The aim of this paper was to develop a model that can characterize the actual micropore structures in coal and gain an in-depth insight into water’s seepage rules in coal pores under different pressure gradients from a microscopic perspective. To achieve this goal, long-flame coals were first scanned by an X-ray 3D microscope; then, through a representative elementary volume (REV) analysis, the optimal side length was determined to be 60
In recent years, rock bursts, coal-gas outbursts, and dust explosion accidents have occurred frequently in underground coal mines [
As coal is usually stored underground, it is fairly difficult to explore its structural properties through observation. Various experimental methods, which mainly include the mercury intrusion method [
In addition, in terms of seepage simulations, Coles and Karacan et al. focused on the gas adsorption and migration characteristics in coal pores and fractures [
Accordingly in this study, a domestic advanced X-ray 3D microscope (nanoVoxel-2000 series, Sanying Precision Instrument Ltd., China) was employed for conducting scanning and microstructural reconstruction on long-flame coals from the Daliuta Coal Mine; then, the coal’s micropore structural model was developed through denoising, rendering, and data segmentation, which were performed on the Avizo platform; finally, appropriate pressure inlet and outlet were set, and the seepage behaviors during the water injection process under different pressure gradients were simulated using finite element software. The seepage characteristics were then analyzed from a microscopic perspective, based on the simulation results. The present study could provide a new way of gaining insights into the nature of water injections in coal seams and contribute to the improvement of water injection efficiency [
In this study, long-flame coals from the Daliuta Coal Mine, Shanxi, China, were tested. The coal samples show low metamorphism degrees and well-developed pores and thus are suitable for investigating the characteristics of pore structures. For each coal sample, an ore core with a diameter of approximately 2 mm and a length of approximately 5 mm was drilled, which was then sealed by wax. This was done to prevent the evaporation of water in coal during scanning, which would then affect the experimental results due to the changes in shape. Through measurements, it was determined that the coal core after sealing was 2.29 mm in diameter, as shown in Figure
Picture of a coal sample.
Picture of the nanoVoxel-2000 series X-ray 3D microscope.
Setting of scanning parameters of the X-ray 3D microscope.
Detector | SOD/ODD (mm/mm) | Voltage (kV) | Current ( |
Number of scanning frames | Consumed time (h) | Exposure time (s) | Penetration rate (%) |
---|---|---|---|---|---|---|---|
20X | 35/13 | 41 | 240 | 900 | 19 | 65 | 57 |
A micro-CT system generally adopts a 3D cone-beam reconstruction algorithm. Among various 3D cone-beam reconstruction algorithms, the approximation algorithm has a number of advantages, including simple mathematical expression and easy implementation, which means it can achieve favorable reconstruction results at relatively small cone angles, and thus, it is widely applied in practice. FDK algorithm is a mainstream algorithm in various approximation algorithms based on a filtered back projection. The FDK algorithm, proposed by Feldkamp et al., is a kind of approximate reconstruction algorithm based on circular orbit scanning. In this study, this algorithm was used to conduct a 3D reconstruction on the scanned images. It is essentially an expansion of the 2D fan-beam filtered back projection algorithm in 3D space and includes the steps of the preweighting of projection data, one-dimensional filtering, and back projection. Specifically, the FDK algorithm includes the following steps: First, weighted processing was conducted on the projection data, using a function similar to the cosine function, in order to modify the distance between the voxel and source point and the angle difference appropriately. Then, one-dimensional filtering was conducted on the projection data from different projection angles along the horizontal direction. Finally, a 3D back projection was performed along the direction of the X-ray. The reconstructed voxel values were the sum of the rays passing the voxel at all projection angles.
The corresponding formulas are written as follows:
The pores should be connected in simulating seepage behaviors during the water injection process. Generally, a larger 3D digital core can provide a more accurate characterization of a core’s micropore structure and more accurate simulation results of its macroscopic physical properties; however, it would place higher requirements on the computer’s storage and calculation capabilities. Since a computer generally has limited storage and calculation capacities, the size of a 3D core cannot be too large. Accordingly, a representative elementary volume (REV) analysis [
Distribution of the selected models using different points as the voxel centers.
