2.2.1. Porosity in the Particle Matrix
Porosity in the matrix of particles was characterized using the combined methods of mercury intrusion porosimetry (MIP) and low temperature nitrogen adsorption.
The MIP experiments were carried out using an Autopore 9510 Mercury Porosimeter (Micromeritics Instrument Corp., Norcross, GA, USA). This instrument can use mercury intrusion pressures from atmospheric pressure to 60,000 psi (414 MPa) and measure pore sizes in the 0.003–6 μm range with a ±0.10% transducer accuracy of full scale. The samples used was about 5–15 mm in size and dried at 110 °C for 24 h before the experiment.
The mercury porosimetry analysis technologies are based on the intrusion of mercury into aporous structure under stringently controlled pressures. They can capture numerous sample pore properties such as pore size distributions, total pore volume, or porosity. The porosity calculation formula is
where
np is the particle matrix porosity;
V1 is the pore volume (mercury volume intruded at the maximum experimental pressure attained, 414 MPa) and
V2 is the sample volume which can be derived by Equation (2)
where
ρHg is the density of mercury at a certain temperature;
w1 is the mass of empty cell;
w2 is the mass of empty cell and sample;
w3 is the mass of mercury, empty cell and sample and after filling with mercury under a certain pressure;
w4 is the mass of mercury and empty cell after empty cell filled with mercury.
Due to compression of mercury, of the sample cell, and of the rest of the instrument components, but also of the sample itself, the mercury intrusion method will have a certain error, especially at higher mercury pressures [
33,
34]. Subtracting an empty cell run from an actual sample analysis is an effective means to correct compression of mercury and system components error (blank correction). For the problem of compressibility of coal under high pressure of mercury intrusion, low temperature nitrogen adsorption was used to instead of MIP to calculate the pore volume which was originally tested with mercury intrusion at high pressure.
The low temperature nitrogen adsorption experiments were carried out using a Micrometrics ASAP 2460 (Micromeritics Instrument Corp., Norcross, GA, USA) gas adsorption instrument. Samples were crushed to 250 μm and dried at 100 °C for 24 h to be used for low pressure isotherm analysis. After outgassing at 150 °C for 8 h, the N2 gas isotherm adsorption measurements were carried out at 77 K (−196 °C). The pore volume and pore size distribution can be obtained from the low temperature nitrogen adsorption experiments.
2.2.2. Total Porosity of Loose Coal
According to the China National Standard [
35], the extended formula for calculating total porosity while under overburden pressure is
where
nt is the total porosity of coal or rock (%);
ρb is the bulk density of coal or rock, i.e., the ratio of mass to total volume of coal or rock (including the volume of skeleton and all pore spaces, g/cm
3) and
ρ is the true density or mineral particle skeletal density of coal or rock (the ratio of mass to skeleton volume, not including the pore spaces, g/cm
3).
The test of true density (ρ) was done with the true density tester. The testing instrument was an AccuPyc 1330 Pycnometer (Micromeritics Instrument Corp., Norcross, GA, USA). The instrument uses the Archimedes principle of helium gas expansion. The molecular diameter of He is 0.26 nm, thus it can penetrate the smallest pores and irregular hollows in the surface of a sample. As a result, it is possible to obtain a skeleton volume very close to the true skeleton volume value, and the calculated true density is therefore a true reflection of the true density value of any given sample.
To determine bulk density (
ρb) of coal samples at different pressures, the UTM5504 universal testing machine was used. The experimental equipment used and a schematic diagram of the method were shown in
Figure 6.
