energies Article
Grain Size Distribution Effect on the Hydraulic Properties of Disintegrated Coal Mixtures Dan Ma 1,2,3, *, Zilong Zhou 1, *, Jiangyu Wu 2 , Qiang Li 2 and Haibo Bai 2 1 2
3
*
School of Resources & Safety Engineering, Central South University, Changsha 410083, Hunan, China State Key Laboratory for Geomechanics & Deep Underground Engineering, China University of Mining & Technology, Xuzhou 221116, Jiangsu, China;
[email protected] (J.W.);
[email protected] (Q.L.);
[email protected] (H.B.) GeoEnergy Research Centre (GERC), University of Nottingham, Nottingham NG7 2RD, UK Correspondence:
[email protected] or
[email protected] (D.M.);
[email protected] (Z.Z.)
Academic Editor: Mehrdad Massoudi Received: 6 April 2017; Accepted: 27 April 2017; Published: 29 April 2017
Abstract: In order to better understand groundwater influx and protection in coal mining extraction works, an in-house water flow apparatus coupled with an industrial rock testing system, known as MTS 815.02, were used to study the effects of grain size mixtures on the compaction and flow properties of disintegrated, or non-cemented, coal samples. From the Reynolds number evaluation of the samples with different grain mixtures, and the relationship between the water flow velocity and pore pressure gradient differences, it was found that seepage through the mixtures are of non-Darcy flow type. The porosity of coal specimens was found to be highly affected by compaction, and the variations of the porosity were also influenced by the samples’ grain size distribution. It was found that the sample porosity decreases with increasing compaction and decreasing grain sizes. Grain crushing during compaction was observed to be the main cause of the appearance of fine grains, and the washing away of fine grains was consequently the main contributing factor for the weight loss due to water seepage. It was observed that during the tests and with the progression of compaction, permeability k decreases and non-Darcy factor β increases with decreasing porosity φ. The k-φ and β-φ plots show that as the sizes of disintegrated coal samples are getting smaller, there are more fluctuations between the porosity values with their corresponding values of k and β. The permeability value of the sample with smallest grains was observed to be considerably lower than that of the sample with largest grains. Non-Darcy behavior could reduce the hydraulic conductivity. It was found that the porosity, grain breakage and hydraulic properties of coal samples are related to grain sizes and compaction levels, as well as to the arrangement of the grains. At high compaction levels, the porosity of disintegrated coal samples decreased strongly, resulting in a significant decrease of the permeability at its full compression state; Non-Darcy flow behavior has the slightest effect in uniform samples, therefore, indicating that disintegrated coal in uniform grain size mixtures could be treated as an aquicluding (water-resisting) stratum. Keywords: water influx; mining; coal grain; hydraulic properties; compaction
1. Introduction Water protection is an important issue for large scope underground mining works, especially in western China, where a large proportion of the coal seams are below arid areas and water resources are quite scarce. Moreover, if the overburden rock strata are sufficiently permeable, surface water and groundwater can flow into the underground mine, which could result in an unsafe mining environment and also deteriorate the region’s already weak ecological environment [1]. Furthermore, in the western China mining area, the overlying rock structures of most of the main coal seams have Energies 2017, 10, 612; doi:10.3390/en10050612
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typical characteristics of shallow depths, overlaid by thick sand layers and underlaid by thin bedrock. Coal exploration works that are taking place in these areas are mostly rather invasive, resulting in strong strata fracture, which could consequently result in significant surface subsidence, water loss, coal seam rock bursts and other hazards. Additionally, deterioration of the existing ecological and environmental systems is among the other negative effects of these mining works [2,3]. Therefore, a better understanding of the hydrogeological responses of coal seam that are widespread in these areas has clear advantages. There are many factors that control and influence the occurrence of water influx within the ground. The main factors are ground stress [4], pore water pressure [5], geological formations and mine dimensions such as mining width and advancing distance [2]. On the other hand, understanding the compaction and flow characteristics of deformed rock layers play a key role in water influx prevention within the coal mines; therefore, studying the evolution of hydraulic properties for porous sedimentary rocks under compaction [6] can certainly be beneficial in the planning of coal mining works. Many of factors, such as lithology, rock texture, and external loading, can affect the compaction level of different non-cemented sedimentary rock [7,8]. There are several other factors that also influence the properties of non-compacted sedimentary rocks mixed grains, including shear strength [9], friction angle [10], permeability [11], etc. During loading, rock grains may be broken [12,13], the degree to which the grains are broken down to, could be related to different factors such as the saturation and drying processes [14,15], the intensity of the applied stress [16] and the initial grading of the rock mixture [12,17]. Historically, many researchers have investigated water flow through non-cemented media (e.g., in dam filter layers) to find out the effect of flow on the grain size ratios and consequently on the hydraulic properties of the grain mixtures [18–20]. More recently, a good number of studies has been carried out to analyze the correlations between the seepage-induced grain rearrangements with seepage forces [21]), grain mixing [22], water table level [23], channel network formation [24] and grain shape and gradation [25]. Furthermore, several experimental studies have been reported in the literature on the investigation of hydraulic properties due to water flux in non-cemented coal samples and other non-compacted sedimentary rocks [26–29]. From studying the variation of the compaction, shearing and flow characteristics of non-cemented rocks, reference [28] proposed a logarithmic equation between the axial pressures and permeability coefficients. They also found that the seepage in non-cemented rock masses does not obey the Darcy law, but it is better explained by the Forchheimer equation [30]. When the rock exhibits a lower porosity, the characteristics of the non-Darcy flow are more clearly observed [28]. For non-cemented coal particles, many theoretical, experimental and numerical methods have been proposed to understand the effect of properties such as grain size, density and ash on fixed characteristics [31–33], coal combustion [34], coal particle moving [35], stable free radicals [36], etc. Permeability is influenced by the stress rate [37], fracture geometry [38], fracture geometry and water-content [39], both presence of water and magnitude of water saturation [40]. In the study carried out by [28], the evolution of permeability within disintegrated rocks under water flow was experimentally investigated; however, in that study the effects of different mixtures of grain sizes were not considered. To capture the compaction and hydraulic properties of disintegrated coal samples with different grain sizes, in this work an experimental setup has been considered for the measurement, calculation, and quantification of the effect of changing grain sizes and axial displacements on the properties of water flow in a non-Darcy condition. The same setup was previously used to study the influence of grain mixture on flow characteristics of disintegrated mudstone [41]; however, the work in this paper is the first study of this type on monitoring and analyzing the compaction and hydraulic properties of coal. In the following sections, the details of experimental apparatus, test specimens and testing procedure are explained.