Calculated results of coal rock porosity using different points (P1, P2, P3, and P4) as the voxel centers.
Size of the volume element ( |
30 | 40 | 50 | 55 | 60 | 65 | 70 | 80 | 90 |
---|---|---|---|---|---|---|---|---|---|
Calculated porosity using P1 as the voxel center (%) | 34.56 | 30.95 | 28.18 | 26.43 | 26.32 | 26.24 | 26.31 | 26.07 | 26.30 |
Calculated porosity using P2 as the voxel center (%) | 32.40 | 30.76 | 29.72 | 28.75 | 28.77 | 28.80 | 28.74 | 28.73 | 28.81 |
Calculated porosity using P3 as the voxel center (%) | 35.74 | 33.19 | 32.01 | 30.27 | 30.10 | 30.13 | 30.09 | 30.15 | 30.20 |
Calculated porosity using P4 as the voxel center (%) | 37.43 | 36.91 | 35.28 | 34.53 | 34.57 | 34.49 | 34.53 | 34.52 | 34.50 |
Variations of the calculated porosity with the increase of volume element size for different models.
It can also be observed from Figure
Various kinds of system noises exist in digital cores after CT scanning, which would not only affect the image quality but also affect the subsequent quantitative analysis. Before image segmentation, the images should be filtered so as to reduce noises, improve the image quality, and thus make it easier for image segmentation and display. The common filtering algorithms include Gaussian filtering, variance filtering, median filtering, recursive exponential filtering, and low-pass linear filtering [
Comparison of the P1 model before and after denoising: (a) before denoising and (b) after denoising.
In order to better distinguish pores from skeletons and make quantitative descriptions, an appropriate binarization should be conducted on the grayscale images. On an Avizo platform, the coal model was first segmented by pressing the “Image Segmentation” button, and then the segmented image was displayed by pressing the “Surface View” button. Thus, the microscopic models of coal pores based on actual coal pore structures were acquired, as shown in Figures
Model of coal’s micropore structure in model P1. (a) Coal sample. (b) Pores and skeletons. (c) Pores (with an absolute porosity of 26.30%).
Model of coal’s micropore structure in model P2. (a) Coal sample (b) Pores and skeletons. (c) Pores (with an absolute porosity of 28.77%).
Model of coal’s micropore structure in model P3. (a) Coal sample. (b) Pores and skeletons. (c) Pores (with an absolute porosity of 30.10%).
Model of coal’s micropore structure in model P4. (a) Coal sample. (b) Pores and skeletons. (c) Pores (with an absolute porosity of 34.57%).
Next, the acquired pore model was imported into ICEM CFD software for grid generation and the establishment of the finite element model [
Settings of boundary conditions.
Grid generation.
After the mesh has been divided effectively, the seepage behaviors in the four different coal microstructure models during the water injection process were simulated under different pressure gradients using CFX15.0 software. In simulations, the nonstationary Navier–Stokes equation, the most basic equation that can accurately describe the fluid’s actual flow characteristics, was used as the control equation. The standard k-epsilon turbulence equation was also used [
Average seepage velocities in coal seams under different pressure gradients.
