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Experimental study on permeability of crushed gangues during compaction
MINPRO-02513; No of Pages 7 International Journal of Mineral Processing xxx (2013) xxx–xxx
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Experimental study on permeability of crushed gangues during compaction Hailing Kong a, Zhanqing Chen b, c, Luzhen Wang a, c,⁎, Haide Shen b a b c
Department of Fundamental Sciences Teaching, Yancheng Institute of Technology, Yancheng 224051, China School of Mechanics and Civil Engineering, China University of Mining and Technology (Xuzhou), Xuzhou 221008, China State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology (Xuzhou), Xuzhou, 221008, China
a r t i c l e
i n f o
Article history: Received 18 October 2012 Received in revised form 24 April 2013 Accepted 27 April 2013 Available online xxxx Keywords: Crushed gangue Compaction Permeability Experimental test
a b s t r a c t Using a crushed rock compaction permeation apparatus and a self-designed seepage circuit, we tested the permeability of crushed gangues with six different particle sizes during compaction on the CMT5305 electronic universal testing machine and analyzed the relationships of seepage velocity, permeability and non-Darcy β factor to the porosity, particle size and diameter distribution. The results show that 1) The seepage flow of crushed gangues during compaction is nonlinear, and their compactability after compaction is related to their final porosity; 2) the seepage velocity of crushed gangues of same size decreases with pressure gradient increase and with porosity decrease, and varies less than that of crushed gangues of same porosity and mixed size or size between 10 and 15 mm. Moreover, the greater the single particle size is, the greater the pressure gradient. In addition, the mixed gangues have the lowest pressure gradient; 3) the permeability of gangues of same size decreases with their size increase and that of the mixed gangues is the largest; 4) the relationship of permeability to porosity can be divided into two stages with porosity decrease. At the stage II, permeability decreases significantly by the magnitude of 2 to 3 compared to that at the stage I. After stage II, the permeability of crushed gangue decreases to the magnitude of 10−15 m2, while the impermeability increases; 5) the non-Darcy β factor is negative for gangues with size larger than 10 mm, while that gradually becomes positive with porosity decrease for mixed gangues and gangues with size less than 10 mm. Moreover, non-Darcyβ factors affect the impermeability of gangues. The results will provide references for gangues as filling materials. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Gangues are solid waste during the production process of coal industry. But its utilization prospect at home and abroad has been more optimistic especially as filling materials for goaf, embankment (dike) and water dams. Thus, their compaction bearer, strength, deformation, impermeability, drainage and seepage have become key issues to be solved urgently. Many scholars at home and abroad have tested the gangues' compaction characteristics experimentally. Butler (1974), Michalski and Skarzynska (1984), Solesbury (1987) and Rainbow and Skarzynska (1987) have pointed out that the available density of gangues is correlated with its particle size distribution. Jiang et al. (1999, 2001) have experimentally studied the compaction characteristics of gangues mixed with coal ash and clay, explored the relationships of its compactability to its crushing degree. Ma et al. (2003, 2004) experimentally summarized the strain, Poisson's ratio and elasticity modulus of loose gangues during compaction process, theoretically analyzed the ⁎ Corresponding author at: Department of Fundamental Sciences Teaching, Yancheng Institute of Technology, Yancheng 224051, China. Tel.: + 86 11 86 15851060692; fax: + 86 11 86 515 88168221. E-mail address: [email protected] (L. Wang).
compacting deformation mechanisms and measured the stress–strain and porosity–stress relationships of the saturated gangues, etc. Qi et al. (2004) tested and discussed the influence of particle sizes of gangues on their compaction characteristics. Tu et al. (2009) experimentally studied the relationship between the filling gangues with different grade of particle sizes and the compaction amount. However, the permeability of gangues during compaction is not well studied. Wang (2006) studied the effects of crushing degree through compaction trials on the permeability of gangues, and found that the exponential function could describe the relationship between the permeability and porosity of gangues and that the permeability decreased significantly with fine particle amount increase. However, he did not further analyze the impact of particle size on this function. Li et al. (2008) tested the permeability of crushed rock including gangues based on the MTS815.02 rock mechanics servo system. However, in their experiments, the MTS turbocharger volume was too small, and the test time for permeability was too short, thus the seepage velocity and pore pressure gradient range were limited, the obtained permeability at the initial loading period was very unstable, and the correlation curve between permeability and porosity of the gangues with larger particle size fluctuated greatly. Liu et al. (2011) utilized the system, obtained the permeability of the graded crushed gangues and concluded that the permeability of the gangues was
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Please cite this article as: Kong, H., et al., Experimental study on permeability of crushed gangues during compaction, Int. J. Miner. Process. (2013), http://dx.doi.org/10.1016/j.minpro.2013.04.012
2
H. Kong et al. / International Journal of Mineral Processing xxx (2013) xxx–xxx
related to their particle size, particle arrangement and pore structure. However, they did not further study the permeability of gangue with different sizes. The study used a self-designed seepage circuit composed of a permeability tester, a gear pump, a pressure relief valve and the CMT5305 electronic universal testing machine, measured the permeability characteristics of crushed gangues with six different sizes during compaction, and provided a theoretical guidance for permeability and impermeability characteristics of gangues as filling materials in engineering projects. 2. Experiment system and method The test system for the permeability characteristics of the crushed gangues under compaction mainly consists of a CMT5305 electronic universal testing machine, crushed rock compaction containing cylinder (Miao et al., 2004) and a self-designed seepage circuit, which is composed of gear pump, pressure gauge, direction valve, cut-off valve, pressure transmitter, flow transmitter, etc, as shown in Fig. 1. The gangues used in this test were collected from LuAn Mine in Shanxi Province. Their mass density ρ was 1526 kg/m 3 and their average uniaxial compression strength was 76.27 MPa as measured by uniaxial compression test. Then the crushed gangues were selected based on their particle diameter and grouped into five groups with diameter of 2.5–5 mm, 5–10 mm, 10–15 mm, 15–20 mm and 20– 25 mm, respectively. The mixed group was composed of those five gangues at mass ratio of 1:1:1:1:1. The permeability of crushed gangues was tested in triplicates and the average was used for analysis. In brief, a certain amount (m) of crushed gangues were packed into the cylinder of inner diameter of 2a (2a = 68) mm and height of 110 mm and connected to the electronic universal testing machine. Its height (ho) under natural pressure was recorded and used to calculate the initial porosity (ϕ0) of
the crushed gangues. Table 1 lists the formula used for porosity calculation and the controlled, recorded and calculated parameters used in the test. Then the load was applied to the piston of the electronic universal testing machine in accordance with the displacement control during the test. Considering the polytropy and complexity of the gangues, the displacement increment of piston was set as five levels (i.e. gangue compaction), for example, from 15 mm, 5 mm, 5 mm, 3 mm to 2 mm, or from 10 mm, 5 mm, 5 mm, 5 mm to 3 mm, depending on the maximum flow in the previous level and flow under the initial pressure of the relief valve at current level, and used to calculate the porosity (ϕi) at each level (i = 1, 2, 3, 4, 5). Under the pressure, the pore structure of the crushed gangues changed. With the axial pressure on crushed gangues increasing, its internal pore space became smaller and smaller. Under each level of compaction, the pore pressure Δρj (j = 1, 2, 3, 4) of the relief valve was set as four levels. When the porosity was large, the increment of the pore pressure of the relief valve was set as 0.5 MPa, meaning the pore pressure was set as 0.5 MPa, 1.0 MPa, 1.5 MPa, and 2.0 MPa at the first level to the fourth level. As the porosity decrease, the increment was set as 1.0 MPa, meaning the pressure was set as 3 MPa, 4 MPa, 5 MPa and 6 MPa. Fig. 2 shows the flowchart of the test. With the pore pressure of the relief valve changes, the pressure gradient Gp and seepage velocity V change accordingly. Under Darcy flow pressure gradient, Gp and V obey the linear relationship, while under the Forchheimer non-Darcy flow pressure gradient Gp and V obey the quadratic polynomial relationship. The relationship of Gp to V was fitted using both linear and quadratic polynomial formula. Meanwhile, the permeability and non-Darcy flow β factor of the crushed gangues were calculated using the least squares fit method (Chen et al., 2010). In this way, seepage velocity, permeability and non-Darcy flow β factor of the crushed gangues with six particle diameters under different porosity level were measured.
