepage fields inin three directions to a certain This is because of thepressure local differences the shape, size,are directions are different to a certain extent. This is because of the local differences in the shape, size, different to a certainas extent. This because of the localpore differences inTo thebe shape, size,one and connectivity, and connectivity, well as theispermeability of the channels. specific, can observe and connectivity, as well as the permeability of the pore channels. To be specific, one can observe as that, well as the permeability of the pore channels. To be specific, one can observeand that,the along the water along the water seepage direction, the pressure decreased gradually maximum that, along the water seepage direction, the pressure decreased gradually and the maximum seepage direction, the pressure decreased gradually and pressure was present pressure was present at the narrow pore near the inlet; at the the maximum narrow pore where water flowed, at thethe pressure was present at the narrow pore near the inlet; at the narrow pore where water flowed, the pressure the inlet; fastest decreased as where a whole (generally, decreased and narrow porevaried near the atand the narrow pore water flowed,the thepressure pressurefirstly varied the fastest and pressure varied the fastest and decreased as a whole (generally, the pressure firstly decreased and then increased), which is mainlythe due to the fact that decreased the pore channel bent sharply and its diameter decreased as a whole (generally, pressure firstly and then increased), which is mainly then increased), which is mainly due to the fact that the pore channel bent sharply and its diameter decreased rapidly. due to the fact that the pore channel bent sharply and its diameter decreased rapidly. decreased rapidly. Figure 11 displays the overall velocity distributions of theofsingle-channel water seepage X, Y, Figure theoverall overall velocity distributions the single-channel water in seepage Figure11 11 displays displays the velocity distributions of the single-channel water seepage in X, Y, and Z directions. Then, different sections at different positions along the axis directions (i.e., x = 0, in and X, Y,Zand Z directions. Then, different sections at positions different along positions along the axis(i.e., directions directions. Then, different sections at different the axis directions x = 0, 12, 24, 36, 48 24, and 60 48 μm; y = 0, 12, and μm; = 0, 60 12, 24, 36, μm, (i.e., = 0, and µm;24, y 36, = 0,48 24,60 48zzand z =48 0,and 12, 60 24, 36, respectively, 48 and 60 µm, 12,x24, 36,12, 48 and36, 60 μm; y =60 0, 12, 24, 36, 4812, and 6036, μm; = 0, 12,µm; 24, 36, 48 and 60 μm, respectively, in which x, y, and z denote the distances from the inlet section) were selected, and the water respectively, in which x, y, and z denote the distances from the inlet section) were selected, the in which x, y, and z denote the distances from the inlet section) were selected, and the and water seepage velocity distributions of different sections were acquired and shown in Figures 12–14. water seepage velocity distributions of different sections were acquired and shown in Figures 12–14. seepage velocity distributions of different sections were acquired and shown in Figures 12–14.
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Figure 12. Water seepage velocity distribution of different sections of the single channel in the X Figure 12.(a) Water distribution of different sections the single channel the X direction: x = seepage 0 seepage μm; (b)velocity xvelocity = 12 μm; (c) x = 24 μm; x = 36 μm; (e) x of =of48 μm; and (f) x = 60 in μm. Figure 12. Water distribution of (d) different sections the single channel in the X direction: (a) x = 0 μm; (b) x = 12 μm; (c) x = 24 μm; (d) x = 36 μm; (e) x = 48 μm; and (f) x = 60 μm. direction: (a) x = 0 µm; (b) x = 12 µm; (c) x = 24 µm; (d) x = 36 µm; (e) x = 48 µm; and (f) x = 60 µm.
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Figure13. 13. Waterseepage seepage velocity distribution distribution of different different sections of Figure of the the single single channel channel in in the the Y Figure 13.Water Water seepage velocity velocity distribution of of different sections sections of the single channel in the YY direction: (a) x = 0 μm; (b) x = 12 μm; (c) x = 24 μm; (d) x = 36 μm; (e) x = 48 μm; and (f) x = 60 μm. direction: (a) x = 0 µm; (b) x = 12 µm; (c) x = 24 µm; (d) x = 36 µm; (e) x = 48 µm; and (f) x = 60 µm. direction: (a) x = 0 μm; (b) x = 12 μm; (c) x = 24 μm; (d) x = 36 μm; (e) x = 48 μm; and (f) x = 60 μm.