Pressure increase (MPa) | Inlet pressure (MPa) | Pressure gradient (109 MPa·m−1) | Average seepage velocities in coal’s different regions (m·s−1) | |||
---|---|---|---|---|---|---|
P1 | P2 | P3 | P4 | |||
0.2 | 0.3 | 3.93 | 1.01 | 1.24 | 1.18 | 0.95 |
0.5 | 7.97 | 1.77 | 2.22 | 2.11 | 1.70 | |
0.7 | 12.14 | 2.40 | 3.07 | 2.91 | 2.30 | |
0.9 | 16.52 | 2.95 | 3.82 | 3.65 | 2.83 | |
1.1 | 21.16 | 3.44 | 4.53 | 4.39 | 3.32 | |
1.3 | 26.77 | 3.98 | 5.19 | 5.35 | 3.79 | |
0.4 | 1.7 | 35.36 | 4.92 | 6.12 | 6.13 | 4.70 |
2.1 | 45.31 | 5.72 | 7.15 | 7.19 | 5.48 | |
2.5 | 53.26 | 6.46 | 8.14 | 7.55 | 6.01 | |
2.9 | 62.47 | 7.14 | 9.04 | 8.42 | 6.31 | |
3.3 | 71.88 | 7.79 | 9.68 | 9.21 | 6.91 | |
3.7 | 82.88 | 8.36 | 10.71 | 9.99 | 7.49 | |
0.6 | 4.3 | 99.06 | 9.21 | 11.95 | 11.12 | 8.32 |
4.9 | 113.87 | 10.02 | 12.63 | 12.20 | 9.11 | |
5.5 | 130.78 | 10.8 | 13.75 | 13.25 | 9.85 | |
6.1 | 148.37 | 11.52 | 14.85 | 14.31 | 10.59 | |
6.7 | 161.51 | 12.24 | 16.27 | 15.37 | 11.31 | |
7.3 | 174.18 | 13.05 | 17.14 | 16.24 | 12.01 | |
0.8 | 8.1 | 196.07 | 13.98 | 18.01 | 17.35 | 12.92 |
8.9 | 230.39 | 14.95 | 18.94 | 18.42 | 13.82 | |
9.7 | 259.86 | 15.84 | 20.84 | 19.45 | 14.66 | |
10.5 | 285.29 | 16.69 | 21.98 | 20.45 | 15.52 | |
11.3 | 310.44 | 17.54 | 23.10 | 21.41 | 16.08 | |
12.1 | 339.06 | 18.39 | 24.20 | 22.35 | 17.37 | |
1.0 | 13.1 | 373.47 | 19.39 | 25.55 | 23.48 | 18.39 |
14.1 | 407.36 | 20.44 | 26.88 | 24.58 | 19.06 | |
15.1 | 443.90 | 21.48 | 28.20 | 25.64 | 19.90 | |
16.1 | 480.27 | 22.40 | 29.50 | 26.68 | 20.72 | |
17.1 | 518.03 | 23.38 | 30.80 | 27.67 | 21.52 | |
18.1 | 556.90 | 24.35 | 32.11 | 28.66 | 22.30 |
The seepage parameters under different conditions are now analyzed based on the simulation results of the water injection seepage under different pressure gradients.
Using CFD-POST software, the average seepage velocities at different water injection pressures were extracted. Table
As shown in Table
Variation of average seepage velocities and pressure gradient.
More evidently, it can be observed that the water seepage velocities in the four different regions increased gradually with the increase of the pressure gradient. Both factors show an obvious nonlinear relationship. Wang et al. found that, under the conditions with quite large pores and fractures or large hydraulic slopes, the Reynolds number of water flow was significant, and the underground water seepage velocity exhibited a complex nonlinear relationship with the hydraulic slope [
The other is the exponential formula:
Compared with the latter formula, the Forchheimer formula possesses more favorable theoretical foundations, which can be derived from the Navier–Stokers equation in fluid mechanics. Therefore, the Forchheimer formula was used in this study for fitting the relationship between the pressure gradient
Through fitting, the values of A and B of different curves were acquired; moreover, both the coefficient of the dynamic viscosity and seepage velocity of water at a normal temperature are constants. Then, according to equation (
Coal’s permeability and non-Darcy coefficients after fitting.
Coal region | Effective porosity | Correlation coefficient | Fitted value of |
Fitted value of |
Permeability ( |
Non-Darcy coefficient ( |
---|---|---|---|---|---|---|
P1 | 18.15% | 0.99967 | 3.64826 | 0.94244 | 2.30 | 942 |
P2 | 15.26% | 0.9995 | 3.44116 | 0.80657 | 2.44 | 807 |
P3 | 14.57% | 0.99912 | 3.40512 | 0.65068 | 2.46 | 651 |
P4 | 20.43% | 0.99926 | 3.35691 | 0.44063 | 2.50 | 441 |
As shown in Table
For analyzing the effects of the water injection pressure on seepage in coal, the model P1 was selected in this study for seepage simulations during water injections under different pressure gradients, in which the injection pressure was set as 0.3 MPa, 1.7 MPa, 4.3 MPa, 8.1 MPa, 13.1 MPa, and 18.1 MPa. Figures
Distributions of pressure fields in model P1 under different water injection pressures. (a) 0.3 MPa. (b) 1.7 MPa. (c) 4.3 MPa. (d) 8.1 MPa. (e) 13.1 MPa. (f) 18.1 MPa.