3. Experiment results and analysis
10 9 8 7 p
6 5 4
3.1. The relationship between pressure gradient and seepage velocity Table 2 lists the test results of pressure gradient and seepage velocity of the crushed gangues with diameters of 15–20 mm with compaction amount increase, the linear fitting formula and its coefficient based on Darcy flow, the quadratic polynomial fitting formula and its coefficient based on Forchheimer non-Darcy flow, and the calculated non-Darcy flow permeability k and non-Darcy flow β factor. Obviously, the quadratic polynomial fitting is better than the linear fitting, indicating that the seepage of crushed gangues under compaction is non-Darcy flow. Fig. 3 shows the curve of pressure gradient vs seepage velocity of the crushed gangues with diameter of 15–20 mm and different porosity. It can be seen that as the porosity decreases, the pressure gradient increases, the seepage velocity reduces from 10−3 ms−1 to 10 −5 ms−1. Obviously, as the crushed gangue being compacted constantly, the
3 2 M
1
Fig. 1. The seepage test system. 1. Oil tank, 2. filter, 3. gear pump, 4. pressure gauge, 5. switch valve, 6. shutoff valve, 7. pressure transmitter, 8. flow transmitter, 9. permeability tester, 10. material testing machine.
Table 1 Parameters used in the test. Parameter
Sign
Unit
Type
Initial height of the crushed gangues Initial porosity Displacement increment of piston Current height of the crushed gangues Porosity Pore pressure of the relief valve Pressure gradient Seepage amount Seepage velocity
h0 ϕ0 ¼ 1− ρπam2 h 0 Δhi hi = h0 − ∑ Δhi
mm None mm mm
Recorded Calculated Controlled Calculated
ϕi ¼ 1− ρπam2 h i Δpj Δp Gp ¼ hi j Q V ¼ πaQ2
None MPa Mpa m−1 mL M s−1
Calculated Controlled Calculated Recorded Calculated
Please cite this article as: Kong, H., et al., Experimental study on permeability of crushed gangues during compaction, Int. J. Miner. Process. (2013), http://dx.doi.org/10.1016/j.minpro.2013.04.012
H. Kong et al. / International Journal of Mineral Processing xxx (2013) xxx–xxx
3
calculate the initial porosity initial load 0.2kN, zero diaplacement start gear pump, injected and saturated
load axial displacement
record the compacted displacement
keep axial displacement
calculate porosity
change pore pressure of the relief valve
change the axial displacement
start relief valve
record pore pressure of the relief valve
keep pore pressure of the relief valve
calculate pressure gradient
seepage liquid
record seepage time and flow
seepage completed
NO
different pore pressure of the relief valve tests completed
NO
different axial displacement tests completed
test completed Fig. 2. The flowchart for testing permeability of crushed gangues.
seepage velocity will reduce and the pressure of the relief valve will increase correspondingly. Fig. 4 shows the curves of pressure gradient vs seepage velocity of the crushed gangues with the same porosity (0.174) but 6 different diameters. As shown, with pressure gradient increasing, the seepage velocity of crushed gangues with diameter smaller than 10 mm is in the magnitude of 10 −4 ms −1; that of crushed gangues with diameter larger than 15 mm is in the magnitude of 10 −5 ms −1; that of crushed gangues with diameter in range of 10–15 mm or with mixed diameter varies greatly from magnitude of 10 −4 to 10 −5 ms −1.
Fig. 4 also shows that when the crushed gangues have uniform diameter, the greater the diameter is, the greater the pressure gradient is; and when the crushed gangues have mixed diameter, their pressure gradient is smaller. The results that the crushed gangues with larger diameter have smaller seepage velocity could be explained as follows. After several compaction stages at certain porosity, the crushed gangues are fragmented. The larger the diameter is, the wider the diameter distributes after compaction. Those crushed gangues with smaller diameter could effectively fill the void spaces between the larger crushed
Table 2 Permeability of the crushed gangues with diameter of 15–20 mm. Compaction Δh/mm
Porosity ϕ
Pressure gradient Gp/Pa.m−1
15
0.402
20
0.331
25
0.241
28
0.174
30
0.122
1.06 2.50 3.19 4.10 2.40 5.10 7.50 9.30 5.50 7.70 9.80 1.14 5.88 9.10 1.22 1.47 1.25 1.56 1.88 2.19
× × × × × × × × × × × × × × × × × × × ×
107 107 107 107 107 107 107 107 107 107 107 108 107 107 108 108 108 108 108 108
Seepage velocity V/m.s−1 2.95 4.63 5.85 1.04 3.92 7.13 1.56 3.31 2.60 3.37 5.18 9.08 1.78 2.19 3.22 5.33 7.91 1.12 1.81 4.11
× × × × × × × × × × × × × × × × × × × ×
10−4 10−4 10−4 10−3 10−5 10−5 10−4 10−4 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−6 10−5 10−5 10−5
Linear fitting and its correlation
Quadratic fitting and its correlation
Non-Darcy flow permeability k/m2
Non-Darcy flow β factor/m−1
Gp = 41 × 1010 V R2 = 0.822
Gp = −1.92 × 1013 V2 + 6.02 × 1010 V R2 = 0.913
3.26 × 10−13
−2.20 × 1010
Gp = 3.35 × 1011 V R2 = 0.680
Gp = −1.30 × 1015 V2 + 7.10 × 1011 V R2 = 0.975E
2.76 × 10−14
−1.49 × 1012
Gp = 1.53 × 1012 V R2 = 0.0579
Gp = −1.61 × 1016 V2 + 2.72 × 1012 V R2 = 0.981
7.21 × 10−15
−1.84 × 1013
Gp = 3.17 × 1012 V R2 = 0.694
Gp = −3.59 × 1016 V2 + 4.71 × 1012 V R2 = 0.938
4.16 × 10−15
−4.11 × 1013
Gp = 6.86 × 1012 V R2 = −2.95
Gp = −2.61 × 1017 V2 + 1.60 × 1013 V R2 = 0.879
1.23 × 10−15
−2.99 × 1014
Please cite this article as: Kong, H., et al., Experimental study on permeability of crushed gangues during compaction, Int. J. Miner. Process. (2013), http://dx.doi.org/10.1016/j.minpro.2013.04.012
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0.403 0.331 0.241 0.174 0.122
pressure gradient Gp/Pam-1
2.50E+08 2.00E+08 1.50E+08 1.00E+08 5.00E+07 0.00E+00 1.00E-06
2.5mm-5mm 5mm-10mm 10mm-15mm 15mm-20mm 20mm-25mm mixed
1.00E-11
permeability k/m2
4
1.00E-12 1.00E-13 1.00E-14 1.00E-15 0.000
1.00E-05
1.00E-04 1.00E-03
0.100
0.200
seepage velocity V/ ms-1
0.300
0.400
0.500
porosity
1.00E-02
Fig. 5. The curve of permeability vs porosity of crushed gangues with different diameters.