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Figure 14 .Water seepage velocity distribution of different sections of the single channel in the Z Figure14. 14 Water .Water seepagevelocity velocity distribution distribution of of different different sections sections of the single channel in Figure the single in the the ZZ direction: (a) x = 0seepage μm; (b) x = 12 μm; (c) x = 24 μm; (d) x = 36 μm; (e) x of = 48 μm; and channel (f) x= 60 μm. direction: (a) x = 0 μm; (b) x = 12 μm; (c) x = 24 μm; (d) x = 36 μm; (e) x = 48 μm; and (f) x= 60 μm. direction: (a) x = 0 µm; (b) x = 12 µm; (c) x = 24 µm; (d) x = 36 µm; (e) x = 48 µm; and (f) x= 60 µm.
As shown in Figures 11–14, under the same pressure drops along the three directions (X, Y, As shown in Figures 11–14, under the same pressure drops along the three directions (X, Y, andAs Z),shown the single-channel seepage velocity distribution alongalong three the directions were different in Figures 11–14, under the same pressure drops three directions (X, Y, due and to Z), and Z), the single-channel seepage velocity distribution along three directions were different due to the differences in the distribution of seepage water pressure, as well as the connectivity and the single-channel seepage velocity distribution along three directions were different due to the the differences in the distribution of seepage water pressure, as well as the connectivity and permeability of pore channels. primary conclusions as follows: differences in the distribution ofThe seepage water pressure, are as as the connectivity and permeability permeability of pore channels. The primary conclusions arewell as follows: of(1) poreInchannels. The primary conclusions are as although follows: all the pores were connected with each the maximum pore-connected cluster, (1) In the maximum pore-connected cluster, although all the pores were connected with each other, the seepage of low-pressure water was observed in only a few pores. The seepage of other, seepagepore-connected of low-pressurecluster, water was observed in only few pores. The seepage of (1) In the the maximum although all the poresa were connected with each low-pressure water firstly selected the paths with large pore radii, short paths, and shorter low-pressure wateroffirstly selected the paths large in pore radii, short paths, shorter other, the seepage low-pressure water waswith observed only a few pores. Theand seepage of distances from the outlet. distances from the outlet.
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(2) (2) In In terms terms of of the the seepage seepage in in aa single single pore pore channel, channel, the the seepage seepage velocity velocity of of low-pressure low-pressure water water decreased in the direction from the pore center to pore wall until it became zero. In terms decreased in the direction from the pore center to pore wall until it became zero. In terms of of the whole structure, the seepage velocity appeared the region low-pressure water firstly selected the paths with large pore radii, shortin paths, and shorter the whole micro-pore micro-pore structure, the maximum maximum seepage velocity appeared in the center center region where water seepage was distances from the outlet. where water seepage was fully fully developed. developed. The The maximum maximum velocities velocities of of the the single-channel single-channel water seepage in the X and Y directions were up to 75.3 and 64.4 m/s, respectively; in the seepage the X and directions were up the to 75.3 and velocity 64.4 m/s,ofrespectively; inwater the ZZ (2) water In terms of theinseepage in a Ysingle pore channel, seepage low-pressure direction, in spite of the gravity effect, the maximum seepage velocity still reached 39.2 m/s. direction, of the gravity effect, the maximum velocity still reached m/s. decreasedininspite the direction from the pore center to poreseepage wall until it became zero. In 39.2 terms of Overall, at the micro-scale, the seepage velocity of low-pressure water in a single-channel was Overall, at micro-pore the micro-scale, the seepage velocityseepage of low-pressure water in ainsingle-channel was the whole structure, the maximum velocity appeared the center region relatively large, with the value near the wall the low-pressure relatively large, with was the minimum minimum value The nearmaximum the pore pore velocities wall where where thesingle-channel low-pressure water water where water seepage fully developed. of the water passed through. passed