Distributions of velocity fields in model P1 under different water injection pressures. (a) 0.3 MPa. (b) 1.7 MPa. (c) 4.3 MPa. (d) 8.1 MPa. (e) 13.1 MPa. (f) 18.1 MPa.
Distributions of mass flows in model P1 on different sections under different water injection pressures. (a) 0.3 MPa. (b) 1.7 MPa. (c) 4.3 MPa. (d) 8.1 MPa. (e) 13.1 MPa. (f) 18.1 MPa.
As shown in Figure
It can be observed from Figure
As shown in Figure
In order to gain an in-depth insight into the water injection seepage rules of the same model under different pressure gradients, 13 sections that were equally spaced were selected, and the seepage parameters, which mainly included the average seepage pressure, average seepage velocity and average mass flow on each section, were simulated, as shown in Table
Simulated results of average seepage pressure, average seepage velocity, and average mass flow on each section under different inlet pressures.
Inlet pressure (MPa) | Seepage parameters | Distance from the inlet section ( | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | ||
0.3 | P1 | 0.30 | 0..29 | 0.29 | 0.26 | 0.23 | 0.21 | 0.18 | 0.16 | 0.15 | 0.13 | 0.12 | 0.11 | 0.10 |
V2 | 0.82 | 0.92 | 1.19 | 1.63 | 1.54 | 1.69 | 1.51 | 1.26 | 1.31 | 1.00 | 1.15 | 1.10 | 1.17 | |
M3 | 13.34 | 3.96 | 4.45 | 5.61 | 5.59 | 6.10 | 5.35 | 4.93 | 4.31 | 4.12 | 4.19 | 4.61 | 5.12 | |
|
||||||||||||||
1.7 | P | 1.70 | 1.69 | 1.62 | 1.38 | 1.05 | 0.87 | 0.71 | 0.50 | 0.44 | 0.30 | 0.25 | 0.15 | 0.10 |
V | 4.20 | 4.58 | 5.96 | 7.93 | 7.77 | 7.99 | 7.43 | 6.73 | 6.70 | 4.61 | 5.82 | 5.27 | 5.31 | |
M | 37.15 | 18.98 | 21.34 | 26.92 | 26.82 | 29.27 | 25.69 | 23.62 | 20.65 | 19.76 | 20.09 | 22.13 | 27.33 | |
|
||||||||||||||
4.3 | P | 4.30 | 4.27 | 4.11 | 3.49 | 2.60 | 2.13 | 1.71 | 1.13 | 1.00 | 0.62 | 0.52 | 0.23 | 0.10 |
V | 7.86 | 8.77 | 10.99 | 14.49 | 14.10 | 14.77 | 14.08 | 13.25 | 12.83 | 8.87 | 11.10 | 9.71 | 9.72 | |
M | 61.01 | 34.00 | 38.23 | 48.22 | 48.04 | 52.43 | 46.01 | 42.31 | 36.99 | 35.40 | 36.00 | 39.65 | 45.55 | |
|
||||||||||||||
8.1 | P | 8.10 | 8.06 | 7.76 | 6.57 | 4.83 | 3.96 | 3.17 | 2.04 | 1.77 | 1.08 | 0.92 | 0.36 | 0.10 |
V | 12.75 | 13.67 | 16.06 | 20.72 | 20.70 | 21.97 | 21.03 | 20.35 | 19.52 | 13.39 | 16.67 | 14.83 | 14.56 | |
M | 84.14 | 49.22 | 55.34 | 69.80 | 69.53 | 75.90 | 66.60 | 61.25 | 53.55 | 51.24 | 52.10 | 57.39 | 64.06 | |
|
||||||||||||||
13.1 | P | 13.25 | 13.08 | 12.48 | 10.54 | 7.75 | 6.39 | 5.13 | 3.26 | 2.68 | 1.67 | 1.47 | 0.55 | 0.10 |
V | 19.55 | 19.46 | 20.88 | 26.97 | 27.91 | 29.31 | 28.25 | 28.26 | 26.69 | 18.29 | 22.77 | 20.15 | 19.47 | |
M | 107.91 | 64.66 | 72.70 | 91.70 | 91.35 | 99.70 | 87.50 | 80.47 | 70.34 | 67.26 | 68.43 | 75.39 | 85.92 | |
|
||||||||||||||
18.1 | P | 18.10 | 18.38 | 17.34 | 14.67 | 10.63 | 8.74 | 7.00 | 4.44 | 3.64 | 2.28 | 2.01 | 0.74 | 0.10 |
V | 26.54 | 26.07 | 25.11 | 32.72 | 34.09 | 35.39 | 33.81 | 34.76 | 32.6 | 22.31 | 27.75 | 24.52 | 23.33 | |
M | 126.26 | 76.67 | 86.21 | 108.74 | 108.33 | 118.24 | 103.77 | 95.43 | 83.41 | 79.75 | 81.15 | 89.4 | 101.49 |
Note: 1P denotes the average seepage pressure, with a unit of MPa, 2V denotes the average seepage velocity, with a unit of m·s−1, and 3M denotes the average mass flow, with a unit of 10−11 Kg·s−1.