Fig. 3. The curve of pressure gradient vs seepage velocity of crushed gangues with different porosities.
gangues. After further compaction, the crushed gangues become denser and denser, so that the seepage velocity becomes smaller and smaller. By comparison, the fragmentation of the crushed gangues with smaller diameter is limited, thus the void space between the crushed gangues with similar diameter may form effective channels, enhancing seepage velocity. For the crushed gangues with mixed diameter, the smaller ones can fully fill the space at the initial stage of charging, which leads to smaller initial porosity compared to those with uniform diameter. With continuous loading, they have higher randomness and uncertainty than those with uniform diameter and probably form a temporary channel in the process of pore structure adjustment under a certain porosity level, leading to larger flow and faster seepage velocity, which could leap two magnitudes with the pore pressure of the relief valve increasing. The seepage velocity of the crushed gangues with diameter in range of 10–15 mm also leaps two magnitudes because their compaction level increased from the first level to the fourth level. As shown in Figs. 3 and 4, seepage velocity is affected by several factors, including particle size, the proportion of mixture, the pore pressure of the relief valve, the compaction level in the previous stages and porosity. Thus, the compaction level of the crushed gangues with different diameter but same porosity is not equal at different seepage condition. As shown in Fig. 5, when porosities is 0.174, the compaction level of the crushed gangues with mixed diameter and diameter in range of 2.5–5 mm is in the third level, while that of other diameters is in the fourth or fifth level. 3.2. The relationship between permeability and porosity
pressure gradient Gp/Pam-1
Fig. 5 shows the relationship curve between the non-Darcy flow permeability k and the porosity of the crushed gangues with different diameters. As shown, the permeability of the gangues with uniform diameter decreases as the diameter increases. In addition, permeability of the gangues with mixed diameters is larger than those with uniform diameter. This phenomenon could be explained as follows. During the compaction process, the crushed gangues experience constant fragmentation, reconstruction and compaction. Those with larger diameter
1.00E+09
2.5mm-5mm 5mm-10mm 10mm-15mm 15mm-20mm 20mm-25mm mixed
1.00E+08 1.00E+07 1.00E+06 1.00E-05
1.00E-04
1.00E-03
seepage velocity V/
1.00E-02
ms-1
Fig. 4. The curve of pressure gradient vs seepage velocity of crushed gangues with same porosity, but different diameters.
have much wider diameter distribution range after fragmentation, thus the crushed gangues with smaller diameter could effectively fill the void space between the crushed gangues with larger diameter. As consequence, the permeability reduces. The randomness and uncertainty of gangues with mixed diameters are larger than those with uniform diameter during the initial stage of charging and loading process, thus a temporary channel is easily formed in the process of pore structure adjustment, lading to increased permeability. It can also be seen from Fig. 5, the non-Darcy flow permeability of the crushed gangues decreases with porosity decrease and is in the magnitude of 10 −12 to 10 −15 m 2 in the compaction process. Thus, the crushed gangues are impermeable eventually and the curve of permeability vs porosity can be divided into two stages on the base of the concavity and convexity of the curve. Fig. 6 is the schematic curve of permeability vs porosity of the crushed gangues with diameter of 15–20 mm. As shown, the curve changes from concavity to convexity with the porosity decreasing in the whole compaction process of the crushed gangues. Obviously, the ratio of permeability alters. The curve is fitted by cubic polynomial as k ¼ 7 10
−11
3
ϕ − 4 10
−13
− 6 10
−11
2
−12
ϕ þ 9 10
ϕ
ð0:122≤ϕ≤0:402Þ
with correlation coefficient of 0.991. The inflection point ϕ = 0.191 is easily conformed when the second derivative of permeability to porosity is zero and used as a piecewise point to divide the curve into two stages. The piecewise point porosities of the crushed gangues with other five diameters also can be conformed similarly and are listed in Table 3. It is obvious that the cubic polynomials used to fit the permeability–porosity curve have better correlation coefficient. The piecewise points porosities of the crushed gangues with different diameters are closely related with their respective porosities in the first and last levels, as shown in Fig. 5. At the stage I, the porosity of the crushed gangues decreases to the piecewise point porosity, at which the crushed gangues start to be compacted. First, the edges and corners of the crushed gangues are crushed off and then the particles are crushed to much finer particles, which then rearrange and fill into the spaces between the larger particles. At this time, the crushed gangues have relatively larger porosity and relatively higher permeability. As the porosity decreases, the permeability reduces greatly from the magnitude of 10 −12 to 10 −14 m 2. It was observed during the experiment that the liquid seepage was more turbid. The reason is that with the pressure gradient increase, finer particles are flushed out. At the stage II, the porosity of the crushed gangues decreases from the piecewise point porosity to that at the last level, at which the crushed gangues remain under pressure, and particles fragment more severely. During this compaction process, small particles are squeezed and become denser and denser. Thus, the porosity is relatively small, and the permeability decreases with the porosity decrease. However,
Please cite this article as: Kong, H., et al., Experimental study on permeability of crushed gangues during compaction, Int. J. Miner. Process. (2013), http://dx.doi.org/10.1016/j.minpro.2013.04.012
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5
permeability k/m2
1.00E-12
1.00E-13
1.00E-14
1.00E-15 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
porosity Fig. 6. The diagram curve of permeability vs porosity of crushed gangues at different stages.