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2. Experimental Equipment and Conditions 2. Experimental Equipment and Conditions 2. Experimental Equipment and Conditions 2.1. Experimental Equipment ExperimentalEquipment Equipment 2.1.2.1. Experimental The MTS 815.02 rock material system and a fluid seepage setup are the two main parts of the The MTS 815.02 rock material system and a fluid seepage are the two main parts the coupled testing equipment (Figure system 1) usedand in this study. The setup schematic illustration theoftesting The MTS 815.02 rock material a fluid seepage setup are the two mainofparts of the coupled testing equipment (Figure 1) used in this study. The schematic illustration of the testing system istesting shownequipment in Figure 2.(Figure An epoxy resin in layer is used to schematic separate the cylindricaloftube (6) and coupled 1) used this(7) study. The illustration the testing system is shown in Figure 2. An epoxy resin layer (7) is used to separate the cylindrical tube (6) and the rockisspecimen and to prevent the radial water flow. one–way is usedtube to connect system shown in (16), Figure 2. An epoxy resin layer (7) is used toA separate thevalve cylindrical (6) and the rock specimen (16), and to prevent the radial water flow. A one–way valve is used to connect the rock cylindrical tube(16), (6) and the triaxial the base of thewater system, which includes valve (1),connect valve core specimen to prevent radial flow. A one–way valve is chest used to the the cylindrical tube (6) and the triaxial base of the system, which includes valve chest (1), valve core (2), mechanical spring (3), triaxial mechanical bolt (4) and base plate (13). The porous disks (9 core and (2), 14) cylindrical tube (6) and the base of the system, which includes valve chest (1), valve (2), mechanical spring (3), mechanical bolt (4) and base plate (13). The porous disks (9 and 14) ensure that water flow is evenly distributed, and the filter pads (8 and 15) can keep the testing mechanical spring (3),flow mechanical (4) and base (13). The (9 and ensure that ensure that water is evenlybolt distributed, andplate the filter padsporous (8 anddisks 15) can keep14) the testing system clear and free of water contamination. The loading plate (12) is utilized to exert the axial water flow is evenly distributed, and the filter pads (8 and 15) can keep the testing system clear and system clear and free of water contamination. The loading plate (12) is utilized to exert the axial pressure. free of water contamination. The loading plate (12) is utilized to exert the axial pressure. pressure.
Figure 1. MTS815.02 system and a fluid seepage apparatus. Figure Figure 1. 1. MTS815.02 MTS815.02 system system and and aa fluid fluid seepage seepage apparatus. apparatus.
Figure 2. Testing system for non-cemented coal. Note: A—pressure sensor; B—load controller; C—relief valve; D—regulator; E—pressure difference sensor; F—drainage; S1~S15—switch. 1—valve Figure 2. Testing system for non-cemented coal. Note: A—pressure sensor; B—load controller; chest;2.2—valve 3—mechanical spring; 4—mechanical 5,11—O—shaped rubber seal rings; Figure Testingcore; system for non-cemented coal. Note: bolt; A—pressure sensor; B—load controller; C—relief valve; D—regulator; E—pressure difference sensor; F—drainage; S1~S15—switch. 1—valve 6—cylindrical tube; 7—epoxyE—pressure resin separation layer; 8,15—filter pad; 9,14—porous disk; 10—piston; C—relief valve; D—regulator; difference sensor; F—drainage; S1~S15—switch. 1—valve chest; 2—valve core; 3—mechanical spring; 4—mechanical bolt; 5,11—O—shaped rubber seal rings; 12—loading 13—base plate; and 16—coal sample. bolt; chest; 2—valveplaten; core; 3—mechanical spring; 4—mechanical 5,11—O—shaped rubber seal rings;
6—cylindrical tube; tube; 7—epoxy 7—epoxy resin resin separation separation layer; layer; 8,15—filter 8,15—filter pad; pad; 9,14—porous 9,14—porous disk; disk; 10—piston; 10—piston; 6—cylindrical 12—loading platen; 13—base plate; and 16—coal sample. 12—loading platen; 13—base plate; and 16—coal sample.
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The The same same experimental experimental setup setup was was formerly formerly applied applied to to study study the the flow flow characteristics characteristics of of disintegrated disintegrated sedimentary sedimentary rocks rocks [4,41]; [4,41]; however, however, the the former former work work did did not not take take into into account account the the effect effect of of grain grain size size distribution distribution on on the the compaction compaction and and water water flow flow properties properties of of sedimentary sedimentary coal coal samples, which is the main focus of this study. samples, which is the main focus of this study. 2.2. 2.2. Experimental Experimental Conditions Conditions In mining, as as shown shownin inFigure Figure3,3,there thereare are four disturbance zones that formed in In longwall mining, four disturbance zones that areare formed in the the overlying strata of a seam coal seam [42]. mining After mining operations, alongthewith the consolidation overlying strata of a coal [42]. After operations, along with consolidation process process around the excavated areas,ofaequilibrium state of equilibrium can bewithin reached the zones disturbed around the excavated areas, a state can be reached thewithin disturbed [43]. zones In these mining-affected areas, addition toof the investigation of the water geological In these[43]. mining-affected areas, in addition to theininvestigation the geological formations, table formations, water table and cavitation percentages of underground openings [44–47], it is also and cavitation percentages of underground openings [44–47], it is also essential to study the hydraulic essential to of study the hydraulic properties of the deformed rocks the constant loading of [48]. the properties the deformed rocks under the constant loading of under the overlying ground layers overlying ground layers [48]. Asgeotechnics, a practical issue in mining geotechnics, studying theconductivity compaction As a practical issue in mining studying the compaction and hydraulic and hydraulic conductivity of deformed strata makes great contribution to problems plan for attributes of deformed strataattributes makes a great contribution to plan foramitigation of potential mitigation of from potential problems that canthe arise from of mining activities. removal of coal that can arise mining activities. With removal coal material, theWith stressthe distribution around material, the stress distribution the the excavated area andarea as acould resultcave the ceiling the the excavated area changes andaround as a result ceiling of thechanges excavated in. The of stress excavated area could cave in. The stress variation within the ground occurs from the seam level all variation within the ground occurs from the seam level all the way up to the ground surface, this can the up to theand ground surface, thispermeability can lead to fractures and changes the permeability of the leadway to fractures changes of the of the adjacent groundofzones by several orders adjacent ground zones by of magnitude [42,49]. result the hydraulic of magnitude [42,49]. As several a resultorders the hydraulic properties of As theaoverburden strata areproperties changed, of the overburden strata are changed, near thepermeability excavated zones, and therefore high particularly near the excavated zones, particularly and therefore high pathways are frequently permeability pathways frequently formed [49,50]; this can cause water influx within the ground. formed [49,50]; this can are cause water influx within the ground.