Variations of average seepage pressure with seepage length under different inlet pressures.
Variations of average velocity with seepage length under different inlet pressures.
Variations of average seepage mass flow with seepage length under different inlet pressures.
By analyzing Table As shown in Figure As shown in Figure As shown in Figure
The porosities of different regions are different even in the same coal sample. Thus, a coal sample may exhibit different water injection processes under the same injection gradient. In this study, the seepage rules of four different models were analyzed with four types of pressure gradients, low pressure (4.3 MPa), medium pressure (8.1 MPa), high pressure (13.1 MPa), and ultrahigh pressure (18.1 MPa). Figures
Distribution of pressure and velocity fields in four different models under a low inlet pressure of 4.3 MPa. (a) Results in model P1. (b) Results in model P2. (c) Results in model P3. (d) Results in model P4.
Distribution of pressure and velocity fields in four different models under a medium inlet pressure of 8.1 MPa. (a) Results in model P1. (b) Results in model P2. (c) Results in model P3. (d) Results in model P4.
Distribution of pressure and velocity fields in four different models under a high inlet pressure of 13.1 MPa. (a) Results in model P1. (b) Results in model P2. (c) Results in model P3. (d) Results in model P4.
Distribution of pressure and velocity fields in four different models under an ultrahigh inlet pressure of 18.1 MPa. (a) Results in model P1. (b) Results in model P2. (c) Results in model P3. (d) Results in model P4.
Table Under an injection pressure of 4.3 MPa, the pressure fields of the four models were different. The maximum pressures all fluctuated around 4.3 MPa and appeared around the inlet; similarly, the minimum pressures fluctuated around 0.1 MPa and appeared around the outlet. Under an injection pressure of 4.3 MPa, the velocity fields of the four models also showed significant differences. The maximum seepage velocities appeared in the intermediate region where the pore diameter was suddenly reduced. In the four models, the maximum seepage velocities differed slightly; specifically, the maximum seepage velocity in the P4 model was greatest, followed by those in the P1 and P2 models, while the value in P3 was smallest. This is mainly because at the center of the small pore channel of the section where the water flowed, the water seepage velocity increased as the pore radius and bending degree decreased. Under the same injection pressure, the total mass flows at different inlet areas were different. At the inlet area of 12.10 × 10−10 m2, the total inlet mass flow was 5.61 × 10−6 kg·s−1; at the inlet area of 9.29 × 10−10 m2, the total inlet mass flow was 10 × 10−6 kg·s−1; at the inlet area of 13.02 × 10−10 m2, the total inlet mass flow was 9.90 × 10−6 kg·s−1; and at the inlet area of 9.60 × 10−10 m2, the total inlet mass flow was 7.13 × 10−6 kg·s−1. When these are ranked in a descending order, the total mass flow in the P2 model is greatest, followed by the values in P3 and P4, and finally by that in P1. Since the present seepage simulations were conducted based on an actual coal pore model, water would flow into the pores that were not connected with the outlet due to the seepage effect and the total mass flows at the outlet were smaller than those at the inlet.