the permeability varies only slightly in the magnitude range of 10−14 to 10−15 m 2. At this stage, the liquid seepage is not turbid. The reason is that after stage I the particles are round enough, so no more edges and corners are off and no fine particles can be flushed out. The permeability of crushed gangues decreases obviously and significantly to 10 −15 m 2 after stage II, and the gangues as a filling material has good impermeable property. Supposing the crushed gangues are compressed continuously in the test, with the porosity further decreasing, their permeability decreases to lower than 10 −15 m 2, which cannot be measured unless increasing pore pressure of the relief valve. Therefore, the crushed gangues will break under high osmotic pressure difference, and instability of seepage flow occurs, indicating that measurement of seepage is insignificant any more, as discussed previously (Wang et al., 2013). 3.3. The relationship between non-Darcy flow β factor and porosity Fig. 7 shows the relationship curve of non-Darcy flow β factor and porosity of the crushed gangues. As can be seen, the absolute value of the non-Darcy flow β factor shows an overall increasing trend with the porosity decrease and is in the magnitude of 10 11–10 14 m −1. When the diameter is below 10 mm, with the porosity decrease, the value of non-Darcy flow β factor changes from negative to positive; while when the diameter is greater than 10 mm, its value is always negative at different porosities. From literature (Wang et al., 2013) we know that negative β factor is prerequisite for seepage instability. Therefore, if the sufficient condition for seepage instability is satisfied (pressure gradient reaches a
Table 3 Piecewise points of the permeability–porosity curve of the crushed gangues with different diameters. Diameters
Fitting function
Correlation coefficient
Piecewise points
2.5–5 mm
k = 5 × 10−10φ3 − 2 × 10−10φ2 + 3 × 10−11φ − 7 × 10−13 (0.0316 ≤ φ ≤ 0.427) k = 9 × 10−10φ3 − 6 × 10−10φ2 + 1 × 10−10φ − 7 × 10−12 (0.122 ≤ φ ≤ 0.432) k = 1 × 10−9φ3 − 9 × 10−10φ2 + 2 × 10−10φ − 2 × 10−11 (0.174 ≤ φ ≤ 0.438) k = 1 × 10−11φ3 − 6 × 10−12φ2 + 1 × 10−12φ − 8 × 10−14 (0.126 ≤ φ ≤ 0.376) k = 7 × 10−10φ3 − 3 × 10−10φ2 + 4 × 10−11φ − 2 × 10−12 (0.0822 ≤ φ ≤ 0.276)
0.998
0.133
0.998
0.222
0.994
0.300
0.998
0.200
0.996
0.143
5–10 mm
10–15 mm
20–25 mm
Mixed diameters
certain value), the crushed gangues with diameter larger than 10 mm at different porosities may lose its impermeable property, while the crushed gangues with diameter less than 10 mm and mixed diameter have strong impermeable property and could loose its permeable property only when the porosity is large enough. 4. Experimental phenomena and discussion In this paper, we changed the pore structure by controlling the axial compression force on the crushed gangues in the cylinder by which further correspondingly changed its seepage velocity, permeability and non-Darcy β flow factor. Obviously, the particle size and distribution have great impacts on the compacted permeability of the crushed gangues. Furthermore, during the compaction process, the change of pore structure is crucial for permeability. However, the final shape of the compacted gangues is unrelated to their size, but only related to their final porosity. As shown in Fig. 8(a), the smaller the final porosity is, the denser the compacted gangues and the higher the integrity are. As shown in Fig. 8(c), the larger the final porosity is, the looser the obtained crushed gangues are. 5. Conclusions By observing and analyzing the experimental phenomena of permeability property crushed gangues in 6 different sizes under different compact pressure, we conclude that: (1) The seepage of the crushed gangues under compaction is nonlinear. (2) The seepage velocity of the crushed gangues is related to their particle size, proportion of mixture, pore pressure of the relief valve, compaction degree in the previous stage and porosity, and in the range of 10 −5 to 10 −3 ms −1. At fixed diameter, the seepage velocity decreases with the porosity decrease and the pressure gradient increase. At fixed porosity, the seepage velocity of the crushed gangues with larger uniform diameter decreases with the pressure gradient increase and the seepage velocity of the crushed gangues with mixed diameter and diameter of 10–15 mm increases from 10 −5 ms −1 to 10 −4 ms −1. For crushed gangues of the same size, the greater the diameter is, the slower the seepage velocity is and the greater the pressure gradient is. Among them the mixed sizes have the lowest pressure gradient. (3) The permeability of the crushed gangues is related to their porosity, particle diameter, particle diameter distribution, and pore structure. The larger the single particle diameter is, the smaller the permeability is. The permeability of the crushed gangues with mixed diameter is the largest. As the porosity
Please cite this article as: Kong, H., et al., Experimental study on permeability of crushed gangues during compaction, Int. J. Miner. Process. (2013), http://dx.doi.org/10.1016/j.minpro.2013.04.012
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(b) 5~10 mm factor
(a) 2.5~5 mm
/m-1
8.00E+12 4.00E+12 0.00E+00 -4.00E+12 -8.00E+12 0.00
0.10
0.20
0.30
0.40
0.50
6.00E+12 4.50E+12
/m-1
1.20E+13
non Darcy flow
6
3.00E+12 1.50E+12 0.00E+00 -1.50E+12 0.00
0.10
0.20
(c) 10~15mm
(d) 15~20 mm non Darcy flow factor
-2.00E+11 -4.00E+11 -6.00E+11 0.10
0.20
0.30
0.40
-2.80E+14 -3.50E+14 0.00
0.50
0.10
0.20
0.30
factor
porosity
factor
-2.00E+13 -4.00E+13 -6.00E+13 0.30
0.40
2.40E+13 1.80E+13
/m-1
0.00E+00
non Darcy flow
non Darcy flow /m-1
0.50
-2.10E+14
(f) mixed gangues
0.20
0.40
-1.40E+14
(e) 20~25 mm
0.10
0.50
-7.00E+13
porosity
-8.00E+13 0.00
0.40
0.00E+00
/m-1
0.00E+00
-8.00E+11 0.00
0.30
porosity
non Darcy flow factor /m-1
porosity
1.20E+13 6.00E+12 0.00E+00 -6.00E+12 0.05
0.10
porosity
0.15
0.20
0.25
0.30
porosity
Fig. 7. The curve of non-Darcy flow β factor vs porosity of crushed gangues with different diameters.
decreases, the permeability decreases and is in the range of 10 −15–10 −12 m 2. (4) The curve of permeability vs porosity can be divided into two stages. At stage I, the permeability of the crushed gangues varies dramatically from 10 −14 to10 −12 m 2. At stage II, the permeability of the crushed gangues varies slightly from 10 −14 to 10 −15 m 2. After stage II, the crushed gangues are under compaction and have better water blocking and impermeable properties. (5) The non-Darcy flow β factor of the crushed gangues is related to the porosity and particle diameter. Its absolute value shows an
overall increasing trend as the porosity reduces and is in the range of 10 11–10 14 m −1. When the crushed gangues have mixed diameter or diameter less than 10 mm, as the porosity decreases, the value of β factor changes from negative to positive; when the crushed gangues have a diameter greater than 10 mm, the value of β factor is negative under any porosity. When certain conditions are met, the crushed gangues with diameter greater than 10 mm may lose their impermeable property, while the crushed gangues with diameter less than 10 mm and mixed diameter have enhanced impermeability as porosity decreases.
Fig. 8. Compaction degree of the crushed gangues after the test.
Please cite this article as: Kong, H., et al., Experimental study on permeability of crushed gangues during compaction, Int. J. Miner. Process. (2013), http://dx.doi.org/10.1016/j.minpro.2013.04.012
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(6) The compaction seepage process of the crushed gangues is associated with fragmentation and reorganization of the particles. With porosity decrease, the shape of the crushed gangues is basically unrelated with their diameter, but is related with their final porosity: the smaller the final porosity, the denser and more compact the crushed gangues are. Acknowledgment The work was financially supported by the National Nature Science Fund (50974107), University Graduate Research and Innovation Project in Jiangsu province (CXZZ12_0924), Applied Basic Research Projects of Yancheng Institute of Technology (XKR2010010) and State Key Laboratory Open Foundation of Deep Geomechanics and Underground Engineering of University of Mining and Technology, China (SKLGDUEK1014). References Butler, E.P., 1974. Utilization of Coalmine Refuse in the Construction of Highway Embankments. Coal and the Environ Tech. Symposium on Mine and Preplant Refuse Dispose. National Coal Association, USA, Louisville, pp. 22–24. Chen, Z.Q., Li, S.C., Pu, H., et al., 2010. Mining Rock Creep and Seepage Coupling Dynamics. Science Press, Beijing. Jiang, Z.Q., Zhao, D.H., Sui, W.H., Guo, Q.Y., 1999. Study on relationship between consolidation compactness and size grade shortage of coal gangue. J. China Univ. Min. Technol. 28 (3), 212–216.