Figure Figure 3. 3. Four Four zones zones of of overlying overlying strata strata above above aa longwall longwall panel panel [42]. [42].
2.2.1. 2.2.1. Sample Sample Preparation Preparation As As shown shown in in Figure Figure 3, 3, the the grain grain sizes sizes of of disintegrated disintegratedcoal coalunderground undergrounddisplay displaylarge largevariety. variety. However, because of the limit of experimental setup-cylindrical tube (its diameter is 100 mm However, because of the limit of experimental setup-cylindrical tube (its diameter is 100 mm and and height is 180 180mm), mm),coal coal was broken 2.5–20 diameter sizethe and the were grains weretomixed to height is was broken intointo 2.5–20 mm mm diameter size and grains mixed decrease decrease the boundary and the testing error. the boundary effect andeffect the testing error. The coal blocks sampled for this The coal blocks sampled for this study study were were taken taken from from aa depth depth of of approximately approximately 340 340 m m at at the the 3 3 1.63××10 m3 3. . site Coal Mine Mine in in China. China. The The dry dry density densityof ofthe thecoal coalblocks blockswas wasρs ρ= site of of Xiaojiawa Xiaojiawa Coal 1.63 10 kg kg/m s = The The coal coal specimens specimens were were broken broken into into grains grains smaller smaller than than 20 20 mm mm in in the the laboratory. The The crushing crushing of of coal coal blocks blocks was was done done in in two two steps. steps. First, First, using using steel steel piercers piercers and and iron iron hammers, hammers, the the coal coal blocks blocks were were hammered into pieces of 60 mm diameter or less. Then, a particular stone breaker was used to break those large pieces into small ones with sizes less than 20 mm in diameter.
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hammered into pieces of 60 mm diameter or less. Then, a particular stone breaker was used to break Energies 2017, 10, 612 5 of 17 thoseUsing large pieces intomachine small ones with sizes less than 20 mm in diameter. a sieving with high-frequency vibration (Figure 4a), the disintegrated coal was Usinginto a sieving machine with high-frequency (Figure 4a), the disintegrated coal was separated four groups with different grain sizevibration ranges, namely mm, 5–10 mm, 10–15 Using a sieving machine with high-frequency vibration (Figure2.5–5 4a), the disintegrated coal mm was separated into four groups with different grain size ranges, namely 2.5–5 mm, 5–10 mm, 10–15 mm and and 15–20into mm.four As groups shown with in Figure 4b, grain the sieves used had round shaped holes,mm, to ensure the separated different size ranges, namely 2.5–5 mm, 5–10 10–15 mm 15–20 mm. As shown in Figure 4b, the sieves used had round shaped holes, to ensure the samples uniformity uniformity of the prepared test samples and that the grains are sieved evenly. Testing in and 15–20 mm. As shown in Figure 4b, the sieves used had round shaped holes, to ensure the of the prepared test samples and that(1:2:1:1), the grains are sieved evenly. Testing samples infrom weight ratios weight ratios of (1:1:1:1), (2:1:1:1), (1:1:2:1) and (1:1:1:2) were prepared the four uniformity of the prepared test samples and that the grains are sieved evenly. Testing samples in of (1:1:1:1),grain (2:1:1:1), (1:2:1:1), (1:1:2:1) and (1:1:1:2) were prepared from the four the groups of grain sizes, groups respectively. simplicity of referencing in this paper above-mentioned weight of ratios ofsizes, (1:1:1:1), (2:1:1:1),For (1:2:1:1), (1:1:2:1) and (1:1:1:2) were prepared from the four respectively. For simplicity referencing in this paper the above-mentioned samples are referred as samples referred as of uniform (1:1:1:1), smallest (2:1:1:1), smaller (1:1:2:1) to and groups ofare grain sizes,to respectively. For simplicity of referencing in this (1:2:1:1), paper thelarger above-mentioned uniform (1:1:1:1), smallest (2:1:1:1), smaller (1:2:1:1), larger (1:1:2:1) and largest (1:1:1:2), the sample largest (1:1:1:2), the sample weight (1:1:1:1), was 1500smallest g. Table(2:1:1:1), 1 provides a summary the samples samples are referred to as uniform smaller (1:2:1:1),oflarger (1:1:2:1)with and weight was 1500 g.ofTable 1 provides a summary of the samples with different amounts of10–15 grain mm size different amounts grain size constituents. An example display of the sieved grains in largest (1:1:1:2), the sample weight was 1500 g. Table 1 provides a summary of the samples with constituents. An example of the sieved grains in 10–15 mm is also shown in Figure 5. is also shown in Figure 5. display different amounts of grain size constituents. An example display of the sieved grains in 10–15 mm is also shown in Figure 5.
Figure 4. 4. A vibration: (a) and (b) (b) aa 10 Figure A sieving sieving machine machine with with high high frequency frequency vibration: (a) sieve sieve machine; machine; and 10 mm mm sieve. sieve. Figure 4. A sieving machine with high frequency vibration: (a) sieve machine; and (b) a 10 mm sieve. Table 1. Coal grain size distribution of each sample. Table 1. Coal grain size distribution of each sample. Table 1. Coal grain size distribution of each sample. Weight to Each Grain Size (g) Sample Weight Ratio to Each Grain Size tomm Each Grain (g) 2.5–5 mmWeight 5–10 10–15Size mm Weight to Each Grain Size (g) 15–20 mm Sample Weight Ratio to Each Grain Size Sample Weight Ratio to Each Grain Size Uniform 1:1:1:1 375mm 5–10 375 375mm 375mm 2.5–5 mm mm 10–15 mm 15–20 mm 2.5–5 5–10 mm 10–15 15–20 Smallest 2:1:1:1 600 300 300 300 Uniform 1:1:1:1 375 375 375 Uniform 1:1:1:1 375375 375 375 Smaller 1:2:1:1 300 600 300 300 Smallest 2:1:1:1 600600 300 300 Smallest 2:1:1:1 300 300 300 Larger 1:1:2:1 300 300 600 300 Smaller 1:2:1:1 300300 600 300 300 Smaller 1:2:1:1 600 300 300 Largest 1:1:1:2 300 300 300 600 Larger 1:1:2:1 300 300 600 300 Larger 1:1:2:1 300 300 600 300 Largest 1:1:1:2 300 300 300 600 Largest 1:1:1:2 300 300 300 600
Figure 5. Grain size (10–15 mm) of non-cemented coal separated by the sieving machine. Figure 5. Grain size (10–15 mm) of non-cemented coal separated by the sieving machine.