Simulated results of seepage parameters in four models under a low inlet pressure of 4.3 MPa.
Model |
|
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|---|
P1 | 4.13 | 0.08 | 97.60 | 10.16 | 12.10 | 5.61 | 8.37 | 5.61 |
P2 | 4.33 | 0.11 | 87.08 | 6.38 | 9.29 | 10 | 8.30 | 9.98 |
P3 | 4.38 | 0.11 | 81.55 | 4.21 | 13.02 | 9.90 | 8.60 | 9.89 |
P4 | 4.32 | 0.11 | 98.70 | 3.28 | 9.60 | 7.13 | 8.53 | 7.13 |
Table The pressure and velocity fields under a medium inlet pressure were similar to those under a low pressure. With the increase of the water injection pressure, the maximum seepage velocity increased to be approximately 125 m·s−1, with basically the same increasing amplitudes in the four models. The maximum seepage velocity in the P4 model was greatest, followed by those in P1 and P3, and finally by the value in P2. Compared with the results at a low inlet pressure (4.3 MPa), the total mass flows at an 8.1 MPa at the inlet and outlet increased. The total mass flow at the inlet in the P2 model was greatest (14.95 × 10−6 kg·s−1), followed by the values in the P3 and P4 models (13.78 × 10−6 kg·s−1 and 10.54 × 10−6 kg·s−1, resp.); finally, the value in the P1 model was smallest (7.40 × 10−6 kg·s−1). Since the inlet area remained unchanged, the total mass flow increased gradually with the increase of pressure.
Simulated results of seepage parameters in four models under a medium inlet pressure of 8.1 MPa.
Model |
|
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|---|
P1 | 8.17 | 0.062 | 145.4 | 17.37 | 12.10 | 7.40 | 8.37 | 7.32 |
P2 | 8.08 | 0.13 | 117.3 | 2.213 | 9.29 | 14.95 | 8.30 | 14.90 |
P3 | 8.12 | 0.11 | 121.8 | 0.9 | 13.02 | 13.78 | 8.60 | 13.78 |
P4 | 8.11 | 0.15 | 150.8 | 6.042 | 9.60 | 10.54 | 8.53 | 10.54 |
Table The seepage behaviors in the four models showed almost the same variation tendencies. The pressures decreased along the seepage direction, which were greatest at the inlet and smallest at the outlet. Although these four models had different porosities, the seepage pressures at both the inlet and outlet fluctuated at around 13.1 MPa and showed slight variations. The average seepage velocities varied significantly in the intermediate regions, and the maximum seepage velocities reached up to 202.4 m·s−1. Compared with the results under low and medium inlet pressures, the total mass flows at the inlet and outlet under a high pressure of 13.1 MPa increased more significantly. Owing to the increase of the water injection pressure, some pores which were originally closed were opened and connected with each other to form seepage channels; thus, more water flowed out compared with the conditions under low and medium pressures. Under a high inlet pressure, the mass flow differences between the inlet and outlet were small. The total mass flow in the P2 model was greatest, followed by the values in the P3 and P4 models, and finally by the value in the P1 model. Similarly, with the increase of the pressure gradient, the total mass flows increased, with almost the same increasing amplitudes in the four models.
Simulated results of seepage parameters in four models under a high inlet pressure of 13.1 MPa.
Model |
|
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|---|
P1 | 13.2 | 0.11 | 191.2 | 14 | 12.10 | 9.56 | 8.37 | 9.49 |
P2 | 13.1 | 0.14 | 256 | 1.37 | 9.29 | 20.26 | 8.30 | 20.1 |
P3 | 13.07 | 0.092 | 161.8 | 3.43 | 13.02 | 19.83 | 8.60 | 19.76 |
P4 | 13.1 | 0.1 | 202.4 | 3.80 | 9.60 | 13.94 | 8.53 | 13.93 |
Table The seepage behaviors showed same variation tendencies in the four models. With the increase of the pressure gradient, the maximum seepage velocity increased steadily. The maximum seepage velocity in the P2 model was as high as 469.9 m·s−1, while the minimum seepage velocity remained at approximately 2 × 10−5 m·s−1. The total mass flow increased steadily with the increase of the pressure gradient. The total mass flows in the four models differed slightly; specifically, the total mass flow in the P2 model was greatest, followed by the values in the P3 and P4 models, and finally by the value in the P1 model. At 18.1 MPa, some pores that originally showed a favorable connectivity might have broken under the impact of the hydraulic pressure, and some large fractures were formed. Thus, fluids flowed out easily. Taking the P1 model as the example, water was more inclined to flow out through the left-center pores and less inclined to flow out through the upper right pores.