To accurately simulate the in situ state of pressure, the experiment was run in four stages:
- (1)
Forward loading stage: A loading speed of 2 mm/min was used, and after the specified pressure (Determined according to the in situ stresses—5, 10, 15, 20, and 25 MPa—was selected in this test because the in situ stress of Guobei Coal Mine 8105-1 working face is 20 MPa) level was reached, the force applied was kept constant for 30 min. The loading time was referenced by some scholars’ briquette compressing schemes [
24,
25,
36,
37]. The forward decreased displacement of indenter
h1 was automatically recorded by the testing machine. At each initial experiment, the coal sample should be filled with the mold, that is, the initial position of the bottom surface of the indenter was flush with the top of the coal briquette mold, as shown in
Figure 6d. The purpose of the operation is to conveniently calculate the height of the coal sample after compressing. After this stage,
hcoal =
h −
h1.
h is the height of the briquette mold excluding the base embedded in the mold.
- (2)
Forward unloading rebound stage: The unloading speeds were set to 15 N/s corresponding to experimental pressures of 5 MPa, 30 N/s→10 MPa, 45 N/s→15 MPa, 60 N/s→20 MPa, and 75 N/s→25 MPa. The purpose is to keep the consistent unloading time at each pressure. When the force returned to zero, the compressed coal sample rebounded and the forward rebound amount of the coal sample h2 was recorded.
- (3)
Reverse loading stage: The briquette mold was reversed, and the pressure was applied continuously. The loading speed was set to 2 mm/min and after the specified pressure level (5, 10, 15, 20, and 25 MPa) was reached the applied force was kept constant for 30 min. The reverse loading parameters were exactly the same as the parameters in the forward loading stage. The reverse decreased displacement of indenter h3 was recorded.
- (4)
Reverse unloading rebound stage: The unloading speeds were set to 15 N/s corresponding to experimental pressures of 5 MPa, 30 N/s→10 MPa, 45 N/s→15 MPa, 60 N/s→20 MPa, and 75 N/s→25 MPa. When the reverse force returned to zero, the compressed coal sample rebounded and the reverse rebound amount h4 was recorded.
- (5)
The mold was again turned upside down and the next level of pressure was applied. The previous four stages were repeated to complete the next pressure level tests.
The bulk density of coal under different pressures was then calculated as shown in Equation (4).
where
ρb is the bulk density of coal under a certain overburden pressure (g/cm
3);
m is the mass in grams of the coal sample in the briquette mold (the coal sample filled the mold at the beginning of the test); and
d is the inner diameter of the briquette mold (cm). The inner diameter used in this experiment was 4.960 cm.
The various heights and displacements are as follows: h is the height of the briquette mold (10.542 cm) excluding the base embedded in the mold; h1 is the forward decreased displacement (cm) of the indenter under a certain overburden pressure; h2 is the forward rebound amount (cm) of the coal sample when the overburden pressure returns to zero; and h3 is the reverse decreased displacement (cm) of the indenter under a certain overburden pressure. The result of h − (h1 + h3 − h2) is the height of the compressed coal samples under each pressure.
It should be noted that Equation (4) applies to the calculation of the bulk density of the independently filling and compressing coal samples under each pressure level, but if the coal sample compression of a certain pressure level continues to circulate on the basis of the previous pressure level, when calculating the height of the compressed coal sample, it is necessary to subtract the influence of the reverse rebound amount h4 of the previous pressure level. For example, in the experiment scheme of this article, when the pressure is 5 MPa, the bulk density can be calculated directly using Equation (4), but when 10 MPa, the reverse rebound amount h4 of 5 MPa needs to be subtracted when calculating the height of the compressed coal sample. Because the 10 MPa forward loading stage was followed by 5 MPa reverse unloading rebound stage.
In the bulk density experiment, the mass of the coal sample was measured using a precision balance (Yuyao Jiming Weighing Calibration Equipment Co., Ltd., Ningbo, China, JM-A20002, MAX = 2000 g, d = 0.01 g) and the height and inner diameter of the mold were measured using a Vernier caliper (Hangzhou Huafeng Big Arrow Tools Co., Ltd., Hangzhou, China, HF-8631215, MAX = 150 mm, d = 0.01 mm). The decreased displacement and rebound amount of the indenter were automatically recorded by the testing machine with a 0.04 μm displacement resolution. The maximum test force of the machine is 50 KN (resolution 1/500,000).