Figure 5. Grain size (10–15 mm) of non-cemented coal separated by the sieving machine. 2.2.2. Water Pressure
2.2.2.In Water Pressure actual mining conditions, the water pressure under coal seam in Xiaojiawa Coal Mine can reachIntoactual 2.3 MPa. Considering the the experimental setup under and geological conditions, 2.3 MPa taken mining conditions, water pressure coal seam in Xiaojiawa Coal was Mine can as the highest water pressure in the test. reach to 2.3 MPa. Considering the experimental setup and geological conditions, 2.3 MPa was taken as the highest water pressure in the test.
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2.2.2. Water Pressure In actual mining conditions, the water pressure under coal seam in Xiaojiawa Coal Mine can reach Energies 2017, 10, 612 6 of 17 to 2.3 MPa. Considering the experimental setup and geological conditions, 2.3 MPa was taken as the highest water pressure in the test. 2.2.3. Compaction Behavior 2.2.3. Compaction Behavior As show in Figure 3, due to the effect of mining, the lower section of coal seam will be disintegrated, porosity thetolower sectionofwill be increased. Therefore, As show the in Figure 3, of due the effect mining, the lower section compaction of coal seamlevel willwas be considered to monitor the variation of porosity on hydraulic properties. disintegrated, the porosity of the lower section will be increased. Therefore, compaction level was considered to monitor the variation of porosity on hydraulic properties. 3. Experimental Procedure 3. Experimental Procedure Before each test, the coal samples were required to be fully saturated with water. To obtain Before each test, the coal samples were required be fullyout saturated with water. To obtain reliable reliable measurements, water flow readings weretocarried after the load (displacement) was measurements, flow readings carried the load (displacement) was remained at remained at a water set value; in other were words, the out loadafter modification and fluid seepage were two aconsecutive set value; in other words, the load modification and fluid seepage were two consecutive testing testing stages. The testing advancement was as follows: stages. The testing advancement was as follows: (1) Calculation of the original length (porosity) of sample before load application. (1) Calculation of the original length (porosity) of sample before load application. First, a coal sample was placed into the cylindrical container, and the loading ram was h0 ofwas installed the sample. shown in container, Figure 6, the original height ram the First,toarudimentarily coal sample compact was placed into theAs cylindrical and the loading installed to rudimentarily compact As shown in Figure 6, the original height h0 h0 = H1the − Hsample. sample can be calculated as 2 − 2H3 − 2H4 + H5 . H1 to H 5 , which are illustrated in of the sample can be calculated as h0 = H1 − H2 − 2H3 − 2H4 + H5 . H1 to H5 , which are Figure 6, are the dimensions of the different components of the sample container setup. As illustrated in Figure 6, are the dimensions of the different components of the sample container setup. H , H , H and H 4 were set before the design of the seepage device, h0 could only be related to As1 H12, H23, H3 and H 4 were set before the design of the seepage device, h0 could only be related to 180−−110 1818 +H H55: :h0h= Therefore, the original porosity of coal sample was fixed. 0 = 5 .H H 180 110 − −44−− +5H=5 48 = +48H+ 5 . Therefore, the original porosity of coal sample was fixed.
Figure 6. 6. Sketch Sketch calculating calculating the the height height of of the thenon-cemented non-cemented coal. coal. Note: Note: H H11: height of the cylindrical cylindrical (180mm); mm);H2H: 2height : height plunger H3 : thickness of the padH(24 : mm); H4: tube (180 of of thethe plunger (110(110 mm);mm); H3 : thickness of the filter padfilter (2 mm); thickness 5 : height of the plunger head exceeds the cylindrical tube; and h0: thickness porous diskH(9 mm); H of porous of disk (9 mm); : height of the plunger head exceeds the cylindrical tube; and h : original 5 0 originalofheight of sample. the coal sample. height the coal
(2) Saturation (2) Saturation of of the the coal coal samples. samples. The water injection capability of the MTS 815.02 test system was used to saturate the coal The water injection capability of the MTS 815.02 test system was used to saturate the coal samples. samples. (3) Application of of the the load. load. (3) Application The sample until its deformation reached to a pre-planned displacement value. samplewas wasloaded loadedaxially axially until its deformation reached to a pre-planned displacement The axial atkept 0.400atMPa during loading; then thethen porosity at each at displacement (i.e., 10,(i.e., 15, value. Thestress axialkept stress 0.400 MPa during loading; the porosity each displacement 20, mm) calculated. The displacement was maintained until step 4 until was finished. 10, 25, 15, 30, 20,35, 25,4030, 35, was 40 mm) was calculated. The displacement was maintained step 4 was finished. (4) Application of the water flow. (4) Application of the water flow.
The loading ram speed could be programmed through the control system of the MTS 815.02 machine. During the experiments, after the final compaction of the sample (i.e., step 3), water pressure was regulated in order to maintain different loading ram speeds of 16.7, 31.3, 62.5, 93.8, 109 µm/s to apply different axial displacements within the range of 10 mm to 40 mm with 5 mm
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The loading ram speed could be programmed through the control system of the MTS 815.02 machine. During the experiments, after the final compaction of the sample (i.e., step 3), water pressure was regulated in order to maintain different loading ram speeds of 16.7, 31.3, 62.5, 93.8, 109 µm/s to Energies 2017, 10, 612 7 of 17 apply different axial displacements within the range of 10 mm to 40 mm with 5 mm intervals. The Theflowchart flowchartin inFigure Figure77summarizes summarizesthe thecomplete completetest testadvancement; advancement;each eachsample samplewas wastested tested four achieve a better levellevel of reliability in thein results. For each case, to increase accuracy, fourtimes timestoto achieve a better of reliability the results. For each case, to test increase test the final result was taken as the average value from the four tests. accuracy, the final result was taken as the average value from the four tests.