Simulated results of seepage parameters in four models under an ultrahigh inlet pressure of 18.1 MPa.
Model |
|
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|---|
P1 | 17.99 | 0.093 | 297.3 | 3.43 | 12.10 | 11.50 | 8.37 | 11.23 |
P2 | 18.02 | 0.13 | 469.9 | 1.97 | 9.29 | 24.96 | 8.30 | 24.42 |
P3 | 18.1 | 0.1 | 198.1 | 3.49 | 13.02 | 23.86 | 8.60 | 23.76 |
P4 | 18.01 | 0.11 | 243.2 | 2.83 | 9.60 | 16.64 | 8.53 | 16.63 |
In this paper, through a REV analysis, the optimum border length of the finite element analysis data was determined to be 0.06 mm, and the water seepage numerical simulation under 30 different pressure gradients was carried out using CFX software. The following results were ascertained: At a microscopic scale, the simulated results of the seepage velocity based on actual pore models exhibited complex nonlinear relationships with the pressure gradient rather than simple linear relationships. The seepage behaviors accorded with Forchheimer’s high-velocity nonlinear seepage rules. The permeability did not necessarily increase with the increase of effective porosity; that is, the positive correlation between them was not absolute. The non-Darcy flow efficient increased gradually with the increase of permeability. In the same model (P1), under different water injection pressure gradients, the following can be concluded: Along the seepage direction (i.e., the positive direction of At a low pressure water injection, the seepage velocities fluctuated evenly; with the increase of the water injection pressure, the average seepage velocities overall showed the variation tendency of increase-decrease-increase-decrease. Although the seepage velocities varied significantly during the entire water injection process, the seepage velocities at the inlet and outlet showed slight variations. At the same seepage length, the average seepage velocities varied significantly under different pressure gradients; the larger the pressure gradient, the greater the average seepage velocity. The average mass flows on the various sections fluctuated evenly. However, as the water injection pressure increased, the average mass flows at various sections fluctuated, notably along the direction of the seepage length; the average mass flow at the inlet (with a seepage length of 0 The overall direction of the seepage is insignificantly influenced by the injection pressure. The seepage pressures decreased gradually along the seepage direction, which were greatest at the inlet and smallest at the outlet. The maximum seepage velocities all appeared in the intermediate regions with suddenly decreased pores. Under the same injection pressure, the total mass flows from the different inlets with different areas also varied. The increase of the total mass flow from the inlet to outlet was more significant under a higher injection pressure.
Computed tomography
ANSYS CFX software
The distance between the X-ray source and the detector
The distance between the stage sample and the detector
ANSYS ICEM CFD software
Computational fluid dynamics
The representative elementary volume
The cross-sectional area and mass flow of the inlet
The cross-sectional area and mass flow of the outlet.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work was financially supported by the National Key Research and Development Program of China (Grant no. 2017YFC0805202), the National Natural Science Foundation of China (Grant nos. 51774198 and 51474139), the Outstanding Youth Fund Project of Provincial Universities in Shandong Province (Grant no. ZR2017JL026), the Taishan Scholar Talent Team Support Plan for Advantaged and Unique Discipline Areas, the Qingdao City Science and Technology Project (Grant no. 16-6-2-52-nsh), the China Postdoctoral Science Foundation Funded Special Project (Grant no. 2016T90642), the China Postdoctoral Science Foundation Funded Project (Grant no. 2015M570602), the Natural Science Foundation of Shandong Province (Grant no. ZR2016EEM36), and the Qingdao Postdoctoral Applied Research Project (Grant no. 2015194).