through. seepage in the X and Y directions were up to 75.3 and 64.4 m/s, respectively; in the Z direction, (3) At different sections, the maximum seepage at center of small pore (3) At sections, the maximum seepage velocity velocity appeared appearedstill at the the center of the the small pore in different spite of the gravity effect, the maximum seepage velocity reached 39.2 m/s. Overall, channel of the section where the water flowed. Moreover, the water seepage velocity increased channel of the section the water flowed. Moreover, the in water seepage velocity increased at the micro-scale, the where seepage velocity of low-pressure water a single-channel was relatively as the and as thepore pore radius andbending bending degree decreased. large, withradius the minimum value degree near thedecreased. pore wall where the low-pressure water passed through. (3) At different sections, the maximum seepage velocity appeared at the center of the small pore 6.2. Seepage Velocity, and Flow ofofSingle-Channel Seepage at Sections 6.2.Pressure, Pressure, Velocity, andMass Mass FlowRate Rate Single-Channel atDifferent Different Sections channelSeepage of the section where the water flowed. Moreover, theSeepage water seepage velocity increased In order to gain an in-depth insight into the rules of single-channel water seepage in X, as the pore radius and bending degree decreased. In order to gain an in-depth insight into the rules of single-channel water seepage in X, Y, Y, and and ZZ directions, several sections at different positions along the axes (i.e., x = 0, 6, 12, 18, 24, 30, 36, directions, several sections at different positions along the axes (i.e., x = 0, 6, 12, 18, 24, 30, 36, 42, 42, 6.2. Pressure, Seepage Velocity, and Mass Flow Rate of54 Single-Channel Seepage at6,Different Sections 48, 54 and 60 μm; y = 0, 6, 12, 18, 24, 30, 36, 42, 48, and 60 μm; and z = 0, 12, 18, 24, 30, 36, 42, 48, 54 and 60 μm; y = 0, 6, 12, 18, 24, 30, 36, 42, 48, 54 and 60 μm; and z = 0, 6, 12, 18, 24, 30, 36, 42,48, 48, 54 60 in yy and denote the inlet were In order to respectively, gain an in-depth insightx, thezzrules of single-channel water seepage in X, Y, and Z 54 and and 60 μm, μm, respectively, in which which x,into and denote the distances distances from from the the inlet section) section) were selected further analyses. Figures 15–17 show the mean mean seepage directions, several sections at different positions (i.e.,seepage x = 0, 6, pressure, 12, 18, 24, 30, 36, 42, 48, 54 selected for for further analyses. Figures 15–17 along showthe theaxes mean seepage pressure, mean seepage velocity, and mean rate at different sections. and 60 µm; y= 0, 6, mass 12, 18,flow 24, 30, 36, 48, 54 and 60 µm; and z = 0, 6, 12, 18, 24, 30, 36, 42, 48, 54 and velocity, and mean mass flow rate at42, different sections. As shown in Figure 15, the mean seepage pressure at sections along directions 60 µm, in which x, ymean and zseepage denote pressure the distances from the inlet section) were selected for Asrespectively, shown in Figure 15, the atdifferent different sections alongdifferent different directions (X, Z) similar variation, i.e., average seepage pressure each further analyses. Figures 15–17trend showand therange meanof seepage pressure, seepage velocity, andat mean (X,Y, Y,and and Z) exhibited exhibited similar trend and range of variation, i.e., the themean average seepage pressure at each section decreased gradually as mass flow rate at different sections. section decreased gradually asthe thedistance distancefrom fromthe theseepage seepageinlet inletsection sectionincreased. increased. Meanseepage seepagepressure pressure(MPa) (MPa) Mean
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Meanseepage seepagevelocity velocity(m/s) (m/s) Mean
Figure cross-sections. Figure 15. Mean pressure at different Figure15. 15.Mean Meanpressure pressureat atdifferent differentcross-sections. cross-sections. 20 20 18 18 16 16 14 14 12 12 10 10 88 66 44 22 00
XXdirection direction YYdirection direction ZZdirection direction
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66 12 18 24 30 36 42 48 54 12 18 24 30 36 42 48 54 Different sections along different directions (μm) Different sections along different directions (μm)
Figure cross-sections. Figure16. 16.Mean Meanseepage seepagevelocity velocityat atdifferent differentcross-sections. cross-sections. Figure 16. Mean seepage velocity at different
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Figure 17. Mean mass flow at different cross-sections.