Figure7. 7. Testing Testingprocedure procedureof ofthe thenon-cemented non-cementedcoal. coal. Figure
ExperimentalResults Resultsand andDiscussion Discussion 4.4. Experimental Testresults resultsare areanalyzed analyzedin inthis thissection, section,which whichinclude includeporosity porosityevolution evolution during during compaction, compaction, Test evaluationof ofthe thenon-Darcy non-Darcyseepage seepageflow, flow,grain graincrushing crushingand andhydraulic hydraulicproperties. properties. evaluation 4.1. Porosity PorosityEvolution Evolutionduring duringCompaction Compaction 4.1. Thesample sampleporosity, porosity,φ,ϕat, at each compaction level can expressed The each compaction level can bebe expressed as:as: mm φ = ϕ1 = −1 − S) ρsρQs Q (h(h0 0−− S
(1) (1)
ρs sample is the sample and is the mass of disintegrated the disintegrated sample, wheremmis the where mass of the coal coal sample, ρs is the densitydensity and h0 is the horiginal 0 is the height of height the sample, is the cross-sectional area of the cylindrical and S istube, the displacement original of theQ sample, Q is the cross-sectional area of thetube, cylindrical and S is the along the vertical axis. displacement along the vertical axis. Based on Equation (1), the evolution of porosity values during compaction could be obtained, as summarized in Table 2, based on which the porosity evolution graphs are plotted in Figure 8. The graphs in Figure 8 illustrate that on the whole, the porosity of disintegrated coal is highly affected by the compaction level (axial deformation) and by different mixtures of grain sizes. For the same sample, the porosity reduces with increasing axial deformation, as the voids in the non-cemented coal parts are reduced during compaction. At the same compaction level (i.e., axial
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Based on Equation (1), the evolution of porosity values during compaction could be obtained, as summarized in Table 2, based on which the porosity evolution graphs are plotted in Figure 8. The graphs in Figure 8 illustrate that on the whole, the porosity of disintegrated coal is highly affected by the compaction level (axial deformation) and by different mixtures of grain sizes. For the same sample, the porosity reduces with increasing axial deformation, as the voids in the non-cemented coal parts are reduced during compaction. At the same compaction level (i.e., axial deformation), Energies 2017, 10, 612 8 of 17 the porosity increases with increasing grain sizes. The largest sample exhibits the maximum porosity Energies 2017, 10, 612 8 of 17 value because the volume of voids in the sample with larger fragments is greater than that in the because the the volume ofgrains. voids in in the samplesample with larger larger fragments is greater greater than that that in the the samples samples with smallerof The uniform exhibits the minimum porosity value because the because volume voids the sample with fragments is than in samples with smaller grains. The uniform sample exhibits the minimum porosity value because the smaller smaller grains fill in the void spaces produced by larger fragments, and as a result the grains are closer with smaller grains. The uniform sample exhibits the minimum porosity value because the smaller grains fill in the the void spaces produced by larger larger fragments, andofas asporosity resultvariation the grains grains are closer to to eachfill other than in other samples. As Figure 9 shows, the rate in are the closer uniform grains in void spaces produced by fragments, and aa result the to each other than in other samples. As Figure 9 shows, the rate of porosity variation in the uniform sample is the most significant, indicating that9the grainthe mixture (original porosity) plays a key each other than in other samples. As Figure shows, rate ofratio porosity variation in the uniform sample is the most significant, indicating that the grain mixture ratio (original porosity) plays a key role during compression under compaction. sample is the most significant, indicating that the grain mixture ratio (original porosity) plays a key role during compression under compaction. role during compression under compaction. Table 2. Porosity evolution during compaction. Table 2. 2. Porosity Porosity evolution evolution during during compaction. compaction. Table Axial Displacement (mm) Axial Displacement Displacement (mm) (mm) Sample Axial Sample Sample 10 10 1515 20 25 30 35 35 40 20 25 30 10 15 20 25 30 35 40 Uniform 0.342 0.321 0.299 0.275 0.249 0.221 0.192 Uniform 0.342 0.321 0.299 0.275 0.249 0.221 Uniform 0.342 0.321 0.299 0.275 0.249 0.221 0.192 Smallest0.346 0.346 0.326 0.326 0.303 0.303 0.279 0.279 0.254 0.2270.227 0.198 Smallest 0.279 0.254 0.2540.227 Smallest 0.346 0.326 0.303 0.198 Smaller 0.354 0.333 0.312 0.289 0.265 0.238 0.354 0.333 0.333 0.312 0.312 0.289 0.289 0.265 0.265 0.238 0.238 0.21 0.21 Smaller 0.354 Smaller LargerLarger 0.362 0.342 0.321 0.299 0.275 0.2750.2490.249 0.362 0.342 0.321 0.299 0.221 Larger 0.362 0.342 0.321 0.299 0.275 0.249 0.221 Largest 0.34 0.319 0.296 0.2960.2720.272 0.379 0.36 0.36 0.34 0.319 0.319 0.246 Largest0.379 0.379 0.36 0.34 0.296 0.272 0.246 Largest
40 0.192 0.198 0.21 0.221 0.246
Figure 8. 8. Porosity Porosity of non-cemented non-cemented coal coal sample sample of of each each axial axial displacement. displacement. Porosity of Figure
9. Porosity change rate of each axial displacement. Figure 9. Figure Porosity change rate of each axial displacement.
4.2. Non-Darcy Non-Darcy Flow Flow Type Type 4.2. There are are two two methods methods to to show show that that the the flow flow within within the the disintegrated disintegrated coal coal samples samples is is of of aa nonnonThere Darcy type: (1) when the Reynolds number calculated for the flow within disintegrated coal samples Darcy type: (1) when the Reynolds number calculated for the flow within disintegrated coal samples is larger larger than than five; five; and and (2) (2) when when the the relation relation between between the the water water pressure pressure gradient gradient and and flow flow rate rate could could is be replicated with a second-order function. be replicated with a second-order function.
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4.2. Non-Darcy Flow Type There are two methods to show that the flow within the disintegrated coal samples is of a non-Darcy type: (1) when the Reynolds number calculated for the flow within disintegrated coal samples is larger than five; and (2) when the relation between the water pressure gradient and flow rate could be replicated with a second-order function. 4.2.1. Reynolds Number Calculation It has been shown that Forchheimer equation [30] provides good estimates of seepage flow within disintegrated hard non-cemented rocks, (e.g., [4,28]); therefore, it was used to model flow in this study. According to this method, for a non-Darcy seepage flow in one dimension, the correlation between pressure variations and flow rate can be defined as:
− ∂p/∂z =
ρw µv + ρw βv2 k
(2)
where ∂p/∂z, p and z are pore pressure gradient, pore pressure and dimensional variable, respectively, ρw is water density, µ is water viscosity (equal to 1.01 × 10−6 m2 /s), k is sample permeability, v is the average flow rate and β is a non-Darcy factor. For the flow to be of Darcy type, β should be almost equal to zero. Equation (2) could be applied to match the water seepage in coal samples as described below [41,51,52]. In this case, the Reynolds number (Re) can be expressed as: Re =
ρw vd µφ
(3)
where d is a characteristic size, in this test, for non–consolidated non-cemented coal, the value for d can be considered as the average diameter of the grains. As mentioned before, the seepage rate, v, can be regulated by maintaining a constant deformation through the loading ram. A previous study has shown that the upper limit of Re that is applicable for Darcy flow is 5, and this limiting value is only moderately different [53] for various porous media. As summarized in Table 2, the minimum and maximum porosity values are found to be 0.192 and 0.379, respectively. In the tests, the minimum and maximum flow velocities were measured as 3.13 × 10−2 mm/s and 1.09 × 10−1 mm/s, respectively. Taking the value of d within the range of 2.5 to 20 mm, and porosity values between 0.192 and 0.379, from Equation (3) we have: (
Remin = Remax =
ρw vmin dmin µφmax ρw vmax dmax µφmin
= 0.37 = 20.2
(4)
Thus, Re values for the flow with the coal samples are between 0.37 and 20.2 as the minimum and maximum values, respectively. Therefore it is possible for the Re to be greater than 5, which means that in particular scenarios the non-Darcy seepage flow could be expected. 4.2.2. Relationship of Flow Rate and Water Pressure Gradient The water pressure gradient, ∂p/∂z, does not change if the variables on the right hand side of Equation (2) are constant with regards to z. In this case the pressure gradient can be verified from the pressure differences at the top p a and bottom pb boundaries of the sample. The bottom end of the specimen was linked with the atmosphere, i.e., pb = 0, in this case: ∂p/∂z = −
p a − pb pa p =− =− L L L
(5)
where L is the length of the coal sample. For the majority steady state flow, when the seepage flow is upward in vertical direction, z, we have:
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p/L =
ρw µv + ρw βv2 k
(6)
Figures 10 and 11 illustrate that the hydraulic properties of non-cemented coal are highly affected by axial displacements and different mixtures of grain sizes. Generally, the pressure gradients versus flow rate plots are nonlinear and can be fitted by second-order relationship, which demonstrates that the second-order relationship, i.e., Equation (2), could be used to match the seepage flow in non-cemented coal during compaction. Energies 2017, 10, 612 10 of 17
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Figure 10. Relation of pore pressure gradient with with flow velocity velocity for the the uniform sample. sample. Figure 10. 10. Relation Relation of of pore pore pressure pressure gradient gradient Figure with flow flow velocity for for the uniform uniform sample.