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Jiang, Z.Q., Ji, L.J., Zuo, R.S., 2001. Research on mechanism of crushing-compression of coal waste. J. China Univ. Min. Technol. 30 (2), 139–142. Li, S.C., Miao, X.X., Chen, Z.Q., et al., 2008. Experimental study on seepage properties of non-Darcy flow in confined crushed rocks. Eng. Mech. 25 (4), 85–92. Liu, Y., Wang, W.K., Jiang, H.Q., Liang, Z.Y., 2011. Experimental Study of Nonlinear Seepage in Mixed Granular Rock. Min. Res. Dev. 31 (5), 27–29 (98). Ma, Z.G., Pu, H., Zhang, F., et al., 2003. Study on compaction characteristics of gangue. Undergr. Press. Manag. 1, 95–96. Ma, Z.G., Xiao, J.H., Wu, Y.L., et al., 2004. Study on compaction characteristics of saturated gangue. Undergr. Press. Manag. 1, 106–108. Miao, X.X., Chen, Z.Q., Liu, W.Q., 2004. Seepage theory of mining rock. Science Press, Beijing. Michalski, P., Skarzynska, K.M., 1984. Compactability of Coal Mining Wastes as a Fill Material. Treatment and Utilization of coal mining wastes. Symposium on the Reclamation. British coal corporation, Durham, England. Qi, A.G., Hu, W., Tao, Y.H., 2004. Experimental study on compaction characteristics of gangue. Min. Technol. 4 (4), 14–16. Rainbow, K.M., Skarzynska, K.M., 1987. Mine stone impoundment dams for fluid fly ash storage. In: Rainbow, A.K.M. (Ed.), 2nd Symposium on the Reclamation, Treatment and Utilization of coal mining wastes. British coal corporation, Netherlands, pp. 219–238. Solesbury, F.W., 1987. Coal wastes in civil engineering works: two case histories from south Africa. In: Rainbow, A.K.M. (Ed.), 2nd Symposium on the Reclamation, Treatment and Utilization of coal mining wastes. British coal corporation, Netherlands, pp. 207–218. Tu, Q., Zhang, X.F., Liu, P.L., et al., 2009. Experimental study on different particle size gradation gangue compaction deformation. Coal. Eng. 11, 68–70. Wang, F.J., 2006. Grain breakage effect on the permeability properties of coal gangue. Geotech. Eng. Tech. 20 (3), 147–150. Wang, L.Z., Chen, Z.Q., Shen, H.D., 2013. Experimental study on the type change of liquid flow in crushed coal. J. China Coal Soc. 19 (1), 19–25.
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International Journal of Mineral Processing journal homepage: www.elsevier.com/locate/ijminpro
Experimental study on permeability of crushed gangues during compaction Hailing Kong a, Zhanqing Chen b, c, Luzhen Wang a, c,⁎, Haide Shen b a b c
Department of Fundamental Sciences Teaching, Yancheng Institute of Technology, Yancheng 224051, China School of Mechanics and Civil Engineering, China University of Mining and Technology (Xuzhou), Xuzhou 221008, China State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology (Xuzhou), Xuzhou, 221008, China
a r t i c l e
i n f o
Article history: Received 18 October 2012 Received in revised form 24 April 2013 Accepted 27 April 2013 Available online xxxx Keywords: Crushed gangue Compaction Permeability Experimental test
a b s t r a c t Using a crushed rock compaction permeation apparatus and a self-designed seepage circuit, we tested the permeability of crushed gangues with six different particle sizes during compaction on the CMT5305 electronic universal testing machine and analyzed the relationships of seepage velocity, permeability and non-Darcy β factor to the porosity, particle size and diameter distribution. The results show that 1) The seepage flow of crushed gangues during compaction is nonlinear, and their compactability after compaction is related to their final porosity; 2) the seepage velocity of crushed gangues of same size decreases with pressure gradient increase and with porosity decrease, and varies less than that of crushed gangues of same porosity and mixed size or size between 10 and 15 mm. Moreover, the greater the single particle size is, the greater the pressure gradient. In addition, the mixed gangues have the lowest pressure gradient; 3) the permeability of gangues of same size decreases with their size increase and that of the mixed gangues is the largest; 4) the relationship of permeability to porosity can be divided into two stages with porosity decrease. At the stage II, permeability decreases significantly by the magnitude of 2 to 3 compared to that at the stage I. After stage II, the permeability of crushed gangue decreases to the magnitude of 10−15 m2, while the impermeability increases; 5) the non-Darcy β factor is negative for gangues with size larger than 10 mm, while that gradually becomes positive with porosity decrease for mixed gangues and gangues with size less than 10 mm. Moreover, non-Darcyβ factors affect the impermeability of gangues. The results will provide references for gangues as filling materials. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Gangues are solid waste during the production process of coal industry. But its utilization prospect at home and abroad has been more optimistic especially as filling materials for goaf, embankment (dike) and water dams. Thus, their compaction bearer, strength, deformation, impermeability, drainage and seepage have become key issues to be solved urgently. Many scholars at home and abroad have tested the gangues' compaction characteristics experimentally. Butler (1974), Michalski and Skarzynska (1984), Solesbury (1987) and Rainbow and Skarzynska (1987) have pointed out that the available density of gangues is correlated with its particle size distribution. Jiang et al. (1999, 2001) have experimentally studied the compaction characteristics of gangues mixed with coal ash and clay, explored the relationships of its compactability to its crushing degree. Ma et al. (2003, 2004) experimentally summarized the strain, Poisson's ratio and elasticity modulus of loose gangues during compaction process, theoretically analyzed the ⁎ Corresponding author at: Department of Fundamental Sciences Teaching, Yancheng Institute of Technology, Yancheng 224051, China. Tel.: + 86 11 86 15851060692; fax: + 86 11 86 515 88168221. E-mail address: [email protected] (L. Wang).