Figure 17. Mean mass flow at different cross-sections. As shown in Figure 16, during the single-channel water seepage processes along the X, Y, and directions, the mean velocity at each section as a whole, withdirections the AsZ shown in Figure 15, seepage the mean seepage pressure at gradually different decreased sections along different increase of the distance from the seepage inlet. However, at three different sections (i.e., 12–18 μm, (X, Y, and Z) exhibited similar trend and range of variation, i.e., the average seepage pressure at each μm, and 48–54 μm,asrespectively), mean velocities exhibited obvious fluctuations. section42–48 decreased gradually the distancethe from theseepage seepage inlet section increased. To be specific, in the X direction, the mean seepage velocity increased significantly at the 12–18 μm As shown in Figure 16, during the single-channel water seepage processes along the X, Y, and section, increased slightly at the 42–48 μm section, and decreased sharply at the 48–54 μm section; Z directions, the mean seepage velocity at each section gradually decreased as a whole, with the in the Y direction, the mean seepage velocity decreased notably at the 12–18 μm section, increased increase of theatdistance the seepage inlet. However, different sections 12–18 greatly the 42–48from μm section, and decreased sharply at in three the 48–54 μm section; and(i.e., in the Z µm, 42–48 µm, and 48–54 µm, respectively), the meansignificantly seepage velocities exhibited obvious fluctuations. direction, the mean seepage velocity decreased in the 12–18 μm and 42–48 μm sections, To be specific, in the greatly X direction, mean 12–18 and increased in thethe 48–54 μmseepage section. velocity Through increased comparisonsignificantly and analysis,at itthe can be µm that the variation seepage velocity the Z direction was at basically contrary to section,concluded increased slightly at thetrend 42–48ofµm section, andindecreased sharply the 48–54 µm section; those in the other two directions. Additionally, the mean seepage velocity in the X direction was the in the Y direction, the mean seepage velocity decreased notably at the 12–18 µm section, largest, followed by that in the Y direction, and the mean seepage velocity in the Z direction was the increased greatly at the 42–48 µm section, and decreased sharply in the 48–54 µm section; smallest, which can also reflect the local difference in permeability. and in the Z direction, the mean seepage velocity decreased significantly in the 12–18 µm and 42–48 µm As shown in Figure 17, the mean mass flow rate during the single-channel seepage processes sections, andX,increased greatly inreached the 48–54 µm section. and analysis, it can be in the Y, and Z directions the maxima at the Through inlet, then comparison decreased gradually, and finally concluded that the variation trend of seepage velocity in the Z direction was basically contrary to those stabilized. The variation trend of mean mass flow rate was similar to that of mean seepage velocity. in the other two directions. Additionally, seepage velocity in themass X direction the X largest, The mean mass flow rate decreased the as amean whole; moreover, the mean flow ratewas in the direction the Ylargest, followed by the Y direction, and the in mean mass flow rate thesmallest, Z followed by thatwas in the direction, and the mean seepage velocity the Z direction wasinthe direction was the smallest. In the Z direction, the mean seepage velocity and mean mass flow rate which can also reflect the local difference in permeability. influenced by gravity to mean a great mass extent.flow rate during the single-channel seepage processes Aswere shown in Figure 17, the in the X, Y, and Z directions reached the maxima at the inlet, then decreased gradually, and finally 6.3. Numerical Simulation on Seepage Characteristics of Dual-Channel and Multi-Channel Seepage stabilized. The variation trend of mean mass flow rate was similar to that of mean seepage velocity. Firstly, we should explain the meanings of dual-channel and multi-channel seepages. The The mean mass flow rate decreased as a whole; moreover, the mean mass flow rate in the X direction former refers to the water injection along the positive directions of X and Y simultaneously and the was thelatter largest, followed by the Y direction, and the mean mass flow rate in the Z direction was the refers to the water injection along the positive directions of X, Y, and Z simultaneously. In this smallest. In the direction, the mean seepage velocity mass flow rate were influenced study, the Z direction of dual-channel is denoted as (X and + Y) mean while the direction of multi-channel is by gravitydenoted to a great extent. as (X + Y + Z), respectively. Numerical simulation was performed to further investigate the dual-channel and
6.3. Numerical Simulation on characteristics Seepage Characteristics of Dual-Channel andcoal Multi-Channel Seepage multi-channel seepage of low-pressure water in the at micro-scale. X and Y
directions (i.e., the positive direction of (X + Y)) were both selected for dual-channel simulation
Firstly, we should explain the meanings of dual-channel and multi-channel seepages. The former while the X, Y, and Z directions (i.e., the positive direction of (X + Y + Z)) were all selected for refers to the water injection along the positive directions of X and Y simultaneously and the latter multi-channel simulation. Figures18 and 19 display the flow conditions and velocity distribution of refers to the water and injection along the positive directions of X, Y, and Z simultaneously. In this study, dual-channel multi-channel seepage. the direction of dual-channel is denoted as (X + Y) while the direction of multi-channel is denoted as (X + Y + Z), respectively. Numerical simulation was performed to further investigate the dual-channel and multi-channel seepage characteristics of low-pressure water in the coal at micro-scale. X and Y directions (i.e., the positive direction of (X + Y)) were both selected for dual-channel simulation while the X, Y, and Z directions (i.e., the positive direction of (X + Y + Z)) were all selected for multi-channel simulation. Figures 18 and 19 display the flow conditions and velocity distribution of dual-channel and multi-channel seepage.