Figure 11. Relation of pore pressure gradient with with flow velocity velocity at axial axial displacement 10 10 mm. Figure 11. 11. Relation Relation of of pore pore pressure pressure gradient gradient Figure with flow flow velocity at at axial displacement displacement 10 mm. mm.
4.3. Grain Mixture Alterations during the Tests 4.3. Grain Mixture Alterations during the Tests Tests Using the sieving machine (Figure 4), the weights of the different grain size ranges in the samples Using the sieving machine (Figure 4), the weights of the different grain size ranges in the samples were determined for for both both before before and and after after the the testing testing (seepage (seepage and and compaction), compaction), and and the the values values are are were determined summarized in Table 3. summarized in Table 3. Table 3. Grain size weight before and after carrying out the tests tests (seepage (seepage and and compaction). compaction). Table 3. Grain size weight before and after carrying out the tests (seepage and compaction). Sample Sample
Sample
Uniform Uniform Smallest Smallest Uniform Smaller Smaller Smallest Larger Larger Smaller Largest Largest Larger
Largest
Weight to Each Grain Size (g) Weight Change (g) WeightWeight to EachtoGrain Size (g) WeightWeight ChangeChange (g) Each Grain (g) 2.5–5 mm 5–10 mm 10–15 mm Size (g)15–20 mm 0–2.5 mm (Increase) Wight Loss 2.5–5 mm 5–10 mm 10–15 mm 15–20 mm Before After Before After15–20 2.5–5After mm Before 5–10 mm Before After 10–15 mm mm 0–2.5 mm (Increase) Loss 0–2.5 mmWight Wight Before After Before After Before After Before After 375 389.3 375 377.9 375 367.4 375 337.8 14.2 13.4 Loss Before After 375Before After Before After 375 389.3 377.9 After 375 Before 367.4 375 337.8 14.2 (Increase) 13.4 600 608.3 300 306.8 300 288.4 300 262.2 18.4 15.9 600 608.3 300 306.8 300 288.4 300 262.2 18.4 15.9 375 389.3 600 375 592.4 377.9 375 367.4 375 337.8 14.2 13.4 309.6 300 294.6 300 280.9 11.3 11.2 300 592.4 300 294.6 300 280.9 11.3 11.2 300 600 309.6 608.3 600 300 288.4 300 262.2 18.4 15.9 319.1 300 300 307.8 306.8 600 583.2 300 264.3 12.4 13.2 300 307.8 600 583.2 300 264.3 12.4 13.2 300 300 319.1 309.6 300 300 294.6 300 280.9 11.3 11.2 316.2 300 600 304.2 592.4 300 283.6 600 573.1 13.6 9.3 300 300 283.6 600 573.1 13.6 9.3 300 300 316.2 319.1 300 300 304.2 307.8 600 583.2 300 264.3 12.4 13.2
300
316.2
300
304.2
300
283.6
600
573.1
13.6
9.3
According to the data in Table 3 and Figure 12, that shows the mass change variations following According to the data in Table 3 and Figure 12, that shows the mass change variations following the tests, it is seen that compared with the original mass distributions, for all of the samples the the tests, it is seen that compared with the original mass distributions, for all of the samples the proportions of the largest grains (15–20 mm) decreased after the completion of experiments. The proportions of the largest grains (15–20 mm) decreased after the completion of experiments. The decreased values indicate that, during compaction, the largest grains were broken into smaller decreased values indicate that, during compaction, the largest grains were broken into smaller particles. The weights of the medium grain sizes, (i.e., 5–10 mm and 10–15 mm) after compaction particles. The weights of the medium grain sizes, (i.e., 5–10 mm and 10–15 mm) after compaction were almost unchanged, which means that during compaction the influence of grain crushing on the were almost unchanged, which means that during compaction the influence of grain crushing on the
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According to the data in Table 3 and Figure 12, that shows the mass change variations following the tests, it is seen that compared with the original mass distributions, for all of the samples the proportions of the largest grains (15–20 mm) decreased after the completion of experiments. The decreased values indicate that, during compaction, the largest grains were broken into smaller particles. The weights of the medium grain sizes, (i.e., 5–10 mm and 10–15 mm) after compaction were almost unchanged, which means that during compaction the influence of grain crushing on the amount of medium size grains were very small. However, after the compaction in all samples there were more grains with the smallest sizes (2.5–5 mm), which suggested that under the compaction part of the largest grain constituents the samples (15–20 mm) were broken into smaller ones, increasing the total weight of Energies 2017, 10, 10,of612 612 11 of of 17 17 Energies 2017, 11 grains within the size ranges of 2.5–5 mm and 5–10 mm. During compaction, compaction, some some of of the the larger larger grains grains were grains, which During compaction, some of the larger grains were broken broken into into fine fine grains, which included included During within the size range of 0–2.5 mm. Water flow through the sample transported out some particles within the size range of 0–2.5 mm. Water flow through the sample transported out some of particles within the size range of 0–2.5 mm. Water flow through the sample transported out some of of the fine grains which was evident from the weight losses observed (see Figure 13). The weight of the fine fine grains grains which which was was evident evident from from the the weight weight losses losses observed observed (see (see Figure Figure 13). 13). The The weight weight of of the the the the fine grains component is highest forsmallest the smallest sample, which could be to due to easy crushing of fine grains component is highest highest for the the smallest sample, which could be due due to easy crushing of 2.5– 2.5– fine grains component is for sample, which could be easy crushing of 2.5–5 mm grains into fine particles. The weight loss is the least for the largest specimen, as it is 5 mm grains into fine particles. The weight loss is the least for the largest specimen, as it is more 5 mm grains into fine particles. The weight loss is the least for the largest specimen, as it is more broken into into fine fine particles. particles. Because, Because, compared compared to others, the the smallest smallest difficult for for the the larger larger grains grains to to be be broken broken into fine particles. Because, compared to others, others, the smallest difficult specimen contained more of the smallest grain sizes (2.5–5 mm), the transport of specimen contained more of the smallest grain sizes (2.5–5 mm), the transport of fine grains in this this specimen contained more of the smallest grain sizes (2.5–5 mm), the transport of fine grains in specimen was more pronounced. specimen was more pronounced.