compacting deformation mechanisms and measured the stress–strain and porosity–stress relationships of the saturated gangues, etc. Qi et al. (2004) tested and discussed the influence of particle sizes of gangues on their compaction characteristics. Tu et al. (2009) experimentally studied the relationship between the filling gangues with different grade of particle sizes and the compaction amount. However, the permeability of gangues during compaction is not well studied. Wang (2006) studied the effects of crushing degree through compaction trials on the permeability of gangues, and found that the exponential function could describe the relationship between the permeability and porosity of gangues and that the permeability decreased significantly with fine particle amount increase. However, he did not further analyze the impact of particle size on this function. Li et al. (2008) tested the permeability of crushed rock including gangues based on the MTS815.02 rock mechanics servo system. However, in their experiments, the MTS turbocharger volume was too small, and the test time for permeability was too short, thus the seepage velocity and pore pressure gradient range were limited, the obtained permeability at the initial loading period was very unstable, and the correlation curve between permeability and porosity of the gangues with larger particle size fluctuated greatly. Liu et al. (2011) utilized the system, obtained the permeability of the graded crushed gangues and concluded that the permeability of the gangues was
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Please cite this article as: Kong, H., et al., Experimental study on permeability of crushed gangues during compaction, Int. J. Miner. Process. (2013), http://dx.doi.org/10.1016/j.minpro.2013.04.012
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related to their particle size, particle arrangement and pore structure. However, they did not further study the permeability of gangue with different sizes. The study used a self-designed seepage circuit composed of a permeability tester, a gear pump, a pressure relief valve and the CMT5305 electronic universal testing machine, measured the permeability characteristics of crushed gangues with six different sizes during compaction, and provided a theoretical guidance for permeability and impermeability characteristics of gangues as filling materials in engineering projects. 2. Experiment system and method The test system for the permeability characteristics of the crushed gangues under compaction mainly consists of a CMT5305 electronic universal testing machine, crushed rock compaction containing cylinder (Miao et al., 2004) and a self-designed seepage circuit, which is composed of gear pump, pressure gauge, direction valve, cut-off valve, pressure transmitter, flow transmitter, etc, as shown in Fig. 1. The gangues used in this test were collected from LuAn Mine in Shanxi Province. Their mass density ρ was 1526 kg/m 3 and their average uniaxial compression strength was 76.27 MPa as measured by uniaxial compression test. Then the crushed gangues were selected based on their particle diameter and grouped into five groups with diameter of 2.5–5 mm, 5–10 mm, 10–15 mm, 15–20 mm and 20– 25 mm, respectively. The mixed group was composed of those five gangues at mass ratio of 1:1:1:1:1. The permeability of crushed gangues was tested in triplicates and the average was used for analysis. In brief, a certain amount (m) of crushed gangues were packed into the cylinder of inner diameter of 2a (2a = 68) mm and height of 110 mm and connected to the electronic universal testing machine. Its height (ho) under natural pressure was recorded and used to calculate the initial porosity (ϕ0) of
the crushed gangues. Table 1 lists the formula used for porosity calculation and the controlled, recorded and calculated parameters used in the test. Then the load was applied to the piston of the electronic universal testing machine in accordance with the displacement control during the test. Considering the polytropy and complexity of the gangues, the displacement increment of piston was set as five levels (i.e. gangue compaction), for example, from 15 mm, 5 mm, 5 mm, 3 mm to 2 mm, or from 10 mm, 5 mm, 5 mm, 5 mm to 3 mm, depending on the maximum flow in the previous level and flow under the initial pressure of the relief valve at current level, and used to calculate the porosity (ϕi) at each level (i = 1, 2, 3, 4, 5). Under the pressure, the pore structure of the crushed gangues changed. With the axial pressure on crushed gangues increasing, its internal pore space became smaller and smaller. Under each level of compaction, the pore pressure Δρj (j = 1, 2, 3, 4) of the relief valve was set as four levels. When the porosity was large, the increment of the pore pressure of the relief valve was set as 0.5 MPa, meaning the pore pressure was set as 0.5 MPa, 1.0 MPa, 1.5 MPa, and 2.0 MPa at the first level to the fourth level. As the porosity decrease, the increment was set as 1.0 MPa, meaning the pressure was set as 3 MPa, 4 MPa, 5 MPa and 6 MPa. Fig. 2 shows the flowchart of the test. With the pore pressure of the relief valve changes, the pressure gradient Gp and seepage velocity V change accordingly. Under Darcy flow pressure gradient, Gp and V obey the linear relationship, while under the Forchheimer non-Darcy flow pressure gradient Gp and V obey the quadratic polynomial relationship. The relationship of Gp to V was fitted using both linear and quadratic polynomial formula. Meanwhile, the permeability and non-Darcy flow β factor of the crushed gangues were calculated using the least squares fit method (Chen et al., 2010). In this way, seepage velocity, permeability and non-Darcy flow β factor of the crushed gangues with six particle diameters under different porosity level were measured.
3. Experiment results and analysis
10 9 8 7 p
6 5 4
3.1. The relationship between pressure gradient and seepage velocity Table 2 lists the test results of pressure gradient and seepage velocity of the crushed gangues with diameters of 15–20 mm with compaction amount increase, the linear fitting formula and its coefficient based on Darcy flow, the quadratic polynomial fitting formula and its coefficient based on Forchheimer non-Darcy flow, and the calculated non-Darcy flow permeability k and non-Darcy flow β factor. Obviously, the quadratic polynomial fitting is better than the linear fitting, indicating that the seepage of crushed gangues under compaction is non-Darcy flow. Fig. 3 shows the curve of pressure gradient vs seepage velocity of the crushed gangues with diameter of 15–20 mm and different porosity. It can be seen that as the porosity decreases, the pressure gradient increases, the seepage velocity reduces from 10−3 ms−1 to 10 −5 ms−1. Obviously, as the crushed gangue being compacted constantly, the
3 2 M
1
Fig. 1. The seepage test system. 1. Oil tank, 2. filter, 3. gear pump, 4. pressure gauge, 5. switch valve, 6. shutoff valve, 7. pressure transmitter, 8. flow transmitter, 9. permeability tester, 10. material testing machine.
Table 1 Parameters used in the test. Parameter
Sign
Unit
Type
Initial height of the crushed gangues Initial porosity Displacement increment of piston Current height of the crushed gangues Porosity Pore pressure of the relief valve Pressure gradient Seepage amount Seepage velocity
h0 ϕ0 ¼ 1− ρπam2 h 0 Δhi hi = h0 − ∑ Δhi
mm None mm mm
Recorded Calculated Controlled Calculated
ϕi ¼ 1− ρπam2 h i Δpj Δp Gp ¼ hi j Q V ¼ πaQ2
None MPa Mpa m−1 mL M s−1
Calculated Controlled Calculated Recorded Calculated
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calculate the initial porosity initial load 0.2kN, zero diaplacement start gear pump, injected and saturated
load axial displacement
record the compacted displacement
keep axial displacement
calculate porosity
change pore pressure of the relief valve
change the axial displacement
start relief valve
record pore pressure of the relief valve
keep pore pressure of the relief valve
calculate pressure gradient
seepage liquid
record seepage time and flow
seepage completed
NO
different pore pressure of the relief valve tests completed
NO
different axial displacement tests completed
test completed Fig. 2. The flowchart for testing permeability of crushed gangues.
seepage velocity will reduce and the pressure of the relief valve will increase correspondingly. Fig. 4 shows the curves of pressure gradient vs seepage velocity of the crushed gangues with the same porosity (0.174) but 6 different diameters. As shown, with pressure gradient increasing, the seepage velocity of crushed gangues with diameter smaller than 10 mm is in the magnitude of 10 −4 ms −1; that of crushed gangues with diameter larger than 15 mm is in the magnitude of 10 −5 ms −1; that of crushed gangues with diameter in range of 10–15 mm or with mixed diameter varies greatly from magnitude of 10 −4 to 10 −5 ms −1.