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Figure 18. 18. Seepage Seepage velocity velocity distribution of dual-channels in the X and Y directions: (a) X direction; Figure distribution of of dual-channels dual-channels in in the the X X and and Y Y directions: directions: (a) X X direction; direction; Figure 18. Seepage velocity distribution (a) and (b) Y direction. and (b) (b) Y Y direction. direction. and
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Figure 19. Seepage velocity distribution of multi-channel in the X, Y, and Z directions: (a) X Figure 19. Seepage Seepagevelocity velocity distribution of multi-channel X, Y, and Z directions: (a) X Figure 19. distribution of multi-channel in theinX,the Y, and Z directions: (a) X direction; direction; (b) Y direction; and (c) Z direction. direction; (b) Y direction; and (c) Z direction. (b) Y direction; and (c) Z direction.
As shown in Figure 18, compared with the results in single-channel water seepage in the As shown in Figure 18, compared with the results in single-channel water seepage in the direction of X or the seepage velocity of the low-pressure water in dual-channel waterin seepage in the As shown in Y, Figure 18, compared with results in single-channel water seepage the direction direction of X or Y, the seepage velocity of low-pressure water in dual-channel water seepage in the direction + Y) increased with the in maximum seepage velocity upintothe 89.6 m/s. Due of X or Y, of the(Xseepage velocity significantly, of low-pressure water dual-channel water seepage direction of direction of (X + Y) increased significantly, with the maximum seepage velocity up to 89.6 m/s. Due to the of water pressure with in Y the direction, 92.36% of water flowup that theDue coaltosample in (X + Y)effect increased significantly, maximum seepage velocity to entered 89.6 m/s. the effect to the effect of water pressure in Y direction, 92.36% of water flow that entered the coal sample in the X direction would flow through the pressure outlet in Y direction. Similarly, due to the effect of of water pressure in Y direction, 92.36% of water flow that entered the coal sample in the X direction the X direction would flow through the pressure outlet in Y direction. Similarly, due to the effect of water pressure in the direction, 90.17% water flow that entered theeffect coal of sample in the Y would flow through theXpressure outlet in Y of direction. Similarly, due to the water pressure water pressure in the X direction, 90.17% of water flow that entered the coal sample in the Y direction would flow through the pressure outlet in the X direction. in the X direction, 90.17% of water flow that entered the coal sample in the Y direction would flow direction would flow through the pressure outlet in the X direction. As shown in Figure 19,incompared with the simulation results of single-channel water seepage through the pressure outlet the X direction. As shown in Figure 19, compared with the simulation results of single-channel water seepage in X,AsY,shown or Z in directions, seepagewith velocity of low-pressure in multi-channels in the Figure 19,the compared the simulation results ofwater single-channel water seepage in in X, Y, or Z directions, the seepage velocity of low-pressure water in multi-channels in the direction of (X + Y + Z) increased significantly, with the maximum seepage velocity up to 140.2 m/s. X, Y, or Z directions, the seepage velocity of low-pressure water in multi-channels in the direction of direction of (X + Y + Z) increased significantly, with the maximum seepage velocity up to 140.2 m/s. Due to the of water pressure in thethe Y and Z directions, of water flow that entered (X +Y Z) effect increased significantly, seepage97.29% velocity to 140.2 Due to the Due to +the effect of water pressure with in the Y maximum and Z directions, 97.29% of up water flow m/s. that entered the coal sample the X direction would flow through theofpressure outlet the Y the andcoal Z directions. effect of waterinpressure in the Y and Z directions, 97.29% water flow thatin entered sample in coal sample in the X direction would flow through the pressure outlet in the Y and Z directions. Similarly, due to the effect of water pressure in the Xinand ZY directions, 95.24% of waterdue flow that the X direction would flow through pressure theZ and Z directions. the Similarly, due to the effect of waterthe pressure inoutlet the X and directions, 95.24%Similarly, of water