Figure 12. 12. Weight Weight change change curves curves after after carrying carrying out out the the tests tests (+ (+ means means increased, increased, − means loss). Weight meansloss). loss). Figure change curves after carrying out the tests (+ increased, −− means
Figure 13. 13. Weight of of the size size (0–2.5 mm) mm) and and losses losses after after carrying carrying out out the the tests. tests. Figure Figure 13. Weight Weight of the the size (0–2.5 (0–2.5 losses
4.4. Non-Darcy Non-Darcy Flow Flow Characteristics Characteristics 4.4. The values values of of kk and and ββ were were evaluated evaluated from from the the relationship relationship between between the the pressure pressure gradient gradient The Λ,, vvi ,,Λ Λ,, vvn and and the the corresponding corresponding steady steady state state and the the seepage seepage rate. rate. For For aa set set of of seepage seepage velocities velocities vv1,,Λ and 1
i
n
Λ,, ppi ,,Λ Λppn ,, the pressure gradients gradients pp1,,Λ the values values of of kk and and ββ could could be be calculated calculated from: from: pressure 1 i n
( vv ) −−
μ μ
n 2 ini==11vvii44 vvii2 = n kk = n n n 2 3 n n n n 2 3 − p v v p v i =1 pivi i =1vi − i =1 pivi i =1vvi44
i =1
n n i =1 i =1
i i
2 3 2 3 i i
i =1 i
n n i =1 i =1
i =1
i i
i =1 i
(7) (7)
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4.4. Non-Darcy Flow Characteristics The values of k and β were evaluated from the relationship between the pressure gradient and the seepage rate. For a set of seepage velocities v1 , · · · , vi , · · · , vn and the corresponding steady state pressure gradients p1 , · · · , pi , · · · pn , the values of k and β could be calculated from:
k=
β=
h i 2 µ ∑in=1 v3i − ∑in=1 v2i ∑in=1 v4i
(7)
∑in=1 pi v2i ∑in=1 v3i − ∑in=1 pi vi ∑in=1 v4i ∑in=1 pi vi ∑in=1 v3i − ∑in=1 pi v2i ∑in=1 v2i h i 2 ρw ∑in=1 v3i − ∑in=1 v2i ∑in=1 v4i
(8)
where n is the total number of the test flow for each sample, 1 ≤ i ≤ n, in these experiments n = 4. Using Equations (7) and (8), the non-Darcy seepage parameters (i.e., k and β) during compaction were calculated and the results are summarized in Table 4. Figure 14 shows the plots of k and β variation with porosity, φ, changes which also provide the comparison of the hydraulic properties of five different non-cemented coal samples with dissimilar grain size mixtures. The figure also shows that during compaction, the value of k increases while that of β decreases with increasing porosity. However, during loading, as the result of the breakage of corners and edges of the grains and the readjustment of the specimens structure, the fracture apertures become more erratic; therefore, both the curves for k-φ and β-φ relationships display some irregular fluctuations; for example, k for the smallest sample in Figure 14a, β for the smallest sample in Figure 14a and the smaller sample in Figure 14b, exhibit local fluctuations, when porosity is between 0.2 and 0.3. The plots of k and β and their variations with φ for different mixture of grains are shown in Figure 15. Generally, the larger the grain sizes in the sample, the greater the permeability value of the sample is due to the larger pores; this also indicates pore and crack closure and narrowing are easier in coal samples with larger grains, e.g., as displayed in Figure 15e, the permeability k of the largest sample is about four times greater than that of the uniform sample in Figure 15a; while, at the same time the non-Darcy factor β value is on average about four times smaller. Evidently, the uniform sample exhibits the minimum permeability value (see Figure 15a), which is mainly because the smaller grains tend to clog the voids of the larger ones, causing the porosity of the sample to be less than that of the others, and in turn results in the minimum value for permeability and the maximum value for the non-Darcy factor β. Furthermore, the variation of k has an opposite trend when compared with β. That means non-Darcy behavior could reduce the hydraulic conductivity of the effective porosity of non-cemented coal samples. Table 4. Non-Darcy flow characteristics during compaction.
Sample
Characteristics
Uniform
Axial Displacement (mm) 10
15
20
25
30
35
40
k (µm2 ) β (mm−1 )
19.344 3.215
16.241 4.367
12.167 9.135
10.13 13.244
5.38 12.983
3.655 19.167
1.234 28.344
Smallest
k (µm2 ) β (mm−1 )
38.167 2.673
24.531 6.314
20.188 3.145
12.28 5.328
16.732 7.73
8.63 7.481
4.529 9.673
Smaller
k (µm2 ) β (mm−1 )
54.135 1.355
32.148 4.432
27.44 2.673
20.128 3.985
12.35 7.872
7.862 11.256
4.583 9.442
Larger
k (µm2 ) β (mm−1 )
62.137 1.235
31.455 3.467
41.263 6.548
23.145 4.32
16.33 9.531
12.15 8.237
6.732 12.258
Largest
k (µm2 ) β (mm−1 )
71.427 3.455
38.135 1.293
29.037 4.673
30.182 2.732
26.355 6.329
19.247 7.383
10.156 10.252
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in considerable drop of the permeability value (e.g., about 16 times for uniform sample when porosity decreased fromdrop 0.34 to Therefore, disintegrated coal 16 seam in the aquiclude (waterin considerable of0.19). the permeability value (e.g., about times for ground uniformform sample when porosity resisting) layers (e.g., [55]), which can be useful for groundwater protection as well as prevention of decreased from 0.34 to 0.19). Therefore, disintegrated coal seam in the ground form aquiclude (waterEnergies 2017, 10, 612 13 of 17 mining-induced groundwater influx. resisting) layers (e.g., [55]), which can be useful for groundwater protection as well as prevention of mining-induced groundwater influx.