Fig. 4 also shows that when the crushed gangues have uniform diameter, the greater the diameter is, the greater the pressure gradient is; and when the crushed gangues have mixed diameter, their pressure gradient is smaller. The results that the crushed gangues with larger diameter have smaller seepage velocity could be explained as follows. After several compaction stages at certain porosity, the crushed gangues are fragmented. The larger the diameter is, the wider the diameter distributes after compaction. Those crushed gangues with smaller diameter could effectively fill the void spaces between the larger crushed
Table 2 Permeability of the crushed gangues with diameter of 15–20 mm. Compaction Δh/mm
Porosity ϕ
Pressure gradient Gp/Pa.m−1
15
0.402
20
0.331
25
0.241
28
0.174
30
0.122
1.06 2.50 3.19 4.10 2.40 5.10 7.50 9.30 5.50 7.70 9.80 1.14 5.88 9.10 1.22 1.47 1.25 1.56 1.88 2.19
× × × × × × × × × × × × × × × × × × × ×
107 107 107 107 107 107 107 107 107 107 107 108 107 107 108 108 108 108 108 108
Seepage velocity V/m.s−1 2.95 4.63 5.85 1.04 3.92 7.13 1.56 3.31 2.60 3.37 5.18 9.08 1.78 2.19 3.22 5.33 7.91 1.12 1.81 4.11
× × × × × × × × × × × × × × × × × × × ×
10−4 10−4 10−4 10−3 10−5 10−5 10−4 10−4 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−6 10−5 10−5 10−5
Linear fitting and its correlation
Quadratic fitting and its correlation
Non-Darcy flow permeability k/m2
Non-Darcy flow β factor/m−1
Gp = 41 × 1010 V R2 = 0.822
Gp = −1.92 × 1013 V2 + 6.02 × 1010 V R2 = 0.913
3.26 × 10−13
−2.20 × 1010
Gp = 3.35 × 1011 V R2 = 0.680
Gp = −1.30 × 1015 V2 + 7.10 × 1011 V R2 = 0.975E
2.76 × 10−14
−1.49 × 1012
Gp = 1.53 × 1012 V R2 = 0.0579
Gp = −1.61 × 1016 V2 + 2.72 × 1012 V R2 = 0.981
7.21 × 10−15
−1.84 × 1013
Gp = 3.17 × 1012 V R2 = 0.694
Gp = −3.59 × 1016 V2 + 4.71 × 1012 V R2 = 0.938
4.16 × 10−15
−4.11 × 1013
Gp = 6.86 × 1012 V R2 = −2.95
Gp = −2.61 × 1017 V2 + 1.60 × 1013 V R2 = 0.879
1.23 × 10−15
−2.99 × 1014
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0.403 0.331 0.241 0.174 0.122
pressure gradient Gp/Pam-1
2.50E+08 2.00E+08 1.50E+08 1.00E+08 5.00E+07 0.00E+00 1.00E-06
2.5mm-5mm 5mm-10mm 10mm-15mm 15mm-20mm 20mm-25mm mixed
1.00E-11
permeability k/m2
4
1.00E-12 1.00E-13 1.00E-14 1.00E-15 0.000
1.00E-05
1.00E-04 1.00E-03
0.100
0.200
seepage velocity V/ ms-1
0.300
0.400
0.500
porosity
1.00E-02
Fig. 5. The curve of permeability vs porosity of crushed gangues with different diameters.
Fig. 3. The curve of pressure gradient vs seepage velocity of crushed gangues with different porosities.
gangues. After further compaction, the crushed gangues become denser and denser, so that the seepage velocity becomes smaller and smaller. By comparison, the fragmentation of the crushed gangues with smaller diameter is limited, thus the void space between the crushed gangues with similar diameter may form effective channels, enhancing seepage velocity. For the crushed gangues with mixed diameter, the smaller ones can fully fill the space at the initial stage of charging, which leads to smaller initial porosity compared to those with uniform diameter. With continuous loading, they have higher randomness and uncertainty than those with uniform diameter and probably form a temporary channel in the process of pore structure adjustment under a certain porosity level, leading to larger flow and faster seepage velocity, which could leap two magnitudes with the pore pressure of the relief valve increasing. The seepage velocity of the crushed gangues with diameter in range of 10–15 mm also leaps two magnitudes because their compaction level increased from the first level to the fourth level. As shown in Figs. 3 and 4, seepage velocity is affected by several factors, including particle size, the proportion of mixture, the pore pressure of the relief valve, the compaction level in the previous stages and porosity. Thus, the compaction level of the crushed gangues with different diameter but same porosity is not equal at different seepage condition. As shown in Fig. 5, when porosities is 0.174, the compaction level of the crushed gangues with mixed diameter and diameter in range of 2.5–5 mm is in the third level, while that of other diameters is in the fourth or fifth level. 3.2. The relationship between permeability and porosity
pressure gradient Gp/Pam-1
Fig. 5 shows the relationship curve between the non-Darcy flow permeability k and the porosity of the crushed gangues with different diameters. As shown, the permeability of the gangues with uniform diameter decreases as the diameter increases. In addition, permeability of the gangues with mixed diameters is larger than those with uniform diameter. This phenomenon could be explained as follows. During the compaction process, the crushed gangues experience constant fragmentation, reconstruction and compaction. Those with larger diameter
1.00E+09
2.5mm-5mm 5mm-10mm 10mm-15mm 15mm-20mm 20mm-25mm mixed
1.00E+08 1.00E+07 1.00E+06 1.00E-05
1.00E-04
1.00E-03
seepage velocity V/
1.00E-02
ms-1
Fig. 4. The curve of pressure gradient vs seepage velocity of crushed gangues with same porosity, but different diameters.
have much wider diameter distribution range after fragmentation, thus the crushed gangues with smaller diameter could effectively fill the void space between the crushed gangues with larger diameter. As consequence, the permeability reduces. The randomness and uncertainty of gangues with mixed diameters are larger than those with uniform diameter during the initial stage of charging and loading process, thus a temporary channel is easily formed in the process of pore structure adjustment, lading to increased permeability. It can also be seen from Fig. 5, the non-Darcy flow permeability of the crushed gangues decreases with porosity decrease and is in the magnitude of 10 −12 to 10 −15 m 2 in the compaction process. Thus, the crushed gangues are impermeable eventually and the curve of permeability vs porosity can be divided into two stages on the base of the concavity and convexity of the curve. Fig. 6 is the schematic curve of permeability vs porosity of the crushed gangues with diameter of 15–20 mm. As shown, the curve changes from concavity to convexity with the porosity decreasing in the whole compaction process of the crushed gangues. Obviously, the ratio of permeability alters. The curve is fitted by cubic polynomial as k ¼ 7 10
−11
3
ϕ − 4 10
−13
− 6 10
−11
2
−12
ϕ þ 9 10
ϕ
ð0:122≤ϕ≤0:402Þ
with correlation coefficient of 0.991. The inflection point ϕ = 0.191 is easily conformed when the second derivative of permeability to porosity is zero and used as a piecewise point to divide the curve into two stages. The piecewise point porosities of the crushed gangues with other five diameters also can be conformed similarly and are listed in Table 3. It is obvious that the cubic polynomials used to fit the permeability–porosity curve have better correlation coefficient. The piecewise points porosities of the crushed gangues with different diameters are closely related with their respective porosities in the first and last levels, as shown in Fig. 5. At the stage I, the porosity of the crushed gangues decreases to the piecewise point porosity, at which the crushed gangues start to be compacted. First, the edges and corners of the crushed gangues are crushed off and then the particles are crushed to much finer particles, which then rearrange and fill into the spaces between the larger particles. At this time, the crushed gangues have relatively larger porosity and relatively higher permeability. As the porosity decreases, the permeability reduces greatly from the magnitude of 10 −12 to 10 −14 m 2. It was observed during the experiment that the liquid seepage was more turbid. The reason is that with the pressure gradient increase, finer particles are flushed out. At the stage II, the porosity of the crushed gangues decreases from the piecewise point porosity to that at the last level, at which the crushed gangues remain under pressure, and particles fragment more severely. During this compaction process, small particles are squeezed and become denser and denser. Thus, the porosity is relatively small, and the permeability decreases with the porosity decrease. However,
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permeability k/m2
1.00E-12
1.00E-13
1.00E-14
1.00E-15 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
porosity Fig. 6. The diagram curve of permeability vs porosity of crushed gangues at different stages.