flowtothat entered the coal sampleininthe the Y direction would flow through the pressure outlet incoal thesample X and in Z effect of water pressure X and Z directions, 95.24% of water flow that entered the entered the coal sample in the Y direction would flow through the pressure outlet in the X and Z directions. Due to the effects of gravity and water pressure in the X and Y directions, most of the the Y direction through the pressure outlet in theinXthe andXZand directions. Due tomost the effects directions. Due would to the flow effects of gravity and water pressure Y directions, of the water flowand thatwater entered the coal sample in Z direction would exit from theflow pressure outlets in the X of gravity pressure in the X and Y directions, most of the water that entered thethe coal water flow that entered the coal sample in Z direction would exit from the pressure outlets in X and Y directions after it flows just a certain distance in the Z direction. sample in Z direction exit from the pressure outlets X and Y directions after it flows just a and Y directions afterwould it flows just a certain distance in theinZthe direction. Compared with the results in dual-channel water seepage along the direction of (X + Y), the certain distance in thethe Z direction. Compared with results in dual-channel water seepage along the direction of (X + Y), the seepage paths and velocities in multi-channel water seepage along the direction of (X + Y), Y + Z) Compared withvelocities the results dual-channelwater waterseepage seepagealong alongthe thedirection direction of of (X (X ++ seepage paths and in in multi-channel Y + the Z) exhibited significant differences. Due to thewater effect of water pressure in Z direction, the paths of seepage paths and velocities in multi-channel seepage along the direction of (X + Y + Z) exhibited exhibited significant differences. Due to the effect of water pressure in Z direction, the paths of multi-channel seepage in Xto and Y directions were significantly shortened compared with the significant differences. the effect of water were pressure in Z direction, the paths of multi-channel multi-channel seepage Due in X and Y directions significantly shortened compared with the dual-channel seepage path in the direction of (X + Y), but the overall seepage velocities along their dual-channel seepage path in the direction of (X + Y), but the overall seepage velocities along their respective directions were multiplied compared with the dual-channel seepage velocity in the respective directions were multiplied compared with the dual-channel seepage velocity in the
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seepage in X and Y directions were significantly shortened compared with the dual-channel seepage path in the direction of (X + Y), but the overall seepage velocities along their respective directions were multiplied compared with the dual-channel seepage velocity in the direction of (X + Y). For example, the maximum seepage velocity in the X and Y directions increased from 89.6 m/s in dual-channel seepage by 1.56 times up to 140.2 m/s in multi-channel seepage. 7. Conclusions The present study focused on the long-frame coal sample collected from the Daliuta Coal Mine, which was scanned by a high-precision X-ray 3D microscope to obtain 3D data. With the use of Avizo, an advanced 3D visualization software, the digital coal body model with actual pore structure characteristics was constructed. Then, the preprocessing and postprocessing functions in ICEM CFD software allowed the model generated by Avizo to be conveniently processed in CFX, a multi-field coupling finite element software. Accordingly, the numerical simulation on single-channel and multi-channel seepage of low-pressure water in coal micro-pore structures was conducted. The following conclusions were drawn. (1)
(2)
(3)