Figure 14. Comparison of of non-Darcy flow characteristics of the (a) k-ϕ (a) curves; (b) Comparison non-Darcy flow characteristics of five the samples: five samples: k-φ and curves; β-ϕ curves. Figure of non-Darcy flow characteristics of the five samples: (a) k-ϕ curves; and (b) and (b) 14. β-φComparison curves. β-ϕ curves.
Figure 15. Non-Darcy flow characteristics for the samples at various porosities: (a) uniform sample; (b) smallest sample; (c)flow smaller sample; (d) larger sample; (e) largest sample Figure 15. Non-Darcy Non-Darcy flow characteristics for thesamples samples at various porosities: uniform sample; Figure 15. characteristics for the atand various porosities: (a)(a) uniform sample; (b) (b) smallest sample; (c) smaller sample; (d) larger sample; (e) largest sample smallest sample; (c) smaller sample; (d) larger sample; andand (e) largest sample.
5. Conclusions 5. Conclusions The closure of pores cracks and the narrowing of the flow compression A series of tests usingand an in-house developed water seepage flowchannels apparatusunder was carried out to surely contribute toof the reduction of thedeveloped permeability and increaseflow incharacteristics the value ofwas β;ofhowever, there studyAthe influence grain size mixture on the flowwater and compaction non-cemented series of tests using an in-house seepage apparatus carried out to could where in value k are observed during certain fluctuations, study be thelocalized influencecases of grain sizeanomalous mixture onrises the flow andof compaction characteristics of non-cemented which are most likely the result of clogging of large grains in broadened cracks that in turn accelerate seepage. At certain axial deformations (15 and 20 mm), secluded fractures can expand and join the
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main interconnected fracture network of the porous medium, consequently at this critical deformation there will be significant sudden increase in permeability. Samples with larger gains, in comparison to samples with smaller particles, seem to show a less notable critical deformation. A possible reason for this could be that samples with larger grain sizes have significantly more effective fractures as flow pathways that their closure and narrowing upon undergoing axial deformation result in more pronounced reduction of permeability. The fluctuations of non-Darcy factor β in uniform sample show slighter than that in other samples; while the fluctuations in smaller and larger samples shows greatest. This is mainly because non-Darcy flow behavior has slightest effect in uniform grain size but greatest effect in middle grains. In short, the hydraulic properties of disintegrated coal samples are related not only to the loading levels (porosity), grain mixture, but also to grain arrangement. In saturated ground, the disintegrated coal seam, due to their high permeability, usually form a water-bearing layer, i.e., an aquifer (e.g., [44,54]). The test results in this study showed that at a high compaction levels, the porosity of crushed and disintegrated coal decreases significantly, that results in considerable drop of the permeability value (e.g., about 16 times for uniform sample when porosity decreased from 0.34 to 0.19). Therefore, disintegrated coal seam in the ground form aquiclude (water-resisting) layers (e.g., [55]), which can be useful for groundwater protection as well as prevention of mining-induced groundwater influx. 5. Conclusions A series of tests using an in-house developed water seepage flow apparatus was carried out to study the influence of grain size mixture on the flow and compaction characteristics of non-cemented coal. The following conclusions can be made: evaluation of the Reynolds number for the test samples and the relationship between the water flow velocities and pore pressure gradient differences showed that the flow of water in non-cemented coal samples is of a non-Darcy nature, and best described by the Forchheimer equation, (i.e., Equation (2)). Generally, the porosity of non-cemented coal is highly related to the compaction (axial deformation) level, as well as to the grain sizes. The porosity decreases with increasing axial displacement and decreasing grain sizes. Water flow through the samples prompts the washing away of some fine grains which in turn causes the weight loss of coal samples. Some of the larger grains (15–20 mm and 10–15 mm) are broken into fine particles (0–2.5 mm) during compaction. The hydraulic properties (k and β) of non-cemented coal samples are highly affected by the grain sizes in the sample mixture and the compaction level. Generally, during compaction, k decreases while β increases with decreasing φ. The k-φ and β-φ plots display that the larger the grain sizes, the less oscillation is observed in the values of hydraulic properties. The permeability, k, of the sample with largest grains is four times greater than that of the sample with smallest grains. This is mainly because the samples with larger grains have many more effective pores and cracks that are filled in or closed while undergoing compression, resulting in lower permeability values for non-cemented samples (that are also producing small grains while undergoing compaction). Non-Darcy behavior could reduce the hydraulic conductivity of the effective porosity. In total, the hydraulic properties of the non-cemented coal samples are relative to their compaction levels, their grain mixture sizes, and also to the structure of their grain arrangements. The disintegrated coal seam usually forms subsurface aquifer layers due to their high permeability. At high compaction levels, due to the considerable decrease of the porosity and permeability, water-bearing strata could become water-resisting (aquicluding) strata. Non-Darcy flow behavior has the slightest effect in uniform samples, suggesting that uniform grain size mixtures could become water-resisting aquicluding strata easier than other samples.
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Acknowledgments: This work was supported by the National Basic Research Program of China (2013CB227902) and the National Natural Science Foundation of China (51674247 and 51404266). The authors would like to acknowledge M. Rezania from University of Nottingham for his language improvement, as well as the anonymous reviewers for their valuable comments, which have greatly improved this paper. Author Contributions: Dan Ma, Zilong Zhou and Haibo Bai conceived and designed the experiments; Dan Ma, Jiangyu Wu and Qiang Li performed the experiments; Dan Ma analyzed the data; Dan Ma and Zilong Zhou wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.
Appendix A d h0 H1 H2 H3
Average diameter of the grains (L) Original height of the coal sample (L) Height of cylindrical tube (L) Height of plunger (L) Thickness of the filter pad (L)
H4
Thickness of the porous disk (L)
i, n k L m p pa
Spatial indices (-) Permeability (L2 ) Sample length (L) Mass of the coal sample (M) Pore pressure (mL−1 ·T−2 ) Pore pressure at the intake boundary (mL−1 ·T−2 ) Pore pressure connected with the atmosphere (mL−1 ·T−2 )
pb
Cross section area of cylindrical tube (L2 ) Reynolds number (-) Axial displacement (L) Time (T) Water flow velocity (L·T−1 ) Vertical axis going through the center of the z sample (L) ∂ Partial differential operator (-) ∂()/∂z Nabla operator (L−1 ) β Non-Darcy factor (L−1 ) µ Viscosity (L2 ·T−1 ) φ Porosity (-) ρs Coal mass density (mL−3 ) Q Re S t v
ρw
Water density (mL−3 )
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