the permeability varies only slightly in the magnitude range of 10−14 to 10−15 m 2. At this stage, the liquid seepage is not turbid. The reason is that after stage I the particles are round enough, so no more edges and corners are off and no fine particles can be flushed out. The permeability of crushed gangues decreases obviously and significantly to 10 −15 m 2 after stage II, and the gangues as a filling material has good impermeable property. Supposing the crushed gangues are compressed continuously in the test, with the porosity further decreasing, their permeability decreases to lower than 10 −15 m 2, which cannot be measured unless increasing pore pressure of the relief valve. Therefore, the crushed gangues will break under high osmotic pressure difference, and instability of seepage flow occurs, indicating that measurement of seepage is insignificant any more, as discussed previously (Wang et al., 2013). 3.3. The relationship between non-Darcy flow β factor and porosity Fig. 7 shows the relationship curve of non-Darcy flow β factor and porosity of the crushed gangues. As can be seen, the absolute value of the non-Darcy flow β factor shows an overall increasing trend with the porosity decrease and is in the magnitude of 10 11–10 14 m −1. When the diameter is below 10 mm, with the porosity decrease, the value of non-Darcy flow β factor changes from negative to positive; while when the diameter is greater than 10 mm, its value is always negative at different porosities. From literature (Wang et al., 2013) we know that negative β factor is prerequisite for seepage instability. Therefore, if the sufficient condition for seepage instability is satisfied (pressure gradient reaches a
Table 3 Piecewise points of the permeability–porosity curve of the crushed gangues with different diameters. Diameters
Fitting function
Correlation coefficient
Piecewise points
2.5–5 mm
k = 5 × 10−10φ3 − 2 × 10−10φ2 + 3 × 10−11φ − 7 × 10−13 (0.0316 ≤ φ ≤ 0.427) k = 9 × 10−10φ3 − 6 × 10−10φ2 + 1 × 10−10φ − 7 × 10−12 (0.122 ≤ φ ≤ 0.432) k = 1 × 10−9φ3 − 9 × 10−10φ2 + 2 × 10−10φ − 2 × 10−11 (0.174 ≤ φ ≤ 0.438) k = 1 × 10−11φ3 − 6 × 10−12φ2 + 1 × 10−12φ − 8 × 10−14 (0.126 ≤ φ ≤ 0.376) k = 7 × 10−10φ3 − 3 × 10−10φ2 + 4 × 10−11φ − 2 × 10−12 (0.0822 ≤ φ ≤ 0.276)
0.998
0.133
0.998
0.222
0.994
0.300
0.998
0.200
0.996
0.143
5–10 mm
10–15 mm
20–25 mm
Mixed diameters
certain value), the crushed gangues with diameter larger than 10 mm at different porosities may lose its impermeable property, while the crushed gangues with diameter less than 10 mm and mixed diameter have strong impermeable property and could loose its permeable property only when the porosity is large enough. 4. Experimental phenomena and discussion In this paper, we changed the pore structure by controlling the axial compression force on the crushed gangues in the cylinder by which further correspondingly changed its seepage velocity, permeability and non-Darcy β flow factor. Obviously, the particle size and distribution have great impacts on the compacted permeability of the crushed gangues. Furthermore, during the compaction process, the change of pore structure is crucial for permeability. However, the final shape of the compacted gangues is unrelated to their size, but only related to their final porosity. As shown in Fig. 8(a), the smaller the final porosity is, the denser the compacted gangues and the higher the integrity are. As shown in Fig. 8(c), the larger the final porosity is, the looser the obtained crushed gangues are. 5. Conclusions By observing and analyzing the experimental phenomena of permeability property crushed gangues in 6 different sizes under different compact pressure, we conclude that: (1) The seepage of the crushed gangues under compaction is nonlinear. (2) The seepage velocity of the crushed gangues is related to their particle size, proportion of mixture, pore pressure of the relief valve, compaction degree in the previous stage and porosity, and in the range of 10 −5 to 10 −3 ms −1. At fixed diameter, the seepage velocity decreases with the porosity decrease and the pressure gradient increase. At fixed porosity, the seepage velocity of the crushed gangues with larger uniform diameter decreases with the pressure gradient increase and the seepage velocity of the crushed gangues with mixed diameter and diameter of 10–15 mm increases from 10 −5 ms −1 to 10 −4 ms −1. For crushed gangues of the same size, the greater the diameter is, the slower the seepage velocity is and the greater the pressure gradient is. Among them the mixed sizes have the lowest pressure gradient. (3) The permeability of the crushed gangues is related to their porosity, particle diameter, particle diameter distribution, and pore structure. The larger the single particle diameter is, the smaller the permeability is. The permeability of the crushed gangues with mixed diameter is the largest. As the porosity
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(b) 5~10 mm factor
(a) 2.5~5 mm
/m-1
8.00E+12 4.00E+12 0.00E+00 -4.00E+12 -8.00E+12 0.00
0.10
0.20
0.30
0.40
0.50
6.00E+12 4.50E+12
/m-1
1.20E+13
non Darcy flow
6
3.00E+12 1.50E+12 0.00E+00 -1.50E+12 0.00
0.10
0.20
(c) 10~15mm
(d) 15~20 mm non Darcy flow factor
-2.00E+11 -4.00E+11 -6.00E+11 0.10
0.20
0.30
0.40
-2.80E+14 -3.50E+14 0.00
0.50
0.10
0.20
0.30
factor
porosity
factor
-2.00E+13 -4.00E+13 -6.00E+13 0.30
0.40
2.40E+13 1.80E+13
/m-1
0.00E+00
non Darcy flow
non Darcy flow /m-1
0.50
-2.10E+14
(f) mixed gangues
0.20
0.40
-1.40E+14
(e) 20~25 mm
0.10
0.50
-7.00E+13
porosity
-8.00E+13 0.00
0.40
0.00E+00
/m-1
0.00E+00
-8.00E+11 0.00
0.30
porosity
non Darcy flow factor /m-1
porosity
1.20E+13 6.00E+12 0.00E+00 -6.00E+12 0.05
0.10
porosity
0.15
0.20
0.25
0.30
porosity
Fig. 7. The curve of non-Darcy flow β factor vs porosity of crushed gangues with different diameters.
decreases, the permeability decreases and is in the range of 10 −15–10 −12 m 2. (4) The curve of permeability vs porosity can be divided into two stages. At stage I, the permeability of the crushed gangues varies dramatically from 10 −14 to10 −12 m 2. At stage II, the permeability of the crushed gangues varies slightly from 10 −14 to 10 −15 m 2. After stage II, the crushed gangues are under compaction and have better water blocking and impermeable properties. (5) The non-Darcy flow β factor of the crushed gangues is related to the porosity and particle diameter. Its absolute value shows an
overall increasing trend as the porosity reduces and is in the range of 10 11–10 14 m −1. When the crushed gangues have mixed diameter or diameter less than 10 mm, as the porosity decreases, the value of β factor changes from negative to positive; when the crushed gangues have a diameter greater than 10 mm, the value of β factor is negative under any porosity. When certain conditions are met, the crushed gangues with diameter greater than 10 mm may lose their impermeable property, while the crushed gangues with diameter less than 10 mm and mixed diameter have enhanced impermeability as porosity decreases.
Fig. 8. Compaction degree of the crushed gangues after the test.
Please cite this article as: Kong, H., et al., Experimental study on permeability of crushed gangues during compaction, Int. J. Miner. Process. (2013), http://dx.doi.org/10.1016/j.minpro.2013.04.012
H. Kong et al. / International Journal of Mineral Processing xxx (2013) xxx–xxx
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Please cite this article as: Kong, H., et al., Experimental study on permeability of crushed gangues during compaction, Int. J. Miner. Process. (2013), http://dx.doi.org/10.1016/j.minpro.2013.04.012