The micro-pore structure model of the digital coal body in the present study had the actual size of 60 µm ˆ 60 µm ˆ 60 µm and contained a total of 219 pores in it. The micro-pore model of the coal had a maximum pore radius of 4.36 µm, a maximum pore volume of 3336 µm3 , a mean pore radius of 1.17 µm, a mean pore volume of 124.23 µm3 , a bulk porosity of 15.47%, a throat number of 311, a maximum throat radius of 2.77 µm, a mean throat radius of 0.62 µm, a maximum throat length of 13.89 µm, a mean throat length of 2.32 µm, a maximum pore-to-throat ratio of 20.50, a mean pore-to-throat ratio of 2.08, a maximum throat volume of 518 µm3 , and a mean throat volume of 14.67 µm3 . During the seepage process of low-pressure water, the water flow did not pass through each path uniformly, but preferentially passed through the paths with large pore radii, short paths, and short distances from the outlet. In terms of a single pore channel, the seepage velocity of low-pressure water decreased gradually along the direction from the pore center to pore wall; in terms of the overall micro-pore structure, the maximum seepage velocity appeared at the center of small pore channel in the coal center region where the water flow was fully developed. For single-channel seepage in different directions, the seepage pressure decreased gradually along the direction of water seepage; moreover, the mean seepage velocity and mass flow rate of the seepage in the X direction were the largest, followed by those in the Y direction, and the mean seepage velocity and mass flow rate of the seepage in the Z direction were the smallest. At the micro-scale, the seepage velocities of low-pressure water in the dual-channel seepage in the direction of (X + Y) and the multi-channel seepage in the direction of (X + Y + Z) were greatly enhanced compared with the velocity in single-channel seepage. Due to the effects of the seepage water pressure and different numbers of channels in different directions, the dual-channel and multi-channel seepage characteristics of low-pressure water exhibited great changes and complex variation rules compared with the characteristics of single-channel seepage. Using the software of Avizo, the related pore and throat data of the coal micro-pore structure model were extracted, and the coal micro-pore structure model could be converted into a geometric model in CAD format. The geometric model was then imported to many types of finite element and discrete element software, such as CFX, COMSOL, and EDEM for numerical simulations. Meanwhile, using 3D printing technology, we can use the coal powders to prepare the samples that can reflect the coal’s actual micro-pore structure for experimental investigation. The present study provides a new idea and a novel way to investigate the seepage rules in the micro-pore structure of coal. It also casts light on exploring the stress and strain analysis, as well as discrete element analysis of the micro-structure of coal.
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Acknowledgments: This work was financially supported by State Key Program of National Natural Science of China (Grant No. U1261205); National Natural Science Foundation of China (Grant No. 51474139); SDUST Research Fund (Grant No. 2014JQJH106); China Postdoctoral Science Foundation Funded Special Project (Grant No. 2016T90642); China Postdoctoral Science Foundation Funded Project (Grant No. 2015M570602); Open Fund of the Key Laboratory of Coal Mine Gas and Fire Prevention and Control of Ministry of Education (Grant No. 2015KJZX02); Science and Technology Project of Huangdao District, Qingdao (Grant No. 2014-1-30); Qingdao Postdoctoral Applied Research Project (Grant No. 2015194); Open Fund of the Key Laboratory of Safety and High-Efficiency Coal Mining of Ministry of Education (Grant No. JYBSYS2014105); The Key Technology Projects of Chinese State Administration of Work Safety for Preventing Major Safety Production Accidents (Grant No. Shandong-0083-2015AQ). Author Contributions: Gang Zhou and Qi Zhang conceived and designed the experiments; Ruonan Bai and Guanhua Ni performed the experiments; Gang Zhou and Qi Zhang analyzed the data; Gang Zhou contributed reagents/materials/analysis tools. Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations The following abbreviations are used in this manuscript: CT FEI CFX X-CT SOD ODD MRT ICEM CFD CFD CAD LBM SDUST
Computerized Tomography Field Electron and Ion Co. ANSYS CFX Software X-Ray Computed Tomography the Distance between the X-Ray Source and the Detector the Distance between the Stage Sample and the Detector Magnetic Resonance Tomography ANSYS ICEM CFD Software Computational Fluid Dynamics Computer Aided Design Lattice Boltzmann Method Shandong University of Science and Technology
Nomenclature linear attenuation coefficient incident intensity intensity of ray attenuated by the object distance(m) mass percentage logarithm of the ratio of input intensity to output intensity
µ I0 I ∆x a p References 1. 2.
3. 4. 5.
6.
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